If a 4 × 16 rectangle has the same area as a square, what is the length of a side of the square?

Answer:

- 4

Step-by-step explanation:

Using the rule of exponents

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

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

[tex](\frac{1}{9}) ^{a+1}[/tex] = [tex]9^{-(a+1)}[/tex] = [tex]3^{-2(a+1)}[/tex]

and right side

= [tex]3^{4(a+1)}[/tex] × [tex]3^{3(2-a)}[/tex]

Hence

[tex]3^{-2a-2}[/tex] = [tex]3^{4a+4}[/tex] × [tex]3^{6-3a}[/tex]

[tex]3^{-2a-2}[/tex] = [tex]3^{a+10}[/tex]

Equating exponents on both sides gives

a + 10 = - 2a - 2 ( add 2a to both sides )

3a + 10 = - 2 (subtract 10 from both sides )

3a = - 12 ( divide both sides by 3 )

a = - 4

Answer:

the answer to the question you is A on edg

Step-by-step explanation:

Answer:

The translation is 4 down.

Step-by-step explanation:

So you have:

25v² + 5v² + 30v + 6

First you combine the like terms (all of the v²)

25v² + 5v² + 30v + 6

= 30v² + 30v + 6                                  (25v² + 5v² = 30v²)

Now notice that the largest common factor of all those numbers is 6. So you can take out a factor of 6:

30v² + 30v + 6  

= 6 (5v² + 5v + 1)  

----------------------------------------------------------

Answer:

25v² + 5v² + 30v + 6

= 30v² + 30v + 6

= 6 (5v² + 5v + 1)

Answer:

Required probability is 0.3025.

Step-by-step explanation:

Given that probability of landing heads up in a toss of bent coin = 0.55

Then probability of getting head in 1st toss = 0.55

2nd toss is independent of the first toss.

Then probability of getting head in 2nd toss = 0.55

Hence probability of getting head in two tosses of the coin = (0.55)(0.55) =0.3025

Hence required probability is 0.3025.

Answer:

0.3025

Step-by-step explanation:

Given:

The probability of landing heads P(h) = 0.55  

The probability of landing heads when the coin is tossed again is 0.55 as both the events are independent and we are given the probability of heads P(h) = 0.55

So,

The probability of getting 2 heads in a row=0.55*0.55

                                                                   =0.3025  

The point-slope equation y - 3 = 2(x + 4) can be rewritten in slope-intercept form by distributing the slope and adding 3 to both sides, resulting in y = 2x + 11, which is option D.

To rewrite the point-slope equation y - 3 = 2(x + 4) into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y. Here is the step-by-step process:

The resulting slope-intercept form of the equation is y = 2x + 11, which corresponds to option D.

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For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle

We have as data that:

[tex]C = 6 \pi[/tex]

So:

[tex]6 \pi = \pi * d[/tex]

Thus, the diameter of the circle is 6, therefore the radius is 3.

The area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

[tex]A = \pi * 3 ^ 2\\A = 9 \pi[/tex]

Answer:

Option B

Answer:

9π in. ²

Step-by-step explanation:

The circumference of a circle is diameter times pi.

To find the area of a circle, you multiply the radius by itself, and the product by pi.

Diameter (6 in.) divided by two equals the radius (3 in.).

3 x 3 = 9 in.²

Then multiply by pi to get, 9π in.²

Hope this helps! :)

Answer:

D.7/80

Step-by-step explanation:

⇒The question is on probability with replacement

⇒The events taken in this probability are independent of each other

⇒Formulae for combined probability of these events is the product of the probabilities of the event

Given;

6 books for fiction, F=6

7 books for humor, H=7

5 books for play, P=5

2 books for adventure, A=2

Evaluating

n(S)=6+7+5+2=20

P(H)=7/20

P(P)=5/20

P(H ∩ P)=P(H)×P(P)

7/20 × 5/20 =7/80

We have that the value of matrix x is  is mathematically given as

Option A

From the question we are told

If X-A=B what is X

Generally the equation for Matrix   is mathematically given as

X=B+A

Therefore

X=B{-9 5; 1 -1}+A{2 -7;6 1}

X={-7 -2;7 0}

Therefore

X={-7 -2;7 0}

Option A

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Answer:

Step-by-step explanation:

The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.

1. When x=-1, then

f(-1)=2\cdot (-1)^3-3\cdot (-1)^2+7=-2-3+7=2.

2. When x=1, then

f(1)=2\cdot 1^3-3\cdot 1^2+7=2-3+7=6.

3. When x=2, then

f(-1)=2\cdot 2^3-3\cdot 2^2+7=16-12+7=11.

Answer:

f(-1)=2

f(1)=6

f(2)=11

Step-by-step explanation:

The given function is [tex]f(x)=2x^3-3x^2+7[/tex]

Substitute x = -1 to find the value of f(-1)

[tex]f(-1)=2(-1)^3-3(-1)^2+7\\\\=-2-3+7\\\\=2[/tex]

Thus, f(-1)=2

Substitute x = 1 to find the value of f(1)

[tex]f(1)=2(1)^3-3(1)^2+7\\\\=2-3+7\\\\=6[/tex]

Thus, f(1)=6

Substitute x = 2 to find the value of f(2)

[tex]f(2)=2(2)^3-3(2)^2+7\\\\=16-12+7\\\\=11[/tex]

Thus, f(2)=11

6,000 - 1,800 = 4,200

4,200 / 1/4 (or 25)

she donated 168.0% of her money.

Answer:

Step-by-step explanation:

6000-1800 = 4200 divided by 1/4 = 1050

the measure of those two angles equals 180 since it forms a line

so you add up both angles and set that equal to 180.

(I'll use x as the variable but it's still the same answer)

5x-3+9+x=180

combine like terms

6x+6=180

subtract 6

6x=174

then divide by 6

x=29

To find the value of angle H in a triangle, you subtract the sum of the other two angles from 180. This is based on the triangle angle theorems which state that the sum of the angles in a triangle always equals 180 degrees.

In triangle angle theorems, the sum of the angles of a triangle always add up to 180 degrees. If you need to find the value of angle H in your triangle, you'll need to know the measures of the other two angles. For example, if one angle measures 60 degrees and the other measures 50 degrees, you would subtract the sum of these two angles from 180 to find the value of angle H.

Sum of angles in triangle = 180 degrees

So, Angle H = 180 - (60 + 50) = 70 degrees

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By setting up a system of equations, it was determined that the local hamburger shop sold 350 hamburgers on Friday.

To determine how many hamburgers and cheeseburgers were sold on Friday at the local hamburger shop, we can set up a system of equations based on the information given. Let H represent the number of hamburgers sold and C represent the number of cheeseburgers sold. According to the problem, H + C = 625 and H = C + 75.

To find the number of hamburgers, we replace C in the first equation with H - 75 from the second equation, so we have H + (H - 75) = 625. Simplifying this, we get 2H - 75 = 625. Adding 75 to both sides gives us 2H = 700. Dividing both sides by 2 gives H = 350. Therefore, 350 hamburgers were sold on Friday.

Answer:

399

Step-by-step explanation:

If you want a polynomial to have the x-intercepts of your choice, you simply have to build a polynomial by multiplying pieces like [tex](x-x_k)[/tex] where [tex]x_k[/tex] is the x-intercept you want.

So, if you want x-intercepts 0 and 4, you have to build the polynomial

[tex](x-0)(x-4) = x(x-4)[/tex]

The function that has x-intercepts at (0, 0) and (4, 0) is f(x) = x (x − 4).

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The x-intercepts of a function are the points where the graph of the function crosses the x-axis.

At these points, the value of the function is zero.

To have x-intercepts at (0, 0) and (4, 0), the function must be zero when x is equal to 0 and 4.

Let's evaluate the given options:

f(x) = x(x − 4):

This function is zero at x = 0 and x = 4, so it has x-intercepts at (0, 0) and (4, 0).

f(x) = x(x + 4):

This function is zero at x = 0 and x = -4, so it does not have an x-intercept at (4, 0).

f(x) = (x − 4)(x − 4):

This function is zero at x = 4, but it also has a double root at x = 4, so it only has one x-intercept at (4, 0).

f(x) = (x + 4)(x + 4):

This function is zero at x = -4, but it does not have an x-intercept at (0, 0).

Therefore,

The function that has x-intercepts at (0, 0) and (4, 0) is f(x) = x(x − 4).

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The percentage of the discount given on television is 17.72%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a $79 television is on sale for $65. The percentage of the discount will be calculated as:-

Discount% = ( Original price - Discounted price ) / Original price

Discount% = ( 79 - 65 ) / 79

Discount% = 17.72%

Therefore, the discount per cent on television is 17.72%.

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Answer: False

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

4!  means multiply all the number from 4 down to 1

4! = 4*3*2*1

   = 24

For this case we have that by definition, the factorial of a number is the product of the "n" consvutive factors from n to 1. The factors are in descending order, that is:

[tex]n! = n (n-1) (n-2) ... 3 * 2 * 1[/tex]

Then, we have the following expression:

[tex]4![/tex]

Applying the definition we have:

[tex]4! = 4 * 3 * 2 * 1 = 24[/tex]

ANswer:

[tex]4! = 24[/tex]

Answer:

Step-by-step explanation:

The sum of the angles in a triangle is 180.  So for the triangle on the right:

36 + 84 + x = 180

x = 60

The two angles in the corner add up to 90.  So:

60 + y = 90

y = 30

Finally, for the triangle on the left:

30 + 86 + z = 180

z = 64

Answer:

She is 66 years old.

Step-by-step explanation:

If you minus 452 from 650, you get 198.

198 (the whole amount taken from 650) and divide it by 3: you get 66.

Answer:

She is 66 years old.

Step-by-step explanation:

If you minus 452 from 650, you get 198.

198 (the whole amount taken from 650) and divide it by 3: you get 66.

Answer:88 degrees

Step-by-step explanation:

88 degrees is the correct answer

Answer: Option B

[3, 5]

Step-by-step explanation:

The function g(x) is a line of slope m = 4. Therefore, its rate of change is constant and equal to 4.

The rate of change of the function f(x) in the interval [tex][x_1, x_2][/tex] is calculated with the following formula

[tex]m =\frac{y_2-y_1}{x_2 - x_1}[/tex]

Note that the rate of change of the function increases as x increases.

For example

For [-1, 0]

[tex]m =\frac{4-3.5}{0 - (-1)}[/tex]

[tex]m =\frac{1}{2}[/tex]

[tex]\frac{1}{2}<4[/tex]

For [0, 2]

[tex]m =\frac{7-4}{2 - 0}[/tex]

[tex]m =\frac{3}{2}[/tex]

[tex]\frac{3}{2}<4[/tex]

For [1, 3]

[tex]m =\frac{11-5}{3-1}[/tex]

[tex]m =3[/tex]

[tex]3<4[/tex]

For [3, 5]

[tex]m =\frac{35-11}{5-3}[/tex]

[tex]m =12[/tex]

[tex]12>4[/tex]

Answer:

x= 0 and x = -1

Step-by-step explanation:

Solving the equation:

[tex]x^2 +3 = 3-x[/tex]

Adding -3 on both sides

[tex]x^2 +3-3 = 3-3-x[/tex]

[tex]x^2  = -x[/tex]

Rarranging

[tex]x^2 +x= 0[/tex]

