Explain one way to verify that the corresponding angles of the two triangles are congruent.
A) Use the slope formula to prove that the slopes of corresponding sides are opposite reciprocals. Therefore, the corresponding angles of the triangles are congruent.
B) Use the distance formula to prove that two corresponding sides of the triangles have the same lengths. Therefore, corresponding angles of the triangles are congruent by CPCTC.
C) Use the distance formula to prove that all corresponding sides of the triangles have the same lengths. Therefore, the two triangles are congruent by SSS. Then, corresponding angles of the triangles are congruent by CPCTC.
D) Use the distance formula to prove that two corresponding sides of the triangles have the same lengths. Therefore, the two triangles are congruent by SAS. Then, all corresponding angles of the triangles are congruent by CPCTC.

Answer:

D: 56 and 77

Step-by-step explanation:

Answer:

151

Step-by-step explanation:

23+26=$49

49+25=74

74+24=98

98+6=104

104+24=128

128+23=151

Alan earned a total of $198 from gardening by adding all individual earnings together.

The student is asking about the total amount earned by Alan from gardening. To find the total, we simply add all the amounts mentioned: 23 + 26 + 25 + 24 + 23 + 24 + 6 + 24 + 23. Adding these up, Alan earned a total of $198 from gardening.

Answer: It is 15/17

Step-by-step explanation:

Tan is adjacent over hypotenuse

Answer:

A. (3 × 4) + (3 × 7)

3(4 + 7)

B. (5 × 9) - (5 × 6)

5(9 - 6)

C. 32 +16 = 48

8 (4 + 2)

D. 4(100 - 3)

97 × 4

E. 7(60 + 6)

66 × 7

Step-by-step explanation:

Answer:

y= -4x-1/3

Step-by-step explanation:

i think. but dont quote me on that. and Stan BTS!!!!!!

Hope you can understand

Answer:

D :If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5. Then the correct option is D.

If the statement is: p ⇒ q

Then the Contrapositive statement will be: ~q ⇒ ~p

p: 3x + 7 = –5 q: 4x + 12 = –4

The value of x in both cases is the same. Then the p and q are converses with each other.

If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.

Then the correct option is D.

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Answer:

18/19 = About 95%

Step-by-step:

If only six are noble gases, 108 are not noble gases.

114-6= 108

So, the probability of not picking a noble gas is 108 out of 114. This simplifies to 18/19 which is about 95%.

Answer:

101

Step-by-step explanation:

360 - (78+91+90)

360- 259 = 101

HOPE THIS HELPS!!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-3y=x-5&\text{subtract x from both sides}\\x+5y=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-3y=-5\\x+5y=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad2y=2\qquad\text{divide both sides by 2}\\.\qquad\qquad y=1\\\\\text{Put the value of y to the second equation:}\\x+5(1)=7\\x+5=7\qquad\text{subtract 5 from both sides}\\x=2[/tex]

The solution of the system of equations is (2, 1).

The elimination method is a process that uses elimination to reduce the simultaneous equations into one equation with a single variable.

The given system of equations  are;

[tex]\rm -3y=x-5\\\\x+5y=7[/tex]

From equation 1

[tex]\rm -3y=x-5\\\\x = -3y+5[/tex]

Substitute the value of x in the equation 2

[tex]\rm x+5y=7\\\\-3y+5+5y=7\\\\2y =7-5\\\\2y=2\\\\y=\dfrac{2}{2}\\\\y=1[/tex]

Substitute the value of y in the equation 1

[tex]\rm -3y=x-5\\\\-3(1)=x-5\\\\-3=x-5\\\\x=5-3\\\\x=2[/tex]

Hence, the solution of the system of equations is (2, 1).

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Answer:

y = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5x - 3y = 4 into this form

Subtract 5x from both sides

- 3y = - 5x + 4 ( divide all terms by - 3 )

y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{4}{3}[/tex] ← in slope- intercept form

with y- intercept c = - [tex]\frac{4}{3}[/tex]

Method 1: Plunging in 0 for x in the equation and solve for y

5(0) - 3y = 4

0 - 3y = 4

-3y= 4

y = [tex]\frac{-4}{3}[/tex]  <<< y - intercept

Method 2: Converting the equation to slope-intercept form ( y = mx + b) and see what b is (that is the y-intercept). Do do this isolate y

-3y = 4 - 5x

y = [tex]\frac{-4}{3} +\frac{5}{3} x[/tex]

[tex]y = \frac{5}{3} x- \frac{4}{3}[/tex]

b = [tex]\frac{-4}{3}[/tex]  <<< y - intercept

Y- intercept : (0, [tex]\frac{-4}{3}[/tex])

Hope this helped!

Answer:

51200 people

Step-by-step explanation:

Multiply the total number by the corresponding decimal to the percentage desired.

64000*.8=51200

Your answer is B. 0.075 m

The answer is B I think

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

The rectangles that make up the net for a prism are six rectangles

two rectangles are L by W ----> 12 cm by 9 cm

two rectangles are L by H ----> 12 cm by 5 cm

two rectangles are W by H ---> 9 cm by 5 cm

Final answer:

The rectangular prism net Darren is painting consists of two 12x5 cm rectangles for the top and bottom, two 9x5 cm rectangles for the front and back, and two 12x9 cm rectangles for the sides.

Explanation:

Darren is working on an art project involving painting a wooden block that is in the shape of a rectangular prism. To understand the net for this prism, we need to describe the rectangles that would make it up when the prism is unfolded into a flat shape.

The net of a rectangular prism is made up of six rectangles, each corresponding to a face of the prism. For Darren's block, which has dimensions of 12 cm in length, 9 cm in width, and 5 cm in height, we can determine the rectangles as follows:

When painting, Darren would treat each of these rectangles as separate sections to ensure complete coverage.

Answer:

See Explanation Below :)

Step-by-step explanation:

To solve a pair linear equations by graphing, you would first need to find the slope and y-intercept of each of the equation and then graph it in a coordinate plane. Then, you would see where the two lines intersect, and the coressponding coordinates for that point will be your solution.

Example:

y = 2x +2

y = x -1

For the first equation we know the slope (m) is 2 becuase y = mx + b, and m is 2. We know that the y intercept (b) is also 2 becuase y = mx + b, and b is 2.

Similarly, for the second equation the slope (m) is 1 and the y-intercept (b) is -1.

When you use this data and plot the two lines, we can see that they intersect on the 3rd quadrant at (-3,-4) which will be your solution. See the attached graph for this example.

Answer:

C. 14 inches

Step-by-step explanation:

The area of a square is given by

A = s^2

We know the area is 196 in ^2

196 in^2 = s^2

Take the square root of each side

sqrt(196) = sqt (s^2)

14 =s

Each side is 14 inc

Answer:

C.14

Step-by-step explanation:

a=length time width so 14*14=196  

Answer:

x = - 6

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] x² = 24 ( multiply both sides by 3 )

2x² = 72 ( divide both sides by 2 )

x² = 36 ( take the square root of both sides )

x = ± [tex]\sqrt{36}[/tex] ← note plus or minus

x = ± 6

solutions are x = - 6, x = + 6

The smallest solution is x = - 6

Answer:

The area of the shaded region is [tex]44.24\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

step 1

Find the area of circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=4\ cm[/tex]

substitute

[tex]A=\pi (4)^{2}[/tex]

[tex]A=16\pi\ cm^{2}[/tex]

step 2

Find the area of rectangle

The area of rectangle is equal to

[tex]A=(3)(2)=6\ cm^{2}[/tex]

step 3

Find the difference

[tex]16\pi\ cm^{2}-6\ cm^{2}[/tex]

assume

[tex]\pi=3.14[/tex]

[tex]16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}[/tex]

Multiply by .88, he paid $792

Answer:

$792

Step-by-step explanation:

Answer:

  F.  4h ≥ 18

Step-by-step explanation:

Liang wants ...

   distance ≥ goal

We know that ...

   distance = speed · time . . . . . . where speed = 4 mph, and time = h hours

Then the appropriate inequality for Liang's goal of 18 miles or more is ...

  4h ≥ 18

Tom takes 1 day to clear 1 acre.

To find out how many days it takes Tom to clear 1 acre, we can calculate the rate at which he clears brush in acres per day.

Let's use the given information:

[tex]\frac{2}{3}[/tex]​  acre cleared in 2 days,

​ [tex]1\frac{2}{3}[/tex] acres cleared in 5 days,

[tex]2 \frac{1}{3}[/tex]  acres cleared in 7 days.

First, let's find the rate in acres per day for each interval:

For the first interval:

​[tex]\frac{\frac{2}{3} }{2} = \frac{1}{3}[/tex] acre per day.

For the second interval:

[tex]\frac{1\frac{2}{3} }{5} = \frac{5}{3} \times \frac{1}{5} = \frac{1}{3}[/tex]  acre per day.

For the third interval:

[tex]\frac{2\frac{1}{3} }{7} = \frac{7}{3} \times \frac{1}{7} = \frac{1}{3}[/tex] acre per day.

It appears that the rate at which Tom is clearing brush is consistent at

[tex]\frac{1}{3}[/tex]  acre per day.

Therefore, Tom takes 1 day to clear 1 acre.

Answer:

{0, 4 and -3}

Step-by-step explanation:

f(x)=x^3-x^2-12x can be factored, starting by taking out the 'x' factor:

f(x)=x^3-x^2-12x = x(x^2 - x - 12), and then by factoring the quadratic:

f(x) = x(x - 4)(x + 3) = 0

Then the zeros are {0, 4 and -3}.

Answer:

The zeros are;

x=-3,x=0, and x=4

Step-by-step explanation:

The given polynomial is

[tex]f(x)=x^3-x^2-12x[/tex]

We equate the function to zero to obtain;

[tex]fx^3-x^2-12x=0[/tex]

We factor the GCF to get;

[tex]x(x^2-x-12)=0[/tex]

We split the quadratic trinomial to get;

[tex]x(x^2-4x+3x-12)=0[/tex]

Factor by grouping

[tex]x(x(x-4)+3(x-4))=0[/tex]

[tex]x(x-4)(x+3)=0[/tex]

The zeros are;

x=-3,x=0, and x=4

Answer:

0.67

Step-by-step explanation:

Answer:

0.63

Step-by-step explanation:

M: The selected dog is a male. P(M) = 24/40 = 0.6

B: The selected dog is a boxer. P(B) = 22/40 = 0.55

M and B: 14/40 = 0.35

P(M/B) = 0.35 / 0.55 = 0.63

Answer:

33 degrees

Step-by-step explanation

I used arcos, ∠A = arccos((a2 + b2 - c2)/2ab)

= 0.5795 rad = 33.203° = 33°12'11"

b, 33 degrees is correct

The correct option that represents the total area of the rectangle using the distributive property is B) (4 x 3) + (4 x 2) = 20 square units.

The correct option that represents the total area of the rectangle using the distributive property is B) (4 x 3) + (4 x 2) = 20 square units.

The distributive property states that when you multiply a number by a sum or difference of numbers, you can multiply each number individually and then add or subtract the products.

In this case, the rectangle has a length of 4 units and a width of 3 units.

So, the area of the rectangle can be found by multiplying the length by the width, which is 4 multiplied by 3. Then, you add the product of the length multiplied by the width, which is 4 multiplied by 2. This gives us a total area of 20 square units.

Answer:

A and E

Step-by-step explanation:

Answer:

answer is b

Step-by-step explanation:

The Scale factor is 2.

A dilation in mathematics is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilatation is a resemblance to the space in Euclidean space.

Given

in pre -- image sides are 4, 5, 3

in the image, the sides are 4(2), 5(2), 3(2)

The scale factor is 2.

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Answer:

[tex]\boxed{1) V = 40 000(0.89)^{n}, \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_{n} = -2^{n}}[/tex]

Step-by-step explanation:

1) Depreciation

The formula for the value V of an asset after depreciation by an annual percentage rate is  

V = P(1 - r)ⁿ

where

P = present value

r = annual percentage rate

n = number of years

Data:

V = 40 000

r = 11 % = 0.11

n = 8 yr

Calculations:

(a) Function model

V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ

The function model is [tex]\boxed{ V= 40 000(0.89)^{n} }[/tex]

(b) Future value

V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746

In eight years, the truck will be worth [tex]\boxed{ \text{\$15 476}}.[/tex]

2) Profit function

Income from 1 lawn = $15

  Income from x lawns =  15x

Less gas and supplies =         -50        

                 Net income = 15x – 50

The function is [tex]\boxed{f(x) = 15x - 50}[/tex].

3) Geometric series

(a) Calculate the common ratio

a₁ = -2

a₂ = -4

a₃ = -8

a₄ = =16

The ratios of consecutive pairs are

a₄/a₃ = -16/(-8)  = 2

a₃/a₂ =   -8/(-4)  = 2

a₂/a₁ =   -4/(-2)  = 2

All adjacent pairs have the same common ratio r = 2.

(b) Write the formula for the series

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

If a₁ = -2, the formula for the series is

aₙ = -2(2)ⁿ⁻¹ = -2ⁿ

The formula for the series is [tex]\boxed{a_{n} = -2^{n}}[/tex].