Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Answer:

A

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to find EF

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

EF² + DF² = DE² ← substitute values

EF² + 12² = 18², that is

EF² + 144 = 324 ( subtract 144 from both sides )

EF² = 180 ( take the square root of both sides )

EF =  → A

Answer:

Step-by-step explanation:

This is because only a reduction can be 0-1, as it will shrink, while if you multiply a number by a number greater than 1, is will largen.

The dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.

(SCALING ZOOMING SIMILAR FIGURES)

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Similarly, Volume of first figure = k³ × volume of second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

As it can be seen in the image below that the red rectangle is the pre-image therefore, it is the original figure.

The blue rectangle is the image of the original figure.

Now, as it can be seen that the pre-image is a smaller rectangle, while the image is a large rectangle, therefore, the dilation made is of enlargement.

Also, it can be observed that the ratio of any corresponding sides of the two rectangles is more than 1.

Hence, the dilation is an enlargement with a scale factor greater than 1. Thus, the correct option is D.

Learn more about Dilation:

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Answer: mp • (3m3 + 8m2p - 2p2)

Step-by-step explanation:

3m4p + 8m3p2 - 2mp3  =   mp • (3m3 + 8m2p - 2p2)

8.2  Factoring    3m3 + 8m2p - 2p2

Picture relating to question has been attached below

Answer:

x = 10 ; y = 15

Step-by-step explanation:

The values for which the park is a parallelogram :

For the quadrilateral to be a parallelogram ; the diagonals will bisect each other such as :

VT = RV and UV = VS

From the diagram :

VT = 3x + 5y

RV = 6x + 3y

UV = 11y + 33 m

VS = 14y - 12 m

VT = RV and UV = VS

3x + 5y = 6x + 3y

3x - 6x = 3y - 5y

-3x = - 2y

3x = 2y

11y + 33 = 14y - 12

11y - 14y = - 12 - 33

-3y = - 45

y = 45/3

y = 15

From ;

3x = 2y

3x = 2*15

3x = 30

x = 30/3

x = 10

Step-by-step explanation:

9!

= 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9

= ... * 2¹ ... * 2² ... * (2 * 3) ... * 2³

= 2⁷ ...

Hence k is 7.

Answer:

the required postulate which should be used here to make the triangles congruent is

C. ASA , okay

Step-by-step explanation:

because, one side and one angle of both triangles are equal and one of angles of the both triangles are vertically opposite angles , hence they are also equal , so we get an angle, a side and one another angle equal to corresponding side and angles of other triangles , so required postulate is C. ASA

I hope it helped

Answer:

ASA

Step-by-step explanation:

you have 2 angles and a side, so it could either be ASA or AAS.

ASA- the side is between 2 angles (image 1)

AAS- I'm not exactly sure how to describe it, but it's like 2 angles without a side between (image 2)

Answer:did you get the answer???

Step-by-step explanation:

    Expression representing total amount collected for the daily fees yesterday will be $(10a + 5c).

 Daily fees for the Fun Town amusement Park are,

If there were 'a' adults and 'c' children in the park yesterday,

Total amount to be paid = $(10a + 5c)

   Therefore, expression for the total amount collected for daily fees yesterday will be $(10a + 5c).

Learn more,

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Answer: A

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

we can start by dividing finding how many times 60 goes into 156.

It goes in 2 times with 120 miles.

we can subtract 120 from 156

this leaves us with 36 miles.

36 > (60 * .5)

between 7:30 and 10:00 there are 2.5 hours.

the car ride would take 2.6 hours meaning Kim wouldn't arrive before 10 am.

9514 1404 393

Answer:

  (h, k) = (9, -8)

Step-by-step explanation:

The function g(x) is "vertex form" for a quadratic whose vertex is (h, k). We are told the vertex is (9, -8), so we have ...

