Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,1). What is the distance from B to B’?

Answer:

A. 60°

Step-by-step explanation:

From the diagram, in triangle ABC,

AB=BC=CA=15 units.

This means triangle ABC is an equilateral triangle.

All angles in equilateral triangle are congruent. The sum of all interior angles in triangle is always 180°, so one angle of equilateral triangle is equal to 60°. Thus,

∠A=∠B=∠C=60°

49 out of 50 drinks were lemonade.

Divide the number of lemonade drinks by total drinks:

49 / 50 = 0.98 = 98%

98% of the drinks were lemonade, so there would be a 98% chance the next drink was lemonade.

Answer:

A. 9

Step-by-step explanation:

F(-2) = 9

We are given the polynomial function;

F(x) = -2x3 + x2 + 4x-3

In order to determine F(-2) using the remainder theorem, we plug in -2 in place of x in the equation and simplify;

F(-2) = -2(-2)^3 + (-2)^2 + 4(-2) - 3

F(-2) = 9

Answer:

A

Step-by-step explanation:

Evaluating F(- 2) gives the remainder on dividing the polynomial by (x + 2)

F(- 2) = - 2(- 2)³ + (- 2)² + 4(- 2) - 3 = 16 + 4 - 8 - 3 = 9 ← remainder

For this case we have that by definition, the Pythagorean theorem states that:

[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]

Where:

c: It is the hypotenuse of the triangle

a, b: They are the legs of the triangle

Then, we verify if the theorem for the given triangles is fulfilled:

Triangle 1:

[tex]\sqrt {13} = \sqrt {2 ^ 2 + 3 ^ 2}\\\sqrt {13} = \sqrt {4 + 9}\\\sqrt {13} = \sqrt {13}[/tex]

It is fulfilled!

Triangle 2:

[tex]25 = \sqrt {2 ^ 2 + (3 \sqrt {2}) ^ 2}\\25 = \sqrt {4+ (9 * 2)}\\25 = \sqrt {22}[/tex]

It is not fulfilled!

Triangle 3:

[tex]43 = \sqrt {2 ^ 2 + (3 \sqrt {3}) ^ 2}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {31}[/tex]

It is not fulfilled!

ANswer:

Triangle A

Answer:

(3,0) and (-2,5)

Step-by-step explanation:

The solutions of the equations are A ( 3 , 0 ) and B ( -2 , 5 ) and the graph is plotted

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as C

Now , the value of C is

Substituting the values in the equation , we get

y = x² - 2x - 3   be equation (1)

y = -x + 3   be equation (2)

On simplifying , we get

-x + 3 = x² - 2x - 3

Adding x on both sides , we get

x² - 3 - x = 3

Subtracting 3 on both sides , we get

x² - x - 6 = 0

On factorizing , we get

( x - 3 ) ( x + 2 ) = 0

So , the two values of x are 3 and -2

Hence , the solutions of equations are A ( 3 , 0 ) and B ( -2 , 5 )

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Choose two points

(4,1) and (-3 , 5)

rise/run = 4/6

Simplify - 2/3

Answer = B) 2/3

Hope this helps!!

we can simply get the slope by using two points off the line, hmmmm say the line passes through (0,3) and (-3,5)

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-3}{-3-0}\implies \cfrac{2}{-3}\implies -\cfrac{2}{3}[/tex]

[tex]|x|+5\leq1\\|x|\leq-4\\x\in\emptyset[/tex]

C

Answer:

927 Cubic Inches.

Answer:

Area of the prism = 927 in²

Step-by-step explanation:

Area of the prism is defined by A = Area of the base × height

Since base of the prism is an octagon with side length = 4 inches

and apothem = 4.83 inches

Now area of the octagonal base = [tex]\frac{1}{2}(\text{Perimeter})(\text{Apothem})[/tex]

= [tex]\frac{1}{2}(4)(8)(4.83)[/tex]

= 77.28 inch²

Now area of the prism = 12×77.28 = 927.36 inch²

Therefore, area of the prism having base in the shape of an octagon is 927 inch²

Answer:

    All values of x are solutions

Step-by-step explanation:

−15x+4 ≤ 109  OR −6x + 70 > −2

-15x ≤ 105       OR -6x  > -72

  -x ≤ 7            OR    -x > - 12

   x ≥ -7           OR     x < 12

Answer

       x ≥ -7           OR     x < 12

       All values of x are solutions

Answer:

x = 2

Step-by-step explanation:

x+3 = -x + 7

x = -x + 4

(2) = -(2) + 4

2 = 2

Answer:

The correct answer is x = 2.

Step-by-step explanation:

To solve this equation, we must get all of the variables (x's) to one side of the equation and get all of the constant terms (numbers only) to the other side.

Starting with this equation, we are going to add x to both sides of the equation.  This will cancel out the -x on the right side of the equation, thereby moving all of the variable x's to the left side of the equation.

x + x + 3 = -x + x + 7

If we simplify by combining like terms, or adding the x's together, we get:

2x + 3 = 7

Next, we should subtract 3 from both sides of the equation in order to move all of the constant terms to the right side of the equation.

2x + 3 -3 = 7 - 3

If we simplify, we get:

2x = 4

Finally, we should divide both sides by 2 in order to get the variable x alone on the left side of the equation, solving it.

x = 2

Therefore, your answer is x = 2.

Hope this helps!

Answer:

opening the bracket, the expression becomes

12x^2-28-19x^2

collect like terms

12x2-19x^2-28

-7x^2-28

-7(x^2+4)

Answer:

52 is the multiple of 13

Step-by-step explanation:

3x+3=156

3x=153

x=52

Answer:

52 is the multiple of 13 out of 51 , 52, 53 numbers​.

Step-by-step explanation:

Given:  Sum of three consecutive integers 156

To find: Three consecutive integers .

Solution: We have given that

Let first consecutive number  x ,

Second consecutive number=   x+1

Third number =  x+2

According to question :

Sum of three consecutive number

x + x+1 +x+2 = 156 .

Combine like term

3x+3 = 156

On subtracting by 3 both side

3x + 3 -3 = 156 - 3

3x = 153

On dividing by 3

x = 51.

X+1 = 51+1

x+1 = 52.

x +3 = 51+2 = 53.

We can see second number 52 is multiple of 13.

Therefore, 52 is the multiple of 13 out of 51 , 52, 53 numbers​.

Answer:

right

Step-by-step explanation:

there is a right angle in the triangle

Answer:

Right

Step-by-step explanation:

Right... the giveaway was the right angle  in the pic

To find the volume multiply the three dimensions:

16 x 25 x 37 = 14,800 cubic meters.

The statements which are true are:

In Trigonometry, the Law of Sine relates the length of sides of a triangle to the angle of a triangle.

According to this law if a,b and c are the sides of a triangle and A,B and C  respectively are opposite angles to the side.

Hence, we have:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

i.e. we have:

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]

This could also be given by:

[tex]a\sin B=b\sin A[/tex]

[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

Answer:its all of them

Step-by-step explanation:

e2020

Answer:

y+13 = 5(x+2)

Step-by-step explanation:

y = 5x-3

The slope is 5 since it is in the form y= mx +b where m is the slope

The point slope form of the equation of a line is

y-y1 = m(x-x1)  where (x1,y1) is the point

y--13 = 5(x--2)

y+13 = 5(x+2)

Answer:

B or y + 13 = 5(x + 2)

Step-by-step explanation:

Answer:

i^88 =  1

Step-by-step explanation:

i^88 = i^ 4*22 = 1    { i^4k = 1 ; i^4k+1 =i ; i^4k+2 = (-1); i^4k+3 = (-i)  }

The equivalent expression for i^88 is 1 as the powers of i cycle every 4. Hence (i^4)^22 which is same as 1^22 ends up being 1.

In complex numbers, i is the imaginary unit with the property i^2 = -1. The powers of i repeat in a cycle: i^1=i, i^2=-1, i^3=-i, and i^4=1. To find the equivalent expression for i^88, we will the fact that i^4=1 and i^88 would be equivalent to (i^4)^22, because 4*22 = 88.

Therefore, (i^4)^22 = 1^22. The equivalent expression for i^88 is 1.

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Answer:

The unit that should be in the denominator is kilometers

Step-by-step explanation:

we know that

[tex]1\ mile=1.6\ kilometers[/tex]

To convert x km to mi

[tex]x\ km*(\frac{1}{1.6})\frac{mi}{km}=\frac{x}{1.6}\ mi[/tex]

therefore

The unit that should be in the denominator is kilometers

Answer:

20 by 20

Step-by-step explanation:

the new dimensions have to be 12 because 12×12 =144 so you would add 8 to 12 and get 20 for each side

Answer:

D) 20 feet by 20 feet

Step-by-step explanation:

Given:

The area of the original grass lawn reduced by 8 feet on each side.

The smaller lawn's area = 144 square feet which is represented by the equation

[tex](x - 8)^2 = 144[/tex], where "x" is the side of the original lawn.

To find the original dimension of the lawn, we need to solve for x from the above equation.

To solve follow the steps.

Step 1:

To get rid of square on the right hand side, we need to take square root on both sides.

Taking the square root on both sides, we get

[tex]\sqrt{(x - 8)^2} = \sqrt{144}[/tex]

[tex](x - 8) = 12[/tex]

Step 2:

Now add 8 on both sides, we get

x - 8 + 8 = 12 + 8

x = 20

Therefore, the original dimensions of the lawn is 20 feet by 20 feet.

For this case we must factor the following expression:

[tex]d ^ 4-81[/tex]

Rewriting the expression:

[tex](d ^ 2) ^ 2-9 ^ 2[/tex]

We factor using the formula of the square difference:

[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]

Where:

[tex]a = d ^ 2\\b = 9[/tex]

So:

[tex](d ^ 2 + 9) (d ^ 2-9)[/tex]

From the second term we have:

[tex]d ^ 2-3 ^ 2 = (d-3) (d + 3)[/tex]

Finally, the factored expression is:

[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]

Answer:

[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]

The complete factorization of the term:

              [tex]d^4-81[/tex] is:

        [tex](d-3)(d+3)(d^2+9)[/tex]

To factor a term means to express is as a product of distinct factors i.e. multiples.

We are asked to factor the algebraic expression which is given by:

[tex]d^4-81[/tex]

We could write this expression as:

[tex](d^2)^2-(3^2)^2=(d^2)^2-(9)^2[/tex]

We know that:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

i.e.

[tex]d^4-81=(d^2-9)(d^2+9)\\\\i.e.\\\\d^4-81=(d^2-3^2)(d^2+9)\\\\i.e.\\\\d^4-81=(d-3)(d+3)(d^2+9)[/tex]

Final answer:

To find the probability of choosing a random non-honor student who is an athlete, subtract the number of non-honor students who are athletes but not in the 3 honor athletes group from the total non-honor students.

Explanation:

The question: A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

Step-by-step explanation:

Answer:

j = 7

Step-by-step explanation:

flip the equation around: instead of using multiplication you use division to find out what j is.

1st step: 42 divided by 6 is 7

2nd step: (check your answer): 7 times 6 does equal 42, therefore j = 7 is correct.

Answer:

[tex]\huge \boxed{J=7}[/tex]

Step-by-step explanation:

Switch sides.

[tex]\displaystyle6j=42[/tex]

Divide by 6 from both sides.

[tex]\displaystyle \frac{6j}{6}=\frac{42}{6}[/tex]

Simplify, to find the answer.

[tex]\displaystyle 42\div6=7[/tex]

[tex]\huge \boxed{j=7}[/tex], which is our answer.

Answer:

the axis of symmetry is x = 4

Step-by-step explanation:

The three coefficients of the polynomial f(x) = 2x^2 - 16x + 27 are a= 2, b = -16 and c = 27.                                                     -b

The formula for the axis of symmetry is  x = ------------

                                                                             2a

                               -(-16)

which here is x = ------------ = 4

                                2(2)

The equation of the axis of symmetry is x = 4.

Answer:

The answer would be 60

Step-by-step explanation:

What you do is if the number if 5 or less (ex 55) you would round down to 50. However it is 56 so you would round up to the next highest tenth, 60.

Hope this helps! Have a great day!

[tex]\text{Hey there}[/tex]

[tex]\text{If you come across: 5, 6, 7 , 8 , \& 9 you're going}\uparrow\text{(up)}[/tex]

[tex]\text{If you come across 1 , 2 , 3 , \& 4 you're going}\downarrow\text{(down)}[/tex]

[tex]\text{In this equation we have a SIX (6) at the end of the equation so we're going UP!}[/tex]

[tex]\boxed{\boxed{\bf{Ansewr: 60}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]

Step-by-step explanation:

Let

x -----> the length of the rectangle

y -----> the width of the rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(x+y)[/tex]

[tex]P=56\ m[/tex]

so

[tex]56=2(x+y)[/tex]

[tex]28=(x+y)[/tex] ------> equation A

[tex]x=y+8[/tex] -----> equation B

Substitute equation B in equation A and solve for y

[tex]28=(y+8+y)[/tex]

[tex]28=2y+8[/tex]

[tex]2y=20[/tex]

[tex]y=10\ m[/tex]

Find the value of x

[tex]x=10+8=18\ m[/tex]

therefore

The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]

Answer:

x=−7/8±129/8

Step-by-step explanation:

Assuming that is a -4x^2, i'll solve it. So, -4x^2 - 7x = -5. This is a quadratic, so move all the numbers to one side (and variables). So, -4x^2 - 7x + 5 = 0. Divide everything by -1, to make the coefficient of the x squared positive. This leaves: 4x^2 + 7x -5 = 0. Now, factoring attempts: (2x-1)(2x+5). This does not work, sadly, so we must find other methods. Using the quadratic formula would be easier than factoring, so use the quadratic formula. This gives us the answers of -7 plus or minus sqrt(129) all over 8. The quadratic formula comes in handy!

Answer:

B

Step-by-step explanation:

A graph skewed right would have LESS dots on the right side

Hope this helped!

Answer:

The correct option is B.  

Step-by-step explanation:

Consider the provided graph.

A skewed right: If the distribution has a long right tail then it is know as skewed right. It is also called the positive-skew distributions. Due to a lengthy tail on the number line in the positive direction. The mean is on the right of the peak as well. See figure 1.

Now, consider the provided graph.

Option A is skewed left, so it is not the correct option.

Option B is skewed right, which is the correct option.

Whereas C and D are neither skewed left or right.

Therefore, the correct option is B.

[tex]\bf (\stackrel{x_1}{7}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-(-5)}{3-7}\implies \cfrac{-9+5}{-4}\implies \cfrac{-4}{-4}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=1(x-7) \\\\\\ y+5=x-7\implies y=x-12[/tex]

Answer:

The probability of the spinner landing on an even number or a multiple of 3 is 0.6667 .

The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is 0.7778 .

Step-by-step explanation:

Be the events

A = even number

B = Multiple of 3

C = Odd Number

D = Number between 4 and 15, both numbers excluded

The sets are as follows:

A = {2,4,6,8,10,12,14,16,18}

B = {3,6,9,12,15,18}

C = {1,3,5,7,9,11,13,15,17}

D = {5,6,7,8,9,10,11,12,13,14}

To calculate the probability that the roulette lands in an even number or in a multiple of 3, we make the union of A and B:

A U B = {2,3,4,6,8,9,10,12,14,15,16,18} = 12 numbers of 18

P (A U B) = 12/18 = 2/3 = 0.6667

To calculate the probability that roulette lands on an odd number or a number between 4 and 15 (both numbers excluded), we make the union of C and D:

C U D = {1,3,5,6,7,8,9,10,11,12,13,14,15,17} = 14 numbers of 18

P (C U D) = 14/18 = 7/9 = 0.7778

The first answer is 0.6667

The second answer is 0.7778

Hope this helps!

Answer:

first one: 2/3

second one: 7/9

Step-by-step explanation:

PLATO

Answer:

Domain {1,5,10,20}

Ranger {4,20,40,80}

Step-by-step explanation:

$1=4 quarters

$5=20 quarters

$10=40 quarters

$20=80 quarters

Domain {1,5,10,20}

Ranger {4,20,40,80}