Solve for a side in right triangles

Answer:

[tex] \frac{11}{20} [/tex]

On the first day, they traveled 30 percents of the total distance. On the second day they traveled one fourth of the total distance. One fourth converted into percentage is 25 percent. Then you add 30 plus 25 because that is the to a

total distance that Murphy's family traveled for 2 days. It will be 55 percents, and you convert 55 percents into fraction will be 55/100, and you simplify it, will be 11/20.

Answer:

  is a function

Step-by-step explanation:

You want to know if the given set of ordered pairs represents a function.

A function cannot map an input value to more than one output value. That means the x-coordinates in a set of ordered pairs must all be different.

No x-values are repeated, so this relation is a function.

Two division expressions equivalent to 61.12 divided by 3.2 are 611.2 divided by 32 and 6.112 divided by 0.32. These are derived by scaling both numbers by the same power of 10, and such scaling does not change the value of the quotient.

When looking for division expressions that have the same value as 61.12 divided by 3.2, we want to maintain the ratio between the dividend and the divisor.

By multiplying both the dividend and the divisor by the same power of ten, we can create equivalent expressions without changing the actual value of the division.

For the given problem, 61.12 ÷ 3.2, two equivalent division expressions from the choices provided are:

Both of these are arrived at by multiplying the original dividend and divisor by 10 and 100 respectively. This operation does not change the value of the quotient but simply scales the numbers involved.

The expressions that have the same value as 61.12 divided by 3.2 are Option1. 611.2÷32 and Option 3.  6.112÷0.32

Given the choices, let's identify the equivalent expressions that will have the same value as [tex]\( 61.12 \div 3.2 \)[/tex]

The original division:

[tex]\[ 61.12 \div 3.2 = 19.1 \][/tex]

We need to find two expressions that also equal 19.1

Let's test the given options:

1. [tex]\( 611.2 \div 32 \)[/tex]

[tex]\[ 611.2 \div 32 = 19.1 \][/tex]

2. [tex]\( 6.112 \div 0.32 \)[/tex]

[tex]\[ 6.112 \div 0.32 = 19.1 \][/tex]

So, the two division expressions that have the same value as  are:

[tex]\[ 611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32 \][/tex]

Thus, the answers are: [tex]\[ \boxed{611.2 \div 32 \quad \text{and} \quad 6.112 \div 0.32} \][/tex]

Full question

Write two division expressions that have the same value as 61.12 divided by 3.2

the following are choice you can pick 2 from

Answer:

Charges per flower delivered by Tina is, y= 2.99 (x) + 5

Step-by-step explanation:

Given:

Tina's charges per flower = 2.99 cents

Delivery charged by Tina = 5 units or 5$

We have fill the blank in terms of 'y'.

We know slope intercept form that is : y = m(x)+b

So here we have to fill numbers according to the slope intercept form.

Let the numbers of flowers sold by Tina be 'x'.

Here slope (m) will be the charge of each flower charged by the florist.

The delivery charge is the fixed rate so its the constant value and will be treated equivalent to y-intercept or b values.

Arranging our values:

[tex]m=2.99[/tex] cents , [tex]b=5\$[/tex]

Then the slope-intercept form :

⇒ [tex]y=m(x)+b[/tex]

⇒ [tex]y= 2.99(x) + 5[/tex]

We have to type only that goes in the blank and that is 2.99(x) +5.

y = 2.99(x) + 5 is our final answer.

Explanation: Linear equations can be written in the form y = mx + b where the multiplier, m, or the coefficient of the x term represents the slope of the line and b represents the y-intercept of the line.

The linear equation y = 5x - 22 has a slope equal to 5

and a y-intercept equal to -22.

Answer:

60

Step-by-step explanation:

I used the guess and change method and subtracting every guessed number for 51.6. I found out that if you subtract 60 by 14%, you'll get 51.6.

Hope this helps :)

Answer:

The percent of decrease is [tex]30\%[/tex]

Step-by-step explanation:

Assuming the number of students enrolled in the photography club decrease from 50 to 35.

Then the change in student enrollment is 35-50=-15.

The percent of change  is given by:

[tex]\frac{Change\:in\:enrollment}{Original\:number}\times 100\%[/tex]

[tex]\frac{-15}{50}\times 100\%[/tex]

[tex]-15*2\%=-30\%[/tex]

Answer: 30

Step-by-step explanation:

i got it right

Answer: 4

Step-by-step explanation:

The sum of 12 and 8 is 12 add 8 which is 20. The difference between 12 and 8 is 12 minus 8 which is 4.

I don't know if this is right but if it is not tell me plz.

:) Thx

Answer:

Therefore the value of the car after 10 year will be = $4,845.34

Step-by-step explanation:

A new car is purchased for $17900. the value of the car depreciates at 12.25% per year.

Since the value of the car depreciates therefore the amount of the car is

[tex]A= P(1-\frac{r}{100})^n}[/tex]

    [tex]=17900(1-\frac{12.25}{100})^{10}[/tex]                [  p = $17900, r = 12.25% and n =10 years]

    = $ 4,845.34

Therefore the value of the car after 10 year will be = $4,845.34

The value of the car be, after 10 years will be $4845.34.

Given that,

A new car is purchased for 17900 dollars.

The value of the car depreciates at 12.25% per year.

We have to determine,

What will the value of the car be, after 10 years.

According to the question,

The value of the car depreciates therefore the amount of the car is determined by the formula,

[tex]A = P (1 -\dfrac{r}{100})^n[/tex]

Where, P = $17900, r = 12.25% and n =10 years

Substitute all the values in the formula,

[tex]A = P (1 -\frac{r}{100})^n\\\\A = 17900(1 -\frac{12.25}{100})^{10}\\\\A = 17900( 1- 0.1225)^{10}\\\\A = 17900(0.8775)^{10}\\\\A = 17900 \times 0.270\\\\A = 4845.34[/tex]

Hence, The value of the car be, after 10 years will be $4845.34.

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Answer:

40π

Step-by-step explanation:

Circumference Formula:  C = 2πr

Step 1:  Divide diameter by 2 to get the radius

40 / 2 = 20 m -> Radius

Step 2:  Plug into the Circumference Formula

C = 2π(20)

C = 40π

Answer:  40π

Answer:

Step-by-step explanation:

The radius of the circle is d/2

The Area of the circle is pi*r^2

The Area of the circle is pi * (d/2)^2

The Area of the circle is A = pi * (40/2)^2

The Area of the circle is A = 400 * pi

Answer:

[tex](3,0),(0,3)[/tex]

Step-by-step explanation:

y-intercept:

[tex]Substitute\ x=0\\\\y=0+3\\\\y=3\\\\Hence\ (0,3)\ is\ on\ the\ graph.[/tex]

x-intercept:

[tex]Substitute\ y=0\\\\0=-x+3\\\\x=3\\\\Hence\ graph\ passes\ through\ (3,0)[/tex]

Answer:

12 U.S teaspoons are in 1/4 cups.

The Formula is to multiply the volume value by 48.

So Since a 1/4 us cup=0.25 we can multiply this by 48.

0.25*48=12

So our awnser is 12 teaspoons

There are 12 teaspoons in 1/4 cups.

To understand this conversion, we need to know the standard conversion factors for cups and teaspoons. There are 16 teaspoons in 1 cup. Therefore, to find out how many teaspoons are in 1/4 cup, we divide the number of teaspoons in a full cup by 4.

Here is the calculation:

1 cup = 48 teaspoons

[tex]\( \frac{1}{4} \times 48 \)[/tex] teaspoons

[tex]\( = \frac{1}{4} \times \frac{48}{1} \)[/tex]

[tex]\( = \frac{48}{4} \)[/tex]

[tex]\( = 12 \)[/tex]

Therefore, there are 12 teaspoons in 1/4 cups.

The gardens perimeter is 12 meters.

Explanation:

        Perimeter = 2 × (4m + 2m) = 2 × (6m) = 12 meters.

Answer:

x = 5/4

Step-by-step explanation:

1. cancel x for log 3x and 2x

2. multiply log 2x-1 by log 2

3.simplify to log 4x-2 = log3

4.logs will cancel out and leave you with 4x-2 = 3

5. solve and get 5/4

Answer:

x = 5/4

Step-by-step explanation:

Answer:

81.625

Step-by-step explanation:

a mean is the average. an average is calculated by adding up all the numbers and then dividing the sum by the amount of numbers there are. these numbers added up = 653. 653 divided by 8 = 81.625. since it only goes up to three decimal places, no need to round.

Final answer:

The mean of the given data set is calculated by summing all the values and then dividing by the number of values. The calculated mean for this data set is 81.625.

Explanation:

To find the mean of the data set, we need to add all the data values together and then divide by the number of data values.

