Given the following Information, find the length of the missing side. Leave your answer as a simplified radical.
Hypotenuse = 10
Long = ?

A. 5
B. 5/3
C. 10
D. 10/3

Answer:

"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.

A possible alternative direction might have been to rewrite without the negative exponent.

Answer:

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

Step-by-step explanation:

using the rule of exponents

•  [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]\frac{y^{-5} }{y^{-4} }[/tex]

= [tex]y^{(-5-(-4))}[/tex]

= [tex]y^{(-5+4)}[/tex]

= [tex]y^{-1}[/tex]

= [tex]\frac{1}{y}[/tex]

Considering the expression of a line, the statements:

about the line that passes through (-2, 0) and (2, -4) are true.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷(x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-2, 0) and (x₂, y₂)= (2, -4), the slope m can be calculated as:

m= (-4 - 0)÷(2 - (-2))

m= (-4)÷ 4

m= -1

Considering point 1 and the slope m, you obtain:

0= -1×(-2) + b

0= 2 +b

-2= b

Finally, the equation of the line that passes through the pair of points (-2,0) and (2,-4) is y= -x -2, wich has a slope of -1. The line intersects the x-axis at (−2, 0).

If x=0, you get:

0= -x -2

2= -x

2÷ (-1)=x

-2= x

Finally, the line line intersects the y-axis at (0, −2).

Your question was incomplete. Please check below the full content.

Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

A. The slope of the line is 1.

B. The line intersects the y-axis at (0, −2).

C. The equation of the line is y = −x − 2.

D. The line intersects the x-axis at (−2, 0).

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Probability - The value of P(AUB) =  0.557

What is Probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

P(A) = 0.2,

P(B) = 0.31 and

P(A/B) = 0.152,

Since, we know that

P(A⋃B) = P(A)+P(B)-P(A⋂B)

So, we have to find P(A⋂B)

We know that,

P(A/B) = P(A⋂B)/P(B)

Putting the values we get,

0.152 = P(A⋂B) / 0.31

P(A⋂B) = 0.152 x 0.31

P(A⋂B) = 0.047

Now, lets find the value of P(A⋃B)

P(A⋃B) = P(A)+P(B)-P(A⋂B)

Putting the values we get,

P(A⋃B) = 0.2 + 0.31 + 0.047

P(A⋃B) = 0.557

Hence the value of P(A⋃B) = 0.557

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The equation as a function of x is y = 9280 -20x

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.

The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]

Now rearranging the function we write

[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]

y = 9280 -20x

The equation as a function of x is y = 9280 -20x

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Jack's percentage decrease on his measurement of painting by 18%.

What is meant by percentage change?

Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.

Given that,

Jack's measurement for his room =  5 ft (taking this as old value)

Actual measurement for Jack's room = 4.1 ft (taking this as new value)

Using formula for Percent change =  [tex]\frac{new - old}{old}[/tex]  × 100% =  [tex]\frac{4.1 - 5}{5}[/tex] × 100%

                                                       =  [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%

                                                       = -18%

Here, minus sign represents the decrease in percentage.

Hence, Jack's percentage decrease on his measurement of painting by 18%.

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Correct question will be :

Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?

The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.

So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.

Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.

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Zach began at 0.2 for the price of one piece of gum on the number line. Has moved eight times. The whole price is $1.60.

Since each hash mark is worth.2, moving eight times will result in 1.6, or eight times $0.20.

This is further explained below.

Generally, A number line is a depiction of a graded straight line that is used to represent real numbers visually.

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line.

How the number on the line may be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point

In conclusion, On the number line, Zach started at 0.2, which was equal to the cost of one piece of gum. Has relocated a total of eight times. The whole cost is a dollar and sixty cents.

Moving eight times will result in 1.6, which is equal to eight times $0.20, given that each hash mark is worth.2.

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The numerical value of each of the four given shapes filled in the rows and columns are;

let

Row 1: There are 2 stars, one pentagon and one spiral shape.

A + 2B + C = 23 .....(equation 1)

Row 2: There are 2 spiral shapes and 2 rectangle shape.

2C + 2D = 16 ......( equation 2)

Row 3: There are 1 star, one pentagon and 2 rectangle shape.

A + B + 2D = 24 ....(equation 3)

Row 4: There are 3 spiral shapes and one star shape.

B + 3C = 15 ....(equation 4)

Column 1:

2C + A + D = 19 ....(equation 5)

Column 2:

2B + C + D = 20 .....(equation 6)

From equation 4;

B = 15 - 3C

From equation 2:

D = 8 - C

A + 2B + C = 23

A + 2(15 - 3C) + C = 23

A + 30 - 6C + C = 23

A = 5C - 7

2C + A + D = 19

2C + (5C - 7) + 8 - C = 19

6C + 1 = 19

6C = 18

C = 3

A = 5C - 7

A = 5(3) - 7

A = 8

B = 15 - 3C

B = 15 - 3(3)

B = 6

D = 8 - C

D = 8 - 3

D = 5

Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.

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The first five terms of the given sequence are 4, 1, 6, 13, 22

We can solve this problem by following a few steps.

The formula to find the next four terms is, a =  (n)²- 3, (n ≥2) as per the question.

Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )

So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1  [As n = 2 for the second term ]

Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6  [ As n = 3 for the third term ] ,

for the 4th term A₄ = 4² - 3 = 16 - 3 = 13  [ As n = 4 for the second term ] ,

for the 5th term A₂ = 5² - 3 = 25 - 3 = 22  [As n = 5 for the second term ]

Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22

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The correct question is :

a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms

Answer:

x =2 y = -3

Step-by-step explanation:

hope it helps!!!!!

Let's begin by listing out the information given to us:

(x, y) = (-2, -3), (5, 7)

The distance between the two points is given by:

The area in square units of the hexagon will be 12√3.

What is Hexagon?

A polygon with six sides are called a hexagon.

Given that;

Jennifer makes a hexagon by arranging 6 equilateral triangles.

The length of one side of a triangle is 4.

Now, To find the area of hexagon, we find the height of the equilateral triangle and then multiply by the 6.

So, In ΔABC;

AB = BC = CA = 4

Then, Measure of DC = BD = 2

Now, using Pythagoras theorem to find height of triangle (AD) as;

AD² = AC² - DC²

AD² = 4² - 2²

AD² = 16 - 4

AD² = 12

Take square root both side;

AD = √12

AD = 2√3

So, The area of hexagon = 6 × Height of triangle

                                      = 6 × 2√3

                                      = 12√3

Thus, The area in square units of the hexagon will be 12√3.

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Answer: THE ANSWER TO THAT IS B

Step-by-step explanation:

The graph of the linear equation:

y = -3x + 4

Can be seen in the image at the end.

Here we know that the equation for the line is:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above line so we get the value of k.

-2 = k*2 + 4

With this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

Then the line is:

y = -3*x + 4

If we evaluate in x = 0, we get:

y = -3*0 + 4 = 4

So, at this point we know that the line passes through points (0, 4) and (2, -2), so to graph the line, we just need to graph these two points and draw a line that connects them, like in the example below.

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Answer: 2x + 8

Step-by-step explanation:

( 6x + 2 ) - ( 4x - 6 ) =

6x - 4x = 2x

2 - -6 = 8

The unit rate he can drive in mile per gallon is 22 miles per gallon.

Unit rate can be defined as the ratio between two measurements with the second term as 1.

In other words, a unit rate describes the ratio of two different units for the quantity of one.

Therefore, the  unit rate in miles per gallon can be calculated as follows:

Hence,

unit rate = number of miles / number of gallons

number of miles = 330 miles

number of gallons = 15 gallons

unit rate = 330 / 15

Therefore,

unit rate =  22 miles per gallon

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Answer:

The value of x will be 90°

By rewritting the 6 as 5 + 1 we will get:

1 + 5 + 5 = 1 + (5 + 5) = 11

One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).

This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:

6 + 5

We can rewrite this as:

6 + 5 = 1 + 5 + 5

Using the associative property we rewrite:

1 + 5 + 5 = 1 + (5 + 5)

1 + (5 + 5) = 1 + 10 = 11

The sum is equal to 11.

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When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1

The equation of function f is given as

f(x) = 2x - 1

The transformation is given as

Horizontal shift of 7 units left.

The above transformation rule can be represented as

Horizontal shift of 7 units left.: (x, y) = (x + 7, y)

When the above rule is applied, we have the following equation

g(x) = f(x + 7)

So, we have

g(x) = 2(x + 7) - 1

Open the brackets

g(x) = 2x + 14 - 1

Hence, the equation of function g is g(x) = 2x + 14 - 1

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1.25 is the probability that the aircraft Will last 100 hours.

The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty. 

Given Data

Mean = 80

Standard deviation = 16

P( x < 100)

P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])

P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])

P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])

P(x < 100) = 1.25

1.25 is the probability that the aircraft Will last 100 hours.

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Solution

find the slope of the line that goes through the given points (-2,-4) (1/4,5)

Therefore the slope of the line = 4

When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.

Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.

The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.

In this case, it should be noted that the value of 5,917 × 29 is 171593.

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The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.

It is given in the question that:-

Money borrowed by the company (Principal) = $68,000

Time period for which the money is borrowed = 8 years

Simple Interest rate = 15.5 %

We have to find the interest paid on the loan and the total amount paid.

We know that,

Simple interest = (Principal * Interest * Rate)/100

Hence, we can write,

Simple interest = (68000 * 15.5 * 8)/100 = $84,320

Also, we know that,

Amount = Principal + Interest

Hence, we can write

Amount = 68,000 + 84,320 = $152,320

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Answer:

$89 dollars per uniform

Step-by-step explanation:

Total amount of money raised= $6,764.

Money spent on new instruments= $6,764÷1/2 = $3382

The number of new uniforms bought with the remaining money= 38.

How much was spent on one= $3,382÷38 = $89

Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.

a. What is her ending balance after the year, to the nearest cent?

b. How much interest does she earn, to the nearest cent?

c. What is her annual percentage yield to the nearest hundredth

Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$4,300

t=1 year

r=2.3%=2.3/100=0.023

n=365

Part a

Find out the value of A

substitute the given values in the formula

A=$4,400.04

Part b

I=A-P

I=4,400.04-4,300

I=$100.04

Part c

we have

4,300 -----> represent 100%

so

Applying proportion

Find out how much percentage is 4,400.04

100/4,300=x/4,400.04

x=(100/4,300)*4,400.04

x=102.33%

therefore

102.33-100=2.33%

Given : Initial deposit or the principal amount = $ 9000

Rate of interest = 3.1 %

Compound interest annually

= principal (1 + r/ 100)^t

here put value principal rate and time period 1, 5 10 and 20 years

and we get the  amount for each time period        

than for interest = amount - principal we get interest    

as that we calculate all value:

given in the attachment

When interest on a balance in a savings or investment account is reinvested, you receive compound interest, which results in higher interest payments. Money makes money, a wise man once said. And money makes money by making more money. Compound interest speeds up the long-term growth of your savings and investments.

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EXPLANATION

Given the expression:

Applying the cubic power to both sides:

Simplifying the cubic root with the cubic power:

Subtracting -a to both sides:

Adding z to both sides:

Simplifying terms:

Switching sides:

The probability of the next car not being a white car is 0.92

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The complete question is added as an attachment

From the attached question, we have the following parameters

P(White Vehicle) = 0.25

P(Car) = 0.36

P(White Car) = 0.08

Using the complement rule of probability, we have the following equation

P(White Car) + P(Not White Car)  = 1

Substitute the known values in the above equation

So, we have the following equation

0.08 + P(Not White Car)  = 1

Subtract 0.08 from both sides of the equation

So, we have

P(Not White Car)  = 1 - 0.08

Evaluate the difference

P(Not White Car)  = 0.92

Hence, the probability that the next car will not be a white car is 0.92

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The quadratic formula is given by th following formula:

where a, b and c are the coefficients of the quadratic equation. In this case, you have:

a = 6

b = 9

c = -22

replace the previous values into the quadratic formula and simplify:

Hence, the solutions for the given equation are 1.31 and -2.81

ANSWER

EXPLANATION

To find the surface area of the hemisphere, we apply the formula for the surface area of a hemisphere (without a base):

where r = radius = 7 ft

Therefore, the surface area of the hemisphere is:

To find the volume of the hemisphere, we apply the formula for the volume of a hemisphere:

Therefore, the volume of the hemisphere is: