Part I- a) y = (x + 25)(x + 9)
b) y = x^2 + 34x + 225
c) y= (x + 17)^2 - 64
d) The y-intercept is (0, 225), The y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.
g) y = 465 square yards
Part II- a) y = (6 + 2x)^2
b) 169 = (6 + 2x)^2
c) x = 3.5 feet
Part I:
a) The equation representing the total area of the pool and the pool deck, using y to represent the total area, can be written as:y = (x + 25)(x + 9)
b) To rewrite the equation in standard form using the FOIL method:
y = x^2 + 9x + 25x + 225
= x^2 + 34x + 225
c) To rewrite the equation in vertex form by completing the square:
y = (x^2 + 34x) + 225
= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2
= (x^2 + 34x + 289) + 225 - 289
= (x + 17)^2 - 64
d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:
0 = (x + 17)^2 - 64
64 = (x + 17)^2
x + 17 = ±√64
x + 17 = ±8
x = -17 ± 8
x = -25, -9
Therefore, the x-intercepts are (-25, 0) and (-9, 0).
The y-intercept is obtained by setting x = 0 in the equation:
y = (0 + 17)^2 - 64
y = 17^2 - 64
y = 289 - 64
y = 225
Therefore, the y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.
g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).
h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:
y = (6 + 17)^2 - 64
y = 23^2 - 64
y = 529 - 64
y = 465 square yards
Part II:
a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:
y = (6 + 2x)^2
b) Substituting the area of the enclosed space (169 square feet) for y in the equation:
169 = (6 + 2x)^2
c) Solving the equation for x:
√169 = √((6 + 2x)^2)
13 = 6 + 2x
2x = 13 - 6
2x = 7
x = 7/2
x = 3.5 feet
Therefore, the width of the deck space around the hot tub is 3.5 feet.
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1. 20x + 14y +6z
2.6x + 2y
3. 1/2(6n - 12m)
Answer:
1. linear equation
2. linear equation
3. algebraic equation
Step-by-step explanation:
1. The expression 20x + 14y + 6z represents a linear equation with three variables: x, y, and z. It consists of three terms: 20x, 14y, and 6z. The coefficients of these terms are 20, 14, and 6 respectively. This equation represents a plane in a three-dimensional coordinate system, where the variables x, y, and z determine the position on the plane.
2. The expression 6x + 2y represents a linear equation with two variables: x and y. It consists of two terms: 6x and 2y. The coefficients of these terms are 6 and 2 respectively. This equation represents a straight line in a two-dimensional coordinate system, where the variables x and y determine the position on the line.
3. The expression 1/2(6n - 12m) represents an algebraic equation with two variables: n and m. It consists of one term: 6n - 12m. The coefficient of this term is 1/2. This equation represents a relationship between the variables n and m, where n and m could be any real numbers.
Find the measure of the indicated angle.
- 20°
161"
61*
73"
H
73
195
E
The measure of the indicated angle formed by a secant and tangent line is 61 degrees.
What is the measure of the missing angle?The outside or external angles theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
It is expressed as;
External angle = 1/2 × ( x - y )
From the diagram:
Intercepted arc GE = y = 73°
Intercepted arc HE = x = 195°
External angle GFE = ?
Plug the given values into the above formula and solve for the indicated angle:
External angle = 1/2 × ( x - y )
External angle GFE = 1/2 × ( 195 - 73 )
External angle GFE = 1/2 × 122
External angle GFE = 61°
Therefore, the outside angle is 61 degrees.
Option C) 61° is the correct answer.
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URGENT
There were 35,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold. If a total of 442,000 copies of the novel were sold in all, how many paperback copies were sold?
The number of paperback copies sold is 366,300.
Let's solve the problem :
Calculate the number of hardback copies sold.
We are given that 35,000 hardback copies were sold before the paperback version was issued.
Calculate the number of paperback copies sold.
From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold.
Let's assume the number of hardback copies sold is H.
Therefore, the number of paperback copies sold would be 9H.
Set up the equation for the total number of copies sold.
The problem states that a total of 442,000 copies of the novel were sold in all. We can set up the equation as follows:
H + 9H + 35,000 = 442,000
Solve the equation for H.
