Which of the following would be a good name for the function that takes the weight of a box and returns the energy needed to lift it ?

Answer: 2/7

Step-by-step explanation: To simplify the fraction 14/49, we need to find the greatest common factor of 49 and 7 and we can divide our fraction by it.

In this case, the greatest common factor of 14 and 49 is 7 so we can divide both our numerator and denominator by 7.

Therefore, 14/49 as a simplified fraction is 2/7.

Image provided.

Answer:

$1694.5

Step-by-step explanation:

Hourly rate for Beau = $26.50

Weekly hours = 40 Hours

Basic earning = 26.50 × 40 = $820

Total number of hours Beau worked in week = 56.5 Hours

Overtime = 56.5 - 40 = 16.5 Hours

Overtime rate = 2 × Hourly rate = 2 × 26.50 = $53

Overtime earning = 53×16.5 = $874.5

Total earning for the week = 820 + 874.5 = $1694.5

Answer:

A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down

Step-by-step explanation:

step 1

Find out the reflection of △RST across the x-axis

we know that

The rule of the reflection of a point across the x-axis is

(x,y) -----> (x,-y)

we have

R(1,3),S(1,1),T(4,1)

Applying the rule of reflection across the x-axis

R(1,3) -----> R''(1,-3)

S(1,1) -----> S''(1,-1)

T(4,1) ----> T''(4,-1)

step 2

Find out the translation of △R''S''T'' 1 unit down

The rule of the translation is

(x,y) -----> (x,y-1)

Applying the rule of the translation

R''(1,-3)-----> R'(1,-3-1)

R''(1,-3)-----> R'(1,-4)

S''(1,-1)----> S'(1,-1-1)

S''(1,-1)----> S'(1,-2)

T''(4,-1) ----> T'(4,-1-1)

T''(4,-1) ----> T'(4,-2)

therefore

A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down

Answer:

193/27

Step-by-step explanation:

8 10/27 - 1 2/9

226/27 - 11/9

= 193/27

Answer:

755

Step-by-step explanation:

The sum of 308+622+381=755

The sum of the numbers 308,622, and 381 is 755.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the numbers are 308, 622 and 381. The sum of the numbers will be calculated by adding all the numbers as below,

Sum = 308+622+381

Sum = 755

Hence, the sum of the numbers will be 755.

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Answer:

The ball will take 4.05 seconds to hit the ground.

Step-by-step explanation:

we have

[tex]h=-16t^{2}+64t+3[/tex]

This is a quadratic equation (vertical parabola) open down

The vertex is a maximum

we know that

The ball hit the ground when h=0

Solve the quadratic equation

For h=0

[tex]-16t^{2}+64t+3=0[/tex]

The formula to solve a quadratic equation of the form

[tex]at^{2} +bt+c=0[/tex] is equal to

[tex]t=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]-16t^{2}+64t+3=0[/tex]  

so

[tex]a=-16\\b=64\\c=3[/tex]

substitute in the formula  

[tex]t=\frac{-64(+/-)\sqrt{64^{2}-4(-16)(3)}} {2(-16)}[/tex]

[tex]t=\frac{-64(+/-)\sqrt{4,288}} {-32}[/tex]

[tex]t=\frac{64(-)\sqrt{4,288}} {32}=-0.05\ sec[/tex]  ---> the time cannot be a negative number

[tex]t=\frac{64(+)\sqrt{4,288}} {32}=4.05\ sec[/tex]

therefore

The ball will take 4.05 seconds to hit the ground.

Answer:

A. 1/5

Step-by-step explanation:

Add all the numbers up, you get 25. There is 5 yellow marbles, so that's a 5/25 chance of picking a yellow one, now you just have to simplify, you then get 1/5, because 5 ÷ 5 is 1, and 25 ÷ 5 is 5.

