Triangle ABC is rotated 45° about point X, resulting in triangle EFD. Triangle A B C is rotated 45 degrees about point X to form triangle E F D. The lengths of sides A C and D E are congruent, the lengths of sides A B and E F are congruent, and the lengths of sides D F and C B are congruent. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB? 3.3 cm 3.6 cm 4.2 cm 4.5 cm

Answer:

D. 1800°

Step-by-step explanation:

The given polygon has 12 sides.

The formula for finding the sum of the interior angles of an n-sided polygon is given as, ( n − 2 ) × 180.

Where n is the number of sides of the polygon.

Thus, the sum of the interior angles of the 12 sided polygon given above is:

(12 - 2) × 180

= 10 × 180 = 1800°

Sum of the measures of the interior angles of the 12-sided polygon is D. 1800°

Answer: The answer is B

Step-by-step explanation:

Answer:

Option B is correct

Step-by-step explanation:

cos (3pi/4) = -cos(pi - 3pi/4) = -cos(pi/4) = -sqrt(2)/2

=> Option B is correct

Answer:

The answer is "Option A"

Step-by-step explanation:

Given:

[tex]\to \frac{(a-5)+a}{2}=x.....(a)\\\\\to \frac{a+(a+9)}{2}=y.....(b)\\\\[/tex]

solve the above equation:

[tex]\to \bold{\frac{(a-5)+a}{2}=x}\\\\\to \frac{a-5+a}{2}=x\\\\\to \frac{2a-5}{2}=x\\\\\to \bold{\frac{a+(a+9)}{2}=y}\\\\\to \frac{a+a+9}{2}=y\\\\\to \frac{2a+9}{2}=y\\\\[/tex]

add both value (x and y):

[tex]\to \bold{x+y}\\\\\to \frac{2a-5}{2}+\frac{2a+9}{2}\\\\\to \frac{2a-5+2a+9}{2}\\\\\to \frac{4a+4}{2}\\\\\to \frac{2(2a+2)}{2}\\\\\to (2a+2)\\[/tex]

average of x and y:

[tex]\to \frac{x+y}{2}\\\\\therefore \bold{x+y= 2a+2}\\\\\to \frac{2(a+1)}{2}\\\\\to \boxed{(a+1)}\\[/tex]

Step-by-step explanation:

Plug in -2 whenever u see x

3(-2) -7= 5(-2-1)

-6-7= -10-1

-13 = -11

Therefore, x is not equal to -2.

Answer:

the value of n will be the range

Step-by-step explanation:

lets just give an example of (9,n) and you had to find the value its actually simple

9 is the domain

n is the range

a part of ordered pair function

got it?

Answer:

[tex]\sqrt{37}[/tex]

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A(- 2, 9) and (x₂, y₂ ) = B(4, 8)

d = [tex]\sqrt{(4+2)^2+(8-9)^1}[/tex]

   = [tex]\sqrt{6^2+(-1)^2}[/tex]

   = [tex]\sqrt{36+1}[/tex]

    = [tex]\sqrt{37}[/tex] ≈ 6.1 ( to 1 dec. place )

Answer:

[tex]x = 2, 12[/tex]

Your correct answer is D, since I don't see a -12.

Step 1: Subtracting 2 from both sides

Since we have to find the value of x, we have to factor the equation. To do so, we first have to subtract the two from both sides of the equation so all the values are on one side of the equation.

[tex]x^2-10x-22(-2)=2(-2)\\x^2-10x-24=0[/tex]

Step 2: Factoring the equation

Part 1

After subtracting 2 from both sides of the equation, we have to factor the polynomial to be able to get it into two sets of parentheses, so in order to do that, we will ignore the equal sign and the 0 for now. We are now left with:

[tex]x^2-10x-24\\[/tex]

First, we find the multiples of the first term, [tex]x^2\\[/tex], and the last term, -24. Since there is an invisible 1 before the first term, we are basically finding the multiples of [tex]1x^2[/tex], which is [tex]1x[/tex] and [tex]1x[/tex], or x and x. Now we have to find the correct set of numbers for -24. Do do that, we have to make sure that when we multiply the first set of numbers (x, x) with the second set (?, ?) and add them together, then we would get the number in the middle (-10x). So: Two of the most obvious multiples for 24 are 6 and 4, 12 and 2, and 3 and 8. But, this is a negative 24, so we have to work ahead to find out which pair we use first. If we multiply 8 and 3 with x and x, we get 8x and 3x. When we add them together, we do not get 10x, but instead, we get 11x, so it is the wrong pair. If we do the same thing to 6 and 4, we would get 10x, but since 24 is negative, it is not correct because we would need one of the numbers to be negative. In this case, they equal to 10x, but one of the numbers would have to be negative because (if 6 was the negative):

[tex]-6 * 4=-24\\[/tex]

But:

[tex]4-6\neq 10\\[/tex]

So this is not the correct set either. Our last set is 12 and 2, and when we multiply by x (12x and 2x) and we set one of the numbers to be a negative (-12) and subtract them, we get -10x, so, therefore, this is the correct number pair.

