Find the sum of the terms.

The numerator of the simplified sum is

Answer:

9

Step-by-step explanation:

;)

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, [tex]40\frac{1}{2}[/tex] square feet = 40.5 square feet

Rate at which he paints the wall =40.5/10

= 4.05 square feet per minute

As we know 1 hour =60 minutes

Now, number of square feet

= 4.05×60

= 243 square feet

Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.

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Answer:

98-5 = 93

Step-by-step explanation:

The number of small size and large size bowls of ice cream sold in the shop is 40 and 22 respectively.

let

Number of small bowl = x

Number of large bowl = y

x + y = 63

2.25x + 3y = 159

From (1)

x = 63 - y

Substitute into (2)

2.25x + 3y = 159

2.25(63 - y) + 3y = 159

141.75 - 2.25y + 3y = 159

- 2.25y + 3y = 159 - 141.75

0.75y = 17.25

divide both sides by 0.75

y = 17.25 / 0.75

y = 23

Substitute y = 23 into (1)

x + y = 63

x + 23 = 63

subtract 23 from both sides

x = 63 - 23

x = 40

In conclusion, The ice cream shop sold 40 small size bowls and 23 large size bowls

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An equation in slope-intercept form of the line perpendicular to y = 2x-4

is y =(-1/2)x+10.

We are aware that there are many types of equations for lines, with the

general type being Ax+ By + C = 0, and the slope-intercept form equation

being y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept is the point (0,b) where the line intersects the y-axis when

x = 0, and the slope is the rate of change of the y-axis relative to the x-axis.

We are aware that the slopes of perpendicular lines are oppositely negative.

The slope of the given line, y = 2x-4, is 2.

Consequently, the given line will pass through point with a slope of (-1/2). (4,8).

∴8= (-1/2)(4)+b

8= -2+b

b = 10.

∴ y =(-1/2)x+10  is our required line.

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Answer: ($9.40) or (d)

Step-by-step explanation:

Step-by-step explanation:

here is your answer to your question

Answer: 20x^4 + 2x³ - 19x² - 28x + 6

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

I’m so smart fr

Function may return true or false.

A continuous function is one in which a continuous variation of the input (i.e., a change without a jump) results in a continuous modification of the function's value. This indicates that there aren't any discontinuities, or sudden changes in value.

Here, the function f(x) is continuous.

It follows that if x = 2 then f(x) = 3,

if x = 5 then f(x) = -9,

if x = 7 then f(x) = -15,

if x = 9 then f(x) = -13.

There are at least two solutions in the interval {2,9} for the graph of the function cross x axis f(x) = 0, hence it is not provided.

Therefore, it may be true or false.

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Answer:

[tex]\frac{x+7}{4}[/tex]

(B) is your answer :)

Step-by-step explanation:

do you need me to work it out?

Answer:

b

Step-by-step explanation: took the test

the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.

The probability of a randomly selected person having a birthday in August is 1/12. There are 12 months in a year and August is one of them. Therefore, The probability of a randomly selected person having a birthday in August is 1/12 because there are 12 months in a year and August is one of them. Each month has an equal chance of being chosen since they all have the same number of days. This probability remains the same regardless of whether or not it is a leap year. Therefore, the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.The probability of a randomly selected person having a birthday in August is calculated by dividing the number of days in August (31) by the total number of days in a year (365). This works out to be 1/12 or 0.0833 rounded to four decimal places.

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Answer: (6, -4)

Step-by-step explanation:

Because it translate right 4 units, so the x increase by 4, so x=6

It up 3, so y increase by 3, so y= -4

Answer:

3/31

Step-by-step explanation:

31 - 28 = 3 left handed students

31 total students

probability that a student chosen at random will be left-handed is 3/31

Your answer will be letter C [-4, ∞)

Check the picture below.

so let's check the middle of the picture, inscribed angle "b" is intercepting the purple arc, wait a second!!! angle 22° is intercepting the same arc! ahaaa!.

now let's check the right of the picture, inscribed angle "a" is intercepting that brown arc, wait a second!!! angle 45° is intercepting the same arc!! ahaa!!.

well, you can see what's "c" and "d".

Answer:

55%

Step-by-step explanation:

first, you set up the problem as two fractions: 11 is to 20 as x is to 100. you cross multiply the 11 and 100, then divide that by 20 which gives you 55, which you divide by 100 for the percentage answer.

The segments that could be the image of segment AB after a sequence of reflections, rotations, and/or translations include:

A. Line segment GH

D. Line segment NP

F. Line segment CD

From the information, the coordinates of the point A is (1, 2), the coordinates of the point B is (5, 2)

Therefore, the length of the line AB = 5 - 1 = 4 units

In this case, the transformations are, reflections, rotations, and/or translations which are rigid transformations, such that the length of the image of AB will be the same as the length of AB

Therefore, the possible images of AB are;

PN with coordinates P(5, -2) and N(9, -2) and length 9 - 5 = 4 units

HG with coordinates H(-4, -4) and G(-4, -8) and length -4 - (-8) = -4 + 8 = 4 units

CD with coordinates C(-4, 6) and D(-4, 2) and length 6 - 2 = 4 units

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Answer:

  (b)  g(x) = 6√x +7

Step-by-step explanation:

You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.

A vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...

  f(x) = √x . . . . original square root function

  h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6

A translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...

  h(x) . . . . . original function

  g(x) = h(x) +7 . . . . . translation upward by 7 units

Our stretched and translated function is ...

  g(x) = 6√x +7

Answer:

Step-by-step explanation:

12 x 3 = 36

answer is 36

Answer:

12 x 3 = 36

Step-by-step explanation:

The mass of the boy removed is 54.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

let's take the weight of five boys is x

so,

x/5 = 62

x = 310

and let's take the weight of four boys is y.

so,

y/4 = 64

y = 256

let's take the weight of a boy which is removed from them is z

so,

x - z = y

x - y = z

310 - 256 = z

z = 54

Hence, the mass of the boy removed is 54.

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Answer:

A- negative

B-positive

C- zero

Step-by-step explanation:

Going up= positive

Going down= negative

Horizontal line= zero

vertical line= undefined

The required radius of the cylindrical can is 4 millimeters.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases.

Given that,

The height of the cylinder h  = 12 cm.

And volume of the cylinder v = 600 mL

Since, 1 mL = cm³

The volume v = 600 cm³.

Let radius of cylinder is r,

To find the radius, use formula,

Volume of cylinder V = π x r² x h

22/7 x r² x 12 = 600

22/7 x r² = 50

r² = 350 / 22

r² = 15.909

r = 3.98

or r =  4 millimeters.

The radius of the cylinder is 4 millimeters.

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Step-by-step explanation: To solve this inequality, we can first isolate the absolute value term on one side of the inequality by subtracting |n-2| from both sides of the inequality. This gives us the inequality -3 + |n-2| > 2. Then, we need to consider two cases: when |n-2| is positive and when |n-2| is negative.

If |n-2| is positive, then we can drop the absolute value bars and rewrite the inequality as -3 + (n-2) > 2. Solving this inequality, we find that n > 7.

If |n-2| is negative, then we must reverse the direction of the inequality because subtracting a negative number is the same as adding a positive number. This gives us the inequality -3 - (n-2) > 2. Solving this inequality, we find that n < -1.

Therefore, the solution to the inequality is the set of all numbers that are greater than 7 or less than -1, which is the interval (-1, 7).

The netball team scored 26 points in their fifth game.

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Let x be the no. of points the netball team scores in the fifth game.

∴ (31 + 31 + 31 + 31 + x)/5 = 30.

(124 + x)/5 = 30.

124 + x = 150.

x = 26.

So, They scored 26 points in their fifth game.

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Answer:

22 rabbits and 50 hens

Step-by-step explanation:

Let H and R stand for the numbers of Hens and Rabbits.  Each hen has two feet and each rabbit has four feet.  Each only has 1 head.

We can set the quantities of feet and heads:

Hens:  2H feet and 1H heads

Rabbits:  4R feet and 1R heads

We are told that:

1.)  "The number of feet of the hens exceeds the number of feet of the rabbits by 12"  Rewrite this as an expression:

  2H - 4R = 12  [feet]

2)  "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"  This is written as:

  1H = 1R + 28  [heads]

Since each critter only has one head, this last expression will tell us, quickly, how many more Hens there are, which is 28.  But by substituting the first expression (the feet) into the second, we can detrermine the exact number of each animal.

Rearrange 2H - 4R = 12 to isolate one of the variables.  I'll choose H:

  2H - 4R = 12

  2H  = 12 + 4R

  H  = (12 + 4R)/2

   H =  6+2R

Now use this definition of H in the second equation:

1H = 1R + 28

1(6+2R) = 1R + 28

6 + 2R = 1R + 28

 R = 22   There are 22 rabbits

Use this in the second equation to find the number of hens:

1H = 1R + 28

1H = 22 + 28

 H = 50  There are 50 hens.

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

Check:

1.)  "The number of feet of the hens exceeds the number of feet of the rabbits by 12."  

 Hens have 100 feet total.  Rabbits have 88 feet.    The hens have 12 more total feet:  This checks

2.)  "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"  

 There are 50 heans and 22 rabbits.  The number of hen heads exceed the number of rabbit heads by 28.  This also checks.

The answer to this question which is based on Trignometry is that we divide when we want to calculate Trignometric Ratios

How many Trignometric ratios are available?

There are six basic trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These ratios are used to calculate angles and sides of a right triangle.

Whenever we need to calculate Trignometric ratios we have to divide the length of 2 sides of a triangle and one more the Trignometric ratios can be only found in Right Angled triangle

Hence we can just find the Trignometric ratios for any Triangle we can only do it for right Triangles

The values of Trignometric ratios can be negative also and it depends on the angle for which we want to find the Trignometric ratios.

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