A.-1/3
B.-1
C.-3/2
D.-2/3

Answer:

15/8

Step-by-step explanation:

for 1 batch=5/2 pounds

for 3/4 batch=[5/2]×(3/4)

Answer: Michael will need 15/8 pounds of apples.

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the amount of apples that a batch of applesauce needs (2 1/2) by the number of batches of applesauce that Michael wants to make (3/4).

Mathematically speaking;

2 1/2 x 3/4 = ([2x2+1] / 2 ) x 3/4 = 5/2 x 3/4 = (5x3) / (2x4) = 15/8  

He will need 15/8 pounds of apples.

Answer:

The answer is C

Step-by-step explanation:

It is nonlinear but you have to look at it compared to the months passed. In three months the total houses built are 33 this would mean each month they build 11 houses but in the fourth month they have built 46 houses because 46-11 dosnt equal 33 it is nonlinear.

Answer:  It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.

Step-by-step explanation:

We say function to be linear if the rate of change in dependent variable (y) with respect to independent variable (x) is constant.

Rate of change =[tex]\dfrac{\text{Change in dependent variable}}{\text{Change in independent variable}}[/tex]

According to the question ,

Independent variable = Number of months

Dependent variable = Total house built

Now rate of change of "Total house built" for month 0 to 3:-

[tex]\dfrac{33-0}{3-0}=\dfrac{33}{3}=11[/tex]                           (1)

Rate of change of "Total house built"fro month 3 to 4:-

[tex]\dfrac{46-33}{4-3}=\dfrac{13}{1}=13[/tex]                         (2)

From (1) and (2), it is clear that the rate of change is not constant

(∵ 11≠ 13 ).

Hence, the correct answer is : It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.

Answer:

40°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for third angle

third angle = 180° - (90 + 50)° = 180° - 140° = 40°

Answer: B. 40

Step-by-step explanation: A triangle’s angles will always add up to 180 degrees. Add the 2 angles that are given. 90 + 50 = 140. Subtract this number from 180. 180 - 140 = 40. The third angle is 40 degrees.

Answer:

2/9

Step-by-step explanation:

f(x)=2*3^x

Let x=-2

f(-2) = 2 * 3^(-2)

When the exponent is negative, it flips from the numerator to the denominator

      = 2 * 1/(3^2)

      = 2 * 1/9

     = 2/9

Answer:

It's 2/9.

Step-by-step explanation:

Replace to x by -2.

y = 2 * 3^(-2)

= 2 / 3^2

= 2/9.

Answer:

240

Step-by-step explanation:

Where P = pages and x = minutes, your rule is as follows:

[tex]P=\frac{10}{3} x[/tex]

Simply plug in your last minute value to find your last page value.

[tex]P=\frac{10}{3} (72)\\P=240[/tex]

Answer:

The scale factor of dilation is 1/2

New coordinates are: (-3, 3/2)

Step-by-step explanation:

a) A dilation maps (4,6) to (2,3)

we see that (4/2,6/2) = (2,3)

So, the scale factor of dilation is 1/2

b) if (-6,3) is under same dilation, their new coordinates will be?

We have to multiply (-6,3) by scale factor of 1/2

(-6*1/2,3*1/2) = (-3,3/2)

So, new coordinates are: (-3,3/2)

To solve this problem, we will complete the following steps:
Step 1: Determine the Scale Factor
We are given that the dilation maps the original point (4, 6) to the dilated point (2, 3). To find the scale factor of the dilation, we consider the ratios of the coordinates of the dilated point to the coordinates of the original point. This ratio should be the same for both the x- and y-coordinates since the dilation is uniform.
Scale factor for x-coordinate:
\( \frac{2}{4} = \frac{1}{2} \)
Scale factor for y-coordinate:
\( \frac{3}{6} = \frac{1}{2} \)
Both x and y scale factors are \( \frac{1}{2} \), confirming that the dilation is uniform, and hence the scale factor is \( \frac{1}{2} \).
Step 2: Apply Dilation to the Point (-6, 3)
Now, we want to apply the same scale factor to another point (-6, 3) to find its new coordinates under the same dilation.
\( \text{New x-coordinate} = -6 \times \frac{1}{2} = -3 \)
\( \text{New y-coordinate} = 3 \times \frac{1}{2} = \frac{3}{2} \) or 1.5
Therefore, when the point (-6, 3) is dilated with a scale factor of \( \frac{1}{2} \), the new coordinates are (-3, 1.5).