Thus, the mean of the data set is 81.625, which when expressed to three decimal places is 81.625.

Answer:

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

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

2x5^2-(4+1)

2x25-5

50-5

45

Answer:

24

Step-by-step explanation:

mEG = 24 units

Hope it helps

Answer:

solution is c

Step-by-step explanation:

look at picture

Lines can be divided into different segments of different lengths using ratios.

The y-coordinate of the point at this ratio is 0

The coordinates of J and K are given as:

[tex]\mathbf{J = (1,-10)}[/tex]

[tex]\mathbf{K = (7,2)}[/tex]

The ratio is given as:

[tex]\mathbf{m:n =5:1}[/tex]

The y-coordinate of the point at this ratio is calculated using:

[tex]\mathbf{y_p = \frac{my_2 + ny_1}{m+n}}[/tex]

So, we have:

[tex]\mathbf{y_p = \frac{5 \times 2 + 1 \times -10}{5+1}}[/tex]

[tex]\mathbf{y_p = \frac{10 -10}{5+1}}[/tex]

Simplify the numerator, and the denominator

[tex]\mathbf{y_p = \frac{0}{6}}[/tex]

Divide the fraction

[tex]\mathbf{y_p = 0}[/tex]

Hence, the y-coordinate is 0

Read more about line segment ratios at:

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The y-coordinate of the point is 0.

The formula for the section formula is

x [tex]= \frac{mx_2 + nx_1}{m + n}[/tex]

y [tex]= \frac{my_2 + ny_1}{m + n}[/tex]

Substituting in the points, we get

x = [tex]= \frac{5(7) + 1(1)}{5 + 1} = \frac{36}{6} = 6[/tex]

y [tex]= \frac{5(2) + 1(-10)}{5 + 1} = \frac{0}{6} = 0[/tex]

Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

Answer: (a) 4x + 10(0) = 76

(b) 29questions

Step-by-step explanation: let the correct answer = x.

4points for correct answer each total 4xpoints

Since no penalty for wrong answers, his total points were 76points.

Equation: 4x = 76

x = 19. He scored 19 correct answers.

Total number of questions on the test = 19 correct answers + 10 wrong answers

29 questions

Answer: 45

Step-by-step explanation:

A^2 + B^2 = C^2

27^2 + 36^2 = x^2

729 + 1296 = 2025

square root of 2025 = 45

X = 45

Answer:

[tex]5\frac{1}{3}\ in[/tex]

Step-by-step explanation:

we know that

The original scale factor is 1/80

That means

1 unit in the drawing represent 80 units in the actual

or

1 inch in the drawing represent 80 inches in the actual

step 1

Find the actual length with the original scale  

using proportion

[tex]\frac{1}{80}=\frac{12}{x}\\\\x=80(12)\\\\x= 960\ in[/tex]

step 2

The new scale drawing is

[tex]\frac{1}{180}[/tex]

That means

1 unit in the drawing represent 180 units in the actual

or

1 inch in the drawing represent 180 inches in the actual

step 3

Find the length of a new scale drawing  

using proportion

[tex]\frac{1}{180}=\frac{x}{960}\\\\x=960/180\\\\x= 5.33\ in[/tex]

Convert to mixed number

[tex]5.33\ in=5\frac{1}{3}\ in[/tex]

The actual length of the house if the scale is 1/80 is = 5 1/3 inches

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

Scale of the drawing =  dimensions of the scale drawing / dimensions of the original image.

Actual length when the scale was 1/80 = 80 x 12 = 960 inches

Actual length when the scale was 1/180 = 960 / 180 = 5 1/3 inches

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Answer: The resulting acceleration of the ball is 80m/s² .

Step-by-step explanation:

Formula for force :     [tex]F= ma[/tex]

,where m = mass pf object and a = the resulting acceleration of object.

As per given , we have

The mass of ball : m= 0.5 kg

Force = 40 N

Let 'a' be the resulting acceleration of the ball.

Substitute all values in formula , we get

[tex]40=(0.5)a\\\\\Rightarrow\ a=\dfrac{40}{0.5}=80\ m/s^2[/tex]

Hence, the resulting acceleration of the ball is 80m/s² .

The acceleration of the ball is 80 Newton per kg.

Given that

A 0.5 kg ball is kicked with a force of 40 N.

We have to determine

What is the resulting acceleration of the ball?