Solving quadratic equation using quadratic formula

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where a = 1 , b =1, c= 0

[tex]x=\frac{-1\pm\sqrt{(1)^2-4(1)(0)}}{2(1)}\\x=\frac{-1\pm\sqrt{1-0}}{2}\\x=\frac{-1\pm\sqrt{1}}{2}\\x=\frac{-1\pm1}{2}\\x = \frac{-1+1}{2} \,\,and\,\, x=\frac{-1-1}{2}\\x=  \frac{0}{2} \,\,and\,\,  x=\frac{-2}{2}\\x=0 \,\,and\,\, x= -1[/tex]

So, x= 0 and x = -1

The answer should be x = [0, -1]

To find the infinite geometric sum of the series 80 + 10 + 1.25 + ..., use the formula S = a / (1 - r), with 'a' as the first term and 'r' as the common ratio. Apply the significant figures principle for accurate rounding when approximating to a certain number of decimal places.

The student's question involves finding the infinite geometric sum of the series 80 + 10 + 1.25 + .... To determine this sum, we use the formula for the sum of an infinite geometric series, S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio between terms. In this series, 'a' is 80, and the common ratio 'r' can be found by dividing the second term by the first term, which is 10/80 or 1/8.

Plugging the values into the formula gives us S = 80 / (1 - (1/8)) which simplifies to S = 80 / (7/8) = 80 * (8/7) = 640/7. Calculating this yields an infinite sum which can be approximated to decimal places as needed.

For precise calculations, especially when rounding to a certain number of decimal places or significant figures, the rules of significant figures must be followed. As the sample information shows, if a number in the tenths place is to be dropped and it's greater than 5, we round up to ensure the final value adheres to the significant figures principle, consistently providing a more accurate and professional result.

3,301927249 = ³√36

As discussed in one of my videos on my channel [USERNAME: MATHEMATICS WIZARD] on the Six Rational Exponential Rules, this one states that with a numerator of 1 in the exponent, you take the multiplicative inverse [reciprocal] of the fraction, and set the whole number equal to the root, bringing your a inside the radical, which is 36.

ⁿ√aᵐ = aᵐ\ⁿ → works for both: numerator ≥ 1

I am joyous to assist you anytime.

Answer:

193.8

Step-by-step explanation:

Add each value together, we get 969.

Divide by the number of values in the set, we get (969)/5, or 193.8

I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you!

Answer:

193.8

Step-by-step explanation:

It looks like the practice ones are all that matter so I'm only going to answer those. If you need the others answered let me know.

1. 5k-9=-3k+7

Add 9 to both sides: 5k-9+9=-3k+7+9

5k=-3k+16

Add 3k to both sides: 5k+3k=-3k+16+3k

(You are adding 3 and 9 instead of subtracting them because in the equation, they are negative numbers and you have to do the opposite operation to get rid of them.)

8k=16

Divide both sides by 8: 8k/8=16/8

k=2

2. 2(w-3)+5=3w-2

Use the distributive property: 2*w-2*3+5=3w-2

2w-6+5=3w-2

Combine like terms: 2w-1=3w-2

Add 1 to both sides: 2w-1+1=3w-2+1

2w=3w-1

Subtract 3w from both sides: 2w-3w=3w-1-3w

-w=-1

Divide both sides by -1: -w/-1=-1/-1

w=1

3. 8t+9=7t+6

Subtract 9 from both sides: 8t+9-9=7t+6-9

8t=7t-3

Subtract 7t from both sides: 8t-7t=7t-3-7t

t=-3

Answer:

1/3

Step-by-step explanation:

Find two corresponding sides that have lengths.

24 in Figure 1 corresponds to 8 in Figure 2.

Divide the length in Figure 2 by the corresponding length in Figure 1.

scale factor = (length in Figure 2)/(corresponding length in Figure 1)

scale factor = 8/24

scale factor = 1/3

Answer:

36π cm cubed

Step-by-step explanation:

Surface area of a cylinder is 2πr^2 + 2πrh

4 cm is the diameter in the image, so the radius is 2 (4/2)

7 is the height

π2(2^2) + π2(2)(7)

8π + 28π

36π

The answer above me is right

Answer:

The measure of angle G is 108 Degrees, hope this helps.

Step-by-step explanation: