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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°).

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Answer:

c

Step-by-step explanation:

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.

https://brainly.com/question/4074088

Answer:

(4y7+7x4)(−4y7+7x4)

Step by Step:

Factor 49x8−16y14

−16y14+49x8

=(4y7+7x4)(−4y7+7x4)

The factor of the expression 49x⁸ − 16y¹⁴ is (7x⁴ - 4y⁷) and (7x⁴ + 4y⁷) after using the identity.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

49x⁸ − 16y¹⁴

As we know the polynomial identity:

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

a² - b² = (a - b)(a + b)

The expression 49x⁸ − 16y¹⁴ can be written as:

= (7x⁴)² − (4y⁷)²

After using the identity: a² - b² = (a - b)(a + b)

= (7x⁴ - 4y⁷)(7x⁴ + 4y⁷)

Thus, the factor of the expression 49x⁸ − 16y¹⁴ is (7x⁴ - 4y⁷) and (7x⁴ + 4y⁷) after using the identity.

Learn more about the expression here:

brainly.com/question/14083225

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Answer:

C

Step-by-step explanation:

We start with the second line;

3x -2y + 4 = 0

3x + 4 = 2y

divide through by 2

3x/2 + 2 = y

Comparing this with standard form of y = mx + c

where m is slope

This means 3/2 is slope of the line

Since this line is perpendicular to the other line, then the product of their slopes is -1

3/2 * slope of second line = -1

Slope of second line = -1 divided by 3/2 = -2/3

We use the point slope form to find the equation of the other line

y-y1 = m(x-x1)

where m = -2/3 and (x1,y1) = (2,-3)

y-(-3) = -2/3 (x-2)

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

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

3y + 9 = -2x + 4

3y + 5 = -2x

3y + 2x + 5 = 0

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 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:

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:

[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:

m^2+m+1

Step-by-step explanation:

HCF= m^2+m+1 which is the factor of all three polynomials

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:

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)

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:

[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:

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:

ANSWER:

3x  + 3y = 0

7x - y = 8

Step-by-step explanation:

Answer:

I would say multiply everything by 2 and you’ll have an equivalent system of equations or multiply by 3  or any number, because im not sure if this is a multiple answer question, so sry

Answer:

(-1,-2)

Step-by-step explanation:

y≥-2x

y>|x+|^?

according to the graph only (-1,-1) are in the shaded area

Answer:

49

Step-by-step explanation:

7 times 4 equals 49.

Answer:

x = Rs 20,833.33

the value of x is Rs 20,833.33

Step-by-step explanation:

Let x,y and z represent the price of the item initially, after one month and after two months respectively.

Given that;

after one month its label price is reduced by 20%

y = x - 20% of x

y = x - 0.20x

y = 0.80x ........1

after 2 months its reduced price is further reduced by 10% and then sold it for Rs 15000.

z = y - 10% of y

z = y - 0.10y

z = 0.90y ........2

Substituting equation 1 into 2;

z = 0.90(0.80x)

z = 0.72x

Also z = Rs 15000

So,

z = 0.72x = Rs 15000

0.72x = Rs 15000

x = Rs 15000/0.72

x = Rs 20833.33333333

x = Rs 20,833.33

the value of x is Rs 20,833.33

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..

f • g denotes the product of f and g, so that

[tex](f\cdot g)(x)=f(x)\cdot g(x)=(3x-8)(-2x+5)[/tex]

Without computing the whole product, just look at the first terms, [tex]-6x^2[/tex]. This tells you that f • g is quadratic, and its graph is a stretched parabola that opens downward.

You can treat the product g • s similarly:

[tex](g\cdot s)(x)=(-2x+5)(4x^2-9x+2)[/tex]

The leading term is [tex]-8x^3[/tex], so the graph should resemble a stretched cubic curve reflected across the x axis.

The leading term is , so the graph should resemble a stretched cubic curve reflected across the x axis.

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:

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: 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:

20

Step-by-step explanation:

y = 35x + c

Put x as 1, and y as 55.

55 = 35(1) + c

55 - 35 = c

20 = c

Answer:

the letter in the green box should be 3.

i believe the full equation should be y= -3/2 x+1

Step-by-step explanation:

the y side keeps decreasing by 1 1/2 which in improper fraction form is -3/2. the x side keeps increasing by 1.

Answer:

X^2-9=0 is x2 = 9

Step-by-step explanation:

Answer:

-x + 3

Step-by-step explains:

Um... You can do it on a computer...

Answer:

x = 1/2

Step-by-step explanation:

-3x + 1 + 10x = x + 4

7x + 1 = x + 4

6x + 1 = 4

6x = 3

x = 3/6

x = 1/2

Answer:

It's (A) [tex]x\frac{1}{2}[/tex]

Step-by-step explanation: