Answers
Answer:
Step-by-step explanation: To find (f+g)(x), we simply add the two functions:
(f+g)(x) = f(x) + g(x)
= (3x - 5) + (7x - 3)
= 10x - 8
Therefore, (f+g)(x) = 10x - 8.
To find (f-g)(x), we subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
= (3x - 5) - (7x - 3)
= -4x - 8
Therefore, (f-g)(x) = -4x - 8.
Related Questions
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
Answers
The coordinates of B' after the sequence of transformations are given as follows:
B'(3,-4).
How to obtain the coordinates of B'?The coordinates of B are given as follows:
B(-3,1).
After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:
B'(3, 1).
The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:
B'(1, -3).
The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:
B'(3,-4).
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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Finally, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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SEE ATTACHED IMAGE
1) 12x^3+8x
2) 18a^2+2a
3) 25b^4+30b^3
1. Factor each term and mark the common factors.
2. Multiply the common factors to find the GCF.
3. Rewrite each term as the product of the GCF and other factors.
4. Rewrite the expression using the factors from the previous step.
5. Use the distributive property: ab ac + = a b( ) +c .
Answers
Step-by-step explanation:
remember the GCF (greatest common factor) ?
every number or term is the product of certain prime numbers (prime factors).
the product of factors that the discussed numbers or terms have in common is the GCF.
1)
12x³ + 8x
12x³ :
12 / 2 = 6
6 / 2 = 3
3 / 2 no
3 / 3 = 1 finished
12 = 2×2×3
x³ = x×x×x
so,
12x³ = 2×2×3×x×x×x
8x :
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1 finished
8 = 2×2×2
x = x
so,
8x = 2×2×2×x
what factors do they have in common ?
2×2×x = 4x
so, the GCF = 4x
that means
12x³ + 8x = 4x×3x² + 4x×2 = 4x(3x² + 2)
2)
18a² + 2a
18a² :
18 / 2 = 9
9 / 2 no
9 / 3 = 3
3 / 3 = 1 finished
18a² = 2×3×3×a×a
2a :
2 / 2 = 1 finished
2a = 2×a
so, they have 2×a = 2a in common.
the GCF = 2a.
that means
18a² + 2a = 2a×9a + 2a×1 = 2a(9a + 1)
3)
25b⁴ + 30b³
25b⁴ :
25 / 2 no
25 / 3 no
25 / 5 = 5
5 / 5 = 1 finished
25b⁴ = 5×5×b×b×b×b
30b³ :
30 / 2 = 15
15 / 2 no
15 / 3 = 5
5 / 3 no
5 / 5 = 1 finished
30b³ = 2×3×5×b×b×b
so, they have 5×b×b×b = 5b³ in common.
the GCF = 5b³
that means
25b⁴ + 30b³ = 5b³×5b + 5b³×6 = 5b³(5b + 6)
On bonfire night at sleepaway camp, Lily's counselor puts marshmallows, graham crackers, and several chocolate bars on the snack table. Lily uses
3/4
of a chocolate bar to make herself a s'more. Now 3 1/4
chocolate bars remain on the table.
Which equation can you use to find the number of chocolate bars b the counselor puts on the table?
3/4b = 3 1/4
b - 3/4 = 3 1/4
b + 3 1/4 = 3/4
b + 3/4 = 3 1/4
Answers
Answer:
The correct equation is:
b - 3/4 = 3 1/4
Explanation:
Lily used 3/4 of a chocolate bar, so the remaining chocolate bars can be found by subtracting 3/4 from the total number of chocolate bars b:
b - 3/4 = remaining chocolate bars
The problem tells us that there are 3 1/4 remaining chocolate bars, so we can substitute this value in the equation and solve for b:
b - 3/4 = 3 1/4
b = 3 1/4 + 3/4
b = 4
Therefore, the counselor put 4 chocolate bars on the table.
Select the correct answer.
Consider functions p and q.
log₂ (x - 1)
p(x)
q (x) = 2* - 1
Which statement is true about these functions?
=
O A.
The x-intercept of function p is the same as the x-intercept of function q.
OB.
The x-intercept of function p is less than the x-intercept of function q.
O C.
The x-intercept of function p is greater than the x-intercept of function q.
OD. The x-intercepts cannot be compared because either p or q does not have an x-intercept
Answers
Answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe
D. The x-intercepts cannot be compared because either p or q does not have an x-intercept.
The function q is a constant function and its graph is a horizontal line passing through y = -1. It does not intersect the x-axis, so it does not have an x-intercept.
