g(x) = -3x - 5, find g(4).

The length of the opposite side XY = 15.2cm

How to calculate the opposite side XY?

From the right- triangle XYZ,

[tex]sin \theta =\frac{opposite}{hypotenuse}\\\\sin 61 ^\circ=\frac{XY}{XZ} \\\\XY = sin 61 ^\circ *XZ\\\\XY = 0.875* 17.4 \\\\XY = 15.2cm[/tex]

The length of the opposite side XY = 15.2cm

What is opposite side of a right-triangle?

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Answer:

================================

Large cake:

Small cake:

The profit is the difference of the cost and selling price.

Find the cost x of large cake:

Find the volume of the pack of smaller cakes, taking the volume of the large cake as a unit:

Cost of the pack of smaller cakes is proportional to the volume:

Profit made on smaller cakes:

Answer:

12.5

Step-by-step explanation:

there are eight triangles and one yellow so 1/8=12.5%

Answer: 12.5%

Step-by-step explanation:

There are 8 sections and 1 of them is yellow so 1 divided by 8 is 0.125 or 12.5%

By applying a rotation of 90° clockwise to square ABCD, we have the following:

A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise direction.

In Mathematics, rotating a point 90° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (y, -x).

By applying a rotation of 90° clockwise to square ABCD, the coordinate of the image of square A'B'C'D' is given by:

(x, y)                           →               (y, -x)

Points at A = (-3, 5)   →  Points at A' = (5, -(3)) = (5, -3)

Points at B = (-7, -2)   →  Points at B' = ((-2), -(-7)) = (-2, 7).

Points at C = (-8, 8)   →  Points at C' = (8, -(-8)) = (8, 8).

Points at D = (-4, 10)   →  Points at D' = (10, -(-4)) = (10, 4).

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Number of biology book sold are 223.

Number of psychology books sold are 183.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given Data

A textbook store sold a combined total of 392 biology and psychology textbooks in a week. the number of psychology textbooks sold was 48 less than the number of biology textbooks sold.

Let number of biology books sold be x

Let number of psychology books sold be (x- 48)

Total book sold = 392

392 = x + x - 48

392 + 48 = 2x

446 = 2x

x = 223

Number of biology book sold are 223.

Number of psychology books sold are 183.

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The completed table is:

Term Number    1       2    3    4   5     6

Term Value       6     10   14   18  22   26

In order to determine the term values, the rate of increase in the number of videos that Violet has at the end of each week has to be determined.

Rate of increase in the number of videos can be determined by dividing the change in the number of videos per week by the change in the number of weeks.

Rate of increase = change in the number of videos / change in the number of weeks

(10 - 6) / (2 - 1)

4 / 1 = 4 videos per week

Number of videos in week 5 = 18 + 4 = 22

Number of videos in week 6 = 22 + 4 = 26

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Answer: $426.20

Step-by-step explanation:

The subtotal is [tex]299.99+191.96+99.99=\$ 591.94[/tex].

[tex](591.94)(0.8)=\$473.552\\\\(473.552)(0.9) \approx \$426.20[/tex]

Riley hit 46 balls and Paul hit 29 balls at the driving range.

According to the question, let

Number of balls hit by Riley be x

Number of balls hit by Paul be y

Together Riley and Paul hit 75 balls

∴x+y=75       (1)

Riley hit 17 more balls than Paul

∴x= y + 17      (2)

Now we have to solve these simultaneous linear equations (1) and (2)

Replacing the value of x from equation (2) into equation (1) we get,

y+17+y=75

⇒2y + 17 = 75

⇒2y = 75 - 17

⇒2y = 58

⇒y = 58/2             (dividing both sides by 2)

⇒y = 29

∴No. of balls hit by Riley = x = y +17 = 29 + 17 = 46         (from equation (2))

Therefore, Riley hit 46 balls and Paul hit 29 balls at the driving range.

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Answer:

y= 2x + 9

Step-by-step explanation:

Given:

The rate of change in volume = 12 cubic feet per minute.

We need to find the rate of change of radius at radius = 6 feet.

Consider the formula to find the volume of the sphere.

Differentiate with respect to t.

Dividing both sides by 144pi, we get

Hence the radius of the balloon increases by 0.03 feet per minute.

Answer:

Since the y axis is increasing at an exponential rate. You can see that it goes from 0.06 to 0.125 to 0.25. If you were to graph that it would be a exponential curve. You can see that it jumps alot.

0.0625 to 0.0625*2 to 0.0625*2*2 to  0.0625*2*2*2

To calculate the future value we need to use the compound formula:

where P is the principal, r is the interest rate in decimal form, n is the number of times the interest is compound in any given time t.

In this case we have that P=901, r=0.035 and since the interest is compound semiannually this means that n=2. Finally t=6. Plugging this values into the equation above we have that:

Therefore the future value would be $1109.53

The correct solution to the equation is -13.

-12x + 12 = -3(5x + 8)

Split the right-hand side,

-12x + 12 = -15x + 24 (This line have error, instead of + there will be - )

Shifted the values of x to the left-hand side and the constant values to the right-hand side,

3x + 12 = 24

3x = 12

x= 4, which is the incorrect value of x.

The correct solution to the equation,

-12x + 12 = -3(5x + 8)

Split the right-hand side,

-12x + 12 = -15x - 24

Shift the values of x to the left-hand side and the constant values to the right-hand side,

3x = -36

The final value of x,

x = -13

Therefore, the value of x is -13.

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Answer:

1953.125

Step-by-step explanation:

(12.5)³

= 12.5 × 12.5 × 12.5

= 1953.125

Answer: 1953.125

(12.5)³

so 12.5 multiplied to itself thrice

12.5x12.5x12.5

which is 1953.125

Answer:

A 100% increase in a total means the final amount is 200% of the initial amount.

A 100% decrease in a total means the final amount is 0% of the initial amount.

Error means that you were a way off from the real value

Step-by-step explanation:

Answer: About 65 minutes.

It changes an average of about 60 degrees Fahrenheit every half hour.

180     120      60    50

 0       30       60     65

Now it is about ten degrees until it's fifty. Since it takes thirty minutes to go down sixty degrees, divide sixty by ten to get six. Then divide thirty by six to get five. So, it should take about 65 minutes to cool down to 50 degrees.

It will take approximately 35 minutes for the custard to cool from 120°F to 50°F.

To determine how long it will take for the custard to cool to 50°F, we need to consider the rate at which it cools. From the given information, we know that the custard cools from 180°F to 120°F in 30 minutes.

To find the rate of cooling, we can calculate the temperature change per minute.

The temperature decreases by 180°F - 120°F = 60°F over 30 minutes. So, the rate of cooling is 60°F / 30 minutes = 2°F per minute. Now, let's use this rate to calculate how long it will take for the custard to cool from 120°F to 50°F.

The temperature difference between 120°F and 50°F is 120°F - 50°F = 70°F. To cool from 120°F to 50°F at a rate of 2°F per minute, it will take 70°F / 2°F per minute = 35 minutes.

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Answer:

34.1%, D

Step-by-step explanation:

To convert a number into a percent, you multiply it by 1, or more precisely, 100%. 100% can be thought of as 100 * 1%
0.341 * 100 * 1 %   = 34.1%

Answer:

Step-by-step explanat

Answer:

1. 25+5c

2. -8y-16

3. (m+1)^9

4. -6a-15

5. 4y+12z

6. (2a+3b)^4

7. 23c

8. 8y+7x

9. 14a+16

10. 16m+16n

Answer: y = -4x + 11

Step-by-step explanation:

y = mx + b

3 = -4(2) + b

3 = -8 + b

11 = b

Given data:

The given expression is f(x)= (-4x+8)/(x^2 -x-2).

The hole of the graph is x=2.

The expression for the vertical asymptode is,

The expression for the horizontal asymptode is,

There is no x-intercept, and y-intercept is,

Thus, the

A function can only have two horizontal asymptotes, hence the answer is no. By examining the degrees of the numerator and denominator, one can find the horizontal asymptote of a rational function.

If limxf(x)=L or limxf(x)=L, a function f(x) will have the horizontal asymptote y=L. Therefore, we simply calculate the function's limit as it approaches infinity and again as it approaches negative infinity to locate horizontal asymptotes. Based on the degree of the numerator, n, and the degree of the denominator, m, horizontal asymptotes adhere to three principles. The horizontal asymptote is y = 0 if n m. The horizontal asymptote is y = a/b if n = m. There is no horizontal asymptote if n > m. As x gets closer to 0, we say that f(xlimit )'s is infinite. A boundary or a limit is now a number.

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Answer:

the answer is y<-17

Step-by-step explanation:

This is actually just like algebra.

y+8<-9

y<-9-8

y<-17

Shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .

What is difference between fraction and mixed number?

Single fraction is represented as [tex]\frac{p}{q}[/tex]   form where p is numerator and q is denominator and value of q can't be zero. Example [tex]\frac{5}{9}[/tex] .

Mixed number contains two part one is an integer and other is fractional part. It is represented as N [tex]\frac{p}{q}[/tex]. Example  5[tex]\frac{1}{2}[/tex] .

According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.

There are three shaded circle and a circle with 7 sector shaded.

So, Total shaded area in single fraction = 1 + 1 + 1+ [tex]\frac{7}{10}[/tex] =   [tex]\frac{37}{10}[/tex]

and total shaded area in mixed number = 1 + 1 + 1 +  [tex]\frac{7}{10}[/tex] = 3 + [tex]\frac{7}{10}[/tex] = 3[tex]\frac{7}{10}[/tex] .

Hence, shaded portion in single fraction is [tex]\frac{37}{10}[/tex] and mixed number is 3[tex]\frac{7}{10}[/tex] .

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In ΔTUV, UV = 14, VT = 19, and TU = 9, The statement about the angles of ΔTUV that must be true is  [tex]m \angle U > m \angle T > \angle V[/tex] Option 5

This is further explained below.

Generally, A triangle's angle is a measurement of the length of the side that is perpendicular to it.

This indicates that if one of the sides is longer in length, then the measure of the angle opposite to it will also be longer.

The angles in the triangle TUV are denoted by the symbols T, U, and V.

The side that is UV, TV, and T U correspondingly is the side that is opposite to these angles.

The length of the opposing sides will immediately determine the measure of the angles, which will be directly proportionate to those angles.

since V T>U V>T U, the arrangement of angles will correspond to this as follows: [tex]m \angle U > m \angle T > \angle V[/tex] Option 5

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CQ

In $\triangle T U V$, UV $=14, V T=19$, and $T U=9$. Which statement about the angles of $\triangle T U V$ must be true?

$\mathrm{m} \angle V>\mathrm{m} \angle T>\mathrm{m} \angle U$

$\mathrm{m} \angle T>\mathrm{m} \angle U>\mathrm{m} \angle V$

$\mathrm{m} \angle U>\mathrm{m} \angle V>\mathrm{m} \angle T$

$m \angle V>m \angle U>m \angle T$

$m \angle U>m \angle T>m \angle V$

$\mathrm{m} \angle T>\mathrm{m} \angle V>\mathrm{m} \angle U$