The scale on a map is 2 cm = 25 miles . Dave measured the distance to the next town at 5cm. How many miles away is the next town?

Similar triangles may or may not be congruent.

Question 1 to 6:

Triangles XYZ and NPQ are similar triangles.

This means that:

Angles Z and Q, lines YZ and PQ, angles P and Y, angles X and N, lines NQ and XZ, lines PN and YX are corresponding sides and angles

Question 7 to 12:

Triangles LMN and CBA are similar triangles.

This means that:

[tex]\mathbf{7z+6 = 5y}[/tex]

[tex]\mathbf{2y-12 = z + 12}[/tex]

Collect like terms

[tex]\mathbf{2y= z + 12+12}[/tex]

[tex]\mathbf{2y= z + 24}[/tex]

Make z the subject

[tex]\mathbf{z = 2y -24}[/tex]

Substitute [tex]\mathbf{z = 2y -24}[/tex] in [tex]\mathbf{7z+6 = 5y}[/tex]

[tex]\mathbf{7(2y -24) + 6 = 5y}[/tex]

[tex]\mathbf{14y -168 + 6 = 5y}[/tex]

[tex]\mathbf{14y -162 = 5y}[/tex]

Collect like terms

[tex]\mathbf{14y -5y = 162}[/tex]

[tex]\mathbf{9y = 162}[/tex]

Divide both sides by 9

[tex]\mathbf{y = 18}[/tex]

Recall that: [tex]\mathbf{z = 2y -24}[/tex]

[tex]\mathbf{z = 2 \times 18 - 24}[/tex]

[tex]\mathbf{z = 12}[/tex]

[tex]\mathbf{L = 60}[/tex]

[tex]\mathbf{LN = 2y - 12}[/tex]

[tex]\mathbf{LN = 2 \times 18 - 12}[/tex]

[tex]\mathbf{LN = 24}[/tex]

[tex]\mathbf{C = L}[/tex]

[tex]\mathbf{C = 60}[/tex]

[tex]\mathbf{AC = LN}[/tex]

[tex]\mathbf{AC = 24}[/tex]

Question 13:

The congruent parts are: KL and RQ,  KJ and RS, QS and LJ

Read more about congruent and similar triangles at:

https://brainly.com/question/19589236

Answer:

y=1/2x - 7

Step-by-step explanation:

Since the lines are parallel, this means that the slopes will be the same, only the y-intercept will change. I graphed this out to find the answer.  

Answer:

it's the number that u end up with at the bottomof the division process. hope this helps...

Step-by-step explanation:

Answer:

[tex] {2x}^{2} + 3x - 11 + \frac{19x + 23}{ {x}^{2} + 2x + 2} [/tex]

Also, the term remaining after the last subtract step is the remainder and must be written as a fraction in the final answer.

Answer:

y=mx+b

Step-by-step explanation:

Answer:

y=mx+b

Explanation:

The slope-intercept formula is y=mx+b. The b represents the y-intercept, which is the point where a line on a graph meets the y-axis. The coordinates for this would be (0,b). The m represents the slope, which is the rate of change. The x represents any x variable that you plug in. The y represents the y variable.

Answer:

D

Step-by-step explanation:

You have 4 chairs originally, added 2 and if you separate the tables you would get T=whatever the number is. i think

Given that,

The three numbers are consecutive

The three numbers are

x

x + 1

x + 2

Also,

x × (x + 1) = (x + 2) + 7

x² + x = x + 9

x² + x - x = 9

x² = 9

x = √9

x = 3

The three numbers

x = 3

x + 1 = 4

x + 2 = 5

The sum of the three numbers

3 + 4 + 5 = 12

Answer:

24% is the answer

Step-by-step explanation:

Answer:

1. x= 5/3 or 1.6 and y= -10

2. x= -1 and y= 2

Step-by-step explanation:

1. y= 6x - 10, 0= 6x - 10, -6x= -10, x= 5/3

2. y= 2x + 2, 0= 2x + 2, -2x= 2, x= -1

Answer:

0.25

Step-by-step explanation:

Answer:

48 cm^2

Step-by-step explanation:

First find the area of each shape.

2 triangles- [bxh]x1/2

(4 times 3)(divided by 2) = 6, but there are 2 triangles so 6+6=12

Square- (l x w)

3 times 3 (You get the other three from the other side of the rectangle) =9

Left rectangle- (l x w)

3 times 4 = 12

Right rectangle- (l x w)

5 times 3 (You get the three from the side of the square) = 15

Total: 2 triangles Area + Square Area  + Left rectangle Area+ Right rectangle Area = Surface Area

12 + 9 + 12 + 15 = 48 cm^2

Hope this helps!!

Answer: 35.4 feet.

Step-by-step explanation:

Given data:

Height of the roof = 24 feet

Height of the ladder = 26 foot

Solution:

c^2 = a^2 + b^2

a = 24

b = 26

c^2 = 24^2 + 26^2

c = √576 + 676

c = √1252

c = 35.4 feet

The foot of the ladder is 35.4 foot away from the top of the ladder.

Answer:

The distance between the base of the ladder and the building is 10 ft

Step-by-step explanation:

Here, we want to calculate the distance between the foot of the ladder and the building

To get this, we need to have a pictorial representation. Please check the attachment for this

From the pictorial representation, we can see a right angled triangle with a hypotenuse of 26 feet and the other side being 24 feet. We now need to get the third side of this triangle which represents the distance we want.

Mathematically, we can calculate the distance using Pythagoras’ theorem which states that the square of the length of the hypotenuse is equal the sum of the squares of the two other sides of the triangle.

Let the distance we are looking for be D

26^2 = 24^2 + D^2

D^2 = 26^2 - 24^2

D^2 = 100

D^2 = 10^2

D = 10 feet

Answer:

Option (C)

Step-by-step explanation:

Domain of a function is a set of x-values (input values) of the function.

Similarly, Range of a function is a set of y-values (output values).

Given set of ordered pairs is {(-2, -1), (2, 1), (1, 5), (-2, 4)}.

Domain → {-2, 2, 1, -2}

Range → {-1, 1, 4, 5}

Option C will be the correct option.

Answer:

Read left to right

Do parenthesis first

-4 ( 1 + 5) ^2

-4 (6) ^2

Then exponent

6^2 = 6 x 6 = 36

-4 x 36 = -144

Then divide

-144 / 6 = -24

Then the next parenthesis

(42+5) = 47

-24 - 47 = -71

Step-by-step explanation:

Answer:

7 1/2 pounds

Step-by-step explanation:

5 x 24 = 120

16oz = 1 pound

120oz = 7 1/2 pounds

Answer:

7.5 lbs of raisins

Step-by-step explanation:

24 x 5 = 120 ounce (oz)

1 lb = 16 oz

120 ÷ 16 = 7.5 lbs

Answer:

WAIT I MESSED UP DONT ANSWER THAT

Step-by-step explanation:

Answer:

[tex]\frac{16}{81}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

4

Step-by-step explanation:

I used desmos

[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{\dfrac{-2(7-15)}{4}}\\\\\mathsf{7-15=-8}\\\\\mathsf{\dfrac{-2(-8)}{4}}\\\\\mathsf{-2(-8)=16}\\\\\mathsf{\dfrac{16}{4} = 4}\\\\\\\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: \boxed{\boxed{\mathsf{\bf{D.\ 4}}}}}}}\checkmark[/tex]

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

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

Answer:

The number is 62

Step-by-step explanation:

Let the digits of the number be T and U;

A 2 digit number is represented as: 10T + U

So,

[tex]T + U = 8[/tex]

[tex]10T + U - (10U + T) = 10 + 10U + T[/tex]

Required

Find the digit

Make U the subject in the first equation

[tex]U = 8 - T[/tex]

Substitute 8 - T for U in the second

[tex]10T + U - (10U + T) = 10 + 10U + T[/tex]

[tex]10T + 8 - T - (10*(8-T) + T) = 10 + 10(8 - T) + T[/tex]

[tex]10T + 8 - T - (80-10T + T) = 10 + 80 - 10T+ T[/tex]

[tex]10T + 8 - T -80+10T - T = 10 + 80 - 10T+ T[/tex]

Collect Like Terms

[tex]10T + 10T - T- T + 8 -80 = 10 + 80 - 10T+ T[/tex]

[tex]18T -72 = 90 - 9T[/tex]

[tex]9T + 18T = 90 + 72[/tex]

[tex]27T = 162[/tex]

[tex]T = 162/27[/tex]

[tex]T = 6[/tex]

Recall that:

[tex]U = 8 - T[/tex]

[tex]U = 8 - 6[/tex]

[tex]U = 2[/tex]

Hence, the number is 62

Answer:

I think 32

I'm not sure

Answer:

s = 54/31

r= -156/31

t= -17/31

Step-by-step explanation:

Answer:

Okay first okay this was not from your math book people actually need help on questions and here you are.

Step-by-step explanation:

Answer:-6x^3y^4+8x^2y^2

Step-by-step explanation:

Answer:

If im correct im pretty sure its 6xy

The GCF of 18xy and 12xy is 6xy.

The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.

18 and 24 share one 2 and one 3 in common.

, so 2 x 3 = 6 is the GCF of 18 and 24.

Given:

18xy and 12xy

now, factoring the above terms

18xy = 2 × 3 × 3 × x × y

12xy= 2 × 2 × 3 × x × y

So, 18xy & 12xy = 2 x 3 xy = 6xy

hence, the GCF of 18xy and 12xy is 6xy.

Learn mor about GCF here:

https://brainly.com/question/11444998

#SPJ2

Answer:

Subtract [tex]7x[/tex]from both sides of the equation.

Step-by-step explanation:

According to the following equation, The first step you would take is to subtract [tex]7x[/tex] from both sides of the equation.

Answer:

142

Step-by-step explanation:

<38 and <6 are vertical angles so they both measure 38

<6 and <5 are same side interior angles so they add up to 180

knowing this, you can simply subtract 38 from 180 to find <5

180 - 38 = 142

Answer:

-1,2

Step-by-step explanation:

4-5=-1

3-1=2  

y2-y1

x2-x1

Answer:

Step-by-step explanation:

AA

Answer:

y=6x-2

Step-by-step explanation:

The equation of the line is y=mx+b

FINDING SLOPE: To find the slope of a given line use the equation [tex]\frac{y2-y1}{x2-x1}[/tex]

So x1=-3, y1=-20 and x2=1, y2=4

Plug those numbers into the equation: [tex]\frac{4-(-20)}{1-(-3)}[/tex]  and we get the slope which is 6.

FINDING Y-INTERCEPT: Then we find the y intercept by plugging in our points (you can choose) I will use (1,4) and solve.

y=6x+b

4=6(1)+b

b=-2

Answer:

the answer is [tex]m=\frac{8}{17}[/tex]

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations (I use it all the time).