Solve the following inequality using both the graphical and algebraic approach: 0.5 x + 3 greater-than-or-equal-to 2 x minus 1.5 Graph A On a coordinate plane, a line goes through (0, 2) and (4, 4). Another line goes through (0, 0) and (2, 6). The lines intersect at (1, 1.5). Graph B On a coordinate plane, a line goes through (0, 3) and (4, 4). Another line goes through (1, 0) and (4, 6). The lines intersect at (3, 4). a. x greater-than-or-equal-to 3 Graph A b. x less-than-or-equal-to 3 Graph A c. x greater-than-or-equal-to 3 Graph B d. x less-than-or-equal-to 3 Graph B
Answers
Answer:
d. x les-than-or-equal-to 3 Graph B
Graph B expressed as follows; The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)
Step-by-step explanation:
The given inequality is expressed as follows;
0.5·x + 3 ≥ 2·x - 1.5
Let y₁ = 0.5·x + 3, and y₂ = 2·x - 1.5, we get;
For x = -1, 0, 1, 2, 3, 4, 5, 6
y₁ = 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6
y₂ = -3.5, -1.5, 0.5, 2.5, 4.5, 6.5, 8.5, 10.5
From the given data, the lines intersect at (3, 4.5)
The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)
Please find attached the required inequality created with MS Excel
Therefore, we have;
3 + 1.5 ≥ 2·x - 0.5·x
4.5 ≥ 1.5·x
∴ 3 ≥ x
x ≤ 3
Therefore, with (typographical) correction, the best option is x les-than-or-equal-to 3 Graph B
Answer:
D
Step-by-step explanation:just took the test
Related Questions
Individual bottles of water are filled by a machine at a factory with an amount of water that is approximately normal with a mean of 505 mL and a standard deviation of 10 mL. A random sample of 16 bottles is selected for a quality inspection What is the probability that the mean amount of water in these 16 bottles is within 5 mL of the population mean? Choose 1 answer: P(500 < < 510) 0.38 B P(500 < t <510) 0.45 P(500 < & <510) 0.88 P(500 <<510) 0.95 We cannot calculate this probability because the sampling distribution is not normal.
Answers
The probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.
The correct answer is: D. P(500 <<510) 0.95.
Here, we have to find the probability that the mean amount of water in the 16 bottles is within 5 mL of the population mean (505 mL), we need to calculate the probability P(500 <x < 510), where x is the sample mean.
Given that the sample size (n) is 16 and the population standard deviation (σ) is 10 mL, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean.
The Central Limit Theorem states that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
The mean of the sampling distribution of the sample mean is equal to the population mean (μ) and the standard deviation of the sampling distribution (standard error) is given by σ/√n, where σ is the population standard deviation and n is the sample size.
In this case:
μ = 505 mL (population mean)
σ = 10 mL (population standard deviation)
n = 16 (sample size)
The standard error (SE) of the sample mean is:
SE = σ/√n = 10/√16 = 10/4 = 2.5 mL
Now, we need to find the z-scores for 500 mL and 510 mL:
z₁ = (500 - μ) / SE = (500 - 505) / 2.5 = -2
z₂ = (510 - μ) / SE = (510 - 505) / 2.5 = 2
Using the z-table or a statistical calculator, we can find the probabilities corresponding to these z-scores:
P(z < -2) ≈ 0.0228
P(z < 2) ≈ 0.9772
Now, to find the probability that the sample mean is within 5 mL of the population mean (P(500 <x < 510)), we subtract the probability corresponding to the lower z-score from the probability corresponding to the higher z-score:
P(500 < x < 510) ≈ P(z < 2) - P(z < -2) ≈ 0.9772 - 0.0228 ≈ 0.9544
So, the probability of the event that the mean amount of water in the 16 bottles is within 5 mL of the population mean is approximately 0.9544, which is closest to 0.95.
The correct answer is: D. P(500 <<510) 0.95
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What will make the expression x² 4x+ a perfect square trinomial?
Answers
In order for an expression, such as x² + 4x + , to become a perfect square trinomial, it must be in the form of a² + 2ab + b².
What is perfect squares?Perfect squares are whole numbers that are the result of multiplying a given number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by itself. Similarly, 9 is a perfect square because it is the result of multiplying 3 by itself. Other examples of perfect squares include 16 (4x4), 25 (5x5), 36 (6x6), and so on.
To do this, you must factor the expression. In this case, the expression can be factored into (x + 2)².
Once the expression has been factored into a perfect square trinomial, it can be written as (x + 2)².
This is a perfect square trinomial because it represents the area of a square, as the length of each side is equal to (x + 2).
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A population of 1,800 cheetahs decreases by 8% per year. How many cheetahs will there be in the population after 13 years? Round your answer to the nearest whole number.
Answers
Answer:
1/2 of an answer is zero answer.
Step-by-step explanation:
What’s 36/6 as a whole number?
Answers
Answer:
It should be 6 because 6x6 is 36
Answer:
6
Step-by-step explanation:
fractions are division so just divide 36 by 6 and you will get 6 which is your answer
36/6 =
36 : 6 =
6
2 Lauren is using 10 pink beads and 5 black a bracelet. Which beads to decorate ratio compares the number of black beads to the total number of beads She is using?
Answers
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
What is ratio?A comparison between two items by means of a number. (arithmetic) comparing two quantities' relative magnitudes (usually expressed as a quotient).
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B. Your ratio will be 5/10, for instance, if A is 5 and B is 10.
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Jessica is wanting to buy a 10.00 box of candy. The sales tax is 5%. How much is the total for the candy?
$15.00
$12.00
$11.00
$10.50
Answers
Answer: To find the total cost of the candy including the sales tax, we first need to calculate the amount of tax by multiplying the cost of the candy by the tax rate.
The cost of the candy is 10.00.
The tax rate is 5%, which can be written as 0.05.
The total cost of the candy would be
10 + (10*0.05) = 10+0.5 = 10.50
So the correct answer is $10.50.
Step-by-step explanation:
Why do we use similarity transformation?
Answers
The goal of using similarity transformations is to make the evaluation of a matrix's eigenvalues less complicated. In fact, the computation of the eigenvalues would be instantaneous if a given matrix could be translated into a similar matrix in diagonal or triangular form.
A geometric similarity or a matrix transformation that produces a likeness are both covered by the term "similarity transformation."
A conformal mapping with a similarity transformation is one whose transformation matrix A' has the formula A'=BAB⁻¹, where A and A' are referred to as similar matrices.
Space-based items are converted to equivalent objects by similarity transformations. Fractals and iterated function systems have a lot to do with similarity transformations and the idea of self-similarity.
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( 40 POINTS AND BRAINLIEST , HELP ASAP !!!!!!!!! )
Brooke and Daniel are playing a game that involves one flip of a coin and one spin of a spinner with 3 sections. They each drew a tree diagram to represent the sample space of possible outcomes.
Whose tree diagram is correct ?
A. Brooke’s
B. Daniel sure
C. Both Brooke’s and Daniel’s
D. Neither Brooke’s nor Daniel’s
Answers
Answer:
Daniel's is correct
Step-by-step explanation:
Daniel split the coin toss into Heads and Tails and has 3 sections for the spinner coming off of each coin toss branch.
For the equation f(x) = -3x7 + 2x- 1, identify the vertex, line of symmetry, and y intercept
Answers
The vertex of the equation is (0, -1), the line of symmetry is x = 0 and the y-intercept is (0,-1).
For the equation f(x) = [tex]-3x^7[/tex] + 2x - 1, the vertex is the highest or lowest point on the parabola and it can be found by completing the square method.
To find the line of symmetry, we can set the function equal to zero and solve for x. The x-coordinate of the vertex is the same as the line of symmetry.
The y-intercept is the point at which the parabola crosses the y-axis, and it can be found by setting x equal to zero and solving for y.
The vertex of the parabola:
The equation is in form f(x) = a[tex](x-h)^2[/tex] + k, where a is -3, h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. In this case, h = 0 and k = -1.So the vertex is (0, -1)The line of symmetry:
We can set the function equal to zero and solve for x:[tex]-3x^7[/tex] + 2x - 1 = 0The x value that makes the equation equal to zero is x = 0So the line of symmetry is x = 0The y-intercept:
We can set x equal to zero and solve for y: f(0) = [tex]-3(0)^7[/tex] + 2(0) - 1 = -1So the y-intercept is (0, -1)To learn more about vertex, line of symmetry, and intercept at
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Given: AAED ≈ ABEC and
AC BD.
Prove: AABD≈ ABAC.
Note: quadrilateral properties are not permitted in this
proof.
Step
1
try
Statement
D
AAED ~ ABEC
AC BD
Type of Statement
E
с
Note: AC and DB are segments.
B
Answers
Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.
How may the ABC def be demonstrated?Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.
The use of labels Triangle ABC is congruent to triangle DEF if the angles of triangles ABC and DEF are AB = DE, AC = DF, and A = D.