Answer:

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the given base

# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3

Step-by-step explanation:

* Lets explain how to solve the problem

- She has three vertices of the parallelogram

- The vertices are (12 , 2) , (5 , 2) , (1 , 5)

∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates

∴ The length of the base of the parallelogram is 12 - 5 = 7 units

- In parallelogram each two opposite sides are equal and parallel

∴ The opposite side to the base is 7

∴ The x coordinate of the missing point equal the x-coordinate of the

  point (1 , 5) + the length of the base

∴ The x coordinate of the missing vertex  = 1 + 7 = 8

∵ The y-coordinate of the missing vertex is the same with the

   y-coordinate of the point (1 , 5)

∴ The y-coordinate of the missing vertex is 5

∴ The missing vertex is (8 , 5)

- The area of the parallelogram is A = bh, where b is the base of it

  and h is the height of this base

- Remember the height must be perpendicular on the base

∵ The perpendicular distance between the two parallel bases is the

  difference between the y-coordinates of the two points each one

  belong to one of the two parallel bases

∴ The height of the parallelogram = 5 - 2 = 3 units

∴ Its area = 7 + 3 = 21 units ²

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the

   given base

# She used a side length of the parallelogram for the height instead

  of a line segment perpendicular to the base; the height should be 3

(2^3)^5

=2^(3*5)

= 2^15

hope it helps

Answer:

A

Step-by-step explanation:

Using the rules of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] and

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

Given

[tex](2^3)^{-5}[/tex]

= [tex]2^{3(-5)}[/tex] = [tex]2^{-15}[/tex] = [tex]\frac{1}{2^{15} }[/tex]

Step-by-step explanation:

It is impossible for a triangle to have side lengths of 4, √415, and 16.

The sum of the shortest two sides must be greater than the longest side.  However, 4 + 16 < √415.  

It is impossible to make a triangle with side lengths  4, √415, and 16 because the two side length of the triangle is always greater than the third length of the triangle.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have side lengths of a triangle.

As we know from the definition of the triangle the sum of the two side length of the triangle is always greater than the third length of the triangle.

Also, the sum of the interior angle of a triangle is 180 degrees.

As the three lengths are 4, √415, and 16

AB + BC < AC

Let suppose:

AB = 4 units

BC = 16 units

AC = √415 units

4 + 16 < √415

Thus, it is impossible to make a triangle with side lengths  4, √415, and 16.

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Answer:

1: C=615.75m

2: 62.83 meters or 60 meters rounded to the nearest tenth

Step-by-step explanation:

1: The circumference of a circle that has radius of 98 meters, using 3.14 for pi, is 615.75m.

Formula: C=2πr

C=2πr=2·π·98≈615.75216m

_______________________________________________

2: The difference in area between circle A and circle B, using 3.14 for pi and rounded to the nearest tenth is 62.83 meters or 60 meters.

The diameter of circle A is 12 cm.

Changing the diameter to radius is going to be easier.

Radius is half of the diameter.

12 ÷ 2 = 6

Therefore, the area of circle A is 113.1.

Formula: A=πr^2

A=πr^2=π·6^2≈113.09734

The diameter of circle B is 8 cm.

Once again, changing the diameter to radius is going to be easier.

Radius is half of the diameter.

8 ÷ 2 = 4

Therefore, the area of circle B is 50.27.

Formula: A=πr^2

A=πr2=π·42≈50.26548

113.09734 - 50.26548 = 62.83 meters or 60 meters.

Answer:

Hi there!

The answer to this question is: B

Step-by-step explanation:

The function for the question is: y=3^x

3^10=59049 and 3^9=19683

Then you just subtract the two numbers to get 39366

ANSWER

B. 39,366

EXPLANATION

The y-values of the exponential function has the following pattern

[tex] {3}^{0} = 1[/tex]

[tex] {3}^{1} = 3[/tex]

[tex] {3}^{2} = 9[/tex]

[tex] {3}^{3} = 27[/tex]

:

:

[tex] {3}^{x} = y [/tex]

Or

[tex]f(x) = {3}^{x} [/tex]

To find the average rate of change from x=9 to x=10, we simply find the slope of the secant line joining (9,f(9)) and (10,f(10))

This implies that,

[tex]slope = \frac{f(10) - f(9)}{10 - 9} [/tex]

[tex]slope = \frac{ {3}^{10} - {3}^{9} }{1} [/tex]

[tex]slope = \frac{59049-19683}{1} = 39366[/tex]

Therefore the average rate of change from x=9 to x=10 is 39366.

