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Solve the equation f(x)=g(x) by graphing the functions f(x)=3^x+1 and g(x)=4 on the same set of coordinate axes.

Which statements about the solution are true?

Select EACH correct answer.

A. The solution to the equation is x=1

B. The ordered pair that contains the solution to the equation lies in Quadrant I

C. The ordered pairs that contain the solutions to the equation like in Quadrants I and II.

D. There are 2 solutions to the equation.

E. The ordered pair that contains the solution to the equation lies in Quadrant II

Answer:

11.7

Step-by-step explanation:

Using the cosine ratio, then

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{h}[/tex]

Multiply both sides by h , the hypotenuse

h × cos40° = 9 ( divide both sides by cos40° )

h = [tex]\frac{9}{cos40}[/tex] ≈ 11.7 ( to the nearest tenth )

Answer:

an = -8 +3(n-1)

an = -11 +3n

f(n) = -11 +3n

Step-by-step explanation:

–8, –5, –2, 1, 4, ...

This is an arithmetic sequence.

We are increasing by 3 each time

-8 +3 = -5

-5+3 = -2

-2 +3 = 1

The common difference is 3

The formula for an arithmetic sequence is

an = a1 +d (n-1)

an = -8 +3(n-1)

an = -8 +3n -3

an = -11 +3n

The nth term is -11 +3n

f(n) = -11 +3n

D. an = an-1+3; a1 = -8

EG. 2020

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

step 1

Find the ratio of the height of shape A to the height of shape B

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area shape A

y----> surface area shape B

so

[tex]z^{2} =\frac{x}{y}[/tex]

substitute

[tex]z^{2} =\frac{4}{25}[/tex]

[tex]z =\frac{2}{5}[/tex]

therefore

the ratio of the height of shape A to the height of shape B is equal to

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

step 2

Find the ratio of the height of shape B to the height of shape C

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> volume shape B

y----> volume shape C

so

[tex]z^{3} =\frac{x}{y}[/tex]

substitute

[tex]z^{3} =\frac{27}{64}[/tex]

[tex]z =\frac{3}{4}[/tex]

therefore

the ratio of the height of shape B to the height of shape C is equal to

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

step 3

Find the ratio of the height of shape A to the height of shape C

we have

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

Multiply

[tex](\frac{hA}{hB})(\frac{hB}{hC})=\frac{hA}{hC}[/tex]

so

[tex](\frac{2}{5})(\frac{3}{4})=\frac{6}{20}=\frac{3}{10}[/tex]

In this problem, we're working with the geometric property of similarity to compare the heights and volumes of different shapes. Using the ratios of their surface areas and volumes, we found that the ratio of the height of Shape A to Shape C is 15:8.

In order to solve this problem, it is necessary to first know that, for similar shapes, the ratio of the areas is actually the square of the ratio of the corresponding length measurements (this includes dimensions such as the height). In this particular case, since shapes A and B are similar, the ratio of their surface areas will give the square of the ratio of the heights:

√(25/4) : 1 => 5 : 2

Now, for shapes B and C, we have the volume ratio given as 27 : 64. Since, for similar shapes, the ratio of the volumes is the cube of the ratio of the corresponding length measurements, the cube root of the volume ratio will give the ratio of the heights:

∛(27/64 : 1) => 3 : 4

Using these two ratios, we can find the ratio of height from shape A to shape C by multiplying together the heights of shape A to B and shape B to C: (5/2) * (3/4) => 15 : 8.

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Answer:

4 1/4 × 3 × 1 1/4

Step-by-step explanation:

To find volume you need to do length×width×height

The expression which can be used to find the volume of the rectangular prism is, Volume = l × w × h

If a three dimensional prism has 6 rectangular faces such that all 3 pair of opposite faces are congruent.

The three dimensions of a rectangular prism are length, width and height.

Let, length of rectangular prism = l unit

Width of rectangular prism = w unit

And the height of rectangular prism = h unit

Then, Volume of rectangular prism = Length × Width × Height

                                                           = l × w × h  cubic unit

Learn more about rectangular prism here :

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There are 7040 yards in 4 miles

Answer:

there is 7040 yards in 4 miles

Step-by-step explanation:

1) 1 Miles = 1760 yards

2) just multiply 1760 times 4 because one Miles is 1760 yards

1760 x 4 = 7040 yards

4 represents miles

Hopes this helps!

The answer is -3, let me know if you want me to give you the steps

The answer would be -3

Answer:

Part A: 379.94

Part B: 254.34

Part C: 125.6

Step-by-step explanation:

The are for the area of a circle is A = Pi*r^2

So for part A, do

A = 3.14 * 11^2

A = 3.14 * 121

A = 379.94

Same thing for Part B, just change the radius:

A = 3.14 * 9^2

A = 3.14 *81

A= 125.6

And for Part C, Subtract the area of the smaller from the area of the larger circle:

379.97 - 254.34 = 125.6

Answer:

I'm just answering this so that you can give them brainlest

Step-by-step explanation: Have a good day

Answer:

I think the answer would be to divide the inches by 4.  So Length would be 3.5 inches and width would be 1.25 inches . I might be wrong but if you have no hope I would go with my answer.

Step-by-step explanation:

Answer:

lenght: 3.5 inches.

width: 1.25 inches.

Step-by-step explanation:

You have the following information:

- The drawing must be 1/4  the size of the original drawing.

- The tree in the original drawing is 14 inches tall and 5 inches wide.

Therefore, keeping the above on mind, you can find the length and width of the tree in Barry's drawing by multiplying the original dimensions by 1/4.

Then, you obtain the result shown below:

[tex]lenght=\frac{1}{4}*14in=3.5in\\\\width=\frac{1}{4}*5in=1.25in[/tex]

$16 / $80 * 100% = 20%.

$16/$80 *100= 20%

answer is 20%

Answer:D)78

Step-by-step explanation:70+71+75+75+88+89/6

Answer: $15.92*6= $95.52

$175.72 - $ 95.52= $ 80.20

Step-by-step explanation:

Answer:

Yes different signs leads to a negative product.

Step-by-step explanation:

So I don't know if this was helpful, but I hope you find it very helpful!

Answer:

the blue one is 1/2 and the red one is 1/4

Step-by-step explanation:

count the bricks and put a "1/" in front of the number of bricks and... BOOM you have your answer

Answer:

-40

Step-by-step explanation:

Try rearranging and factoring -8y-2c-2b-8x-2a:

This is equal to -8(x + y) -2(a + b + c).

Since x + y = 7, we have:

                            -8(7) -2(a + b + c)

and since a + b + c = 8, we end up with:

                             -56 - 2(8), or

                               -56 - 16    = -40

Answer:  104°

Step-by-step explanation:

Since ∠JKL and ∠LKM are supplementary, then their sum is 180°.

∠JKL + ∠LKM = 180

2x + 4 + x + 26 = 180

            3x + 30 = 180

            3x         = 150

              x         =  50

∠JKL = 2x + 4

        = 2(50) + 4

        = 100 + 4

        = 104

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5   <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

[tex]\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}[/tex]

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

[tex]\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}[/tex]

we also know that the expanded 3rd term is 240x², therefore we can say that

[tex]\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480[/tex]

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

[tex]\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft[/tex]

Answer:

y=cos(0.4x)

Step-by-step explanation:

Answer:

The equation of the graph given is:

                  [tex]y=\cos(0.4x)[/tex]

Step-by-step explanation:

Clearly from the graph of the function that is provided to us we see that the graph repeats itself after every 5π.

i.e. the period of the function is: 5π.

Now we will check in each of the given options whose period is 5π.

We know that the period of a cosine function of the type:

[tex]y=cos(bx)[/tex] is given by:

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

1)

[tex]y=\cos(\dfrac{x}{0.4})[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi[/tex]

Hence, option: 1 is incorrect.

2)

[tex]y=\cos (5x)[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi[/tex]

Hence, option: 2 is incorrect.

4)

[tex]y=\cos (\dfrac{x}{5})[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi[/tex]

Hence, option: 4 is incorrect.

3)

[tex]y=\cos(0.4x)[/tex]

The period of this function is:

[tex]Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi[/tex]

        Hence, option: 3 is the correct option.

Answer: -2x²-11x-35

Step-by-step explanation:

-2(p+4)²-3+5p

-2(x²+8x+16)-3+5x

-2x²-11x-35

To simplify the expression -2(p+4)^2-3+5p, it's important to distribute, multiply, and combine like terms. The simplified expression is -2p^2 -11p -35.

To simplify the expression -2(p+4)^2-3+5p, it's easier to break it down step by step:

This is the simplest form of the original expression.

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Answer:

f(x)+1 = x^2 + 1

Step-by-step explanation:

The graph of f(x)+1 will be given by adding 1 to the initial function f(x)

f(x)+1 = x^2 + 1

See the attachment for the graph;

➷ Substitute it into the equation:

3 = 2x + 5

Subtract 5 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

The other coordinate is -1

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

-1

Step-by-step explanation:

1.We know that the equation of the line is y=2x+5 ( with a gradient of 2 and a

y-intercept of 5) and the y coordinate is 3 so we must work out x (x,3).

2.We know y=3 so

3 = 2x+5

3. Solve the equation

3=2x+5

(-5 from both sides)

-2=2x

(Divide both sides by 2 to isolate x)

-1 = x so x = 1

Hope this helps:)

5INGH

[tex] - 7 {v}^{2} - 25v - 12 \\ = - 7 {v}^{2} - 21v - 4v - 12 \\ = - 7 v (v + 3) - 4(v + 3) \\ = ( - 7v - 4)(v + 3) \\ = - (7v + 4)(v + 3)[/tex]

Answer:

B and C

Step-by-step explanation:

Use the Pythagorean Theorem a^2+b^2=c^2.

We can see in B that 8^2 is 64 and 15^2 is 225 which adds to 17^2 which is 289.

In C, the sqrt of 2 squared is just 2 and adding that by another sqrt 2^2 results in 4 which is also the value of 2^2.

Answer:(use the Pythagorean formula)

Step-by-step explanation:

Find the two smaller sides. Square each one them add them together. Then square the third side (the biggest side). If your two answers match, it's a right triangle!

Make sure that you don't make the mistake of adding the two smaller sides together before squaring.

Answer:

[tex]6^{\frac{7}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponents

• [tex]\sqrt[n]{a^{m} }[/tex] ⇔ [tex]a^{\frac{m}{n} }[/tex]

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Hence

[tex]\sqrt[3]{6}[/tex] = [tex]6^{\frac{1}{3} }[/tex] and

6² × [tex]6^{\frac{1}{3} }[/tex] = [tex]6^{\frac{7}{3} }[/tex]

Answer:

210

Step-by-step explanation:

The general formula for picking k items from a total of n is

[tex]_{n}C_{k} = \frac{n! }{(n-k)!k! }[/tex]

Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is

[tex]_{10}C_{6} = \frac{10! }{(10-6)!6! }[/tex]

[tex]= \frac{10! }{4!6! }[/tex]

[tex]= \frac{10\times9\times8\times7}{4\times3\times2\times1 }[/tex]

[tex]= \frac{5040 }{24 }[/tex]

= 210

The committee can be selected in 210 separate ways.

Answer:

b

Step-by-step explanation:

Answer:

a. [tex]8^{8}\sqrt{8}[/tex]

Step-by-step explanation:

The given expression is

[tex]\sqrt{8^{17}}[/tex]

We rewrite the radicand to obtain;

[tex]\sqrt{8^{16}\times 8}[/tex]

Split the radicand;

[tex]\sqrt{8^{16}}\times \sqrt{8}[/tex]

[tex]\sqrt{(8^{8})^2}\times \sqrt{8}[/tex]

[tex]8^{8}\sqrt{8}[/tex]

Answer:

y intercept is 1  1/3

equation is y = -1/6x + 4/3

x coordinate is -70  (-70,13)

Step-by-step explanation:

find M

m = 1 - (-1)/ 2 -1 4

m = -2/12 = -1/6

Find y intercept--Plug m and one point from above into y = mx + b

1 = - 1/6 (2) + b

1 = -2/6 + b

1  2/6 = b

1  1/3 = b

4/3 = b

To find the x coordinate if y is 13

13 = -1/6 x + 4/3

11 2/3 = -1/6 x

-70 = x

The y intercept of line AB = [tex](0,\dfrac{4}{3})[/tex]

The equation of line AB will be

[tex] y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]

The x-coordinate of C = 4

The slope of line AB with coordinates of A and B are (14, -1) and (2, 1)

[tex]m_1=\dfrac{1-(-1)}{2-14}=\dfrac{2}{-12}=\dfrac{1}{-6}[/tex]

The equation of line AB will be

[tex](y-1)=\dfrac{1}{-6}(x-2)\\\\\Rightarrow y=\dfrac{1}{-6}(x-2)+1\\\\\Rightarrow\ y=\dfrac{-1}{6}x+\dfrac{1}{3}+1\\\\\Rightarrow y=\dfrac{-1}{6}x+\dfrac{4}{3}[/tex]

Put x=0, we get the [tex]y=\dfrac{4}{3}[/tex] i.e. [tex](0,\dfrac{4}{3})[/tex] is the y intercept of line AB.

Since, Line AB and Line BC form a right angle at their point of intersection, B. The the product of their slope must be -1.

Therefore, the slope of BC =[tex]m_2=\dfrac{-1}{m_1}=6[/tex]

Let x coordinate of C be a,then the coordinates of C = (a,13)

Now, slope of BC with points B(2,1) and C(a,13) will be

[tex]\dfrac{13-1}{a-2}=6\\\\\Rightarrow\ a-2=\dfrac{12}{6}\\\\\Rightarrow\ a-1=2\\\\\Rightarrow\ a=4[/tex]

Hence, the x-coordinate of C = 4

Answer:

The correct answer is third option

(10x² - 4) - (7x² + 3)

Step-by-step explanation:

From the given option we get the correct answer is  third option.

(10x² - 4) - (7x² + 3)

Check the correct answer

(10x² - 4) - (7x² + 3) = 10x² - 4 - 7x² - 3)

 = 10x² - 7x² - 4 - 3 = 3x² - 7

Therefore the correct answer is third option

(10x² - 4) - (7x² + 3)

The correct answer is C on edg

:)

Answer:

The answer is A. [-4/3]

For the second part the answer is a rotation 90 CCW about origin

Hope this helped!

Answer:

The correct option is B.

Step-by-step explanation:

From the given graph it is clear the x-coordinate of the vector is 3 and y-coordinate of the vector is 4 in the coordinate plane.

The given vector can be defined as

[tex]A=\begin{bmatrix}3 & 4\end{bmatrix}[/tex]

Translation vector is

[tex]B=\begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

We need to find the resulting vector,

[tex]AB=\begin{bmatrix}3 & 4\end{bmatrix}\cdot \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}3(0)+4(1) & 3(-1)+4(0)\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}4& -3\end{bmatrix}[/tex]

Therefore the correct option is B.

Answer:

Step-by-step explanation:

The general equation for a circle of radius r with center at (h, k) is

(x - h)² + (y - k)² = r²

Here, this equation becomes:

(x - 1)² + (y - 2)² = 3²

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius. The equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

The center point of the given circle is (1,2).

The length of the radius of the circle is 3 units.

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius.

The standard form of the equation of the circle is,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here,

(h,k) is the center of the circle.

[tex]r[/tex] is the radius of the circle.

Put the values given in the problem in the standard form of the equation of the circle. Thus,

[tex](x-1)^2+(y-2)^2=3^2[/tex]

[tex]x^2+1-2x+y^2+4-4y=9[/tex]

[tex]x^2+y^2-2x-4y+5-9=0[/tex]

[tex]x^2+y^2-2x-4y-4=0[/tex]

Thus the equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

Learn more about the equation of the circle here;

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Answer:

v = -2.5

Step-by-step explanation:

9(9-2v) = -12(v-8)

81−18v= −12v+96

So move -18v to the other side and change the sign. Same to 96.

81-96 = -12v + 18v

-15 = 6v

v = -2.5