The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.

Answer:

∠ RST = 22°

Step-by-step explanation:

since ∠ RSU = 91°

and ∠ TSU = 69°

so ∠ RST = 22°

HOW:

given that;

∠ RSU = 91°

and

∠ TSU = 69°

we would subtract 69° from 91°

91°-69°= 22°

The laws of exponents are useful to solve algebraic expression as shown below.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

The laws of exponents (sometimes referred to as the rules of exponents) allow us to simplify expressions by using our understanding of what an exponent implies.

The goal is to write algebraic expressions as simply as you can in both situations.

Recall that an exponent indicates the number of times to multiply a number, variable, or expression by itself.

[tex]x^4=x \cdot x\cdot x\cdot x[/tex]

and, [tex](x+5)^3=(x+5)(x+5)(x+5)[/tex]

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Answer: 2/3

Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.

Answer: 2/3

Step-by-step explanation:

total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)

Answer:

(4, - 8 )

Step-by-step explanation:

9x + y = 28 ( subtract 9x from both sides )

y = 28 - 9x → (1)

3x + 3y = - 12

substitute y = 28 - 9x into (2)

3x + 3(28 - 9x) = - 12 ← distribute parenthesis on left side and substitute

3x + 84 - 27x = - 12

- 24x + 84 = - 12 ( subtract 84 from both sides )

- 24x = - 96 ( divide both sides by - 24 )

x = 4

substitute x = 4 into (1)

y = 28 - 9(4) = 28 - 36 = - 8

solution is (4, - 8 )

Based on the distance of the entire trip, the fraction of the trip that the car has travelled is 514 ²/ ₇.

The diagram is divided into 7 parts which means that each part can be said to be:

= 1/7 of the journey

The car is in the 4th part so that means that the fraction of the trip that has been traveled is:

= 4 / 7

Given the total miles of the trip, this would be:

= 4/7 x 900

= 514.29

= 514 + 29 / 100

= 514 ²/ ₇

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Answer:

154 feet squared

Step-by-step explanation:

1. Divide 14 by 2

2. Use the equation pie times radius squared

3. Answer is 153 foot squared

Answer:

14

Explanation:

To evaluate the expression, we need to replace x by 4. So, the expression is equal to:

3x + 2

3(4) + 2

12 + 2

14

Therefore, the value of the expression is 14

If each driver’s distance (miles) is shown for the same elapsed time (hours) of the trip. The person that had a head start is: Rita had a 28-mile head start.

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (130 - 65) / (2 - 1)

Slope for speed= 65 / 1

Slope for speed= 65 mph

Determining Roger's starting position if Roger distance is 65.

Hence,

Mile of head start = Slope of speed - Roger distance

Mile of head start = 65 mph - 65 miles

Mile of head start = 0 miles

Rita  starting position if Rita distance is 93

Slope for speed = (y² - y1) / (x² - x1)

Slope for speed = (158 - 93) / (2 - 1)

Slope for speed = 65 / 1

Slope for speed = 65 mph  

Mile of head start = Slope of speed - Rita distance

Mile of head start =  93 - 65

Mile of head start= 28 miles

Therefore we can conclude that Rita has a head start of 28 miles.

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Answer:

Rita had a 28-mile head start.

Step-by-step explanation:

EDGE

Answer:

1.25

Step-by-step explanation:

5 X 1.25 is 6.25 and 5 + 1.25 is 6.25

Step-by-step explanation:

the triangles are congruent out at least similar, so both have the same angles.

therefore,

2x = 80

x = 40

The solutions to the rational equation x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1) are 7 and - 4, respectively.

In this problem we find a rational equation that must be solved for x by means of algebraic properties. The complete procedure is shown below:

Step 1 - We have the following expression:

x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1)

Step 2 - Factor x² + 3 · x - 4:

x / (x + 4) = 20 / [(x + 4) · (x - 1)] + 2 / (x - 1)                

Step 3 - By existence of multiplicative inverse, modulative, associative and commutative properties:

[x · (x - 1)] / [(x + 4) · (x - 1)] = 20 / [(x + 4) · (x - 1)] + [2 · (x + 4)] / [(x + 4) · (x - 1)]

Step 4 - By compatibility with multiplication, existence of multiplicative inverse, modulative, associative and commutative properties:

x · (x - 1) = 20 + 2 · (x + 4)                                            

Step 5 - By distributive property:

x² - x = 20 + 2 · x + 8                                                  

Step 6 - By compatibility with addition, distributive, modulative and associative properties:

x² - 3 · x - 28 = 0  

Step 7 - Factor x² - 3 · x - 28:

(x - 7) · (x + 4) = 0                                                        

Step 8 - By understanding the factors found in the previous, we get the folowing result:

x = 7 or x = - 4                                                               Result

The solution to the equation are 7 and - 4.

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The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively

The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.

mean= sum of data in the collection/ number of data

= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)

standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data

finding (x- mean)^2 for each value of x

(20-59.125)^2=848.266

(33-59.125)^2=682.516

(44-59.125)^2=228.766

(53-59.125)^2=37.516

(69-59.125)^2=102.516

(75-59.125)^2= 260.016

(89-59.125)^2= 907.516

(90-59.125)^2= 968.766

S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =

√504.484

Therefore S.D =22.461 ( to the nearest thousandth)

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The number of cups of bananas is represented by x

The number of cups of strawberries is represented by y

Note that:

27/5 cups of strawberry is used for 27/25 cups of banana

1 cup of strawberry is used for x cups of banana

x = 27/25 ÷ 27/5

x = 27/25 x 5/27

x = 1/5

1/5 cups of banana is used for 1 cup of strawberry

Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:

y = 5x

where k = 5

The constant of proportionality = 5

The function is given below

What is a function?

The value of a function f at an element x of its domain is indicated by f(x); the numerical value resulting from the function evaluation at a given input value is expressed by substituting x with this value; for example, the value of f at x = 4 is denoted by f(x) (4). When the function is not named and is represented by an expression E, the function's value at, say, x = 4 can be expressed by E|x=4. In science, engineering, and the bulk of the mathematical disciplines, functions are commonly used. Functions are claimed to be "the central objects of research" in most branches of mathematics.

The given function is

f(x) = x - 6/2

The function in gf is

g{f(x)} = √(x - 6/2) - 4

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The value of the required composite function is [tex]g(f(x))=\sqrt{x-\frac{6}{2} } -4[/tex].

What is a composite function?

When the result of one function is utilized as the input for another, a composite function is created.

Given that:

[tex]f(x)=x-\frac{6}{2}[/tex] and [tex]g(x)=\sqrt{x}-4[/tex]

To find the composite function [tex]g(f(x))[/tex], it is required to use the output of the first function as the input of the second function. It means that replace [tex]x[/tex] by  [tex]f(x)[/tex]  in the second function as:

[tex]g(x)=\sqrt{x}-4\\g(f(x))=\sqrt{f(x)}-4[/tex]

Now, substitute the value of  [tex]f(x)[/tex] on the right side of the above equation as:

[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]

Hence, the required answer is:

[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]

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Answer:

total distance = 654.5

Total gas used = 27.5

Distance per gallon = 654.5 ÷ 27.5 = 23.8

We drove 23.8 miles for each gallon of gas

The absolute value expressions of the echo sounder are |r - w| and |w - r|

The statement in the question is represented as

The accuracy of an echo sounder is the positive difference between ...

To solve further, we use the following representations

Depth of water reading = r

Actual depth = w

So, the statement becomes

The accuracy of an echo sounder is the positive difference between r and w

The difference can be represented as

Difference = r - w or Difference = w - r

Represented as absolute value expressions

Difference = |r - w| or Difference = |w - r|

Hence, the expressions are |r - w| and |w - r|

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Answer:

Step-by-step explanation:

12%

Answer:

12.5%

Step-by-step explanation:

The place value of 9 in 194.6 is tens or 90.

According to the question,

We have the following expression:

194.6

Now, we know that place value of any digit can be found easily. The place value of the digit at the right most corner (of a number without any decimal point) is unit, left to this digit we have place value of tens, then we have hundred, then thousand, ten thousand, etc.

Now, in this case, we have a decimal point. So, we will look at the last digit before the decimal point because it's place value is unit place. And the next left digit to this is tens.

Hence, the place value of 9 in 194.6 is tens.

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The spaces with inputs; 5 has an output of 16 × 4 + 6 × 25, 100 has an output of 16 × 99 + 6 × 10000, and p has an output of 16 × (p-1)+ 6 × p².

Following the given three examples of the outputs from inputs 1, 3 and 7, we will discover a pattern of subtracting 1 from an input, multiply the result by 16, and then add the square of the input multiplied by 6 to it.

We will derive the missing outputs as follows;

For input 5:

5 - 1= 4

16 × 4

16 × 4 + 6 × 5²

16 × 4 + 6 × 25

For input 100:

100 - 1 = 99

16 × 99

16 × 99 + 6 × 100²

16 × 99 + 6 × 10000

For input p:

p - 1

16 × (p - 1)

16 × (p - 1) + 6 × p²

Hence, the input 5 gives an output 16 × 4 + 6 × 25, input 100 gives an output 16 × 99 + 6 × 10000 and input p gives an output of 16 × (p - 1) + 6 × p² from the reasoned pattern.

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Answer:

1 hour

Step-by-step explanation:

Since the penguin supposedly walks a 1 mile per hour, it would take one hour to achieve 1 mile

Answer: -4 (-4/1)

Step-by-step explanation:

Slope is the rate of change, or rise over run. So in this case it is negative because to get from p to v we have to go down. Sow e go down 4, and across one, but we just say -4.

Answer:

x/1

Step-by-step explanation:

8=-4x-4

4=-4x

(divide by -4)

1=x

Answer:

[tex]-1\geq x[/tex]

Step-by-step explanation:

[tex]8\leq -4(x-1)[/tex]

[tex]8\leq -4x+4[/tex]

[tex]8-4=-4x+4-4[/tex]

[tex]4\leq -4x[/tex]

[tex]\frac{4}{-4} \leq \frac{-4x}{-4}[/tex]

Inequality is reversed:

[tex]-1\geq x[/tex]

Hope this helps

Answer:

4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{48}[/tex] is not in simplest form, however, 48 contains a perfect square as a factor, that is 16 × 3

using the rule of radicals

[tex]\sqrt{ab}[/tex] ⇔ [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{48}[/tex]

= [tex]\sqrt{16(3)}[/tex]

= [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex]

= 4[tex]\sqrt{3}[/tex] ← in simplest form

Answer:

brand A. The bag weights for brand A have less variability than the bag weights for brand B

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

The idea of an expression number makes use of the method of allocating single-digit numbers (1 to 9) to the letters of the English alphabet, starting with A. The main mathematical advancements utilizing these number patterns are highlighted in the next section.

An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign.

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Answer:

B' (-3,11)

Step-by-step explanation:

B(2,3)  The rule is saying subtract 5 from x and 8 add to y

(2 -5, 3 + 8)

(-3,11)