[tex]-12*2=-24\\2-12=-10[/tex]

Part 2

With all that done, we now have to factor the numbers. We take the first numbers (x and x), and we place them in front of each of the two parentheses.

[tex](x,?)(x,?)[/tex]

Now, we place -12 and 2 in those places.

[tex](x,-12)(x,2)[/tex]

To find x, we have to plug in the equal sign and 0 from the beginning.

[tex](x,-12)(x,2)=0[/tex]

Since they both have to equal to 0, then that means there would be two different answers because, for example: 12 - 12 = 0, but 12 - 2 ≠ 0.

To find both solutions, we treat the numbers in each of the parentheses as its own equation, and we solve it from there.

x - 12 = 0

12 - 12 = 0

x - 2 = 0

2 - 2 = 0

12 and 2 are our solutions! Hope this helps :)

Answer:

12  and 2

Step-by-step explanation:

factor the euqation x^2-10x-22=2 and you get (x,-12)(x,2)=0 and when you solve that you get 12 and 2

Answer:

C.

Step-by-step explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7

Answer:

Option C is the correct option.

Step-by-step explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

[tex] \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} [/tex]

Plug the values

[tex] \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} [/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} [/tex]

Add the numbers

[tex] \frac{y + 1}{x - 2} = \frac{6}{4 - 2} [/tex]

Subtract the numbers

[tex] \frac{y + 1}{x - 2} = \frac{6}{2} [/tex]

Reduce the numbers with 2

[tex] \frac{y + 1}{x - 2} = 3[/tex]

Apply cross product property

[tex]3x - 6 = y + 1[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex]3x - y = 1 + 6[/tex]

Add the numbers

[tex]3x - y = 7[/tex]

[tex] - 3x + y = - 7[/tex]

Hope this helps...

Best regards!

Answer:

49

Step-by-step explanation:

7 times 4 equals 49.

Answer:

9x + 8.

Step-by-step explanation:

2(x - 3) + 7(x + 2)

= 2x - 6 + 7x + 14

= 2x + 7x - 6 + 14

= 9x + 8.

Hope this helps!

Answer

y= 12.5x + 210,000

Step-by-step explanation:

This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b

The value of function that represents the situation is,

⇒ P = 210,000 (1.125)ⁿ

Where, n is number of years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The situation is,

⇒ A population of 210,000 increases by 12.5% each year​.

Now, Let number of years = n

Hence, The value of function that represents the situation is,

⇒ P = 210,000 (1 + 12.5%)ⁿ

⇒ P = 210,000 (1 + 0.125)ⁿ

⇒ P = 210,000 (1.125)ⁿ

Learn more about the mathematical expression visit:

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Answer:

m∠1 + m∠2 = 180°

Step-by-step explanation:

An interior angle and its exterior angle are supplementary (they add up to 180°).

I would really appreciate it if you would mark me brainliest!

Have a blessed day!

Answer:

c

Step-by-step explanation:

Answer:

6,8

Step-by-step explanation:

Answer:

Hey there!

Eight years ago, Manuel's age was 36/2, or 18.

Now, his age is 18+8, or 26 years old.

So, he is 26 years old now.

Hope this helps :)

Answer: 4:3.

Step-by-step explanation:

Given: Point P is [tex]\dfrac{4}{7}[/tex] of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

[tex]\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}[/tex]

As per given,

[tex]\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}[/tex]

Hence, P partition the directed line segment from M to N in 4:3.

Answer: After 210 seconds they with next flash at the same time.

Step-by-step explanation:

Given: Ardem has two lights.

One flashes every 15 seconds the other flashes every 42 seconds.

If they started flashing at the same time, then the number of seconds after that they with next flash at the same time = LCM (15, 42)   [LCM - Least common multiple]

Prime factorization of 15 = 3 x 5

Prime factorization of 42 = 2 x 3 x 7

Then, LCM (15, 42) = 2 x 3 x 5 x 7 = 210

i.e. After 210 seconds they with next flash at the same time.

Answer:

Third choice is correct

Step-by-step explanation:

-2x-y=-2

-y=2x-2

y=-2x+2

3x-y=-2

-y=-3x-2

y=3x+2

These two lines intersect at (0, 2)

Answer:

17 nickels

Step-by-step explanation:

To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:

quarters= 0.25

dimes= 0.10

nickels= 0.05

pennies= 0.01

(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where

x= the quantity of nickels

Now, you can solve for x:

4.75+3.9+0.05x+0.58=10.08

0.05x=10.08-4.75-3.9-0.58

0.05x=0.85

x=0.85/0.05

x=17

According to this, the answer is that there are 17 nickels in the cup holder.

Answer:

(-6, 0) and (2, 0)

Step-by-step explanation:

To find the x-intercepts, we can factor the expression:

f(x) = x² + 4x - 12

2 factors of -12 that add up to 4 are 6 and -2

(x + 6)(x - 2)

Set each factor equal to 0 and solve for x:

x + 6 = 0

x = -6

x - 2 = 0

x = 2

So, the x intercepts are (-6, 0) and (2, 0)

Answer:

It's the first option, (-6, 0) (2, 0)

Step-by-step explanation:

100% on Edge

Answer: The tank which has 3 m side.

Step-by-step explanation: A cube is a form that has equal sides. To calculate the volume of it, multiply all three sides:

V = length*width*height

Since they are all the same, volume will be:

V = s³

One tank has a 3 m side, so its volume is:

V = 3³

V = 27 m³

The other has half of the first one side, then s = [tex]\frac{3}{2}[/tex] and volume will be:

V = [tex](\frac{3}{2})^{3}[/tex]

V = [tex]\frac{27}{8}[/tex] m³

As you can see, the volume of the second tank is [tex]\frac{1}{8}[/tex] smaller than the first one. Therefore, the tank which has 3 m side can store more water than the  tank with side measuring half of the first.

Answer:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Company A will charge $ 37 less than Company B

Part C:

Company A will charge $ 65 less than Company B

Step-by-step explanation:

Part A:

Equation for Company A:

x = Number of days renting a car

35x + 15

Equation for Company B:

x = Number of days renting a car

42x + 10

Part B:

Renting a car for 6 days

Company A:

35 * 6 + 15 = 210 + 15 = $ 225

Company B:

42 * 6 + 10 = 252 + 10 = $ 262

Company A will charge $ 37 less than Company B

Part C:

Renting a car for 10 days

Company A:

35 * 10 + 15 = 350 + 15 = $ 365

Company B:

42 * 10 + 10 = 420 + 10 = $ 430

Company A will charge $ 65 less than Company B

Step-by-step explanation:

This question requires the Pythagorean theorem.

Car A travels north 100km in two hours.

Car B travels west 160km in two hours.

Imagine a triangle the line going up is 100km

the line going left is 160km

the formula for the Pythagorean theorem is

a^2+b^2=c^2

100^2+160^2=c^2

10000+25600=c

35600=c

√35600=c

You can draw a diagram.

Answer:

(squareroot2^2) times 27 (1/2)

Step-by-step explanation:

Answer:3z^2/9

Step-by-step explanation:

Answer: -1/1

Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.

Answer:

[tex] \frac{97pi}{18} m [/tex]

Step-by-step Explanation:

==>Given:

radius (r) = 10 m

m<VCW = 97°

==>Required:

Length of arc VW

==>Solution:

Formula for length VW is given as 2πr(θ/360)

Using the formula, Arc length = 2πr(θ/360), find the arc length VW in the given circle

Where,

θ = 97°

r = radius of the circle = 10 m

Thus,

Arc length VW = 2*π*10(97/360)

Arc length VW = 20π(97/360)

Arc length VW = π(97/18)

Arc length VW = 97π/18 m

Our answer is,

[tex] \frac{97pi}{18} m [/tex]

Answer:

36

Step-by-step explanation:

Let's call the # of boys and girls 5x and 3x respectively. We can write:

5x = 3x + 24

2x = 24

x = 12 so the # of girls = 12 * 3 = 36

Answer:

solution,

Let the number of girls be X

Number of boys be 'x+24'

Now,

[tex] \frac{x + 24}{x} = \frac{5}{3} \\ or \: 3(x + 24) = 5x \\ or \: 3x + 72 = 5x \\ or \: 3x - 5x = - 72 \\ or \: - 2x = - 72 \\ or \: x = \frac{ - 72}{ - 2} \\ x = 36[/tex]

hope this helps..

Good luck on your assignment..

The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five

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Answer:

The answer is x=7/5

Step-by-step explanation:

because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5

Answer:

360 degrees

Step-by-step explanation:

The sum of all exterior angles in any convex polygon is 360 degrees.

Answer:

360 degrees.

Step-by-step explanation:

The sum of exterior angles of every polygon is 360 degrees so the What is the sum of the exterior angles of a 14-gon is also equal to 360 degrees.

Answer:

The numbers at 13 and 13

Step-by-step explanation:

The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.

The two numbers are (13, 13).

Given that,

The sum of the two numbers is 26.

And the sum of their square is minimum.

We have to determine,

The two numbers are.

According to the question,

Let, the first number be x,  

and the second number be y.

The sum of the two numbers is 26.

[tex]x + y = 26[/tex]

And The sum of their squares is a minimum.

[tex]x^2 + y^2 = h[/tex]

Solving both the equation,

[tex]x + y = 26\\\\x = 26-y[/tex]

Substitute the value of x in equation 2,

[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]

Then, The vertex of the parabola is,

[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]

The minimum value of the parabola is 13, which is also the sum of squares.

Therefore, The two number is x = 13 and y =13.

To know more about Parabola click the link given below.

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