ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)

Answer:

1). True

2). x = 16.4 m^2

3). A = 24, h = 4

4). A = 18.39

5). 162

Step-by-step explanation:

I took this quiz on K12 and got everything correct! Brainliest welcome! :)

The average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

What is average change?

The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b].

Here, we have

Sea level changes by -73.5 ft in 3 minutes

So, we apply the average change formula, and we get

= -73.5/3

= - 24.5 ft per minute

And the otter goes deeper because - 24.5 < 0

Hence, the average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

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Answer:

Use AAA congurency rule

Step-by-step explanation:

1 angle=52

2 angle=58

3 angle=78

The result of the expression (-3/10) + -9 × 9/10 is -42/5

The expression is

(-3/10) + -9 × 9/10

The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.

The expression is

(-3/10) + -9 × 9/10

Here we have to do the suitable arithmetic operations

First do the multiplication in the given expression

= (-3/10) + (-9×9)/10

= (-3/10) + -81/10

Add the terms in the expression

Here the denominator of the both term is equal so we just need to add the numerators

= (-3 + -81) / 10

= (-3 - 81) / 10

= -84 / 10

Divide both numerator and denominator by 2

= -42/5

Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5

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The statement which must be true given the premise that; T is the midpoint of RS and V lies between R and T is; Choice A; RV + VT = TS.

It follows from the task content that the answer choice which represents a true statement regarding the given description be identified.

Since it is given that T is the midpoint of RS, it follows that;

RT = TS.

Also, it is given that point V lies between R and T; it therefore obviously follows that the equation which is true about RV and VT is;

RV + VT = RT.

Therefore, since segments RT and TS are equal;

It follows from the substitution property of equality that;

RV + VT = TS.

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If a person deposits $8,000 into a savings account at 6.5% interest compounded quarterly for 12 years, the balance (future value) will be $17,342.70.

The future value is the compounded present value of an investment for a future period.

The future value can be computed using the FV formula, table, or an online finance calculator as below.

N (# of periods) = 48 quarters (12 years x 4)

I/Y (Interest per year) = 6.5%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $17,342.70

Total Interest = $9,342.70

Thus, the future value of a present investment of $8,000 at 6.5% interest compounded quarterly for 12 years is $17,342.70.

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The least number of balls we require to take out to be sure that we have two green or two red balls is 14.

In the bag, there are a total number of balls of;

Total number of balls = 12 + 7 = 19 balls

Inside the bag, we have 12 red balls and 7 green balls.

The balls are selected without replacement, and this means that they are removed from the bag, and replaced back.

In theory, we could pick 12 balls, and all 12 being red, while also 13, with 12 red and 1 green e.t.c

Therefore, at least 14 balls are needed to guarantee that there are at least 2 green or two red balls

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Peter will take 47.5 minutes to clean the room.

In the question ,

it is given that ,

Peter and Parker are working for a cleaning crew ,

let the time taken by Parker to clean the room is = x minutes .

So ,according to the question ,

time taken by Peter to clean the room is = (x - 15) minutes .

Working together, they clean two rooms in 110 minutes

which is represented  , by the equation  ,

x + x - 15 = 110

2x = 110 + 15

2x = 125

x = 125/2

x = 62.5

Parker takes 62.5 minutes and Peter takes 47.5 minutes .

Therefore , Peter will take 47.5 minutes to clean the room .  

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If they observes a blood sample with a compound microscope that has a 10x ocular lens and a 40x objective lens. The larger that the blood cells appear under the microscope is: 400x.

Given data:

Blood sample has:

10x ocular lens

40x objective lens

Using this formula to determine how large the blood cells appear

Blood cells = ocular lens × objective lens

Let plug in the formula

Blood cells =  10x × 40x

Blood cells = 400x or 400 times larger

Therefore the blood cells appear 400 times larger.

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400 times larger

The unit rate of cups of lemonade per lemon is in the ratio of 6:1.

The unit rate is the ratio of two or more quantities or values that are compared to one another.

Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.

The number of lemons required to make 18 cups of lemonade = 3 lemons

Rate of lemonade per lemon = 18/3 = 6/1

Ratio = 6:1 or 1:6

Conversely, the rate of lemon per cup of lemonade = 1/6

Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.

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Answer:

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

The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s

Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle

Height of the woman = 6 ft.

The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman

Height of the street light = 30 ft.

Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;

[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;

[tex]y = \dfrac{x}{4}[/tex]

The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;

[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]

[tex]\dfrac{dx}{dt} = 8[/tex]

Therefore, dx = 8·dt

x(t) = 8·t

Writing the function for the l in terms of time t gives;

[tex]l = \dfrac{5\cdot x}{4}[/tex]

[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]

The speed at which the tip of the shadow is moving,

[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]

The speed of the shadow dl/dx = 10 ft./s

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Answer:

Step-by-step explanation:

Yes, you did it right.

x = 5/2 and x = -25/2 are the solutions to the equation 4x (x + 10) + 55 = 180.

Given the equation in the question;

4x (x + 10) + 55 = 180

To solve for x, apply distributive property to eliminate the parenthesis.

4x (x + 10) + 55 = 180

4x(x) + 4x(10) + 55 = 180

4x² + 40x + 55 = 180

4x² + 40x + 55 - 180 = 0

4x² + 40x - 125 = 0

Now, we use the quadratic formula to solve the quadratic equation.

x = (-b±√(b² - 4ac)) / (2a)

From 4x² + 40x - 125 = 0

Plug these into the formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -40 ± √( (40)² - ( 4 × 4 × -125))) / ( 2 × 4 )

x = ( -40 ± √( 1600 - ( -2000) )) / ( 8 )

x = ( -40 ± √( 1600 + 2000 )) / ( 8 )

x = ( -40 ± √( 3600 )) / ( 8 )

x = ( -40 ± 60) / ( 8 )

x = ( -40 - 60) / ( 8 ), ( -40 + 60) / ( 8 )

x = ( -100 )/( 8 ), ( 20 )/( 8 )

x = -25/2, 5/2

Therefore, the solution to the quadratic equation is x = -25/2, 5/2.

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Answer:

Ten million, Four hundred eighty-three thousand, one hundred ninety

Step-by-step explanation:

Break it down! into the tens digit, hundreds digit, etc.

Answer: 2 ft.

Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2

Answer: its 18,0000

Step-by-step explanation: Be smart  2x9= 18+ three 0,s?

An equation modeling the population, p, of Ohio given the year, t is,

p = 0.04t + 10.98.

What is population?

The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through. This indicator reveals how many people typically reside in a certain area. Growth rates are the population changes that occur each year as a result of births, deaths, and net migration.

Given: In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the population of Ohio was 11.66 million people.

From this we get, two points (0, 11.03) and (17, 11.66).

First to find the slope using the above two points.

[tex]m=\frac{11.66 - 11.03}{17-0} = \frac{0.63}{17} = 0.04[/tex]

Now to find the equation,

Consider,

p - 11.66 = 0.04(t - 17)

p - 11.66 = 0.04t - 0.68

          p = 0.04t - 0.68 + 11.66

          p = 0.04t + 10.98

Therefore, the equation modeling the population, p, of Ohio given the year, t is, p = 0.04t + 10.98

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When it rains at the same rate for 15 more minutes, the fraction of the rain gauge that will be filled is 2/15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

From the information, after raining for 3/4 of an hour, a rain gauge 2/5 of the way full. It's important to note that 3/4 is (3 × 1/4).

Therefore, we will divide 2/5 by 3 and this will be:

= 2/5 ÷ 3

= 2/5 × 1/3

= 2/15

This is the value of the rain gauge.

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Answer:

y = x^2 + 6       given equation

y = m x + b        equation of straight line required

dy/dx = 2 x       tangent to given curve

dy/dx = slope = 2 * 5 = 10

Thus our line must be of the form

y = 10 x + b

31 = 10 * 5 + b       at the point required

b = 31 - 50 = -19

Then our final equation becomes

y = 10 x - 19

a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The variables are listed as follows:

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

The sample size and the estimate are given as follows:

[tex]n = 150, \pi = \frac{15}{150} = 0.1[/tex]

The margin of error is of:

[tex]M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%[/tex]

The interval is given by the estimate plus/minus the margin of error, hence:

For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}[/tex]

[tex](\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2[/tex]

n = 271 (rounded up).

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The numerical value of p in the equation p = mv, when m = 5 and v = 23 is 115.

Given the equation in the question;

To determine the value of p, plug in the values of m and v and simplify.

p = mv

Plug in m = 5 and v = 23

p = 5 × 23

Multiply 5 and 23

p = 115

Therefore, the value of p is 115.

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Answer:

115

Step-by-step explanation:

m = 5

v = 23

p = mv

p = (5)(23)
p = 115

Answer:

x intercepts= (6,0)

y intercepts= (0,-6)

Step-by-step explanation:

I graphed the points.

Answer:

A: Independent contractor

Step-by-step explanation:

Answer: x = 4. This solution relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.

Step-by-step explanation:

    To solve, we will isolate the variable with inverse operations.

    Given:

3x - 12 = 0

    Add 12 to both sides of the equation:

(3x - 12) + 12 = (0) + 12

3x = 12

    Divide both sides of the equation by 3.

(3x) / 3 = (12) / 3

x = 4

        This solution, x = 4, relates to the original equation because when you substitute x for 4, the equation will simplify correctly as 0 = 0.

Answer:

x=4

Step-by-step explanation:

3x-12 = 0

Solve the equation

Add 12 to each side using the addition property of equality

3x-12+12 = 0+12

3x= 12

Divide each side by 3 using the division property of equality

3x/3 = 12/3

x = 4

The solution is what satisfies the original equation

1. 35 signed up for only mathematics

2. 20 signed up for only English

3. 85 or 70 is English or mathematics

4. Neither math or English is 45

5. English and Math is 50

1. How many signed for only mathematics

We have to define only mathematics as x

while we have math = m

English as E

Math and English as ME

only math

X = M - ME

= 85 - 50

= 35

2. Only English

E - ME

= 70 - 50

= 20

3. English or mathematics =

85 or 75

4. Neither English nor Mathematics

150 - (85 + 70 - 50)

= 45

5. The number for math and English is what is the intersection = 50

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