Find the value of each variable. a,b,c,d,e

Proved that the length of AB ≅ the length of CD

The conditions are given that

The line BC and the line AD are parallel lines

The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other

Similarly

The measure of angle BAD is equal to the measure of angle DCB

If angle BAD = angle DCB, then we can say that the given shape is a parallelogram

In the parallelogram the opposite sides will be equal

Then the length of the length of AB equal to the length of CD

Hence, proved that the length of AB ≅ the length of CD

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Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.

[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]

Answer:

[tex]-4x^2-4x+20[/tex]

Step-by-step explanation:

To find the difference of the two quadratic expressions, subtract the second expression from the first expression:

[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]

Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]

[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]

Collect like terms:

[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]

Combine like terms:

[tex]\implies -4x^2-4x+20[/tex]

Therefore, the difference of the two quadratic expressions is:

[tex]\large \boxed{-4x^2-4x+20}[/tex]

Answer:

y = 8/5

Step-by-step explanation:

Formula we use,

→ y = kx

Then the value of y will be,

→ y = kx

→ y = (-2/5) × (-4)

→ y = (-2 × -4)/5

→ [ y = 8/5 ]

Hence, the value of y is 8/5.

Answer:

Assuming w=2 and r=3, we plug in these values

2+5*3 = 2+15 = 17

Step-by-step explanation:

The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds

Let x represent the number of pounds of Chamomile tea needed.

We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.

Therefore,

9x + 6(8) = 7.8(8 + x)

9x + 48 = 62.4 + 7.8x

9x - 7.8x = 62.4 - 48

1.2x = 14.4

x = 14.4/1.2

x = 12

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The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%

Given,

P = $720

A = $2440

t = 18 years.

r = n[(A/P)^1/nt - 1]

r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]

r = 0.06799764

Then convert r to R as a percentage.

R = r × 100

R = 0.06799764 × 100

R = 6.8%/year

Hence the rate of interest is 6.8%

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The correct numbers from the box below are 5/6 - 1/3 = 1/2.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A table with five different fractions.

Now, 5/6 - 1/3 we will check and the result must fall in the fractions given in the table.

5/6 - 1/3.

= (5 - 2)/6.

= 3/6.

= 1/2.

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Answer:

[tex]y=3x-13[/tex]

Step-by-step explanation:

Parallel lines have the same slope. So, the equation is:

[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]

There are 33 numbers that are less than 200 and divisible 4 but not divisible 12. this can be solved with the help of simplification.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Main body:

Given that,

To determine how many natural numbers less than 200 are divisible by 4, but not divisible by 12.

Here,

Let the largest number divisible by 4 less than 200 is 198

The total numbers divisible by 4 and less than 200 is,

= 198 / 4 = 49

Similarly

The total number divisible by 12 and less than 200 is,

= 192/ 12 = 16

So the numbers that are less than 200 but divisible 4 not by 12 is,

= 49 - 16

= 33

Hence, there are 33 numbers that are less than 200 and divisible 4 but not divisible 12.

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Harold's solution for the given division problem is not valid because it is not accurate.

We are given two numbers. The numbers are given in scientific notation. The first number is 8.4×10^(-7). The second number is 3.6×10^(-2). We need to find the result of the division of the first number by the second number. Let the result of division be denoted by the variable "Q".

Q = [8.4×10^(-7)] ÷ [3.6×10^(-2)]

Q = [(8.4/3.6)×10^(-7 - (-2))]

Q = [(8.4/3.6)×10^(-7 + 2)]

Q = 2.33×10^(-5)

Harold solved this division problem by first rounding the numbers. His result is 2×10^(-5).

Harold's result differs a lot from the actual result. So, his result is not accurate. Hence, his solution is not valid.

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Answer: 44.35

Step-by-step explanation:

0.07x20=1.4

45.75-1.4

a. The discount amount of the exercise machine is $3.39.

b. The exercise machine's sale price will be $561.61

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:

= Discount percentage × Price

= 6% × $565

= $3.39

The exercise machine's sale price will be:

= Original price - Discount

= $565 - $3.39

= $561.61

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Answer:

x = 6

Step-by-step explanation:

2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )

- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )

x = - 3 × - 2 = 6

x = 6

Answer:

-1.1

Step-by-step explanation:

:)

Answer:

12a + 13b

Step-by-step explanation:

3(5a + 4b) - 3a + b

multiply 3 by 5a and 4b

15a + 12b - 3a + b

Now add the a terms together and b terms together

15a - 3a + 12b + b

12a + 13b

Answer:

12a + 13b

Step-by-step explanation:

3(5a+4b)-3a+b

To simplify the expression, we need to distribute the 3 to all terms inside the parentheses

3*5a+3*4b-3a+b

15a+12b-3a+b

Combine like terms

12a + 13b

Answer:

(x - 3)

Step-by-step explanation:

4x² - 12x ← factor out 4x from each term

= 4x(x - 3)

the factors are 4x and (x - 3)

The corresponding standard deviation percentage area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%

To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:

-2 to -1

The gap between -2 and -1 is 1 step, you will subtract -1 from -2:

-2 to -1 =>  0.4772 - 0.3413 = 0.1359 = 13.59%

Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others

0 to +1

Check the value under 1. That is 0.3413 = 34.13%

0 to +2

Check the value under 2. That is 0.4772 = 47.72%

+1 to +3

The gap between +1 and +3 is 2 steps, you will subtract  1 from 3:

+1 to +3 =>  0.4987-0.3413 = 0.1574 = 15.74%

-1 to +2

-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:

-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%

Therefore, the Standard Deviation Percentage Area for -2 to -1,  0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively

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A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.

This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.

This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.

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Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.

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Answer:

a

Step-by-step explanation:edge

The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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The equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.

Given: A line is perpendicular to line y = 4x – 7  and passes through point A (8, 2).

We know that,

Slope of line perpendicular to another line is negative reciprocal of its slope.

So, m(slope) = -1/4

Equation of line is given as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/4(x - 8)

y + (1/4)x = 4

Therefore, the equation of line perpendicular to line y = 4x – 7  and passing through point A (8, 2) is y + (1/4)x = 4.

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The ball hits the ground after x = 6 seconds.

Two or more expressions with an equal sign are defined as an equation.

The given equation is h(x) = -2x² + 8x + 24.

(a) when the ball is thrown, the time is t = 0 sec.

Therefore, the height of the ball when it is thrown is,

h(0) = -2(0)² +8(0) +24

h(0) = 24

(b) The derivative of the function is,

h'(x) = -4x + 8

Substitute h'(x) = 0 into the above equation,

0 = -4x +8

4x = 8

x = 2

The second derivative of the function is,

h''(x) = -4

Since the second derivative of the function is negative, the function is maximum at x = 2.

(c) The maximum height of the ball is,

h(2) = -2(2)² + 8(2) +24

h(2) = -8 +16 +24

h(2) = 32

(d) The ball hits the ground when h(x)= 0, therefore,

0 = -2x² +8x +24

0 = -2x² +12x - 4x + 24

0 = -2x(x - 6) - 4(x - 6)

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

(x - 6) = 0 or (-2x-4) = 0

x = 6 or x = -2

Since time cannot be negative, it follows, x = 6 seconds.

Hence, the ball hits the ground after x = 6 seconds.

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Protein intake, if he consumes 9 egg whites a day is 32.4 grams.

Given:

Candice eats six egg whites a day with a protein content of 21.6 grams.

6 egg white = 21.6 grams.

1 egg white = 21.6/6

= 216/10/6

= 216/10*6

= 216/60

= 3.6 grams.

9 eggs white = 9 * 3.6

= 9 * 36/10

= 324/10

= 32.4 grams.

Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.

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Answer:

the exact form is 419/104

decimal for:4.02884615...

mixed number form: 4 3/104

Step-by-step explanation:

calculator

The dimensions that will minimize the cost is

h= 2.82876 and r = 1.06078

Given That, C₁ = $10 and C₂= $10 and C₃ = $15

lets multiply the top and bottom, we get,

C₁ × C₂ = $10 ×$ 20 = $ 30

The total cost is,

C = (2πr²) C₁ + (2πrh)C₂

Here,  r is base radius and h is the side length.

The volume is given by and the volume to 20 m³

∴ V = πrh² ⇒ πr²h = 20

So, h = 20/πr²

Now, the problem can be  stated as

minimum h, r C(h, r) restricted to V(h, r) = V₀

Using language multiplier it reads,

L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]

Solving for h, r, λ, we get,

h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)

λ = -2 ∛2πC₁C₂² /V₀

or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214

We know that is a minimum because,

(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r

d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³

and for the found solution has the value

d²/dr² (C₀V) (r) = 240 π > 0

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Jamal need to invest $35838.77 in an account.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.

The compound interest formula is,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365

Plug the values in the above formula,

[tex]54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77[/tex]

Hence, Jamal need to invest $35838.77 in an account.

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A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.

The jar is filled with marbles that have a volume of 20 in³.

(a) The volume of the cylindrical jar be,

Volume = πr²h

Volume = (3.14)(6)²(10)

Volume = 1130.97 in³

(b) Now, if each marble has the volume of 20 in³

then, the number of marbles that can be fit in the jar be,

The number of marbles = 1130.97/20

The number of marbles = 56.

Hence, the volume of the cylindrical jar be 1130.97 in³.

Also, 56 whole marbles can fit in the jar.

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