Evelyn is 2.5 years younger than James. Two times the sum of their age is 57. Write and solve an equation to find Evelyn age.

Step-by-step explanation:

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

therefore,

2x = 80

x = 40

The difference of 0.27 is not statistically significant.

A statistically significant difference indicates if the responses of one group differ significantly from those of another when using statistical testing.

Now we know that any data of t-statistic that is greater than 1.96 is statistically significant.

Now the difference is 0.27. Hence it is not statistically significant.

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Answer:

Substitute x = 4 into the equation to find y.

2(4) + y = 2

8 + y = 2

y = -6

To check if it satisfies the equation, substitute values of x and y into the equation.

2(4) + (-6) = 2

8 - 6 = 2

Since, it satisfies the equation, the missing coordinate is -6.

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:

A. [tex]\frac{c}{11} *7-48[/tex]

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

5 X 1.25 is 6.25 and 5 + 1.25 is 6.25

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

The base of the garden is 14.4 feet.

The height of the garden is 6 feet.

Given,

Corey is designing a rectangular garden;

The diagonal of the garden = 15.6 feet

Ratio  between garden's base and height = 12:5

We have to find the length of base and height of the garden.

Here,

Diagonal of a rectangle, d = [tex]\sqrt{base^{2}+ height^{2} }[/tex]

Base = 12x

Height = 5x

Then,

Diagonal, 15.6 = [tex]\sqrt{(12x)^{2} + (5x)^{2} }[/tex]

15.6 = [tex]\sqrt{144x^{2} +25x^{2} }[/tex]

15.6 = √169x²

15.6 = 13 √x²

15.6 = 13x

x = 15.6/13

x = 1.2

Then,

Base of the garden = 12 x 1.2 = 14.4 feet

Height of the garden = 5 x 1.2 = 6 feet

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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.

Step 1

The number of pieces for 5 cuts is

Step 2

The general formula Tn, for the number of rope pieces is

Step 3

How many rope cuttings will make up 153 rope pieces

Step 4

How many ropes pieces will result from 11 cuttings

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:

104 children and 195 adults

Step-by-step explanation:

let a represent number of adults and c represent number of children , then

a + c = 299 → (1)

7a + 2c = 1573 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate c

- 2a - 2c = - 598 → (3)

add (2) and (3) term by term to eliminate c

5a + 0 = 975

5a = 975 ( divide both sides by 5 )

a = 195

substitute a = 195 into (1) and solve for c

195 + c = 299 ( subtract 195 from both sides )

c = 104

104 children and 195 adults were admitted

Answer:

x = 9

Step-by-step explanation:

using the rule of indices

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

[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]

since bases on both sides are equal, both 5 , then equate indices

x = 9

Answer: .63

Step-by-step explanation: y(11)=7

y(11)/11=7/11

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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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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The exponential model A=64.5e^0.02t describes the population, A of a country in millions, t years after 2003. The population of the country will be 108 million in

we have the expression

A=64.5e^0.02t

For A=108

substitute

108=64.5e^0.02t

108/64.5=e^0.02t

Apply ln both sides

ln(108/64.5)=ln(e^0.02t)

ln(108/64.5)=0.02t(ln(e))

ln(108/64.5)=0.02t

solve for t

t=ln(108/64.5)/0.02

t=26 years

therefore

2003+26=2029

answer is

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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Answer:

Step-by-step explanation:

12%

Answer:

12.5%

Step-by-step explanation:

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 )

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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Given the credit card options:

• Chase Sapphire Reserve

• Wells Fargo Propel Card

• American Express Blue Cash Everyday

• Citi Double Cash Card

• Chase Freedom

• Chase Amazon Prime Rewards Card

• Bank of America Cash Rewards Visa

• American Express Platinum

Then, there are 8 options.

If you want to apply for 3 credit cards and the order does not matter, you can use combination to see how many options you have.

The formula for combination of r elements out n elements is:

In this question:

n = 8

r = 3

Answer: 56 ways.

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 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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Answer:

x = -12

Step-by-step explanation:

Hello!

The sentence can be represented as (x + 5)-(2x) = 17.

We can solve for x by isolating the variable.

The value of x is -12.

the width of the wall is 21 3/8 = 171/8

the width of a tile is 4 1/2 = 9/2

so the number of tiles is

(171/8) / (9/2) = 171x2 / (9 x8) = 4.75

so the no of tiles needed is 5.

In order to a set o points define a function, a value of x can't have two different values of y.

Looking at every option, we have in the option C that the value of x = 0 has two different values of y (1 and -1), therefore this set of points do not define a function.

So the answer is C.