Answer:

[tex]\frac{63}{2}[/tex]

Step-by-step explanation:

The n th term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - [tex]\frac{1}{2}[/tex] and d = 4, thus

[tex]a_{9}[/tex] = - [tex]\frac{1}{2}[/tex] + (8 × 4) = - [tex]\frac{1}{2}[/tex] + 32 = [tex]\frac{63}{2}[/tex]

Answer:

The least number of questions a student can answer correctly is 32

Step-by-step explanation:

Let

x -----> the number of questions answered correctly

y ----> the  total number of questions on a test

[tex]ratio=\frac{x}{y}[/tex]

we know that

For a student to earn and A or B on a test, the ratio  must be greater than or equal to 0.8

so

[tex]\frac{x}{y} \geq 0.8[/tex]

For y=40 questions

Find the value of x

substitute

[tex]\frac{x}{40} \geq 0.8[/tex]

solve for x

Multiply both sides by 40

[tex]x \geq 0.8(40)[/tex]

[tex]x \geq 32[/tex]

so

The least number of questions a student can answer correctly is 32

Verify the ratio

For x=32, y=40

[tex]\frac{32}{40}=0.8[/tex]

Compare

[tex]0.8 \geq 0.8[/tex] ----> is ok

Final answer:

This math question involves determining the minimum number of questions a student needs to answer correctly to earn an A or B grade based on a specific ratio criterion.

Explanation:

Mathematics: In this question, we are dealing with a scenario where a teacher evaluates students' test performance based on a specific ratio criterion to determine if they earn an A or B grade. The focus is on determining the minimum number of questions a student must answer correctly to achieve the desired grades.

Step-by-step explanation:

Given that the ratio of correct answers to the total questions must be greater than or equal to 0.8 to earn an A or B.

We know the total number of questions on the test is 40.

To find the least number of questions a student must answer correctly, we calculate 0.8 x 40 = 32.

Therefore, the student needs to answer at least 32 questions correctly to earn an A or B on the test.

A linear pair is supplementary.

It always helps to draw out a diagram with the information you have - it makes the solving process more visual and sometimes easier. I have attached a diagram of this linear pair.

So, since a linear pair is supplementary, we know these two angles add to equal 180°. Let's write this in an equation.

(5n + 15) + (4n + 21) = 180

Solve for n.

(5n + 15) + (4n + 21) = 180

5n + 15 + 4n + 21 = 180

9n + 36 = 180

9n = 144

n = 16

We're not done yet - now we have to plug this in for n to find the angle measures.

5n + 15

5(16) + 15

80 + 15

95

4n + 21

4(16) + 21

64 + 21

85

Lastly, check your work by adding the angle measures.

95 + 85 = 180

m∠EFG = 95°

m∠GFH = 85°

Answer: The radius is 14 units.

Step-by-step explanation:

Start by finding the diameter, the formula for circumference is πd, So set up an equality:

28π=c

28π=πd

Divide both sides by π:

28π/π = 28πd/π

Cross out π:

28 = d

diameters twices largest radius, divide your diameter by 2 to get radius.

D/2 = r = 28/2 = 14

Therefore, your radius is 14 units.

Answer:

Step-by-step explanation:

First, the graph is flattened, and secondly, the whole resulting graph is translated upward by 9 units.

Answer:

2(6x - 2 + x - 1) = 2(7x - 3) = 14x - 6

Greetings!

This is how your double number line should look:

 (lbs)     0      1       2      3     4      5

              ↓-----↓-----↓-----↓-----↓-----↓

              0    3.5    7    10.5  14   17.5          (dollars)

Hope this helps!  

Answer:

The smaller angle is 18 degrees

The larger angle is 72 degrees

Step-by-step explanation:

x = smaller angle

y = larger angle

y = 4x ---> one angle is 4 times larger than other one.

y + x = 90 ----> the sum of complementary angles is 90 degrees

4x + x = 90 ----> plug in 4x for the larger angle (y) and then solve

5x = 90

x = 18 ----> the smaller angle is 18 degrees

y = 90 - 18

y = 72 ----> the larger angle is 72 degrees

The smaller angle is 18.

The complementary angle is the angle that adds up to 90 degrees always, so when we say that two angles are complementary it means that the sum of the angle or the combined angle is equal to ninety degrees.

The larger angle is 4 times the smaller angle so let the smaller angle be 'x' and the larger angle be 4x.

Hence the sum of both the angle is 90 degrees from the definition of complementary

so 4x+x=90, 5x = 90

dividing the equation by 5

x = 18

Hence the smaller angle is 18 degrees

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2,438 3,026 4,209 4,703

Answer: 2,438  3,026  4,209 4,703

Step-by-step explanation:

Answer:

Step-by-step explanation:

D 36 is the answer

Answer:

x=$150,000

4th person invested $550,000

Step-by-step explanation:

100,000+x+2x+(100,000+x+2x)=1,100,000

200,000+6x=1,100,000

6x=900,000

x=150,000

The investment of the fourth person is 100,000+3x

=100,000+450,000

=$550,000

The amount invested by the fourth person was $550,000.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Given that a person invested $100,000. Two others invested in the ratio x:2x and the fourth person invested an amount equal to the other three investors combined.

We have to determine an expression for the amount invested by the fourth person.

The total investment = $1,100,000.

So an expression for the amount invested by all people as:

⇒ 100,000 + x + 2x + (100,000+x+2x) = 1,100,000

⇒ 200,000 + 6x = 1,100,000

⇒ 6x = 900,000

⇒ x = 150,000

So the investment of the fourth person as

⇒ 100,000 + 3x

⇒ 100,000 + 450,000

⇒ $550,000

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Answer:  b ≤ -18

Step-by-step explanation:

Isolate the variable by multiplying both sides by -3.  Remember that when you multiply or divide by a negativem the symbol flips.

[tex]\dfrac{b}{-3}\geq6\\\\\\\dfrac{b}{-3}(-3)\geq6(-3)\\\\\\\large\boxed{b\leq-18}[/tex]

Hey!

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

Solution:

Remember to follow PEMDAS.

= (68 * 95) + 90 / 10

= (6,460) + 90 / 10

= 6,460 + 9

= 6,469

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

Answer:

6,469

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

Hope This Helped! Good Luck!

In order to find the answer to the question you will have to use PEMDAS and then solve.

[tex](68\times95)+90\div10[/tex]

Using PEMDAS:

[tex]68\times95=6460[/tex]

[tex]6460+90\div10[/tex]

[tex]90\div10=9[/tex]

[tex]6460+9[/tex]

[tex]6460+9=6469[/tex]

[tex]=6469[/tex]

Therefore your answer is "6469."

Hope this helps.

Answer:12b^4 + 6b - 18

Step-by-step explanation:

Area of a rectangle is width x height

(4b^4 + 2b - 6) x 3

Multiply the coefficients by 3

So you get

12b^4 + 6b - 18

Answer:

-6

Step-by-step explanation:

Answer:

Is it 15 Minus 21 (Or) 15 x -21

Step-by-step explanation:

Answer: 2/5 3/5 2/3 13/15

Step-by-step explanation:

2/3, 3/5, 13/15, 2/5

The least common denominator is: 15.

Rewriting as equivalent fractions with the LCD:

10/15, 9/15, 13/15, 6/15

Ordering these fractions by the numerator in order from least to greatest:

6/15 < 9/15 < 10/15 < 13/15

Therefore, your input in order from least to greatest is:

2/5 < 3/5 < 2/3 < 13/15

Answer:

0.3

Step-by-step explanation:

7 is greater than 5 therefore round the tenths value up to 3

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=37.68 \end{cases}\implies 37.68=2\pi r\implies \cfrac{37.68}{2\pi }=r \\\\\\ \stackrel{assuming~\pi =3.14}{\cfrac{37.68}{2(3.14)}}=r\implies \boxed{6=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi (6)^2\implies A=36\pi \implies A\approx 113.10[/tex]

If ( t = -3 ), then [tex]\( 3t^2 + 5t + 6 \)[/tex] equals 0.

To find the value of [tex]\( 3t^2 + 5t + 6 \)[/tex] when ( t = -3 ), substitute (-3) for ( t ) in the expression:

[tex]\[ 3(-3)^2 + 5(-3) + 6 \][/tex]

= 3(9) - 15 + 6

= 27 - 15 + 6

= 12 - 15

= -3

Therefore, when ( t = -3 ), \[tex]( 3t^2 + 5t + 6 \)[/tex] evaluates to (-3).

Understanding how to substitute values into algebraic expressions is fundamental in algebra. In this case, replacing ( t ) with (-3) allows us to find the specific value of the expression for that given input.

It's worth noting that this expression equals 0 for ( t = -3 ). This is an interesting mathematical result, indicating that the expression [tex]\( 3t^2 + 5t + 6 \) factors as \( (t + 3)(3t + 2) \),[/tex] making it equal to 0 when either \[tex]( t = -3 \) or \( t = -\frac{2}{3} \).[/tex] This connection between factors and roots is a crucial concept in algebra.

Answer:

10x - 17

Step-by-step explanation:

Perimeter is the sum of all sides

5x - 7 + (3x - 4) + (2x - 6)

10x - 7 - 4 - 6

10x - 17

Answer:

The required diagram is shown below:

Step-by-step explanation:

Consider the provided expression.

0.27+0.23= 1/2

We can draw the model of the provided expression.

Step 1: Shade 27 boxes out of 100 boxes,

This will show 0.27

Step 2: Shade 23 more boxes with another color.

This will show 0.23.

The total shaded boxes are 27+23=50.

Which represents 0.27 + 0.23 = 1/2 (1/2=0.50)

The required diagram is shown below:

To visually show the equation [tex]\(0.27 + 0.23 = \frac{1}{2}\)[/tex], see the diagram attached.

To represent the equation [tex]\(0.27 + 0.23 = \frac{1}{2}\)[/tex], follow the steps:

1. Draw a horizontal line to represent the number line.

2. Label the line with points 0, 0.2, 0.4, 0.6, 0.8, and 1.

3. Mark a point at 0.27, slightly past the midpoint between 0.2 and 0.4.

4. Mark another point at 0.23, slightly before the midpoint of 0.2 and 0.4.

5. Draw a vertical line connecting these two points to represent their sum.

6. Label the top of this line with "0.27 + 0.23."

7. Draw a horizontal line segment from the vertical line's top point to the middle of the line, intersecting at the value 0.5.

8. Label this intersection point as [tex]"\(\frac{1}{2}\)"[/tex] to show that [tex]\(0.27 + 0.23\)[/tex]indeed equals[tex]\(\frac{1}{2}\).[/tex]

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Answer: 36 3/14 miles per hour

Step-by-step explanation:

multiply the speed of a human (5 4/7) by 6 1/2 or 6.5 and you get your answer

To find the fish's speed, convert the mixed numbers 5 4/7 and 6 1/2 to improper fractions and multiply them. The result, 507/14, converts back to a mixed number as approximately 36.21 miles per hour.

To solve this question, we need to multiply the person's swimming speed with the mentioned relative speed of the fish. A person can swim at a speed of 5 4/7 miles per hour, and since the fish can swim 6 1/2 times faster, we multiply 5 4/7 by 6 1/2.

The first step is to convert these mixed numbers to improper fractions. 5 4/7 becomes 39/7 and 6 1/2 becomes 13/2.

Multiplication of fractions involves multiplying the numerators together to get the new numerator and the denominators together to get the new denominator. So the multiplication (39/7)*(13/2) leads to a result of 507/14.

This can be now converted back to a mixed number, giving us an approximate answer of 36.21. Therefore, the fish swims at a speed of approximately 36.21 miles per hour.

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Answer:

C. Paige's soccer ball.

Step-by-step explanation:

When you graph y = 3x^2 + 6x + 3, you can see that the max of the parabola is around 6. This is lower compared to Paige's soccer ball's max height shown in the image.

Answer:

Step-by-step explanation:

To solve this problem, we just need to graph Viola's function to know the altitude she reached, and then compare it with Paige's altitude.

So, we know that Viola's function is [tex]y=-3x^{2}+6x+3[/tex], as an extra solution, we can calculate the vertex of this quadratic function, that will give us Viola's max altitude.

[tex]V(v_{x};v_{y})\\V(\frac{-b}{2a};f(v_{x} ))[/tex]

Where b and a are from the general quadratic function: [tex]y=ax^{2} +bx+c[/tex].

So, in this case, a = -3; b = 6. Replacing this values, we find the vertex:

[tex]V(\frac{-b}{2a};f(v_{x} ))[/tex]

[tex]v_{x}= \frac{-b}{2a}=\frac{-6}{2(-3)}=1[/tex]

Then, we use the function to calculate the vertical coordinate of the vertex:

[tex]v_{y}=f(1)=-3(1)^{2}+6(1)+3=-3+6+3=6[/tex]

Therefore, the max altitude reached by Viola is 6 meters.

Now, from the graph, we observe that Paige's max altitude is around 7.5 meters.

Therefore, Paige reached the higher height. The answer is C.