The coordinates of the vertices of a rectangle are given by R(- 3, - 4), E(- 3, 4), C (4, 4), and T (4, - 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal _ET . a. Use the Pythagorean Theorem to find the exact length of _ET . b. How can you use the Distance Formula to find the length of _ET ? Show that the Distance Formula gives the same answer.

Answer:

If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X

The equation is x^2-8 x-15=0.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Given, sum of the roots of a quadratic equation is 8 and their product is 15 We know that the quadratic equation is given as [tex]$\mathrm{x}^2-$[/tex](Sum of the roots) [tex]$\mathrm{x}+$[/tex] (product of the roots)[tex]$=0$[/tex] [tex]$\Rightarrow x^2-8 x-15=0$[/tex]

Hence, the equation is x^2-8 x-15=0.

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Answer:

  x² +8x -15 = 0

Step-by-step explanation:

You want a quadratic such that the sum of the roots is -8 and their product is -15.

When the roots of a quadratic are p and q, its factored form is ...

  (x -p)(x -q) = 0

The expanded form of this is ...

  x² -(p+q)x +pq = 0

That is, the coefficient of x is the opposite of the sum of the roots, and the constant is the product of the roots.

Here, we want the sum of roots to be -8, so the x-coefficient will be the opposite of that: 8. The constant will be the product of the roots: -15. That makes the desired quadratic be ...

  x² +8x -15 = 0

__

Additional comment

The attachment shows the quadratic, its roots, and their sum and product.

Answer:

formula. for  circumference of a circle is. : 2πR. if you have the radius.

As the diameter is twice the radius,  then  circumference is. diameter π

then : 18*π≈ 56.52

the mistake was to take the diameter as the radius.

Step-by-step explanation:

check answer

The probability that the blood pressure of woman is more than 130 by given normal distribution is 0.9505

What is z-value?

The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean.

We are given a normal distribution with a mean value 115 and standard deviation 9

And we are asked to find the probability that a woman selected at random has blood pressure greater than 130

We first find the z-value

z= (x-μ)/σ

z= (130-115)/9

z= 15/9

z= 1.6666

Now the corresponding value is

Probability is 0.95

Hence the probability is 95%

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Answer:

b = 4

Step-by-step explanation:

y = mx + b represents the equation of a line

m represents the slope

b represents the y-intercept

Based on what we're given, we could determine that 4 is our y-intercept or b.

Answer:

9 ; $234

Step-by-step explanation:

the maximum revenue is the vertex of the parabola

a) -53/(2*-3)

-53/-6

53/6

8.833333

9

b

-3(53/6)^2 + 53(53/6)

-3(2809/36) + 2809/6

-2809/12 + 2809/6

(-2809 + 5618)/12

2809/12

234.083333

234

Each person will have 3 quects when they have the same amount

Given that:

Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour.

The equation of a line is of the form y = mx+c

where m is the slope and c is the y-intercept

For Lee

y =mx+c

c = 12

m = 12-8/0-1 = 4/( -1) = -4

y = -4x+12

For Andrea

y =mx+c

c = 2

m = 2-1/0-1.5 = 1/(-1.5) = -2/3

y = -2/3 x + 2

At the same amount y = -4x+12 is equal to y = -2/3 x + 2. Thus:

-4x+12 = -2/3 x + 2

4x-2/3 x = 12-2

10/3 x = 10

10x = 30

x = 30/10 = 3

Therefore, at 3 quects each person will have when they have the same amount

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Answer:

475$

Step-by-step explanation:

Answer:

16/24

Step-by-step explanation:

To raise a fraction, we have to multiply by 24/3, which is 8:
2 * 8 / 3 * 8 =

16/24

Answer:

i don't know but its not B or D and my guess is A

Step-by-step explanation:

Answer:

i think A is a function because when you search what it looks like it looks kind of like A so i am sure it is A

Step-by-step explanation:

The value of G = F/MH for H

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent all of the numerical constants, variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

According to the given information

F = MGH

we need to find the value for G

Dividing the above equation by MH

F/MH = MGH/MH

SO

G = [tex]\frac{F}{MH}[/tex]

So the value of G = F/MH for H

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12. The customer should use 120 units in a quarter for company A to be      cheaper.

What is cost management?

Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.

Solution:

Company A charges $14 for first 100 units = 14×100

                                                                        = $1400

After that 11% of 14 = 1.54 per unit

Company B charges $12 per unit so for 100 units = $12×100

                                                                                     = $1200

For company A to be cheaper, customer must use 120 units of electricity from company B as expense for 120 units from company B will be  $12×120 = $1440

and,

For 120 units of electricity from company A would be

$14×100 + 1.54×20 as after 100 units company A will charge 11%.

∴ for 120 units = 1400 + 30.8

                        = $1430.8

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13. For taxi company A to be cheaper customer must travel a minimum of 6 miles.

What is cost management?

Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.

Solution:

Given:

Company A charges $2.25 for a minimum of 2 miles journey and after that 85 cents per mile.

Company B charges 95 cents per mile without any minimum mile condition.

Let's assume

no. of miles = 4

fare from A = $2.25(2 miles) + 85 cents(1 mile) + 85 cents(1 mile)

                  = $3.95

fare from B = 95 cents × no. of miles

                  =  95 cents × 4

                  = $3.8

∵ Fare of company A is greater than B, minimum number of miles should be greater than 4.

now,

Let's assume

no. of miles = 5

fare from A = $2.25 + 85 cents + 85 cents + 85 cents

                  = $4.8

fare from B = 95 cents × no. of miles

                  =  95 cents × 5

                  = $4.75

∵ Fare of company A is greater than B minimum number of miles should be greater than 5.

now,

Let's assume

no. of miles = 6

fare from A = $2.25 + 85 cents + 85 cents + 85 cents + 85 cents

                  = $5.65

fare from B = 95 cents × no. of miles

                  =  95 cents × 6

                  = $5.7

∵ Fare of company A is less than B.

∴ Minimum number of miles should be 6.

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Step-by-step explanation:

I just answered this with all explanations.

the 2 solutions are

x = 6

x = -12

The value of z-score of a person who scored 115 on the exam will be;

⇒ z - score = - 1

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The scores are normally distributed with a mean of 135 and a standard deviation of 20.

Now,

Since, The scores are normally distributed with a mean of 135 and a standard deviation of 20.

We know that;

⇒ z - score = X - μ / σ

Substitute all the values, we get;

⇒ z - score = 115 - 135 / 20

⇒ z - score = - 20/20

⇒ z - score = - 1

Thus, The value of z-score of a person who scored 115 on the exam will be;

⇒ z - score = - 1

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All values of t for which the ball's height is 8 feet are 0.82 or 0.305.

What is quadratic equation?

Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.

Main Body:

The actual equation is

h=  4- 18t +16t²

initial height of ball = 4 ft

The problem asks for a time when the ball's height will be 8 ft. To find these times, I plug 8 in for h and solve for t:

8 = 4+18t -16t²

16t² - 18t +4 =0

Using the quadratic equation:

t = {18 ±√((18)² - 4*16 *4 )}/2*16

t = 18 ± √(324 - 256)/32

t = (18 ± √68) /32

t = (18±8.24)/32

t =  0.82 or 0.305

Hence ,all values of t for which the ball's height is 8 feet are 0.82 or 0.305.

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1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that A survey of 2000 subscribers to a certain news paper revealed that 1800  people subscribe to the daily morning edition  

And 1000 subscribe to both the daily and the sunday editions.  

Let x denote the number who subscribe to the Sunday edition.  

Then the addition rule with overlap tells us that is;

1800 + x – 1000 = 2000

800 + x = 2000  

x = 1200  

so, 1500 subscribe to the Sunday edition and 1200 – 1000 = 200 subscribe to the Sunday edition only.

Hence, 1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

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The required value of y for the given inverse relation is 30.78

What is the inverse variation?

Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.

In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.

Given, y varies inversely as [tex]x^{2}[/tex]

That is, y∝ 1/ [tex]x^{2}[/tex]

or, y = k/ [tex]x^{2}[/tex]

or,  [tex]x^{2}[/tex]y = k

And, y=38 when x=18

Then,  [tex]18^{2}[/tex]*38 = k

k = 12312

Now, if x=20 then y=?

[tex]x^{2}[/tex]y = 12312

or,  [tex]20^{2}[/tex]*y = 12312

or, 400y = 12312

or, y = 12312/400 = 30.78

Hence, the required value of y is 30.78

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Answer: 64

Step-by-step explanation:

43 = (4)(4)(4)

=64

OR

4x4x4=64

Answer:

Slope = 2

y-intercept = -1

Step-by-step explanation:

In the slope-intercept form of the equation of a line (y=mx+b), m equals the slope and b represents the y-intercept.

So, for this problem, m=2 and b=-1.  This means the slope is 2 and the y-intercept is -1.

Answer:

$592.92

Step-by-step explanation:

Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?

47 ones = $47

22 fives = $110

9 tens = $90

17 twenties = $340

67 pennies = $0.67

12 nickels = $ 0.60

9 dimes = $0.90

15 quarters = $3.75

$47 + $110 + $90 + $340 + $0.67 + $ 0.60 + $0.90 + $3.75 = $592.92

The value of x has been solved as 6.4

We would have EG = EF + FG

where EG = 70

EF = 4x-3

FG =  6x+9

We would have to put these values in the equation that we have above, such that we would have, To the respective variables, connect the related terms:

70 = (4x-3) + (6x+9)

Separate the x variable. Because of the equal symbol, everything you do on one side also affects the other.

Open the brackets

70 = 4x + 6x -3 + 9

70 = 10x + 6

70 - 6 = 10x

64 = 10x

divide through by 10

x = 64 / 10

x = 6.4

Hence the value of x would be given as 6.4

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Answer:

B

Step-by-step explanation:

assuming you mean [tex]8C_{6}[/tex]

using the definition

n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n! = n(n - 1)(n - 2) × 3 × 2 × 1

then

8[tex]C_{6}[/tex]

= [tex]\frac{8!}{6!(8-6)!}[/tex]

= [tex]\frac{8!}{6!(2!)}[/tex]

= (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (6 × 5 × 4 × 3 × 2 × 1 × 2 × 1

cancel (6 × 5 × 4 × 3 × 2 × 1 ) on numerator / denominator

= (8 × 7 ) / 2 × 1

= 56 ÷ 2

= 28

Apologies for formatting.

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04

The margin of error is a statistic that describes how much random sampling error there is in survey results.

Given in question,

n = 400

p = 317/400

  = 0.7925

Confidence Level = 95%

                          = 0.95

Formula for margin error, E = [tex]z\sqrt{\frac{p(1-p)}{n} }[/tex]

Confidence level corresponding to 95 % confidence interval, z = 1.96

Therefore,

Margin Error, E = [tex]1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }[/tex]

                         = 0.0397

                         ≈ 0.04

Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.

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Answer: 11.36

Step-by-step explanation:

↓ Please look in the screenshot below...

The equation of the function represented by the graph is (d) g(x) = √(x + 9) - 1

From the question, we have the graph that can be used in our computation:

The parent function of the graph is a square root function

This is represented as

f(x) = √x

First, we have the transformation to be:

The function is translated left by 9 units

Next, we have:

The function is translated down by 1 unit

Mathematically, this can be represented as

g(x) = f(x - 9) - 1

When represented as an equation, it is

g(x) = √(x + 9) - 1

Hence, the transformation is (d) g(x) = √(x + 9) - 1

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Answer: 14.0328

Step-by-step explanation:

Answer: 14.032

Step-by-step explanation: you just have to move the decimal point

Answer:

(x-2)(x^2+1)

do not exist the answer, so check your question

Step-by-step explanation:

(x^3-2x^2)+(x-2) = x^2(x-2)+(x-2)

= (x-2)(x^2+1)