Draw a triangle that has degrees of 30, 60, and 90. Measure the side lengths.

The equation solved for the variable are;

h = S- 2B/p

b = S - hp/2

To determine the equation, we need to know that the subject of formula for  an equation is described as the variable that is made to stand on one end of the equality sign.

It is the variable that is being worked out.

From the information given, we have that;

S= hp + 2B.

To make the height with the variable 'h' the subject, we have;

collect the terms

hp = S - 2B

Divide by the coefficient

h = S- 2B/p

For b, we have;

S - hp = 2b

divide by the coefficient

b = S - hp/2

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Step-by-step explanation:

\(y = \frac{4}{x} + \sqrt{x + 0.2} - 5x\)

\(x = \frac{4}{5} \)

\(y = \frac{4}{1} \div \frac{4}{5} + \sqrt{ \frac{4}{5} + 0.2} - 5 \times \frac{4}{5} \)

\( \frac{4}{1} \times \frac{5}{4} + \sqrt{0.8 + 0.2} - 4\)

\(5 + \sqrt{1} - 4\)

\(5 + 1 - 4 \\ 6 - 4 = 2\)

Answer:

A

Step-by-step explanation:

Answer:

108.75km

Step-by-step explanation:

please find attached the diagram

total displacement can be determined by using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

length of x =

20² + 40²

= 400 + 1600

2000

square root of 2000

= 44.72km

length of y

40² + 50²

1600 + 2500 = 4100

square root of 4100

64.03km

total displacement = 44.72 + 64.03 = 108.75

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, 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 (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

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

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

It should be -3.125%

Step-by-step explanation:

(124 - 128)/128 × 100

-4/128 × 100 = -3.125%

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

$21840

Step-by-step explanation:

24000*0.91=21840

Answer:

Quadrant 2

Step-by-step explanation:

Given

\(\theta = 115^o\)

Required

The quadrant

We have:

\(0^o < \theta < 90^o\) --- quadrant 1

\(90^o < \theta < 180^o\) --- quadrant 2

\(180^o < \theta < 270^o\) --- quadrant 3

\(270^o < \theta < 360^o\) --- quadrant 4

So, by comparison; we have:

\(90^o < \theta < 180^o\)

Substitute 115 for \(\theta\)

\(90^o < 115 < 180^o\)

The above is true for quadrant 2

The X-Cordinate is 4

Hi!

I can help you with joy!

In order to solve a proportion, all you should do is cross-multiply:

Cross-multiplying is exactly what it sounds like.

In this case, we Multiply

4 times 7

5 times y

28=5y

Divide both sides by 5:

5.6

Hope it helps!

-Nature

Given in the question, \(\frac{4}{5} =\frac{y}{7} \\\), using the concept of direct proportion, y = 5.6

Direct proportion is the concept of proportionality where one variable increases/decreases when another increases/decreases and vice versa. The rate of increase/decrease can be measured through the constant ratio. The two quantities which are directly proportional are related by a Direct Proportion symbol '∝'.

Given in the question,

\(\frac{4}{5} =\frac{y}{7} \\\)

multiplying 7 on both sides,

\(\frac{4}{5}*7 = \frac{y}{7} *7\\ \\ \frac{28}{5} = y \\\\y = 5.6\)

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Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

A) (x-4)(x+16)

Step-by-step explanation:

\(x^2+12x-64\\=x^2-4x+16x-64\\=x(x-4)+16(x-4)\\=(x+16)(x-4)\)

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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The probability that all 4 cards are face cards is 0.00182842367.

The face cards are the King, Queen, and Jack (sometimes known as the Knaves). There are 12 face cards in the 52-card deck of playing cards.

The cards are drawn without replacement,

The probability of getting a face card in first draw is 12/52.

As it is without replacement, in the second draw the probability is 11/51.

In third draw, it is 10/50.

In the fourth draw the probability is 9/49.

We have to draw all the four cards, so we multiply the probabilities, to get the final probability.

=12/52x 11/51 x 10/50 x 9/49

=0.00182842367.

Therefore, the probability that all 4 cards are face cards is 0.00182842367.

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Answer:

Step-by-step explanation:

Let stock be s, then we get the equation below for the stock value:

Answer:

I've written it in the photo

Answer:

5

Step-by-step explanation:

5^3= 125

1/5^2= 1/25

125 * 1/25 = 125/25 = 5

Check the picture below.

Answer:

A=2pi(9) I think

Step-by-step explanation:

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

Answer:

33084

Step-by-step explanation:

22056 divided by 2 =11028

altogether (on sunday and monday) the total amount would be..

22056+11028=33084

Answer:

33084

Step-by-step explanation:

If 22056 people came to the game on Sunday and Half as many people came on Monday, you do

22056 divided by 2. this is how many people cam on monday

Add this answer to 22056 and this is how many people came on both days.

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

Answer : 8$

you have 1$ left

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Answer:

x=99

Step-by-step explanation:

Move all terms not containing  x  to the right side of the equation.

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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