Point E is the midpoint of AB and point F is the midpoint of CD .



Which statements about the figure must be true? Check all that apply.


AB is bisected by . CD

CD is bisected by . AB

AE = 1/2 AB

EF = 1/2 ED

FD= EB

CE + EF = FD

Answer:

4x² - 4xy + y²

Step-by-step explanation:

For clarity it is essential that you use (2x - y)^2 or (2x – y)² to indicate the square of (2x - y).

Since we're squaring (2x - y), we expect 3 terms in the expansion.

(2x - y)(2x - y) = 4x^2 - 4xy + y^2, or 4x² - 4xy + y²

Next time you see "the following," please share the answer choices.  Thank you.

Answer:  b) 18.37

Step-by-step explanation:

Since the intial t-value is 1960 and the final t-value is 1990, then t = 30

[tex]P(30)=\dfrac{100}{1+400\cdot e^{-0.15(30)}}\\\\\\.\quad =\dfrac{100}{1+400\cdot e^{-4.5}}\\\\\\.\quad =\dfrac{100}{1+400(0.0111)}}\\\\\\.\quad =\dfrac{100}{1+4.4436}}\\\\\\.\quad =\dfrac{100}{5.4436}}\\\\\\.\quad =\boxed{18.37}[/tex]

Answer:

25 - y

Step-by-step explanation:

"subtract" = "-"

"subtract y" means to "- y"

"from 25" implies that 25 is in the front.

Put the phrases together:

"subtract y from 25" = 25 - y

25 - y is your answer.

~

Answer:

y = -3; x = 6

Step-by-step explanation:

-2y - y = 9

-3y = 9

y = -3

Solutions of the linear equations given are x = 6 and y = -3.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given are two linear equations.

x = -2y

x - y = 9

We have to solve this by substitution method.

Substituting x = -2y in x - y = 9, we get,

-2y - y = 9

-3y = 9

y = -3

Substituting y = -3 in x = -2y,

x = -2 × -3 = 6

Hence the values of x and y are 6 and -3 respectively.

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Answer:

y = (2/3)x + 7/3

Step-by-step explanation:

First we want to isolate 3y on the left side.  To accomplish this, add 2x to both sides.  The result will be 3y = 2x + 7.

Next we divide all three terms by 3 to complete the isolation of y on the left side:

y = (2/3)x + 7/3

Answer:

y = ⅓(2x + 7)

Step-by-step explanation:

3y - 2x = 7

3y = 2x + 7

y = ⅓(2x + 7)

Answer: Option B

Step-by-step explanation:

By definition, only those functions that are one to one have an inverse function.

A function is one by one if there are not two different input values, [tex]x_1[/tex] and [tex]x_2[/tex], that have the same output value y

Note that the function [tex]f(x)= \frac{|x+3|}{5}[/tex]  is not a one-to-one function

When x=2  [tex]f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1[/tex]

When x=8  [tex]f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1[/tex]

Note that the function [tex]f(x)= \frac{x^4}{7}+ 27[/tex]  is not a one-to-one function

When x=1 [tex]f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]

When x=-1  [tex]f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}[/tex]

Note that the function [tex]f(x)= \frac{1}{x^2}[/tex]  is not a one-to-one function

When x=1 [tex]f(x)= \frac{1}{(1)^2}\ ,\ \ y=1[/tex]

When x=-1  [tex]f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1[/tex]

Then the answer is the option B.

You can verify that The function [tex]f (x) = x ^ 5-3[/tex] is a one-to-one function and therefore its inverse is a function

Answer:

Step-by-step explanation:

She has a total of 3 + 3 + 2 choices which is 8

She chooses the first one that has 3 members in it.

3/8 is the probability of that fact.

She chooses the second one from a group that also has 3 members only now there are only 7 choices total. That fact is

3/7

So your total probability is

3/8 * 3/7 = 9/56

Those two numbers are prime to one another.

ANSWER

C.

[tex]{f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]

EXPLANATION

The given function is

[tex]f(x) = 2 \arccos(x)[/tex]

Let

[tex]y= 2 \arccos(x)[/tex]

Interchange x and y.

[tex]x= 2 \arccos(y)[/tex]

Divide both sides by 2.

[tex] \frac{x}{2} = \arccos(y)[/tex]

We take cosines to get,

[tex] \cos( \frac{x}{2} ) = y[/tex]

[tex] {f}^{ - 1} (x) = \cos( \frac{x}{2} ) [/tex]

Answer: 50% chance that a randomly chosen student will be a boy

Answer:

Step-by-step explanation

total number of student= 526

total number of girl= 263

total number of boy= 526 - 263 = 263

Probability that chosen student will be boy = number of favorable items/ total number of possible outcome= 263/526 = 1/2

For this case we evaluate the series for each value of "n" from 0 to 3:

So:

[tex](0x + 2) + (1x + 2) + (2x + 2) + (3x + 2) =\\(0 + 2) + (x + 2) + (2x + 2) + (3x + 2) =\\2 + x + 2 + 2x + 2 + 3x + 2 =[/tex]

We add similar terms and we have the result of expanding the series is:

[tex]8 + 6x[/tex]

ANswer:

Option C

[tex]6x + 8[/tex]

Answer: Third option.

Step-by-step explanation:

Given  [tex]3\\\sum(nx+2)\\n=0[/tex], We know that indicates that we need to start with [tex]n=0[/tex] and finish with [tex]n=3[/tex],

In order to expand the series, the procedure is the following:

[tex]3\\\sum(nx+2)=(0x+2)+(1x+2)+(2x+2)+(3x+2)\\n=0\\\\3\\\sum(nx+2)=2+x+2+2x+2+3x+2\\n=0\\\\3\\\sum(nx+2)=6x+8\\n=0[/tex]

This result matches with the third option.

Answer:

The answer is B

Step-by-step explanation:

75 + x = 90

First, Virginia had to write an equation to solve for x.

75 - 75 + x = 90 - 75

Second, Virginia used the subtraction property of equality to isolate x.

x = 15

Third, "x = 15" was the answer Virginia got after subtracting 90 and 75.

75 + 15 = 90

Finally, she had to verify her answer

13/50 is the probability

1st step: 13/25 times 1/2 = 0.26

2nd step: 0.26 as a fraction is 13/50

Answer:

[tex]\frac{1}{3a}[/tex]

Step-by-step explanation:

Given

[tex]\frac{a-3}{15a}[/tex] × [tex]\frac{5}{a-3}[/tex]

Cancel the factor (a - 3) on the numerator and denominator

Cancel the 5 and 15 by dividing both by 5, leaving

[tex]\frac{1}{3a}[/tex]

Answer:  The required answer is [tex]\dfrac{1}{3a},~a\neq 3.[/tex]

Step-by-step explanation:  We are given to find the following product :

[tex]P=\dfrac{a-3}{15a}\times\dfrac{5}{a-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since (a - 3) is present in both numerator and denominator, so we can divide them if

[tex]a-3\neq 0\\\\\Rightarrow a\neq 3.[/tex]

Then, we get from (i) that

[tex]P\\\\\\=\dfrac{(a-3)}{15a}\times\dfrac{5}{(a-3)}\\\\\\=\dfrac{5}{15a}\\\\\\=\dfrac{1}{3a}.[/tex]

Thus, the required answer is [tex]\dfrac{1}{3a},~a\neq 3[/tex]

Answer:

D

Step-by-step explanation:

d/dx(8 - 24/x^2) = 48/x^3

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Indefinite integral assuming all variables are real:

integral(-24/x^2 + 8) dx = 8 x + 24/x + constant

Open code

Limit:

lim_(x-> ± ∞) (8 - 24/x^2) = 8

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Answer:

D, All real numbers

Step-by-step explanation:

Answer:

The corresponding point is (-4.-1)

Step-by-step explanation:

we know that

The point (-4,2) is on the graph of f(x)

so

For x=-4

f(x)=2

therefore

For x=-4

-(1/2)f(x)=-(1/2)*2=-1

The corresponding point is (-4.-1)

Answer:

I attach the missing image from your question.

To easily solve this question, we must realize that the graph of the relation is very similar to that of the expression

y = √(x-a) , where a>0

If we take a look at the image attached, we have plotted the graph of

y = √(x-1) , and its correspondent inverse function.

This means that the answer is the first option

Answer:

The two cars will be almost 188 miles far from each other.

Step-by-step explanation:

Travel Time for Car 1 = t = 3.5 hours

Travel time for Car 2 = t-1 = 3.5 - 1 = 2.5 hours

Average speed of car 1 = 40 mph

Average speed of car 2 = 50 mph

Distance traveled by Car 1 = 40*3.5 = 140 miles

Distance Traveled by Car 2 = 50*2.5 = 125 miles

As both the roads are at a 90 degree angle. The path of the two cars and the joining line of their final position forms a right angle triangle where:

altitude = a = 140

base = b = 125

Distance of cars after 3.5 hours = c = ?

According to Pythagoras theorem:

c^2 = a^2 + b^2

c^2 = 140² + 125²

c² = 19600+15625

c = √35225

c = 187.68

Almost 188 miles.

Answer:

You can find the quotient of the expression in the images below, together with more information and a full analysis

(2x^4-3x^3-3x^2+7x-3)/(x^2-2x+1)

Answer:

The quotient is: 2x^2+x-3

Step-by-step explanation:

we need to divide (2x^4-3x^3-3x^2+7x-3) by (x^2-2x+1)

The division is attached in the figure below.

The quotient is: 2x^2+x-3

The remainder is: 0

[tex]\bf \sqrt{24}\qquad \approx \qquad 4.899~\hfill \underset{\textit{nope, is outside}}{~\hfill \stackrel{\sqrt{24}}{4.899}}\rule[0.35em]{2em}{0.25pt}\boxed{5}\rule[0.35em]{10em}{0.25pt}\boxed{6}[/tex]

Answer:

ellipse

Step-by-step explanation:

Yea that's pretty much the definition of an ellipse. The points in this case would be the "foci"

The term that best describes the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant is an ellipse. This can be obtained by understanding what an ellipse is.

A set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant.

Hence the term that best describes the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant is an ellipse.

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Answer:

about 1325 mph

Step-by-step explanation:

average speed = total distance / total time= (distance uphill + distance downhill)  / (time uphill + time downhill)

time uphill = 606060 minutes / 60 = 10101 hours

path = 666 mph * 10101 hours = 6727266 m

time downhill = 6727266 m / 10101 hours = 55.5 h

average speed = (6727266 m + 6727266 m) / (10101 hours + 55.5 h) = about 1325 mph

Answer:

8

Step-by-step explanation:

Answer:

answers in pictures

Step-by-step explanation:

The greatest common factor of group 1 will be 2x so option C is correct.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution of the given equation will be as follows:-

=  2x² + 6x + 5x + 15

=  2x ( x + 3 )  + 5 ( x + 3 )

=  ( x + 3 ) ( 2x + 5 )

We can see in the second step the first group have a common factor of 2x.

Therefore greatest common factor of group 1 will be 2x so option C is correct.

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Answer:

The Multiplication  property

Step-by-step explanation:

The Multiplication  property by a constant was used

For real numbers a and b, and c different from zero:

If c is positive and [tex]a <b[/tex] then [tex]a*\frac{1}{c} <b*\frac{1}{c}[/tex].

If c is negative and [tex]a <b[/tex] then [tex]a*\frac{1}{c} >b*\frac{1}{c}[/tex].

In this case we have

[tex]5x<100[/tex]  Then  [tex]\frac{5}{5}x<\frac{100}{5}[/tex]

Finally

[tex]x<20[/tex]

Answer: Infinitely many

Step-by-step explanation:

First simplify the right side by adding 5 and 2

now you have the equation 4y+7=7+4y

That is the exact same thing so any number works.

just to add to the great reply above.

[tex]\bf \begin{matrix} 4y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}+7=5+2~~\begin{matrix} +4y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\implies 7=7[/tex]

whenever you end up with something like 0 = 0, or 7 = 7, is a flag that both equations are exactly the same, in this case, the one on the right-hand-side is really the one one the left-hand-side in disguise.

So the graph of one, is the same as the graph of the other, or put in another words, let's say the graph the first one, the second one when graphed, will just be pancaked on top of the first one, and any point whatsoever on the second one, matches with the first one, and since both lines continue infinitely, then infinitely many solutions.

Answer: 10,000

Step-by-step explanation:

If you round to the nearest ten thousand, you round the number that makes it ten thousand in the first place.

Answer: From the right, you count 1 number, 0, then 2 numbers, 7, then 3 numbers, 8, then 4 numbers, and you get rid of those to make it 10,000.

Step-by-step explanation: Because 3, next to the 1 there rounds down, it makes 3,870 be rounded down overall.

First you add all the numbers together. So you add 82+93+75+89 to get 339. Once you get that, you divide it by the amount of numbers there are. In this case, it's 4. 339 divided by 4 is 84.75.

HOPE THIS HELPS!!

Answer:

The average of the John scores is 84.75.

Step-by-step explanation:

Formula of average is given as :

[tex]A=\frac{\text{Sum of all the terms}}{\text{Number of terms}}[/tex]

We have:

Test grades of John: 82, 93, 75, and 89

Number of terms - 4

Average of the score of the John;

[tex]a=\frac{82 + 93 +75 + 89}{4}=84.75[/tex]

The average of the John scores is 84.75.

Answer:

{O c N}

Step-by-step explanation:

Answer:

The profit after 4 seasons is 14.938 units

Step-by-step explanation:

To quickly solve this problem, we can use a calculator or any graphing tool

to examine both graphs

Revenue

t(x)=5x

Cost

r(x)=(1.5)^x

Profit

P = Revenue - costs = t(x) -r(x)

P = 5x - (1.5)^x

The profit after 4 seasons is 14.938 units

Answer:

14.9

Step-by-step explanation:

Answer:

2940

Step-by-step explanation:

Surface Area of a rectangular prism is 2(LW)+2(HW)+2(LH)

We have that the surface area is 1414 where L=c , H=20, W=7

Let's plug all of this in to solve for c:

2(LW)+2(HW)+2(LH)=1414

2(c*7)+2(20*7)+2(c*20)=1414

14c+280+40c=1414

54c+280=1414

54c=1414-280

54c=1134

c=1134/54

c=21

Now the volume of a rectangular prism is V=L*W*H

So plug in our values L=21, H=20, W=7

V=21*20*7=2940

[tex]x^2-9x+14 =x^2-2x-7x+14=x(x-2)-7(x-2)=(x-7)(x-2)[/tex]

Answer:

(x - 7)(x - 2)

Step-by-step explanation:

Consider the factors of the constant term (+ 14) which sum to give the coefficient of the x- term (- 9)

The factors are - 7 and - 2, since

- 7 × - 2 = + 14 and - 7 - 2 = - 9, hence

x² - 9x + 14 = (x - 7)(x - 2) ← in factored form