Combining like terms, we have:
10H + 35,000 = 442,000
10H = 442,000 - 35,000
10H = 407,000
H = 40,700.
Calculate the number of paperback copies sold.
We already know that the number of paperback copies sold is 9 times the number of hardback copies sold.
Therefore, the number of paperback copies sold would be:
9H = 9 [tex]\times[/tex] 40,700 = 366,300
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A research study claims that 68% of adults drink regularly. Edward conducts a random sample of 200 people and finds that 140 people drink regularly.
z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction
Using the formula and data provided, what is the value of the z-test statistic? Answer choices are rounded to the hundredths place.
a.)
0.41
b.)
0.61
c.)
0.39
d.)
0.59
Using the z-statistic relation given, the value of the z-statistic in the scenario would be 0.61
Z - statistic relationshipThe Z-statistic relation is written thus:
z = (phat - p) / √(p * q / n)phat = 140 / 200 = 0.7
p = 0.68
q = 1 - p = 0.32
n = 200
Inputting the values into our formula
z = (phat - p) / sqrt(p * q / n)
= (0.7 - 0.68) / sqrt(0.68 * 0.32 / 200)
= 0.02 / 0.0583
= 0.61
Therefore, Z-statistic is 0.61
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 Randomly selecting a diamond or 3
The probability of randomly selecting a diamond or a 3 is
The probability of randomly selecting either a diamond or a 3 from the bag is 100%.
Random selection refers to the process of selecting elements from a group with equal probability of selection.
Probability is a measure of the likelihood of an event occurring, which is usually expressed as a fraction or a decimal.
When it comes to random selection of a diamond or 3, we can use probability to determine the likelihood of either event occurring.
For instance, suppose we have a bag containing 10 numbered balls: 5 of them are diamonds and 5 are threes.
To find the probability of randomly selecting a diamond, we divide the number of diamonds by the total number of balls: P(Diamond) = Number of diamonds/ Total number of balls = 5/10 = 0.5 or 50%
This means that the probability of randomly selecting a diamond from the bag is 50%.
To find the probability of selecting either a diamond or a 3, we add the probability of selecting a diamond to the probability of selecting a 3, since the events are mutually exclusive: P(Diamond or 3) = P(Diamond) + P(3) = 5/10 + 5/10 = 1
This means that the probability of randomly selecting either a diamond or a 3 from the bag is 100%.
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Which explains whether or not the graph represents a direct variation?
The graph has a constant of variation of 3, so it represents a direct variation.
The graph has a slope of 3, so it represents a direct variation.
The graph has a positive slope, so it does not represent a direct variation.
O The graph does not begin at the origin, so it does not represent a direct variation.
Save and
0
Question #3
Solve for x
10
6x + 8
K
U
N
L
122°
M
194°
Answer:
be more clear of what u mean edit the question and explain more of u mean
Answer:
(b) 7
Step-by-step explanation:
You want to find the value of x in the figure where chords that cross at an angle of 122° intercept arcs of 195° and (6x+8)°.
Crossing angleThe angle where the chords cross is half the sum of the measures of the intercepted arcs:
(194° +(6x +8)°)/2 = 122°
101 +3x = 122 . . . . . . . . . . divide by °, simplify
3x = 21 . . . . . . . . . . . subtract 101
x = 7 . . . . . . . . . . divide by 3
The value of x is 7.
__
Additional comment
The measure of arc KU is 50°.
<95141404393>
Mark this and return
Graph A
Graph B
Which graph represents a density curve, and why?
O graph A only, because the area under the curve
equals 1, and the curve is above the horizontal axis
O graph B only, because the area under the curve
equals 2, and the curve is above the horizontal axis
O both graph A and graph B, because both curves are
above the horizontal axis, and their areas are positive
neither graph A nor graph B, because, even though
both curves are above the horizontal axis, their areas
are not the same value
O
Save and Exit
Next
Submit
Only Graph A satisfies the criteria for a density curve, making it the correct answer.
Graph A represents a density curve because the area under the curve equals 1, and the curve is above the horizontal axis. In a density curve, the total area under the curve represents the probability, and it should always equal 1.
This indicates that the curve represents a probability distribution, where the probability of an event occurring within a certain range is given by the area under the curve within that range.
The fact that the curve is above the horizontal axis indicates positive values, which is consistent with a density curve representing a probability distribution.
On the other hand, Graph B does not represent a density curve because the area under the curve equals 2, which is not valid for a probability distribution. The area under a density curve should always equal 1, indicating that the total probability is accounted for.
As a result, only Graph A meets the requirements for a density curve, making it the right response.
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Q
P
N
M
7.
The triangles are similar. Write a similarity statement for the triangles.
R
Triangles ZWN and ZXY are similar by the SAS congruence theorem.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
In this problem, we have that the angle Z is equals for both triangles, and the two sides between the angle Z, which are ZW = ZY and ZV = ZX, form a proportional relationship.
Hence the SAS theorem holds true for the triangle in this problem.
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i need help in geometry 1
The expression/equation as written in the question is ∠A ≈ ∠C
How to write the expression/equation as expressedFrom the question, we have the following parameters that can be used in our computation:
∠A ≈ ∠C
The above expression means that
The angles A and C are congruent
From the question, we understand that
The question is not to be solved; we only need to write out the expression
Hence, the expression/equation as written is ∠A ≈ ∠C
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with 34
Is AB tangent to the circle? Explain..
Answer:
AB is not tangent to the circle.
Step-by-step explanation:
A tangent is a straight line that touches a circle at only one point.
The tangent of a circle is always perpendicular to the radius.
Therefore, if AB is tangent to the circle, it will form a right angle with the radius, CA.
To determine if AB is tangent, we can use Pythagoras Theorem.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
If AB is tangent, then angle CAB will be a right angle. So AC and AB would be the legs of the right triangle, and BC would be the hypotenuse.
Therefore:
[tex]AC^2+AB^2=BC^2[/tex]
Substitute the values into the equation:
[tex]7^2+12^2=15^2[/tex]
[tex]49+144=225[/tex]
[tex]193 = 225 \; \leftarrow\; \sf not\;true[/tex]
As 193 ≠ 225, the equation does not hold, hence proving that AB is not tangent to the circle.
Question 1 of 35
Colleen is buying a $279,000 home with a 30-year mortgage at 4.5%. Because
she is not making a down payment, PMI in the amount of $134.25 per month
is required for the first 2 years of the loan. Based on this information, what is
the total cost of this loan?
OA. $475,415
OB. $512,136
OC. $508,914
OD.
$493,776
SUBMIT
Answer:
Step-by-step explanation:
add it then subtract the value
Km = km/h÷km + h . find the consistency of the equation.
Jalen's checking account balance last month was $2505. If his checking
account pays 1% interest monthly and has a $15 service fee, how much was
the credit to his account?
A. $15.00
B. $10.05
C. $15.05
D. $25.05
(cosecx+2)(2cosx-1)=0
The solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.
To solve the given equation, we can make use of zero-product property. The zero-product property states that if the product of the two factors is equal to zero, then one of the factors has to be equal to zero. So, now we will equate each factor to zero to find the solution.
1. (cosec(x)+2) = 0
= cosec(x) = -2
Taking reciprocal on both the sides:
= 1/cosec(x) = -1/2
= sin(x) = -1/2
The solutions for sin(x) = -1/2 occur when x = -π/6 + 2πn and 7π/6 + 2πn, where 'n' is an integer.
2. (2cos(x)-1) = 0
= 2cos(x) = 1
= cos(x) = 1/2
The solutions for cos(x) = 1/2 occur when x = π/3 + 2πn and 5π/3 + 2πn, where 'n' is an integer.
Therefore, the solutions to the equation (cosec(x)+2)(2cos(x)-1) are x = -π/6 + 2πn, 7π/6 + 2πn, x = π/3 + 2πn, 5π/3 + 2πn.
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The complete question is: Find out the possible solutions of the equation (cosecx+2)(2cosx-1)=0.
Quincy used this linear system to represent a situation involving a collection of $5 bills and $10 bills:
f+t=70
5f + 10t = 575
a) What problem might Quincy have written?
b) What does each variable represent?
So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70. And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.
a) Quincy might have written a problem involving the number of $5 bills (represented by variable 'f') and the number of $10 bills (represented by variable 't'), with certain constraints and conditions.
Quincy might have written a problem related to a scenario where he needed to determine the number of $5 bills and $10 bills. The problem could involve a specific situation.
b) In this linear system:
'f' represents the number of $5 bills.
't' represents the number of $10 bills.
So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70.
In the linear system, 'f' represents the number of $5 bills Quincy has, while 't' represents the number of $10 bills. The equation 'f+t=70' implies that the total number of bills. The second equation, '5f + 10t = 575', represents the condition that the total value of the $5 bills (5f) and the $10 bills (10t) together amounts to $575.
And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.
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Select all the correct answers.
Which four inequalities can be used to find the solution to this absolute value inequality?
3 ≤ x + 2 ≤ 6
x + 2 ≤ 6
x + 2 ≥ -6
x + 2-3
|x ≥ 1
|x + 2 ≤ -3
x + 22 -6
x + 2 ≥ 3
|x ≤ 4
Answer:
Step-by-step explanation:
x + 2-3
|x ≥ 1
|x + 2 ≤ -3
x + 22 -6
Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Bumper Boats and the Parachute Plunge.
15 units
225 units
8 units
63 units
Answer:the answer is 15 units
Step-by-step explanation:
just took the test
pls help !!!!!! geometry
Suitable average for averaging the shoe sizes of children is
Select one:
a. Mean
b. Harmonic Mean
c. Geometric Mean
d. Percentile
e. Mode
Question 4(Multiple Choice Worth 5 points)
(01.02 MC)
A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts. Which economic questions does this statement
answer?
O How much to produce? How much to charge?
How to produce? How much to produce?
Owhat to produce? For whom to produce?
Owhat to produce? How to produce?
The correct answer is: O How to produce? How much to produce?
The statement "A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts" answers the economic questions of "How to produce?" and "How much to produce?"
How to produce: The statement indicates that the manufacturing firm has chosen to employ workers to monitor and maintain specialized machines. This suggests that they have made a decision regarding the production process and how they will go about manufacturing the small metal parts.
How much to produce: The fact that the manufacturing firm has employed workers to monitor and maintain the machines implies that they have determined a level of production that is deemed appropriate or necessary. The number of workers and the capacity of the machines can influence the quantity of small metal parts produced.
Therefore, the correct answer is: O How to produce? How much to produce?
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Since the mode is the most frequently occurring data value, it
Select one:
a. is always larger than the mean
b. can never be larger than the mean
c. must have a value of at least two
d. is always larger than the median
e. None of these answers is correct.
Any answer without justification will be rejected automatically.
The correct answer is option (e): None of these answers is correct.
The statement "the mode is the most frequently occurring data value" is true. However, none of the options provided accurately describes the relationship between the mode and the mean.
The mode and the mean are different measures of central tendency and can have different values. There is no general rule or guarantee that the mode will always be larger or smaller than the mean. The relationship between the mode and the mean depends on the specific dataset and its distribution. Therefore, none of the provided options correctly describes the relationship between the mode and the mean.
Need help with the vector page
Answer:
Only one scalene triangle with side lengths of 12 in, 15 in, and 18 in exists. Therefore, exactly one unique triangle exists with the given side lengths.
Step-by-step explanation:
Pamela is buying a $242,000 home with a 30-year mortgage. She will make
an 8% down payment. Use the table below to find her monthly PMI payment.
Base-To-Loan %
95.01% to 97%
90.01% to 95%
85.01% to 90%
85% and Under
OA. $96.48
OB. $144.72
OC. $157.30
OD. $151.01
Fixed-Rate Loan
30 yrs. 15 yrs.
0.90% 0.79%
0.78% 0.26%
0.52% 0.23%
0.32% 0.19%
ARM 2% +1 Year Cap
30 yrs.
15 yrs.
n/a
0.92% 0.81%
0.65%
n/a
0.37%
0.54%
0.26%
Sketch the graph of y=-2x²+x+1 using your graphing calculator. What are the x-intercepts of this graph?
a. (1, 0) and (-0.5, 0)
c. There are no x-intercepts
b.
(-2.5, 0) and (-2, 0)
d.