The correct answer is B.

Answer:

6

Step-by-step explanation:

[tex]-\frac{2}{3} x+9=\frac{4}{3} x-3\\\\[/tex]

First, multiply both sides by 3.

[tex]-2x+27=4x-9\\[/tex]

Next, combine like terms.

[tex]-2x+27=4x-9\\-2x+36=4x\\36=6x[/tex]

Solve for x.

[tex]36=6x\\6=x[/tex]

The value of "x" in the equation is 6.

To find the value of "x" in the equation -2/3x + 9 = 4/3x - 3, we need to isolate "x" on one side of the equation. Let's solve step-by-step:

Step 1: Get rid of fractions by multiplying all terms by the least common multiple (LCM) of the denominators, which is 3.

3 * (-2/3x) + 3 * 9 = 3 * (4/3x) - 3 * 3

Simplify:

-2x + 27 = 4x - 9

Step 2: Move "4x" and "27" terms to one side and " -2x" and " -9" terms to the other side.

Add 2x to both sides:

-2x + 2x + 27 = 4x - 9 + 2x

Simplify:

27 = 6x - 9

Step 3: Move the constant term " -9" to the other side of the equation by adding 9 to both sides:

27 + 9 = 6x - 9 + 9

Simplify:

36 = 6x

Step 4: Solve for "x" by dividing both sides by 6:

x = 36 / 6

x = 6

The value of "x" in the equation is 6.

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to get the equation of a straight line, all we need is two points, hmmm say this line runs over (0 , -2) and (3 , 0), so let's use those.

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-0}{0-3}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{2}{3}(x-3)\implies y=\cfrac{2}{3}x-2[/tex]

Answer:

g(x) = x + 2 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the translation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

* Lets solve the problem

∵ The parent function f(x) = x + 6

∵ f(x) is shifted four units to the right

- The translation of a function by h units to the right change the x in

  the function by subtracting h from it

∴ The x in f(x) will change to (x - 4)

∴ The new function = (x - 4) + 6

- Simplify the function

∴ The new function = x + 2

∵ The new function is g(x)

∴ g(x) = x + 2

Answer:

Step 3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Let n be the number

product of seven and a number

7n

is negative 21

7n = -21

Divide each side by 7

7n/7 = -21/7

n = -3

The number is -3

Answer:

36 meters

Step-by-step explanation:

Using pythagorean theorem, 36² - 15² = 1296. √1296 = 36 meters

Answer:D. 36 m

Step-by-step explanation: Use the Pythagorean Theorem, which is a^2 + b^2 = c^2 to find the missing side. C is the hypotenuse. Plug in the numbers.

15^2 + b^2 = 39^2

Simplify.

225 + b^2 = 1521

Subtract 225 from each side.

b^2 = 1296

Square root each side to isolate b.

b = 36

The height of the support beam is 36 m.

The correct answer is c. 1-2 sin^2 x.

The correct answer is c. 1-2 sin^2 x.

To find the value of sin 2x, we can use the double angle formula for sine, which states that sin 2x = 2sin x cos x. Therefore, b. 2 sin x cos x is the correct answer choice.

Correct option is (b) 2sinxcosx

Now using the trigonometric identity of 'sin(a+b)' we can find out the value of sin2x

sin (a + b) = sin a cos b + sin b cos a,

where 'a' and 'b' are angles

let 'a'='x' and 'b'='x'

[tex]sin2x=sin(x+x)\\sin2x=sinx*cosx+sinx*cosx\\sin2x=2sinxcosx[/tex]

Thus 2sinxcosx is the required answer

Answer:

1)A'(8,-10), B'(10,-8), C'(2,-4)

2)A''(8,-4), B''(10,-6), C''(2,-10

Step-by-step explanation:

Given:

Points A(8,8) B(10,6) C(2,2)

reflection over y=-1

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3

after reflections, the perpendicular distance will be 18,14,6 and the points will be at

A'(8,-10), B'(10,-8), C'(2,-4)

Now  

Points A(8,-10), B(10,-8), C(2,-4)

reflection over y=−7

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3

after reflections, the perpendicular distance will be 6,2,6 and the points will be at

A''(8,-4), B''(10,-6), C''(2,-10) !