According to the question

The acceleration of the ball is determined by the following formula;

[tex]\rm Acceleration = \dfrac{Force}{Mass}[/tex]

The mass of the ball is 0.5 kg.

The force applied to the ball is 40 N.

Therefore,

The acceleration of the ball is,

[tex]\rm Acceleration = \dfrac{Force}{Mass}\\ \\ \rm Acceleration = \dfrac{40}{0.5}\\ \\ \rm Acceleration = 80 \ Newton \ per \ kg[/tex]

Hence, The acceleration of the ball is 80 Newton per kg.

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Answer:

8 seconds

Step-by-step explanation:

Given

h = - 5t² + 40t

When the object hits the ground then h = 0

Substitute h = 0 into the function and solve for t

- 5t² + 40t = 0 ← factor out - 5t from each term

- 5t(t - 8) = 0

Equate each factor to zero and solve for t

- 5t = 0 ⇒ t = 0

t - 8 = 0 ⇒ t = 8

t= 0 denotes the time of launch

t = 8 denotes the time it hits the ground

Step-by-step explanation:

We have,

[tex]\dfrac{20}{31}[/tex]

Show that [tex]\dfrac{20}{31}[/tex] is closer 66 % or 75 %.

∴ The percentage of [tex]\dfrac{20}{31}[/tex]

= [tex]\dfrac{20}{31}\times 100[/tex]

= [tex]\dfrac{2000}{31}[/tex]

= 64.516 %

≈ 66 %, shown.

Because the percentage of [tex]\dfrac{20}{31}[/tex] is 66 percent (%).

Thus, [tex]\dfrac{20}{31}[/tex] is closer 66 percent (%) , shown.

The fraction 20/31 is closer to 66%.

To determine which percentage 20/31 is closer to, we first need to convert the percentages into fractions and then compare them with 20/31.

66% can be written as a fraction as 66/100. Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2 in this case:

[tex]\[ \frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50} \][/tex]

Further simplifying by dividing both by 11, we get:

[tex]\[ \frac{33}{50} = \frac{33 \div 11}{50 \div 11} = \frac{3}{5} \][/tex]

75% as a fraction is 75/100. Simplifying this fraction by dividing both the numerator and the denominator by 25, we get:

[tex]\[ \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \][/tex]

Now we compare the fraction 20/31 with 3/5 and 3/4. To compare these fractions, we can find a common denominator or convert them to decimal form.

Converting to decimal form:

[tex]\[ \frac{20}{31} \approx 0.645 \] \[ \frac{3}{5} = 0.6 \] \[ \frac{3}{4} = 0.75 \][/tex]

Now we can see that 0.645 is closer to 0.6 than it is to 0.75. Therefore, 20/31 is closer to 66% (or 3/5) than it is to 75% (or 3/4).

Alternatively, we could also cross-multiply to compare the fractions directly:

For 20/31 and 3/5:

[tex]\[ 20 \times 5 = 100 \] \[ 31 \times 3 = 93 \][/tex]

Since 100 is greater than 93, 20/31 is greater than 3/5, but not by much.

For 20/31 and 3/4:

[tex]\[ 20 \times 4 = 80 \] \[ 31 \times 3 = 93 \][/tex]

Since 93 is much greater than 80, 20/31 is less than 3/4 by a larger margin than its difference with 3/5.

Thus, by both methods, we conclude that 20/31 is closer to 66%.

Answer:

There were 8 people on the bus when Paulina got on.

Step-by-step explanation:

Answer:

a = 2 ; b = 12

Step-by-step explanation:

p(x)=x⁴ + ax³ - 7x² - 8x +b

p(x) is exactly divisible by (x + 2). So p(-2)=0

(-2)⁴ + a(-2)³ - 7(-2)² - 8(-2) +b = 0

16 - 8a - 7*4 +16 + b =0

16 - 8a - 28 + 16 + b =0

4 - 8a + b = 0

-8a +  b = -4 -----------(i)

p(x) is exactly divisible by (x + 3). So p(-3)=0

(-3)⁴ + a(-3)³ - 7(-3)² - 8(-3) +b = 0

81 -27a - 63 + 24 + b =0

42 - 27a + b = 0

-27a + b = -42 ------------(ii)

                    -8a +  b = -4 -----------(i)

                    -27a + b = -42 ------------(ii)

subtract            19a = 38

                           a = 38/19 = 2

a=2

Substitute a value in equation (i)

-8*2 + b= -4

-16 + b = -4

       b = -4 + 16

       b = 12