Rachel is trying to find the length of the lake shown on the diagram. She knows that if the two triangles are similar, she can use a proportion to solve for the length. How can Rachel justify that the triangles are similar? What is the length of the lake? A) Corresponding sides of the two triangles have the ratio of 4:1, which proves SAS similarity.The length of the lake is 212 m. B) Corresponding sides of the two triangles have the ratio of 4:1, which proves SSS similarity. The length of the lake is 132 m.
C) Corresponding sides of the two triangles have the ratio of 3:1, which proves SSS similarity. The length of the lake is 159 m. D)
Corresponding sides of the two triangles have the ratio of 4:1, which proves AAS similarity. The length of the lake is 240 m.

Answer: the last one

Step-by-step explanation:

Answer:

y=6 is the correct answer

Answer:

x=34    y=-87     (34,-87)

Step-by-step explanation:

3x+y=15              rewrite to solve for y  ----->    y=15-3x

5x+2y=-4

Plug y=15-3x into 5x+2y=-4

So, 5x+2 (15-3x)=-4

Distribute: 5x+30-6x=-4

Combine like terms: 30-x=-4

Solve for x   -x=-34

Solve for x   x=34

Then, to solve for y, plug "x" into 3x+y=15

So, 3(34)+y=15

Distribute: 102+y=15

Solve for y  y=-87

Answer:

8

Explanation:

3x-7=x^2-7x+18

X= 5

Y=3(5)-7 aka 15-7

=8

Answer: 2n + 1 = n + 11

9514 1404 393

Answer:

  a) no

  b) yes

Step-by-step explanation:

a) You cannot draw the graph around x=0 without lifting your pencil. The function is not continuous at x=0.

__

b) You can draw the graph around x=1 without lifting your pencil. The function is continuous at x=1.

_____

Additional comment

In technical terms, the limit from the left at x=0 is 2; the limit from the right is 3. These are different, so the function is not continuous there.

On the other hand, the left and right limits at x=1 are the same (both 2), and are equal to the value of the function at that point (f(1)=2). Hence, the function is continuous at x=1.

Answer:

15

Step-by-step explanation:

3 × 5 = 15

Hope this helped <3

Answer:

A, B, E, F

Step-by-step explanation:

A polygon is ANY shape formed with only straight lines.

Answer:

15

Step-by-step explanation: 20+10+3+30 =30

Answer:

The second job

Step-by-step explanation:

Divide 72 by 8 which equals 9

(72÷8=9)

Divide 57 by 6 which equals 9.5

(57÷6=9.5)

The job earns half more than than the  first job in a hour

Answer:

50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

The formula to find the area of a circle is [tex]\pi r^{2}[/tex]. The radius of this circle is 4 because the radius is half the diameter. Since [tex]\pi[/tex] is an irrational number (whose digits goes on forever without repeating), people use use the first three numbers which are 3.14. Substitute 4 for r and 3.14 for [tex]\pi[/tex] into the formula, and you’ll get 50.24, and the answers also have the [tex]m^{2}[/tex] part too because your finding the area of a shape.

Hope this helps! :)

15/20

Figure out what number to use for simplify

Which is 5

Divide the numerator and denominator by 5

15/5=3

20/5=4

Answer:3/4

Answer:

80?

Step-by-step explanation:

Answer:

(8+4)x5

Step-by-step explanation:

Answer:

The distance between the two points is [tex]\sqrt{65} \ \text{units}.[/tex]

Step-by-step explanation:

In order to find the distance between two coordinate pairs, we can use the distance formula:

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

Our coordinate pairs need to be labeled accordingly, so we can use this naming system:

[tex]\bullet \ \ \ (x_1, y_1), (x_2, y_2)[/tex]

This assigns a name to our points:

Therefore, we can plug these into the formula and solve:

[tex]d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}[/tex]

Therefore, the distance between the two points is [tex]\sqrt{65} \ \text{units}[/tex].

Answer:

= 105

Step-by-step explanation:

Answer:

here ya go

Step-by-step explanation:

a

9

=

105 I think

omg thank u sooo much for the points!! :D

Answer:

- 2

Step-by-step explanation:

Add 5 From Both Sides

Simplify

Subtract 9x from both sides of the equation

Simplify

Divide both sides of the equation by the same term

Simplify

Solution

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Step-by-step on how to solve it is in the picture below ↓

Hope this helps! :)

Answer:

1/4 yards squared

Step-by-step explanation:

Area of a rectangle equals length times width.

1/3 x 3/4 = 3/12, or 1/4

Answer:

It would be 1/4 and if not try 3/12

Step-by-step explanation:

I hope this helped

Answer:

4.5 is the answer 9/2=4.5

Step-by-step explanation:

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.) FACTS: An exterior ∠ is equal to the addition of the two Δ angles not right next to it.

Answer:

its 273 rounded but say 270

Step-by-step explanation:

The estimate is 270.

Answer:

2

Step-by-step explanation:

Answer: Steve's bedroom has the greater area.

Step-by-step explanation: The formula for area is Area = Length x Width.

So all you have to do to figure this out is multiply the Width of the rooms by the length.

So Steve's room is 12ft X 13ft = 156ft

Ricardo's room is 8ft X 14ft = 112ft

156ft > 112ft

Steve's room has a greater area.

Answer:

The equation of the parabola is (x + 4)² = -16(y + 1)

Step-by-step explanation:

The standard form of the equation of the parabola is (x - h)²  = 4p(y - k), where

∵ The focus at (-4, -5)

∴ h = -4

∴ k + p = -5 ⇒ (1)

∵ The directrix at y = 3

∴ k - p = 3 ⇒ (2)

→ Add equations (1) and (2) to find k

∴ 2k = -2

→ Divide both sides by 2 to find k

∴ k = -1

→ Substitute it in equation (1) to find p

∵  -1 + p = -5

→ Add both sides by 1

∴ -1 + 1 + p = -5 + 1

∴ p = -4

→ Substitute the values of h, k, and p in the formula above

∵ (x - -4)² = 4(-4)(y - -1)

∴ (x + 4)² = -16(y + 1)

∴ The equation of the parabola is (x + 4)² = -16(y + 1)

Answer:

4

Step-by-step explanation:

[tex]\frac{32}{4x2}[/tex]

[tex]\frac{32}{8}[/tex]

[tex]\frac{16}{4}[/tex]

[tex]\frac{4}{1}[/tex]

4

Answer:

yo are you talking about like absolute value?  then it's  | -15 | and | -25 |

Step-by-step explanation:

Answer:

the slope is 2/3

Answer:

Step-by-step explanation: First you determine if the slope if positive (increasing) or negative (decreasing). Second you use two points on the line, calculate the rise and the run and express it as a fraction (rise over run).  Rise is the change in the y-value and Run is the change in the x-value.

Answer:

the answer is 10

Step-by-step explanation:

Answer:

the is option d cause big number is divided by small ones.

Step-by-step explanation:

hope it's right

                                Retail Price      Quantity     Total Price

Twister Pen                   .35          *        2        =     $0.70

Mini Fish Eraser            .50          *        1         =     $0.50

Happy Cap Eraser        .05          *        5        =     $0.25

Erasing Grip                  .35          *        3        =     $1.05

                                                                               ---------

Subtotal                         .7 + .5 + .25 + 1.05    =     $2.50

Sales Tax Amount (unknown because we aren't given a tax value)

Total (also unknown for the same reason)

                                             Retail Price      Quantity     Total Price

Twister Eraser                            .35          *        3        =      $1.05

Astral Wonders Pencils             .20          *        4        =      $0.80

Criss Cross Critters                    .15           *       2        =      $0.30

Traction Mechanical                      

Pencil                                         .35           *       2        =      $0.70

Muchin Mike Sharpener           .50           *       2        =      $1.00

                                                                                            ----------

Subtotal                                 1.05 + .8 + .3 + 0.7 + 1    =     $3.85

Sales Tax Amount (unknown because we aren't given a tax value)

Total (also unknown for the same reason)

Best of Luck!