Anna's remaining marbles are worth 175 + 6k cents, where k is the worth of a large marble in cents.

Here's a step-by-step solution: Anna initially had 5 small marbles that are worth 25 cents each and 8 large marbles that are worth k cents each. So, her total value in cents would be 5×25 + 8×k which equals 125 + 8k.

After trading 3 large marbles for 1 large marble and 6 small marbles, she now has 6 (8-3+1) large marbles and 11 (5 + 6) small marbles. The worth of her marbles now becomes 6×k (6 large marbles worth k cents each) + 275 (11 small marbles worth 25 cents each), totalling to 275 + 6k.

Anna then gives 4 small marbles to Henry. Now, she is left with 7 small marbles and 6 large marbles. Therefore, the worth of her remaining marbles in cents is 6k (6 large marbles worth k cents each) + 175 (7 small marbles worth 25 cents each), which on simplifying gives A + Bk = 175 + 6k.

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To find the value of the marbles Anna has left in terms of k, calculate the total value of the marbles started, subtract the value lost, and simplify the equation. The value of the marbles Anna has left is 275 cents + 10k cents.

To find the value of the marbles Anna has left, we need to calculate the total value of the marbles she started with and then subtract the value lost through trading and giving marbles to Henry.

1. Total value of the small marbles: 5 small marbles x 25 cents each = 125 cents.

2. Total value of the large marbles: 8 large marbles x k cents each = 8k cents.

3. Value gained through trading: 3 large marbles - 1 large marble = 2 large marbles.

4. Value gained through trading (small marbles): 6 small marbles.

5. Value lost through giving marbles to Henry: 4 small marbles.

6. Value remaining: (125 cents + 8k cents) + (2 large marbles x k cents) + (6 small marbles x 25 cents) - (4 small marbles x 25 cents)

Simplifying the equation, we get: 125 cents + 8k cents + 2k cents + 150 cents - 100 cents = 275 cents + 10k cents. Therefore, the value of the marbles Anna has left, in terms of k, is A + Bk, where A = 275 and B = 10.

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The perimeter of the rectangle is 6x + 2

The formula for the perimeter of  rectangle is expressed as;

P =2 ( l + w)

Such that the parameters are;

Now, substitute the values, we get;

Perimeter = 2( 2x + 3 + x - 2)

collect the like terms, we get;

Perimeter = 2(3x + 1)

expand the bracket

Perimeter = 6x + 2

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Answer:

The hourly fee charged by the teacher was $32.10.

Step-by-step explanation:

A music teacher charged for [tex]2\frac{1}{2}[/tex] hour = $80.25

To calculate the hourly fee of the teacher, we have to divide 80.25 by 2.5

Therefore, hourly fee of the teacher [tex]=\frac{80.25}{2.5}[/tex]

                                                            = $32.10

The hourly fee charged by the teacher was $32.10.

Answer:

the answer is 42.875

Step-by-step explanation:

3.5^3 = 42.875

Answer:

[tex]\large\boxed{V=42\dfrac{7}{8}\ ft^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cube:

[tex]V=a^3[/tex]

a - edge

We have

[tex]a=3\dfrac{1}{2}\ ft[/tex]

Convert to the improper fraction:

[tex]a=\dfrac{3\cdot2+1}{2}=\dfrac{7}{2}\ ft[/tex]

Substitute to the formula of a volume:

[tex]V=\left(\dfrac{7}{2}\right)^3=\dfrac{7^3}{2^3}=\dfrac{343}{8}=42\dfrac{7}{8}\ ft^3[/tex]

Answer:

29

Step-by-step explanation:

Simplify the following:

21 + 49/7 + 1

Hint: | Reduce 49/7 to lowest terms. Start by finding the GCD of 49 and 7.

