The coordinates of △ABC are A(−11,7), B(−5,−3), C(−2,3). After a dilation, the coordinates are A'(22,−14), B'(10,6), C'(4,−6). Find the scale factor.

Answer:

G !!! Have a good day BLOODY

Answer:

3+(6-2)*4=19

Step-by-step explanation:

Due to PEMDAS, it would first be required to do "6-2", which is 4.

Then, the 4 in the parenthesis is multiplied by the 4 on the outside, making 16.

Finally, 3 would be added to 16, making 19.

To find the volume of a rectangular prism, multiply the length by the width by the height.

Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3

All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3

To find the volume of a rectangular prism, multiply the length by the width by the height.Volume = 2.2 x 3.1 x 1.2 = 8.184 cm^3All the dimensions are one decimal place, so if you round the answer to one decimal place it would be 8.2 cm^3

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (3, 7) and (15, 16). Substitute:

[tex]d=\sqrt{(15-3)^2+(16-7)^2}=\sqrt{12^2+9^2}=\sqrt{144+81}=\sqrt{225}=15[/tex]

Answer:

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

Step-by-step explanation:

Let us graph the two equations one by one.

1. [tex]f(x)=-2x+1[/tex]

If we compare this equation with the slope intercept form of a line which is given as

[tex]y=mx+c[/tex]

we see that m = -1 and c =1

Hence the slope of the line is -2 and the y intercept is 1. Hence one point through which it is passing is (0,1) .

Let us find another point by putting x = 1 and solving it for y

[tex]y=-2(1)+1[/tex]

[tex]y=-2+1 = -1[/tex]

Let us find another point by putting x = 2 and solving it for y

[tex]y=-2(2)+1[/tex]

[tex]y=-4+1 = -3[/tex]

Hence the another point will be (2,-3)

Let us find another point by putting x = -2 and solving it for y

[tex]y=-2(-2)+1[/tex]

[tex]y=+1 = 5[/tex]

Hence the another point will be (-2,5)

Now we have two points (0,1) ,(1,-1) ,  (2,-3) and (-2,5) we joint them on line to obtain our line  

2.

[tex]g(x)=y=x^2-2x-3[/tex]

[tex]y=x^2-2x+1-1-3[/tex]

[tex]y=(x-1)^2-4[/tex]

[tex](y+4)=(x-1)^2[/tex]

It represents the parabola opening upward with vertices (1,-4)

Let us mark few coordinates so that we may graph the parabola.

i) x=0 ; [tex]y=y=(0)^2-2(0)-3=0-0-3=-3[/tex] ; (0,-3)

ii)x=-1 ; [tex]y=(-1)^2-2(-1)-3=1+2-3=0[/tex] ; (-1,0)

iii) x=2 ; [tex]y=(2)^2-2(2)-3 = 4-4-3 =-3[/tex] ;(2,-3)

iii) x=1 ; [tex]y=(1)^2-2(1)-3 = 1-2-3 =-4[/tex]  ;(1,-4)

iii) x=-2 ; [tex]y=(-2)^2-2(-2)-3 = 4+4-3 =5[/tex]  ;(-2,5)

Now we plot them on coordinate axis and line them to form our parabola

When we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.

Answer:

so you dont have to suffer lol heres a screenshot

Step-by-step explanation:

Answer:

The equation in slope-intercept form is y=-2x+6.

The equation in standard form is 2x+y=6.

The equation in point-slope form is y-2=-2(x-2).

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

Parallel lines will have the same slope and different y-intercept.

Anyways the slope of y=-2x+1 is -2.

So the equation of our line we are looking for is -2.

So we know our equation is in the form y=-2x+b.

We must inf b using y=-2x+b with (x,y)=(2,2).

y=-2x  +b  with (x,y)=(2,2)

2=-2(2)+b

2=-4+b

Add 4 on both sides:

2+4=b

Simplify:

6=b

The equation is y=-2x+6.

Now it didn't say what form it wanted.

There are some forms I can give you like standard and point-slope form.

There is also general form but it is not too much different from standard form.

Standard form is ax+by=c where a,b, and c are integers if possible.

Point-slope form is y-y1=m(x-x1) where (x1,y1) is a point on the line and m is the slope.

So let's go for standard form (ax+by=c) first:

y=-2x+6

add 2x on both sides:

2x+y=6

This is standard form because it is in the form

ax+by=c.

Ok we know point (2,2) is on our line and we also know we have slope,m, is -2.

Point-slope form is

y-y1=m(x-x1)

y-2=-2(x-2)

B -median

Hypotenuse is only right triangles and legs are sides of a triangle. A bisector divides something in half evenly . Altitude is height of a triangle and median is the same segment

:

The altitude of an isosceles triangle is the same segment in the triangle as the bisector.

The bisector is a line that divides a line or an angle into two equivalent parts. The bisector of a segment always contains the midpoint of the segment.

In an isosceles triangle,

Bisector of vertex angle = midline of base side = altitude

The altitude of an isosceles triangle is the same segment in the triangle as the bisector.

Option C is correct.

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Answer:

[tex]\large\boxed{\frac{1}{1}\,\text{or}\,1}[/tex]

Step-by-step explanation:

In this question, we're trying to find the slope with the given points.

To find the slope, we're going to need to sue the slope formula.

Slope formula:

[tex]\text{Slope}=\frac{y2-y1}{x2-x1}[/tex]

You would plug in the coordinates to its right spot.

Plug in -2 to x1, 3 in y1, 2 in x2, and 7 in y2.

Your equation should look like this:

[tex]\text{Slope}=\frac{7-3}{2-(-2)}[/tex]

Now, you will solve:

[tex]\text{Slope}=\frac{7-3}{2-(-2)}\\\\\text{Slope}=\frac{4}{2-(-2)}\\\\\text{Carry the minus sign over to the -2, turning it to a positive 2}\\\\\text{Slope}=\frac{4}{2+2}\\\\\text{Slope}=\frac{4}{4}\\\\\text{Divide}\\\\\text{Slope}=\frac{1}{1}=1[/tex]

When you're done solving, you should get 1.

This means that the slope of the line is 1/1 or 1

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =7\\y_{1} =3\\x_{2} =2\\x_{1} =-2[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{7-3}{2 - (-2)}[/tex]

[tex]\frac{4}{4}[/tex]

^^^This can be further simplified down to...

1

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: B

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

We are looking for an exponential function [tex]y=a(r)^x[/tex] where r is less than 1.

a works because it is in the form [tex]y=a(r)^x[/tex] where r is less than 1.

b is in the form [tex]y=a(r)^x[/tex] but r is more than 1.

c. and d. are not even exponential functions.

c. is a polynomial

d. is a constant polynomial (no variable)

Answer:

Slope = 2

Step-by-step explanation:

Slope is the change in y/change in x. So (8-4)/4-2)=2.

Answer: Using the formula below you will get -4/-2 which is slope of 2

Step-by-step explanation:

So you would use the slope formula which is y_{2}- y_{1} / x_{2}-x_{1}  

Answer:

B)

Step-by-step explanation:

First, lets try to build the second equation, it has the general shape

[tex]y=m *x+b[/tex]

Where b is a constant (a number) and m the slope, another constant.

Using the given condition (0,-7) you can find the first constant of our second equation, just put "0" where you see "x", and put -7 where there is a "y".

That gives us that b is equals to -7.

Now we only need to know that the condition for 2 linear equations to be parallels is that their slope have to be the same or multiple between each others, this means that "m" of our second equation has to be equal to 1/2

thus, our second equation is [tex]y=\frac{1}{2}*x-7[/tex]

Another way to see this is that you can compare two linear equations y1=m1*x1 + b1, and y2=m2*x2+b2, if these two intersect in somewhere, this condition should meet:

X= (b1-b2)/(m2-m1).

If the slopes are the same, the above equation gives us an error, meaning that the linear equations are, in fact parallels.

Answer:

-28

Step-by-step explanation:

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

We going to use PE(MD)(AS).

So P means ( ).

We do have operations to perform in the ( ).

We have [tex]2-2^3[/tex] in the first set of ( ) and (-2) in the second set of ( ).

There are no operations in the second  set containing -2.

So we are just focusing on the [tex]2-2^3[/tex] right now.

You have subtract and exponent here.

Exponents come first in PE(MD)(AS) so we will perform that first.

[tex]2-2^3=2-8=-6[/tex]

Let's go back to the original problem now.

[tex]-(2-2^3)^2-4 \cdot (-2)[/tex]

[tex]-(-6)^2-4 \cdot(-2)[/tex]

Now there are no longer any operations grouped together by use of ( ).

It on to the rest of PE(MD)(AS).

So now we are doing the E part, the exponents.

[tex]-(36)-4 \cdot(-2)[/tex]

Now there is multiplication and subtraction left.

(MD) comes before (AS) so we do the multiplication and then the subtraction.  So I'm going to do 4(-2) now:

[tex]-(36)-(-8)[/tex]

Subtraction is addition of the opposite so you could write:

[tex]-(36)+8[/tex]

We don't really need ( ) around the first number:

[tex]-36+8[/tex]

36-8 is 28 but since 36>8 and 36 has a negative sign on it, the answer is -28.

Answer:

Lara's share = 25000

Step-by-step explanation:

Partnership's income = 50,000

Lara's guaranteed payment = 20,000

As the Income 50,000 is larger than Lara's guaranteed payment i.e 20,000. Since Lara is 50% partner so she will receive half the amount of the partnership's income.

Partnership's Income = 50,000  

Half of Partnership's income = 50,000/2

                                                = 25,000

Therefore, Lara's distributive share is 25,000.

!!

Answer:

f(-5) = -33

Step-by-step explanation:

f(x) = {-x^2+2x+2 if  x ≤  - 5

        {-3/4x+3 if   x > 1

find what f(-5) = ​

If x=-5, we use the first equation

f(-5) =  -x^2+2x+2  since it has the equal to part

       = - (-5)^2 +2(-5) +2

        =  -25 -10+2

        = -35+2

         =-33

Answer: -1/7

Step-by-step explanation: The reciprocal of -7 is -1/7. Flip -7 to get the answer. -7 is the same as -7/1, so flip the numbers to find the reciprocal.

Answer:

No.

Step-by-step explanation:

The circle of that equation lies on the point (3,1) as its furthest point to the right (x-axis) and therefore could never also lie on the point (3,-1).

Your equation is in center radius form, which is as follows:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Noting that your radius is 4 (since your radius squared is 16).

To graph your circle, simply go to your origin (h, k) which in this case is (-1, 1) and then count out in any direction (up, down, left, or right -- no diagonals) 4 units (since your radius is 4). This will give you the four outermost edges of your circle. Simply fill in the gaps from there, and you'll have sketched your circle.

No. The circle of that equation lies on the point (3,1) as its furthest point to the right (x-axis) and thus could never  lie on the point (3,-1).

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

The equation is in center radius form, which is as follows:

(x - h)² + (y - k)² = r²

the radius is 4 (since your radius squared is 16).

Substituting 3 for x and -1 for y:

(3 + 1)^2 + (-1 - 1)^2 = 16

4^2 + (-2)^2 = 16

16 + 4 = 16

20 = 16

Hence, we can see 20 is clearly not equal to 16, so we know the point (3, -1) can’t lie on that circle.

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Answer:

210

Step-by-step explanation:

Here comes the problem from Combination.

We are being asked to find the number of ways out in which 3 students may sit on 7 seats in a row. Please see that in this case the even can not be repeated.

Let us start with the student one. For him all the 7 seats are available to sit. Hence number of ways for him to sit = 7

Let us see the student second. For him there are only 6 seats available to sit as one seat has already been occupied. Hence number of ways for him to sit = 6

Let us see the student third. For him there are only 5 seats available to sit as two seat has already been occupied. Hence number of ways for him to sit = 5

Hence the total number of ways for three students to be seated will be

7 x 6 x 5

=210

Answer:

[tex]\large\boxed{y-5=-\dfrac{2}{3}(x+3)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope [tex]m=-\dfrac{2}{3}[/tex] and the point [tex](-3,\ 5)[/tex].

Substitute:

[tex]y-5=-\dfrac{2}{3}(x-(-3))\\\\y-5=-\dfrac{2}{3}(x+3)[/tex]

[tex]\bf \begin{cases} 2.34\\ 2.341 \end{cases}\implies \begin{cases} 2.340\\ 2.341 \end{cases}\implies \begin{cases} 2.3400\\ 2.3410 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \boxed{2.3400}\rule[0.35em]{8em}{0.25pt}2.3403\rule[0.35em]{10em}{0.25pt}\boxed{2.3410}[/tex]

Answer:

See attachment

Step-by-step explanation:

We want to graph [tex]f(x)=|x|-12[/tex] on the interval -10 to 10.

Let [tex]g(x)=|x|[/tex] be the parent absolute value function.

We can easily graph [tex]f(x)=|x|-12[/tex], if we use translation.

When the parent function is shifted downwards by 12 units, we obtain the graph of [tex]f(x)=|x|-12[/tex].

The parent function is a v-shaped graph with vertex at the origin.

We shift the parent function down so that its vertex is now at (0,-12) to get the graph of [tex]f(x)=|x|-12[/tex] .

See attachment for the graph of [tex]f(x)=|x|-12[/tex]  on the specified interval.

Answer:

Which of the following did you include in your response?

No, you will not see the graph.

When x is 0, y is –12, which is outside the viewing window.

Because the function has been reflected, it opens down.

From x = –10 to x =10, the y-values range from –22 to –12.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

=======================================

We have the points (-2, 1) and (-4, -3). Substitute:

[tex]m=\dfrac{-3-1}{-4-(-2)}=\dfrac{-4}{-2}=2[/tex]

[tex]y=2x+b[/tex]

Put the coordinates of the point (-2, 1) to the equation:

[tex]1=2(-2)+b[/tex]

[tex]1=-4+b[/tex]           add 4 to both sides

[tex]5=b\to b=5[/tex]

Finally:

[tex]y=2x+5[/tex]

Answer: A. 1.55 repeating.

Step-by-step explanation: Since 5/9 is not going to end as .5, the answer would be 1.55 repeating. 5/10 would make the answer be 1.5.

The mixed fraction number 1  5/9 is equal to the decimal number 1.55.... Then the correct option is A.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

The mixed fraction number is given below.

⇒ 1  5/9

Convert the mixed fraction number into the fraction number. Then we have

1  5/9 = 14 / 9

Convert the fraction number into a decimal number, then we have

⇒ 14/9

⇒ 1.55......

The mixed fraction number 1  5/9 is equal to the decimal number 1.55.... Then the correct option is A.

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Answer:

Law of Cosines; A ≈ 61°, B ≈ 89°, C ≈ 30°

Step-by-step explanation:

In this problem the given values are the length sides of the triangle, therefore, the triangle should be solved by beginning with the Law of Cosines

step 1

Applying the law of cosines find the value of angle C

we know that

[tex]c^{2}=a^{2}+b^{2}-2(a)(b)cos(C)[/tex]

we have

[tex]a = 8, b = 7, c = 4[/tex]

substitute the values and solve for cos(C)

[tex]4^{2}=8^{2}+7^{2}-2(8)(7)cos(C)[/tex]

[tex]16=64+49-112cos(C)[/tex]

[tex]16=113-112cos(C)[/tex]

[tex]112cos(C)=113-16[/tex]

[tex]cos(C)=97/112[/tex]

[tex]C=arccos(97/112)=30\°[/tex]

step 2

Applying the law of cosines find the value of angle B

we know that

[tex]b^{2}=a^{2}+c^{2}-2(a)(c)cos(B)[/tex]

we have

[tex]a = 8, b = 7, c = 4[/tex]

substitute the values and solve for cos(B)

[tex]7^{2}=8^{2}+4^{2}-2(8)(4)cos(B)[/tex]

[tex]49=64+16-64cos(B)[/tex]

[tex]49=80-64cos(B)[/tex]

[tex]64cos(B)=80-49[/tex]

[tex]cos(B)=31/64[/tex]

[tex]B=arccos(31/64)=61\°[/tex]

step 3

Find the measure of angle A

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

we have

[tex]C=30\°[/tex]

[tex]B=61\°[/tex]

substitute and solve for A

[tex]A+61\°+30\°=180\°[/tex]

[tex]A+91\°=180\°[/tex]

[tex]A=180\°-91\°=89\°[/tex]

Answer:

[tex]6+\frac{i}{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3\imath}-(-6+\frac{2}{3\imath})[/tex]

[tex]\frac{1}{3\imath}+6-\frac{2}{3\imath}[/tex]

taking like terms together

[tex]\frac{1}{3\imath}-\frac{2}{3\imath}+6[/tex]

taking LCM

[tex]\frac{1-2}{3\imath}+6[/tex]

[tex]\frac{-1}{3\imath}+6[/tex]

taking LCM

[tex]\frac{-1+18\imath}{3\imath}[/tex]

splitting the term

[tex]\frac{-1+18\imath}{3\imath}[/tex]

splitting the term

[tex]-\frac{1}{3\imath}+\frac{18\imath}{3\imath}[/tex]

[tex]-\frac{1\times3\imath}{3\imath \times \imath}+6[/tex]

[tex]-\frac{i}{3\imath^2}+6[/tex]

we know that

[tex]\imath^2=-1[/tex]

putting this value in above equation

[tex]\frac{\imath}{3}+6[/tex]

Answer:

8x+1

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

7x−5(x+6)

=7x+(−5)(x)+(−5)(6)

=7x+−5x+−30

=7x+−5x+−30

=(7x+−5x)+(−30)

=2x+−30

-2x=-30

x=15

Answer:

Step-by-step explanation:

Givens

Tan(60) = opposite / adjacent

adjacent = 26

Cos(39) = adjacent / hypotenuse

Solution

Tan(60) = opposite (which is the height) / 26            Multiply both sides by 26

26*tan(60) =  opposite                                                  Multiply the left.

tan60 = 1.732

26 * 1.732 = opposite

45.033

====================                

Cos(39) = adjacent / hypotenuse

cos(39) = 0.7771

0.7771 = 45.0333 / x              Multiply both sides by x

0.7771*x = 45.0333                Divide by 0.7771

x = 45.0333 / 0.7771

x = 57.94

Answer:

option C

Step-by-step explanation:

We  have to find the value of x

[tex]tan\theta=\frac{perpendicular side}{base}[/tex]

[tex]tan60^{\circ}=\frac{height}{26}[/tex]

We know that [tex] tan60^{\circ}=\sqrt3[/tex]

[tex]\sqrt3=\frac{height}{26}[/tex]

[tex]height=1.732\times 26[/tex]

Where [tex]\sqrt3=1.732[/tex]

Height=45.032

Height=45.0

[tex]cos\theta=\frac{bas}{hypotenuse}[/tex]

[tex] cos 39^{\circ}=\frac{45}{x}[/tex]

[tex]0.777=\frac{45}{x}[/tex]

[tex]x=\frac{45}{0.777}[/tex]

x=57.9

Hence, option C is true.

Answer:

22 feet below sea level

Step-by-step explanation:

If she goes down by 20 and back up by 7 the overall effect is going down by 13 and then going down 9 more feet makes it a total of 22 feet.

Answer:22

Step-by-step explanation:

-20+7-9= -22 ft, or 22 ft below sea level

Answer:

10.5 units

Step-by-step explanation:

Since M is the centre of the circle. The measure to the edge is the radius.

Which in this case is 10.5 units

Answer: A. 10.5 units

Step-by-step explanation: The answer would be 10.5 units because the radius is equal to half the circle. MS is a radius, and MR is a radius. A radius has one point in the center, and one point on the circle.

The segment bisects \AEC because \AEB and \BEC are both 45\u00b0, proven using the Angle Addition Postulate and the Subtraction Property of equality.

To prove that the segment bisects \AEC, begin by acknowledging the given information that m\AEB = 45\u00b0 and \AEC is a right angle with a measure of 90\u00b0. According to the Angle Addition Postulate, m\AEB + m\BEC = m\AEC. Substitute the known values to get 45\u00b0 + m\BEC = 90\u00b0. Utilizing the Subtraction Property of equality allows us to solve for m\BEC, finding it to also be 45\u00b0. This means that \BEC ≅ \AEB which leads us to conclude that since they have equal measures, the segment indeed bisects \AEC.