ABC=CDE: a) in accordance with the conditions BC=CD and AC=CE; b) BCA=m (DCE).
If ABC = CDE, then m(BAC) = m(DEC), and m(ABC) = m (CDE).
If m(BAC)=m(DEC), then AB || DE, or if m(ABC)=m(CDE), then AB || DE.
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is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by
Answers
The scale factor of segment AB was 1.94.
What is scale factor?Scale factor is a number by which a given set of measurements is multiplied in order to increase or decrease the size of the measurements. It can be used to enlarge or reduce the size of an object, image, or diagram. It is a useful tool in many areas of mathematics, including geometry, engineering, and computer graphics.
The scale factor for segment AB can be found by taking the ratio of the lengths of the two segments. To calculate this, use the distance formula to find the length of segment AB and A'B' and set them equal to each other.
The distance formula is: d = √[(x2-x1)^2 + (y2-y1)^2]
The coordinates of A and B are (0, 0) and (6, 9), respectively. The coordinates of A' and B' are (0, 6) and (6, 9), respectively.
For segment AB, the distance formula becomes: d = √[(6-0)^2 + (9-0)^2], which simplifies to d = √[36 + 81], which simplifies to d = √117.
For segment A'B', the distance formula becomes: d = √[(6-0)^2 + (9-6)^2], which simplifies to d = √[36 + 9], which simplifies to d = √45.
The scale factor is then found by taking the ratio of the two distances, √117/√45, which simplifies to √117/3, or approximately 1.94. Therefore, the scale factor of segment AB was 1.94.
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show a²-4= (a+ 2)(a-2) in diagram
Answers
The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
What is Factorization?Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.
In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.
Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.
Given:
The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).
This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
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If Y=6 and X=10 then find the value of y when x=8
Answers
Answer:
when x=10 & y=6
10-6=4 so,
x=8
y=4
Solve the system by graphing.
y=2x+6
y=−2x−4
Answers
Answer:
(-5/2, 1)
Step-by-step explanation:
i hope this helps :)
The High Roller in Las Vegas is now the world’s tallest Ferris wheel. The Ferris wheel has 520 ft. diameter, and the top of the Ferris wheel is 550 ft. off the ground. What would the vertical shift (k) be for this Ferris wheel?
Answers
Answer:
30
Step-by-step explanation:
how do i graph for this, i struggle
Answers
The equation of line passes through the point (2, 3) will be;
⇒ y = 1/2x + 2
And, Graph of this equation of line is shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (2, 3).
And, The perpendicular line is,
⇒ y - 4 = - 2 (x + 3)
⇒ y - 4 = - 2x - 6
⇒ y = - 2x - 2
Now,
Since, The equation of line passes through the point (2, 3).
So, We need to find the slope of the line.
Since, The product of slope of the perpendicular line is - 1.
Hence, Slope of the given perpendicular line is,
⇒ y = - 2x - 2
m = dy/dx = - 2
m = - 2
So, The slope of line is,
⇒ m₂ = - 1/m
= 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 3 = 1/2 (x - 2)
⇒ y - 3 = 1/2 (x - 2)
⇒ y - 3 = 1/2x - 1
⇒ y = 1/2x - 1 + 3
⇒ y = 1/2x + 2
Therefore, The equation of line passes through the point (2, 3) will be;
⇒ y = 1/2x + 2
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Let ABC be a triangle, and
M, N, and K represent the midpoints of sides AB, BC, and AC respectively.
If area of the triangle ABC is 6.0 square feet, then what is the area of the triangle MAK?
Answers
Step-by-step explanation:
please refer to the sketch
what is the following is a like radical to 3/6x^2?
NO FILES WILL BE REPORTED!!!
Answers
Answer:
I guess is this but Im not sure
Solve for X:????????????????????????
Answers
Answer:
x = 7
Step-by-step explanation:
Given 2 congruent arcs then the chords are congruent , that is
VW = XY , substitute values
9x - 34 = 4x + 1 ( subtract 4x from both sides )
5x - 34 = 1 ( add 34 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
To divide 572 4, Stanley estimated to
place the first digit of the quotient. In which
place is the first digit of the quotient?
Answers
Answer:
The hundreds place
Step-by-step explanation:
143, first digit is , 1 is in the hundreds place
Find the value of x.
Answers
Answer:
35
Step-by-step explanation:
x + 55 = 90
x = 90 - 55
x = 35
10 students took 9 days to weed a school
compound. How long would it take 15
students to weed the same compound if
they weed at the same rate?
Answers
Answer:
It would take 15 students 6 days to weed the school compound
Step-by-step explanation:
This first step to solving this question is to break down the given rates.
We are told that 10 students take 9 days to weed the school compound. From here we can simplify this by figuring out how long it would take 1 student to weed the compound. Having less people would mean taking a longer time.
1 person is a 1/10 of 10 people. Since we have 10x less people, it should take 10x as long. Therefore it would take 1 person 9x10=90 days to weed a school.
Now the question asks how long it would take 15 people. 15 people is 15x as many as 1 person, so it should take 15x less time to weed the compound. 90/15 = 6
It would take 15 students 6 days to weed the school compound.
Similarly you could have just divided 9 by 1.5 as 15 is 1.5x10, but it is easier to explain the process using the above method.
Hope this helped!
A plane slices a double-napped cone parallel to the slanted edge of the cone. Which conic section is formed?
Circle
Ellipse
Hyperbola
Parabola
Answers
It is both of the pair of intersecting lines and degenerate hyperbola.
What is conic section?A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.
Here,
It consists of a pair of intersecting lines as well as a degenerate hyperbola.
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Is 10 24 26 a right triangle?
Answers
Yes, A triangle has sides of lengths 10, 24, and 26 is a right triangle.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
Properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.consider c=26 a=10, b=24 substitute in above formula:
26²=10²+24²
⇒676=100+576
⇒676=676
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Aida, Bernado and Cristiano need $30000 to start a business. a I They borrow & of this amount.
Show that they still need $18000.
They provide the $18000 themselves in the ratio
Aida: Bernado : Christiano = 5: 4: 3.
Calculate the amount each of them provides.
b i Office equipment costs 35% of the $30000.
Calculate the cost of the equipment. ii Office expenses cost another $6500.
Write this as a fraction of $30 000.
Give your answer in its lowest terms. iii How much remains of the $30000 now?
c They invest $12500.
After one year this has increased to $15500.
Calculate this percentage increase.
Answers
Answer:
aida:$7500
Bernardo:$6000
Christiano :$4500
b.i $10500
b.ii 13/60
b.iii $13000
c. 24%
PLEASE HELP ME, ILL BRAINLIEST YOU
Answers
Find the value of x.
x 13 39
Answers
Answer:
13x-39=39
13x=78
the answer is x=6
A jet accelerates from rest to 300 m/s over a time of 23 seconds. What is its acceleration?
Answers
Answer:
13.04m/s^2
Step-by-step explanation:
v=u+at
therefore
a=v-u÷t
300m/s-0÷23s
=13.04m/s^2
What is the length of the longest side ?
Answers
Answer:
11 feet (Option C)
Step-by-step explanation:
Let the longer side be l and the shorter side be b.
We know that,
→ Perimeter of rectangle = 2 ( longer side + shorter side )
Here,
Perimeter of rectangle is 32 feet.→ 32 = 2 (l + b)
→ 32 = 2l + 2(5)
→ 32 = 2l + 10
→ 32 - 10 = 2l
→ 22 = 2l
→ [tex] \sf \dfrac{22}{2} [/tex] = l
→ 11 = l
→ 11 feet = longer side
[tex] \therefore [/tex] Length of the longer side is 11 feet.
What should be added in the polynomial x³ 6x² 11x 8 so that it is completely divisible by X² 3x 2?
Answers
The number that should be added in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] , so that it is completely divisible by [tex]x^{2} -3x+2[/tex] is -14 .
What are Polynomials ?
A polynomial is defined as a type of algebraic expression where the exponents of all the variables is a whole number.
The exponents of the variables in any polynomial is a non-negative integer. A polynomial consists of constants and variables.
the polynomial expression is ⇒ [tex]x^{2} -3x+2[/tex], which can be written in factor form as : [tex](x-1)(x-2)[/tex] ,
that means the polynomial is divisible by both x = 1 and x = 2 ;
So , on substituting [tex]x=1[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]1^{3}-6\times1^{2} +11\times 1+8[/tex] = 14 ;
on substituting [tex]x=2[/tex] in the polynomial [tex]x^{3}-6x^{2} +11x+8[/tex] ,
we get , [tex]2^{3}-6\times2^{2} +11\times 2+8[/tex] = 14 ;
So , the remainder is 14 .
Therefore , -14 should be added in the given polynomial .
The given question is incomplete , the complete question is
What should be added in the polynomial x³ -6x² +11x +8 so that it is completely divisible by x² -3x +2 ?
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