The gcd of 49 and 7 is 7, so 49/7 = (7×7)/(7×1) = 7/7×7 = 7:

21 + 7 + 1

Hint: | Evaluate 21 + 7 + 1 using long addition.

| 2 | 1

| | 7

+ | | 1

| 2 | 9:

Answer:  29

Answer:

the solution set of n2 - 14n = -45 is {5, 9}

Step-by-step explanation:

We have the following equation: n^2 - 14n = -45

Rearrange:

n^2 - 14n +45 = 0

Factorizing:

(n-9)(n-5) = 0

Therefore, the solution set of n2 - 14n = -45 is {5, 9}

Answer:

The factored form of the equation is (x + 4)(x – 6) = 0.

Step-by-step explanation:

(x – 4)(x + 2) = 16

Foil the left side

x^2 +2x-4x-8 =16

Combine like terms

x^2 -2x-8 = 16

Subtract 16 from each side

x^2 -2x-8-16 =16-16

x^2 -2x-24 =0

Factor the left hand side

What two numbers multiply to -24 and add to -2

-6*4 =-24

-6+4 = -2

(x-6) (x+4) =0

Solving using the zero product property

x-6 =0   x+4=0

x=6        x=-4

Answer:

C: on ed

Step-by-step explanation:

Answer:

1 square inch to 16 square feet

Step-by-step explanation:

The real patio area is

[tex]20\cdot 16=320\ ft^2[/tex]

The dimensions of the scale drawing are

[tex]20:4=5\ in\text{ and }16:4=4\ in,[/tex]

so the area of the scale patio is

[tex]5\cdot 4=20\ in^2[/tex]

The ratio of the area of the scaled drawing to the actual area of the patio is

[tex]20:320=1:16[/tex]

or 1 square inch to 16 square feet.

Answer:

I hope this helps

Step-by-step explanation:

To work out the central angle, you just re-arrange the equation for the length of an arc:

Equation for length of an arc:

[tex]\frac{angle}{360}[/tex] × [tex]diameter[/tex] × π = [tex]length of arc[/tex]

We can arrange this to work out the central angle, q.  But first, lets substitute in all of the values that we know:

angle = q

diameter = 5 x 2 = 10 ft

length of arc = 7

[Substitute in]

[tex]\frac{q}{360}[/tex] × [tex]10[/tex]π = [tex]7[/tex]       (Now just rearrange for q)

[tex]\frac{q}{360}[/tex] = [tex]\frac{7}{10\pi }[/tex]     (multiply both sides by 360 to get q)

[tex]q[/tex] = [tex]\frac{7}{10\pi }[/tex] × [tex]360[/tex]  (now just simplify)

[tex]q[/tex] = [tex]\frac{252}{\pi }[/tex]

   = [tex]80.214[/tex]   (rounded to 3 decimal places)

______________________________

Therefore:

The equation that gives you ange q is:

[tex]q[/tex] = [tex]\frac{length.of.arc}{diamater.times.\pi }[/tex] × [tex]360[/tex]

and q = 80.214  when all of the values are substituted in.

Answer:

B q=7/5

Step-by-step explanation:

Well Q=s/r and they said a Radius of 5 Which puts 5 at the bottom.

Then an arc length of 7 Which =S. so q=7/5

Answer:

[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]

Step-by-step explanation:

You only need two points on a line to find the equation for that line.

We are going to use 2 points that cross that line or at least come close to. You don't have to use the green points... just any point on the line will work.  You might have to approximate a little.

I see ~(67.5,67.5) and ~(64,65).

Now once you have your points, we need to find the slope.

You may use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] are points on the line.

Or you can line up the points vertically and subtract then put 2nd difference over 1st difference.

Like this:

(  64  ,   65  )

-( 67.5, 67.5 )

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

-3.5        -2.5

So the slope is -2.5/-3.5=2.5/3.5=25/35=5/7.

Now use point-slope form to find the equation:

[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line.

[tex]y-65=\frac{5}{7}(x-64)[/tex]

Distribute:

[tex]y-65=\frac{5}{7}x-\frac{5}{7}\cdot 64[/tex]

Simplify:

[tex]y-65=\frac{5}{7}x-\frac{320}{7}[/tex]

Add 65 on both sides:

[tex]y=\frac{5}{7}x-\frac{320}{7}+65[/tex]

Simplify:

[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &4 \end{cases} \\\\\\ I=(300)(0.10)(4)\implies I=120[/tex]