The function p is a logarithmic function, and its x-intercept is the point at which the graph of p intersects the x-axis. To find the x-intercept of p, we need to set p(x) = 0 and solve for x.
log₂ (x - 1) = 0
2^0 = x - 1
1 = x - 1
x = 2
So the x-intercept of p is x = 2.
Since q does not have an x-intercept, we cannot compare the x-intercepts of p and q. Therefore, the correct answer is D.
Step-by-step explanation:
hope its help <:
Find the equation of the line.
Use exact numbers.
Answers
Which of the following sets of numbers could not represent the three sides of
a triangle?
{14, 24, 37}
{15, 30, 43}
{9, 21, 32}
{10, 19, 26}
Answers
The triangle that would not represent the three sides of a triangles is: {9, 21, 32}
How do determine this triangleWe can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.
With this in mind, we have that for each of this
14 + 24 > 37
15 + 30 > 43
9 + 21 < 32
10 + 19 > 26
Hence the third option does not fulfill the rule
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ABCD Is a rectangle that represents a park.
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 15m.
Calculate the shortest distance from A to C across the park,using only the lines shown.
Answers
The circumference's shortest distance between points A and C is 102.91m.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle with four equally long sides.
As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.
So, we know that:
AC = 80 m
CD = 50 m
Apply the Pythagorean theorem to the right triangle using ADC.
AC = √AD² + CD²
AC = √80² + 50²
AC = 94.34m
The shortest path through the park from point A to point C must only follow the lines depicted in the diagram.
Hence, we must deduct AC by 15 meters in diameter.
94.34m - 15m = 79.34m
The shortest distance is 79.34 miles plus one-half a circle's circumference.
As the circle's diameter is 15 meters, the radius is 15/2 = 7.5m.
The circumference would be:
2*π*r = 47.14m
The half circumference would be:
47.14/2 = 23.57m
Then,
79.34m + 23.57m = 102.91m
Therefore, the circumference's shortest distance between points A and C is 102.91m.
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find the area of this shape (4.5 ft 3 ft 3ft)
Answers
Answer:assuming its a rectangle its 13.5
Step-by-step explanation: L x H = Area
Help please! For 2 and 3
Answers
1. Answer (a) Positive. The leading coefficient of the polynomial on the right is positive.
Answer (b) 3, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. Answer (a) 2, Answer (b) 1
3. Answer (a) 3, Answer (b) 1 and 5
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can have constants and variables, and they usually have multiple terms that are separated by addition or subtraction.
1. The leading coefficient of a polynomial is the coefficient of the highest degree term. In the graph, the highest degree term is x3, and it is positive. Therefore, the leading coefficient of the polynomial on the right is positive.
The degree of a polynomial is the highest power of the variable in the equation. In the graph, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. The number of real zeros of a polynomial is the number of times the polynomial crosses the x-axis. In the graph, the polynomial crosses the x-axis twice, so it has 2 real zeros.
The number of imaginary zeros of a polynomial is the number of times the polynomial bounces off the x-axis. In the graph, the polynomial bounces off the x-axis once, so it has 1 imaginary zero.
3. The polynomial p(x) bounces off the x-axis at x=3 because the polynomial changes direction at this point.
The polynomial p(x) crosses the x-axis at x=1 and x=5 because the polynomial intersects the x-axis at these points.
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Use the given dimensions to nd the areas of the vehicle and chairs. Then determine if the vehicle
could be used to haul both chairs in a single trip.
Answers
The 5 ft by 8 ft dimensions of the car and the (width) 2 ft by (height) 3 ft dimensions of the chair, indicates that the vehicle can haul both chairs in one trip.
What are the dimensions of a rectangularly shaped solid?The dimensions of rectangularly shaped solid are the height, the width and the length of the solid.
The possible dimensions of the vehicle and the chair obtained from a similar online question are;
Length of the vehicle = 8 feet
Width of the vehicle = 5 feet
The height of one chair = 3 feet
The width of one chair = 2 feet
Therefore;
The width of the vehicle of 5 feet indicates that the vehicle can contain the two chairs placed side by side with their widths of 2 feet each, to get;
Width of the two chairs = 2 feet + 2 feet = 4 feet < 5 feet
The two chairs placed horizontally, such that we get;
The total length of the horizontally placed chairs = 3 feet + 3 feet = 6 feet
The combined height of the two chaires, of 6 feet is less than the length of the car which is 8 feet, therefore;
The car can haul both chairs placed horizontally in a single trip.
The vehicle could therefore be used to haul both chairs in a single trip.
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Null and alternative hypothesis for the study are (in the photo)
! Thank you , 100 points!!
A) test statistic T equals -1.952; P value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
B) test statistic, T equals 0.3619. P value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
C) test statistic, T = -1.952; p value, 0.0509. There is sufficient evidence to reject the no hypothesis of no difference between a triglyceride test levels.
D) test statistic T equals 0.3651. P value, 0.6425. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
Answers
The correct answer is A) test statistic T equals -1.952; P value, 0.0414.
How would you define hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.
The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.
With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).
The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.
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For the following exercises, start with the graph of f (x) = 4x. Then write a function that results from the given
transformation.
32. Shift f (x) 4 units upward
33. Shift f (x) 3 units downward
34. Shift f (x) 2 units left
35. Shift f (x) 5 units right
36. Refl ct f (x) about the x-axis
37. Refl ct f (x) about the y-axis
Answers
32. g(x) = 4x + 4
This transformation shifts the graph
of f(x) 4 units upward.
33. g(x) = 4x-3
This transformation shifts the graph
of f(x) 3 units downward.
34. g(x)=4(x+2)
This transformation shifts the graph
of f(x) 2 units left.
35. g(x) = 4(x-5)
This transformation shifts the graph
of f(x) 5 units right.
36. g(x) = -4x
This transformation reflects the graph
of f(x) about the x-axis.
37. g(x) = -4x
This transformation reflects the graph
of f(x) about the y-axis.
chatGPT
The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 48 miles apart. When the satellite is on one side of the two stations, the angle of elevation at A Is 87° and the angle of elevation at B Is 84°.
How far is the satellite from station A?
How High is the satellite above the ground?
Round all answers to 3 decimal places.
Answers
The distance of the satellite from station A is approximately 47 miles
The satellite is approximately 911 miles above ground
How to find the distanceLet the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48
Using trigonometry
tan 87 degrees = height of the satellite above the ground, h / a
tan 87 degrees = h / a
h = a * tan 87
while
tan 84 degrees = h / a + 48
h = (a + 48) tan 84
substituting for h
a * tan 87 = (a + 48) tan 84
a (tan 87 - tan 84) = 48 tan 84
a (9.567) = 48 tan 84
a = 48 tan 84 / 9.567
a = 47.436
The distance of the satellite from station A is approximately 47 miles
The height above ground
h = a * tan 87
h = 47.436 * tan 87
h = 910.857 miles
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What’s 4559.886 rounded to the nearest inch
Answers
Answer:
Step-by-step explanation:
Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:
4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)
To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:
179.72467632 in rounded to the nearest inch is 180 in.
Therefore, 4559.886 rounded to the nearest inch is 180.
John can mow a lawn in 90 minutes. Bullwinkle can mow the same lawn in 60 minutes. How long does it take for both John and Bullwinkle to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answers
Answer:
32
Step-by-step explanation:
Evaluate the following expressions.
Answers
Accοrding the given expressiοns this is the right answer (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
(1/5)³= 1/5 × 1/5 × 1/5 = 1/125
What is an expressiοn?In mathematics, an expressiοn is a cοmbinatiοn οf numbers, variables, and οperatοrs that represents a mathematical relatiοnship οr fοrmula. It can include numbers, variables, and mathematical οperatοrs such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts. Fοr example, 2x + 3y is an expressiοn that includes the variables x and y, and the οperatοrs additiοn and multiplicatiοn. Expressiοns can be simplified, evaluated, οr used tο represent mathematical relatiοnships.
a) (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
b) (1/5)³ = 1/5 × 1/5 × 1/5 = 1/125
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2. Solve based on the diagram below.
What is the value of angle x? How do you know (what type of angle pairs are they)?
Answers
Answer: 160
Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.
You deposit $1000 each year into an account earning 8% compounded annually.How much will you have in the account in 10 years?
Answers
Answer:
If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.
Given,
Annual deposit = $1000
Rate = 8% compounded annually
Time(n) = 10 year
Amount = ?
As we know the formula ,
Amount = P(1+r/100)ⁿ
Amount = 1000(1+8/100)¹⁰
Amount = 1000(1+0.08)¹⁰
Amount =1000(1.08)¹⁰
Amount = 1000 × 2.15892
Amount = $2158.92
Hence, amount in 10year will be $2158.92
Steps for solving t|u prove mt=mu
Answers
We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.
How to solve the problem?Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.
To get mt = m, substitute u = tk into mt = mu (tk).
Rewrite m(tk) as (mt)k using the associative property of multiplication.
To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.
Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.
Since 1 Equals k, we get u = tk = t(1) = t.
We get mt = mt by substituting u = t into the original equation mt = mu.
As a result, we have demonstrated that mt = mu when t | u.
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Find the surface area obtained by rotating the curve [tex]y=4e^2^x[/tex] on the interval x=0 to x=2 about the x-axis
Answers
what is a number halfway between 8.34 and 8.35
Answers
Answer:
8.345
Step-by-step explanation:
(8.34+8.35)/2 = 16.69/2
= 8.345
Pee Dimensional Figures) CARGO A = lw Area of base_____ A trailer has a volume of 2,112 cubic feet and a height of 12 feet. If the width of the trailer's base 8 feet, find the area and then the length of the trailer's base. A = bh DELIVERY V = Bh
Answers
The area of the trailer's base is 176 square feet.
What is volume?Volume is a measure of the amount of space that an object occupies. It is a three-dimensional quantity that is usually measured in cubic units, such as cubic meters, cubic feet, or cubic centimeters.
According to question:We have a cargo trailer with a volume of 2,112 cubic feet, a height of 12 feet, and a width of 8 feet. We want to find the area and length of the trailer's base.
Since the volume of the trailer is given by V = lwh, we can write:
2,112 = lw(12)
Simplifying this equation, we get:
l = 2,112 / (w x 12)
l = 2,112 / (8 x 12) [Substituting the value of w as 8 feet]
l = 22
Therefore, the length of the trailer's base is 22 feet.
To find the area of the trailer's base, we can use the formula A = lw:
A = l x w
A = 22 x 8
A = 176 square feet
Therefore, the area of the trailer's base is 176 square feet.
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I’m so confused please help me
Answers
We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.
what are angles?An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.
The interior angle of a regular polygon with n sides is calculated as follows:
(n-2) * 180° / n = interior angle
The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:
144° = (n - 2) * 180° / n
144° * n = (n - 2) * 180°
144° * n = 180° * n - 360°
144° * n + 360° = 180° * n
360° = 36° * n
n = 10
As a result, the regular polygon has ten sides.
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(1 − cos 0) (1 + cos 0)= 1/csc²0
Answers
Step-by-step explanation:
lol sorry for untidy work
please help me. somebody solve this question
Answers
Answer:
5.5 or 5 1/2 inches
Step-by-step explanation:
The longest is 12 3/4
The two smallest combined are 3 and 4 1/4 = 7 1/4
12 3/4 - 7 1/4 = 5 1/2
Leo is drawing a map of the recess area at his school on a coordinate grid. If the scale of the map is 1 grid = 5 feet, what is the distance from the jungle gym to the four-square courts? Round your answer to the nearest tenth if necessary.
Answers
if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them. the four-square courts are approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
What are the coordinates of two points?The distance formula is:
[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.
For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:
[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]
[tex]= sqrt(6^2 + 4^2)[/tex]
[tex]= sqrt(36 + 16)[/tex]
[tex]= sqrt(52)[/tex]
[tex]\approx 7.2[/tex]
Therefore, the distance from the jungle gym to the four-square courts is approximately [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).
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A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?
A. 8.78
B. 9.12
C. 9.64
D. 9.68
Show answer.
Answers
Answer: D. 9.68
Step-by-step explanation:
145.2 oz/ 15 cups = 9.68 oz per cup
You move up 7 units and down 4 units. You end at (-2, -2). Where did you start?
Answers
Answer:-2,-5
Step-by-step explanation:
7-4=3
You move 3 units up
You land on -2, -2
the higher units you move up, the higher the number gets to.
please help! the question is in the picture ! PLEEAASSEE
Answers
If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.By critically observing the graph of this circle, we have the following parameters:
Radius, r = 3 units.Center, (h, k) = (-3, 2).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - 2)² = 3²
(x + 3)² + (y - 2)² = 9.
By dilating with a scale factor of 2, we have:
(x + 3)² + (y - 2)² = (9 × 2)
(x + 3)² + (y - 2)² = 18
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Christy is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 7.5 miles each day. During a 5-day training period, she jogs and rides a total of 53 miles. How many miles does Christy jog each day during training? Explain how you solved the problem.
Answers
5 miles each day so 5×7=35 miles a week