(-1.5, 0) and (-0.5, 0)
Please select the best answer from the choices provided
From the graph, we can see that the parabola intersects the x-axis at two points, which are approximately (-0.5, 0) and (1, 0).
Therefore, the correct answer is: a. (1, 0) and (-0.5, 0)
To sketch the graph of the quadratic function y = -2x² + x + 1 and determine the x-intercepts, we can use a graphing calculator or analyze the equation directly.
Here's the visualization and explanation of the graph:
The graph of a quadratic function is a parabola.
The general form of a quadratic equation is y = ax² + bx + c,
where a, b, and c are constants.
In this case, we have y = -2x² + x + 1.
The coefficient of x², which is -2, tells us that the parabola opens downward.
The vertex of the parabola can be found using the formula x = -b / (2a). Plugging in the values from our equation, we get x = -(1) / (2[tex]\times[/tex] (-2)) = 1/4.
So, the x-coordinate of the vertex is 1/4.
To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation: y = -2(1/4)² + (1/4) + 1 = -1/8 + 1/4 + 1 = 1 + 1/4 - 1/8 = 1 + 2/8 - 1/8 = 1 + 1/8 = 9/8.
Now that we have the vertex of the parabola, which is (1/4, 9/8), we can sketch the graph.
-1/2 1/4 1/2
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Indicate in standard form the equation of the line passing through the given points. S(, 1), T(, 4) x = 1/2 y = 1/2 -2x + y = 0
The equation of the line in standard form is 3x + y - 4 = 0.
To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept.
Given the points S(, 1) and T(, 4), we need to determine the slope (m) and the y-intercept (b).
The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Substituting the values, we get:
m = (4 - 1) / ( - ) = 3 / ( - ) = -3
Now that we have the slope, we can substitute it into the equation y = mx + b and use one of the given points to solve for the y-intercept (b).
Using the point S(, 1):
1 = (-3)(1) + b
1 = -3 + b
b = 4
Therefore, the equation of the line passing through the points S and T is:
y = -3x + 4
Converting it to standard form Ax + By + C = 0, we rearrange the equation:
3x + y - 4 = 0
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A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length AC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
41
B
85
Answer:
76 units
Step-by-step explanation:
You want the length of AC in the given triangular pyramid.
Pythagorean theoremThe Pythagorean theorem can be used to find the lengths of AD and CD.
AD² + 40² = 41²
AD² = 41² -40² = 81 . . . . . = 9²
and
CD² +40² = 85²
CD² = 85² -40² = 5625 . . . . . = 75²
It can also be used to find AC:
AD² + CD² = AC²
81 + 5625 = AC²
AC = √5706 = 3√634 ≈ 76
The length of side AC is about 76 units.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.
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Donna joined a club that costs $80 per month with a $60.50 yearly
membership fee. Is the cost over time a proportional or non-proportional
relationship?
The cost of Donna's club membership exhibits a non-proportional relationship over time.
The cost of Donna's club membership can be analyzed to determine whether it exhibits a proportional or non-proportional relationship over time.
In this scenario, Donna pays a monthly fee of $80, along with a yearly membership fee of $60.50. To assess the proportionality, we can examine how the cost changes relative to time.
In a proportional relationship, the cost would increase or decrease at a constant rate. For example, if the monthly fee remained constant, the total cost would be directly proportional to the number of months of membership.
However, in this case, the presence of a yearly membership fee indicates a non-proportional relationship.
The yearly membership fee of $60.50 is a fixed cost that Donna incurs only once per year, regardless of the number of months she remains a member.
As a result, the cost is not directly proportional to time. Instead, it has a fixed component (the yearly fee) and a variable component (the monthly fee).
In summary, the cost of Donna's club membership exhibits a non-proportional relationship over time. While the monthly fee is a constant amount, the yearly membership fee introduces a fixed cost that is independent of the duration of her membership.
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On a coordinate plane, a triangle has points F (3, 4), D (5, negative 3), and E (1, negative 2).
What are the coordinates of the image of vertex D after a reflection across the x-axis?
(5, 3)
(–5, –3)
(–3, 5)
(3, –5)
Answer:
(5, 3 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
D (5, - 3 ) → (5, - (- 3) ) → (5, 3 )
Answer:
(5,3)
Step-by-step explanation:
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