  (h, k) = (9, -8) . . . . the values of h and k

Answer:

x = 1/20 = 0.050

x = 0

Step-by-step explanation:

either of those

Answer:

Hey bro,

The answer should - 39x i.e minus 39x

Answer: y - 3= -1/2 * (x - 8)

Answer:

y=-1/2x+3

Step-by-step explanation:

Slope intercept form is written: y=mx+b...

y=doesn't change, but you need it by itself

m=slope

x=the variable right next to the slope

b=y-intercept

Also, don't worry! This is super simple ^^

The question gives us -1/2 as the slope, so it needs to be plugged into the equation as m (next to x). Now our equation looks like this:

y=-1/2x+b

Next, we can figure out b. B is the y-intercept and we can figure this out by looking at the ordered pair (8, 3). The y is the second number, which is 3, so that is the y-intercept! We can now plug in 3 into b. Our final equation looks like this:

y=-1/2x+3

Hope this helps!! Have an awesome day ❤

Answer:

x=b-8a/8

x=b+8a/a

x=2-2c/c

look at the step by step explanation.

Step-by-step explanation:

Triangle inequality theorem - the sum of the two shorter sides has to be greater than the longest side, which is 8. This is not possible because the sum of the two shorter sides is 8 which is not greater than the longest side.

Answer:

Complicated answer.

Step-by-step explanation:

So, if one side length is 8 the perimeter of a triangle cannot be 16 this is because a triangle has three sides and 8 multiplied by three would not be 16 so we have two possible conclusions.

1. The perimeter is actually 24

2. The side lengths are actually 4

Hope I helped! Have a silver dollar day! :) Please give me brainliest! Thanks Adios!

Answer:

[tex]x=7,\\y=6[/tex]

Step-by-step explanation:

The segment [tex]UV[/tex]consists of [tex]UZ[/tex] and [tex]VZ[/tex]. Therefore, we can write the following equation:

[tex]3y-5+2y+2=27,\\5y-3=27,\\5y=30,\\y=\fbox{$6$}[/tex].

Since [tex]UV[/tex] bisects [tex]TW[/tex], [tex]TZ\cong WZ[/tex].

Therefore,

[tex]3x+3=3y+6,\\3x+3=3(6)+6,\\3x+3=18+6,\\3x+3=24,\\3x=21,\\x=\fbox{$7$}[/tex]

Answer:

Please check explanations

Step-by-step explanation:

The equation of a circle can be represented as;

(x-h)^2 + (y-k)^2 = r^2

r is the radius while (h,k) represents the coordinates of the center

Thus, we have that;

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

That would give;

x^2 - 4x + 4 + y^2 + 6y + 9

The sum of values with no coefficient is;

4 + 9 = 13

If we take this to the other side, we can have 13 + 3 = 16

The square root of this is then 4

Mathematically, we can therefore express the equation of the circle as;

(x-2)^2 + (y-+3)^2 = 4^2

By expansion, we will get the original given equation

Answer:

12

Step-by-step explanation:

12

Answer:

It doesn't make sense and their no picture that provides us with clear evidence on how to answer this better then how your explaing

Step-by-step explanation:

I don't know how to  know how to answer this lol, because I need a better explination

Answer:

5/100×$1500= 75 dollar

as it is annual income we can solve the answer relative to year and considering it as 1 so the interest would be 75 annually

Answer:

rational as it can be expressed as the quotient of two integers

Answer:

that is a rational number

Step-by-step explanation:

A rational number is a number that can be express as the ratio of two integers. ... Likewise, any integer can be expressed as the ratio of two integers, thus all integers are rational.

Example: 17 and −34 are rational numbers. (Note that there is more than one way to write the same rational number as a ratio of integers. For example, 17 and 214 represent the same rational number.) All integers are rational numbers.

An irrational number is real number that cannot be expressed as a ratio of two integers. ... The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. Many square roots are also irrational since they cannot be reduced to fractio

Answer:

the slope is 0

Step-by-step explanation:

m=0

Answer:

0

Step-by-step explanation:

y2 - y1/ x2 - x1

10 - 10 = 0

6 - (-8) = 14

0/14 = 0

ANSWER #1:

x = -1.666666667

x = 0.5

STEP-BY-STEP:

Simplifying

6x2 + 7x + -5 = 0

Reorder the terms:

-5 + 7x + 6x2 = 0

Solving for variable 'x'.

(-5 + -3x)(1 + -2x) = 0

SUBPROBLEM 1

Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying

-5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + -3x = 0 + 5

Combine like terms:

0 + -3x = 0 + 5

-3x = 0 + 5

Combine like terms:

-3x = 5

Divide each side by '-3'.

x = -1.666666667

Simplifying

x = -1.666666667

SUBPROBLEM 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying

1 + -2x = 0

Move all x terms to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -2x = 0 + -1

Combine like terms:

0 + -2x = 0 + -1

-2x = 0 + -1

Combine like terms:

-2x = -1

Divide each side by '-2'.

x = 0.5

Simplifying

x = 0.5

ANSWER #2:

x = -7

x = 2

STEP-BY-STEP:

Simplifying

x2 + 5x + -14 = 0

Reorder the terms:

-14 + 5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-7 + -1x)(2 + -1x) = 0

SUBPROBLEM 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all x terms to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms:

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms:

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

SUBPROBLEM  2

Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying

2 + -1x = 0

Solving

2 + -1x = 0

Move all x terms to the left, all other terms to the right.

Add '-2' to each side

2 + -2 + -1x = 0 + -2

Combine like terms:

0 + -1x = 0 + -2

-1x = 0 + -2

Combine like terms:

-1x = -2

Divide each side by '-1'.

x = 2

Simplifying

x = 2

ANSWER #3:

x = 3.25

x = -0.92

STEP-BY-STEP

Simplifying

3x2 + -7x + -9 = 0

Reorder the terms:

-9 + -7x + 3x2 = 0

Solving for variable 'x'.

Divide each side by '3'.

-3 + -2.333333333x + x2 = 0

Add '3' to each side

-3 + -2.333333333x + 3 + x2 = 0 + 3

Reorder the terms:

-3 + 3 + -2.333333333x + x2 = 0 + 3

Combine like terms:

0 + -2.333333333x + x2 = 0 + 3

-2.333333333x + x2 = 0 + 3

Combine like terms:

-2.333333333x + x2 = 3

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).

Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side

-2.333333333x + 1.361111112 + x2 = 3 + 1.361111112

Reorder the terms:

1.361111112 + -2.333333333x + x2 = 3 + 1.361111112

Combine like terms:

1.361111112 + -2.333333333x + x2 = 4.361111112

Factor a perfect square on the left side:

(x + -1.166666667)(x + -1.166666667) = 4.361111112

Calculate the square root of the right side: 2.088327348

Break this problem into two subproblems by setting

(x + -1.166666667) equal to 2.088327348 and -2.088327348.

SUBPROBLEM 1

x + -1.166666667 = 2.088327348

Simplifying

x + -1.166666667 = 2.088327348

Reorder the terms:

-1.166666667 + x = 2.088327348

Solving for variable 'x'.

Move all x terms to the left, all other terms to the right.

Add '1.166666667' to each side

Combine like terms:

0.000000000 + x = 2.088327348 + 1.166666667

x = 2.088327348 + 1.166666667

Combine like terms:

2.088327348 + 1.166666667 = 3.254994015

Simplifying

x = 3.254994015

SUBPROBLEM 2

x + -1.166666667 = -2.088327348

Simplifying

x + -1.166666667 = -2.088327348

Reorder the terms:

-1.166666667 + x = -2.088327348

Solving

-1.166666667 + x = -2.088327348

Solving for variable 'x'.

Move all x terms to the left, all other terms to the right.

Add '1.166666667' to each side of the equation.

-1.166666667 + 1.166666667 + x = -2.088327348 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000

0.000000000 + x = -2.088327348 + 1.166666667

x = -2.088327348 + 1.166666667

Combine like terms: -2.088327348 + 1.166666667 = -0.921660681

x = -0.921660681

Simplifying

x = -0.921660681

ANSWER #4:

x = -5

x = 5

STEP-BY-STEP:

Simplifying

x2 + -25 = 0

Reorder the terms:

-25 + x2 = 0

Solving

-25 + x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side

-25 + 25 + x2 = 0 + 25

Combine like terms: -25 + 25 = 0

0 + x2 = 0 + 25

x2 = 0 + 25

Combine like terms: 0 + 25 = 25

x2 = 25

Simplifying

x2 = 25

Take the square root of each side:

x = {-5, 5}

Answer:

An actual distance of 360 miles correspond to 9 inches on the map

Step-by-step explanation:

From the question, we have a scale of 0.5 inches representing 20 miles

Now, we want to relate an actual distance of 360 miles to a measurement on the map using the scale

From here, we have that;

0.5 inches = 20 miles

x inches = 360 miles

x * 20 = 0.5 * 360

20x = 180

x = 180/20

x = 9 inches

OK so dont know srry bout that