Marsha deposited ​$7,500 into a savings account 4 years ago. The simple interest rate is 5​%. How much money did Marsha earn in​ interest?

Answers

Answer 1

Answer: Marsha earned $375 in interest. ✅

Step-by-step explanation:

Multiply the amount Marsha deposited, which was $7,500, by the interest rate, which was 5%. 5% of $7,500 is $375, so that's the amount of interest Marsha earned.


Related Questions

Lesson 13:Find a Sequence
Describe a sequence of reflections, rotations, and translations that takes ABCD onto
A'B'C'D'.

Answers

The sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

How to Identify the Transformation?

We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.

Looking at the given image, the sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

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telephone poll administered by a computer randomly generating numbers to call, found that 68% of Americans in the sample of 2000 were in favor of legalizing recreational marijuana use. Thus, almost 70% of Americans favor legalizing recreation marijuana use.

Answers

The method that was used to arrive at the approximate population probability is called; a reasonable statistical generalization

What is statistics generalization?

Statistical generalization is a concept that involves inferring the results from a sample and applying it to a population. Carrying out this means that the sample must be selected randomly and be representative of the population.

Now, in this case, we see that the sample gave a probability of 68% to represent those were in favor of legalizing recreational marijuana use.

Now, since the conclusion was approximated to 70% to reflect the probability of the population then we can say that a reasonable statistical generalization was utilized.

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A line passes through points (2,5) and (6.-7) and has a y-intercept at (0,3). Write the linear equation of this line​

Answers

Answer: -9/4.

The slope formula of the line passing through the points

Drag each tile to the correct box.
Each function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?

Answers

The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .

There are some rules for transformation of graph of various functions which are as follows :-

For F(x) →f(−x) = Reflection about the y-axisFor F(x) → f(ax) =  It will depend upon value of a chosenIf |a|>1 then f(ax) is f(x) squashed horizontally by a factor of aIf 0<|a|<1 then f(ax) is f(x) is stretched horizontally by factor of aIf a<0 then is f(ax) is  f(x) also reflected in the y-axis

 By keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.

Thus the first graph represents sin(2x), the second graph represents

sin(-x) and the third graph represents sin(x/2)

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X + 2/3 = 8/9 x=? /////////////////////////////////////////

Answers

The value of x is  2/9

Given equation x +2/3 = 8/9

We need to find the value of x

Simplifying the equation is

x+2/3 = 8/9

x = 8/9 -2/3

Taking L.C.M of the denominators 3 and 9

The L.C.M is 9

So we will multiply the numerator and denominator with 1 in 8/9

And we will multiply the numerator and denominator with 3 in 2/3

Hence the new equation formed = 8/9-6/9

Solving this equation we get

8-6 / 9

= 2 / 9

Hence the value of x is 2/9

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There are n cities in a OneWayCountry (country in which every road is a One-Way road). Every pair of cities is connected by exactly one direct one-way road. Show that there exists a city which can be reached from every other city either directly or via at most one other city.

Answers

The cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

What is mathematical induction method?

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n. By generalizing this in form of a principle which we would use to prove any mathematical statement is 'Principle of Mathematical Induction'.

The question says that between any two cities X and Y, either there’s an

one-way road from X to Y or from Y to X, but not both. Then show that

there is a path from some city A which visits all the cities exactly once.

This problem is very similar to the Football league problem #7 in Homework 1. This problem can be modeled as a directed graph in which cities

are represented as vertices and there’s an edge from vertices X to Y if

there’s a road from cities X to Y. And then, our goal is to find a path

in this graph which visits every vertex in the graph.

The rest of the solution is very similar to the argument in Problem 7 of

homework 1. We use induction of number of cities, say n.

As a base case, if n = 2, there are only two cities X and Y and the path

is simply the edge between X and Y.

For induction hypothesis, assume that the statement is true for any set

of n cities. That is’ for any set of n cities, we can find a path which visits

all the cities exactly once.

Let’s prove the statement for n + 1 cities. Leave out n + 1 th city (say,

[tex]c_{n}+1[/tex]) and for the remaining n cities, by induction hypothesis, we can find a path which visits all these n cities exactly once. Let us label the cities such that this path is [tex]C_{1}[/tex] → [tex]C_{2}[/tex] → [tex]C_{3}[/tex] . . . → [tex]C_{n}[/tex]. Now, if all roads are going towards [tex]c_{n}+1[/tex], then add  [tex]c_{n}+1[/tex] at the end of this path. Otherwise, let [tex]C_{i}[/tex] be the first city in this path such that there is a road from  [tex]C_{i}[/tex]-1 to  [tex]c_{n}+1[/tex] and from  [tex]c_{n}+1[/tex] to  [tex]C_{i}[/tex]. Place  [tex]c_{n}+1[/tex] between  [tex]C_{i}[/tex]−1 and  [tex]C_{i}[/tex] to get the desired path.

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slope and why intercept?

Answers

Answer:

Slope: -1/3

Y-intercept: 0

Step-by-step explanation:

The lines passes the y-axis at 0, and since the line is going downwards, the slope will be negative.

I hope it helps! Have a great day!

bren~

URGENT!, will mark brainiest!

Use the box plots comparing the number of male pets and number of female pets attending doggy daycare each day for a month to answer the questions. Two box plots shown.

The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.

The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown

Part A: Estimate the I Q R for the males' data. (2 points)

Part B: Estimate the difference between the median values of each data set. (2 points)

Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)

Answers

The IQR for the males' data is equal to 12.The difference between their median's values is 8.The male's data has an outlier while the female's data doesn't have.

How to estimate the IQR?

For the males' data, we can logically deduce the following data elements:

Upper quartile (Q₃) = 14Lower quartile (Q₁) = 2

Mathematically, the male IQR can be calculated by using this formula:

IQR = Q₃ - Q₁

IQR = 14 - 2

Male IQR = 12.

Next, we would find the difference between the median values:

Note: The median of male's data is equal to 10 while median of female's data is equal to 18.

Difference, d = 18 - 10

Difference, d = 8.

The distribution of data.

The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.

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Answer: s

Step-by-step explanation:

Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. www represents the volume of water andrei uses (in liters) if he uses nnn marbles. w=32-0.05nw=32−0.05nw, equals, 32, minus, 0, point, 05, n what is the volume of each marble?

Answers

Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

The volume of a solid revolution generated by rotating the curve y = f(x) and x = f(y) between x = a and x = b , y = a and y = b through 360 degrees about the x-axis and y-axis is given
[tex]V_{x} =\int\limits^b_a {\pi y^{2} } \, dx[/tex] and [tex]V_{y} =\int\limits^b_a {\pi x^{2} } \, dy[/tex]

The diagram shows the line y = 1, the line y = 4 and part of the curve [tex]y=3x^2[/tex]. The shaded region is rotated through 360 degrees about the y-axis. Find the exact value of the volume of revolution obtained. Leave your answer in pi.

Answers

Answer:

[tex]\dfrac{5}{2}\pi[/tex]

Step-by-step explanation:

Rotation about the y-axis

[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]

where:

b = upper limita = lower limitx is a function of y

Given function of y:  [tex]y = 3x^2[/tex]

Rewrite the given function as a function of y:

[tex]\implies x^2=\dfrac{1}{3}y[/tex]

Substitute the values into the formula:

[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Take out the constant and integrate:

[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]

Therefore, the exact value of the volume of revolution is:

[tex]\dfrac{5}{2}\pi[/tex]

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For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx$ have exactly one real solution? express your answer as a list of numbers, separated by commas. thank you!

Answers

The values of 'j' are -11,5.

What is a Quadratic Equation?

Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .

Here, the given equation is (2x+7)(x-5) = - 43 + jx

On simplifying the equation we get,

[tex]2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 2

b = - (3 + j)

c = 8

Therefore,

[tex](-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\[/tex]

Take the square root of both sides,

[tex]\sqrt{(3+j)^{2} }=\sqrt{64} \\[/tex]

3 + j = ±8

Therefore,

3 + j = 8

j = 8 - 3        

j = 5

or

3 + j = -8

j = -8 - 3

j = -11

Hence, the possible values of 'j' are -11,5.

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pls help math problem pls

Answers

Answer: The fourth choice

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) = 4[tex]x^{2}[/tex] - 5x - (3[tex]x^{2}[/tex] + 6x - 4) = [tex]x^{2}[/tex] - 11x + 4

The function h(x) is given below.
h(x) = {(3,-5), (5, -7), (6, -9), (10, -12), (12,-16)}
Which of the following gives h¹(x)?
O ((3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
O ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
O ((3,-5), (5,-7), (6, -9), (10, -12), (12,-16)}
O ((5, 3), (7,5), (9, 6), (12, 10), (16, 12)}

Answers

Answer: Option (2)

Step-by-step explanation:

The inverse of a function swaps the domain and range.

The inverse of the function h(x) is

B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

Option B is the correct answer.

We have,

The function h(x) is given as:

h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)}

To find h¹(x) (the inverse of h(x)), we need to swap the x and y values in each ordered pair.

The inverse function will have the y-values of h(x) as the x-values, and the x-values of h(x) as the y-values.

So,

h¹(x) would be:

h¹(x) = {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

Thus,

The inverse of the function h(x) is

B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

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The figure shows an example of a multiplication problem where the numbers are coded by letters. Same letter represents same digits, and different letters represent different digits. Which digit does the letter x represent?

Answers

Based on the information provided, it can inferred that letter A is equivalent to 4.

What is the value of letter B?

The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.

What is the value of the letter A?

It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).

Note: This question is incomplete below I add the missing image.

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Δ

X

Y

Z
and
Δ

A

B

C
are similar triangles. Given the dimensions shown in the diagram, what is the area of
Δ

A

B

C
? Express the answer in square units.

Answers

Answer:

3.528

Step-by-step explanation:

the scale factor from the large triangle to the smaller triangle is 1/2.  All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.

A = 1/2 (bh)  The area of a triangle.  I need to know the base and the height of the little triangle to figure out the area.  If I use AC as the base, the length is given to me.  It is 4.2.  I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me.  It is 3.36, if I divide that by 2, I get 1.68.  Now I know all that I need to find the area.

A = 1/2(4.2)(1.68)

3.528Units^2

Please help me on this geometry question

Answers

Answer:

? = 3

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{?}{6}[/tex] = [tex]\frac{2}{4}[/tex] ( cross- multiply )

4? = 12 ( divide both sides by 4 )

? = 3

Answer:

3

Step-by-step explanation:

Because the triangles are similar

6/4 = (?+6)/(2+4)

6/4 = (?+6)/6

Cross multiply

36 = 4?+24

4?=12

?=3

The number of rows in an auditorium can be represented by the function f(x) = 80x. the number of seats in each row can be represented by the function g(x) = x 7. which function represents the total number of seats, h(x) = f(x)g(x)? h(x) = 136x h(x) = 80x2 560x h(x) = 80x 560 h(x) = 80x2 560

Answers

Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

How polynomial functions are multiplied?

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

f(x) = 80x.g(x) = x + 7.

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

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Answer:

The answer is b

Step-by-step explanation:

:)

Mr. Krueger wanted a square platform built in the drama room at
school. He provided the carpenter with the desired area of the platform
to be built. Which function can he use to determine the side length of
the square platform?

F(x)=x²

F(x)=√x

F(x) = -=-=

F(x) = |x|

Answers

Answer: F(x) = sqrt(x)

Explanation: inverse of square is square root. Since the area is the side length squared, take the square root of the area to find the side length.

PLEASE HELP quickly ​

Answers

Answer:

C. Radius or diameter must be known.

Step-by-step explanation:

The radius or diameter must be known so you can use the formula.

Hope this helps!

Which graph represents the solution to x<6?

Answers

The answer is last one

1. Chris takes 25 minutes to replace one car tyre.
Jim takes 5 minutes less to replace one car tyre.
At a car workshop, there are a total of x tyres to be replaced.
Jim replaces three more tyres than Chris, without exceeding the time Chris takes.
Form an inequality in x and solve it to find the minimum number of tyres to be replaced.

Answers

Chris and Jim must replace a total quantity of 17 tyres.

What is the minimum number of tyres to be replaced?

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

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You measure 46 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population is normally distributed with a standard deviation of 12.2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers correct to at least two decimal places. Lower Limit = Upper Limit =

Answers

Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).

What is a z-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given as follows:

[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]

Hence the lower and upper bound of the interval are given, respectively, by:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 77 - 2.575\frac{12.2}{\sqrt{46}} = 72.37[/tex][tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 77 + 2.575\frac{12.2}{\sqrt{46}} = 81.63[/tex]

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Instructions: Given the coordinates, Complete the translation (x,y)→(x+2,y−2) C(−5,−1) D(−4,3) E(−3,2) F(−2,0)

Answers

the translations is,

               C(-5,-1) → (-3,-3)

               D(-4,3) → (-2,1)

               E(-3,2) → (-1,0)

               F(-2,0) → (0,-2)

What is Translation ?

The changes in the value of the x and y  coordinates is known as translation.

Calculation:

The given points are C(-5,-1), E(-4,3), F(-3,2), F(-2,0).

according to the question (x,y)→(x+2,y-2)

 this means x coordinate changes by addition of 2

 And the y coordinate changes by subtraction of 2  

 Addition and Subtraction in the Coordinates,

             C(-5,-1) → (-5+2,-1-2) → (-3,-3)

             D(-4,3) → (-4+2,3-2) → (-2,1)

             E(-3,2) → (-3+2,2-2) → (-1,0)

             F(-2,0) → (-2+2,0-2) → (0,-2)

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Find the area of a circle with radius, r =
7.4m.
Give your answer rounded to 2 DP.
r
C
The diagram is not drawn to scale.

Answers

Answer:

172.03 m²

Step-by-step explanation:

Hello!

Area of a circle: [tex]A = \pi r^2[/tex]

A = areaπ = pir = radius

Plug in the radius into the formula to find the area.

Find the Area[tex]A = \pi r^2[/tex][tex]A = \pi (7.4)^2[/tex][tex]A = 54.76\pi[/tex][tex]A = 172.0336137106 \approx 172.03[/tex]

The area is approximately 172.03 m².

To calculate the radius of this circle, we must take into account that:

Data:

R = 7.4 π = 3.14

To calculate the area of the circle, we apply the following formula:

A = π * r², where

a = area

π = pi

r = radius

Substituting the values of the equation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*(7.4 \ m)^{2} \end{gathered}$}[/tex]

Taking the square root

[tex]\large\displaystyle\text{$\begin{gathered}\sf A=3.14*54.76 \ m^{2} \end{gathered}$}[/tex]

Multiplying

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf A=171.95 \ m^{2} \end{gathered}$}}[/tex]

Answer: The approximate area of the circle is 171.95 m².

use the graph to the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 10

Answers

The coordinates of QRTW after dilation by factor 10 are (-20,30),(-30,10),(20,-10),(-20,40).

Given that coordinates of QRTW before dilation are (-2,3),(-3,1),(2,-1),(-2,4) and figure QRTW is dilated by factor 10.

We know that if a figure is dilated its area, increases. The new coordinates can be calculated as x*factor from which it is dilated.

Coordinates are the points on the graph surface.

In our figure Q(-2,3), R(-3,1), S(2,-1), T (-2,4).

We have to just multiply each value with 10 to get the new coordinates of QRTW after dilation.

Q after dilation=(-2*10,3*10)=(-20,30)

R after dilation=(-3*10,1*10)=(-30,10)

S after dilation=(2*10,-1*10)=(20,-10)

T after dilation=(-2*10,4*10)=(-20,40)

Hence the vertices of the image QRTW after dilation are (-20,30),(-30,10),(20,-10),(-20,40).

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find the domain and range of f^-1 where f(x)=x+1/6x+7

Answers

Answer:

Step-by-step explanation:

hello here is an solution

The domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=(x+1)/6x+7

Let f(x)=y

(x+1)/6x+7=y

x+1=y(6x+7)

x+1=6xy+7y

6xy-x=7y-1

x(6y-1)=7y-1

Divide both sides by 6y-1

x=7y-1/6y-1

So f⁻¹(x)=1-7x/6x-1

The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}

The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}

Hence, the domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

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PLEASE HELP WILL GIVE YOU ALL MY POINTS In the picture, t || s, mz1 = 10x + 2, and mz2 = 12x - 22. Find the measure of angle 2.

Answers

Answer:

[tex]\huge\boxed{\sf < 2 = 122\°}[/tex]

Step-by-step explanation:

From the figure,

∠1 = ∠2 (Alternate angles are equal)

We know that:

∠1 = 10x + 2∠2 = 12x - 22

So,

10x + 2 = 12x - 22

Add 22 to both sides

10x + 2 + 22 = 12x

10x + 24 = 12x

Subtract 10x to both sides

24 = 12x - 10x

24 = 2x

Divide 2 to both sides

12 = x

OR

x = 12

Given that,

∠2 = 12x - 22

Put x = 12

∠2 = 12(12) - 22

∠2 = 144 - 22

∠2 = 122°

[tex]\rule[225]{225}{2}[/tex]

Answer: 122°

Step-by-step explanation:

∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.

Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.

[tex]10x+2=12x-22[/tex]

[tex]-2x=-24[/tex]

[tex]x=12[/tex]

Putting x in the expression 12x-22, we get

[tex]12(12)-22\\144-22\\122[/tex]

Hence, the value of ∠2 is 122°.

Round 5 358 708 to the nearest million​

Answers

Answer:5 million

Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.

Is x+2 a factor of the polynomial f(x)=2x^4-3x^2-4x+1?

a. f(2)=0, so (x+2) is a factor.
b. f(-2)=29, so (x+2) is not a factor.
c. f(-2)=0, so (x+2) is a factor.
d. f(2)=13, so (x+2) is not a factor.

Answers

Answer:

B

Step-by-step explanation:

the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)

so if x=-2 ,f(-2) = 29

x+2=0 f(0) = 1

f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor

what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.

Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.

Answers

The true statements are:

Points A, B, and D are on both planes. Point H is not on plane R. Points C, D, and A are noncollinear. The line containing points F and G is on plane R.

What is the intersection of 2 planes?

If two planes are said to have intersect each other, the intersection will be regarded as a line.

Hence, looking at the image attached, you will see that Points C, D, and A are noncollinear and the line containing points F and G is on plane R.

Note that when a line and a plane are said to intersect each other , the intersection will be a single point, or say a line. So Points A, B, and D are on both planes.

Therefore, option 1, 2, 4 and 5 are correct.

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Answer: option 1 , 2 , 4 , 5

Step-by-step explanation: edge 2022

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