Which part of the proof does the fourth statement and reason represent?

Given: AB ≅ BC
BC ≅ EF

Prove: EG = AB + FG





It is part of the given information.
It is part of the argument.
It is the conclusion.
It is an assumption.

Answer:

The length of each side is 12.2 ft

Answer: 17.14 ft

Step-by-step explanation:

The area of the flower bed is 60 ft x 80 ft = 4800 ft²

The perimeter of the sidewalk that surrounds the flower bed is:

The area of the sidewalk is:

area of sidewalk = area of flower bed

280w = 4800

[tex]\text{w}=\dfrac{4800}{280}[/tex]

  [tex]=\dfrac{120}{7}[/tex]

  ≈ 17.14

Answer:

Option A is correct

Values of P = -2 and Q = -31

Step-by-step explanation:

Given the equation: [tex]2x+Q= Px-31[/tex]

Now, we put the given values

A.

Q = -31 and P = -2

2x + (-31) = -2x - 31

2x - 31 = -2x -31  

4x = -31 + 31

4x = 0

x = 0    [one solution]

B.

Q = 31 and P = 2

2x + Q = Px -31

2x + 31 = 2x -31

Subtract 2x from both sides we get

31 = -31        False.

C.

Q = -31 and P = 2

2x + (-31) = 2x - 31

2x - 31 = 2x - 31     [More than one solutions, for any x]

D.

Q = -2 and P = 2

2x + Q = Px -31

2x + (-2) = 2x -31

2x -2 = 2x -31

2x - 2x = -31 + 2      

Combine like term;

0 = -29       False.

Therefore, the values of P and Q results in an equation with exactly one solution is; P = -2 and Q = -31

Answer:

It takes 2.5 seconds for the ball to reach its  highest point

Maximum height is 196 feet

Step-by-step explanation:

h(t) = -16t^2+80t +96

a=-16, b= 80, c=96

To find the maximum height , we need to find vertex

Let find x coordinate of vertex

[tex]t=\frac{-b}{2a}[/tex]

Plug in the values

[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]

It takes 2.5 seconds for the ball to reach its  highest point

Now plug in 2.5 for t to find maximum height

[tex]h(t) = -16t^2+80t +96[/tex]

[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]

Maximum height is 196 feet

Answer:

(0, 10)

Step-by-step explanation:

x=1 y=9

Up 1 means add 1 to the y coordinate

Left 1 means subtract 1 from the x coordinate

(1-1, 9+1)

(0, 10)

Answer:

{1}

Step-by-step explanation:

We find determinant for the given matrix and set it equal to -1

To find determinant we apply formula

[tex]|A| = a_{11}(a_{22}a_{33} − a_{32}a_{23}) - a_{12}(a_{21}a_{33} − a_{31}a_{23})+a_{13}(a_{21}a_{32} - a_{31}a_{22})[/tex]

[tex]|A| = x(1x - 2) - 0(7-7) + 0(14-7x) [/tex]

|A| = x^2 - 2x

Now we set the determinant = -1

[tex]x^2 - 2x=-1[/tex]

Add 1 on both sides

[tex]x^2 - 2x + 1=0[/tex]

Now factor it

(x-1)(x-1) = 0

Set each factor =0  and solve for x

x- 1=0 so x=1

Equation: 300+35x=1700; where x represents the amount of teams participating in the tournament

Answer: 40 teams competed in the lacrosse tournament

How to solve-

300+35x=1700

300-300+35x=1700-300

35x=1400

35/35x=1400/35

x=40

Answer:

y = 2x^2 + 8x + 8

Step-by-step explanation:

The graph touches the x axis at only one point.

so there is only one real solution.

If there is only one real solution then determinant =0

Now we find out the equation that has determinant 0

Determinant is [tex]b^2 - 4ac[/tex]

Let find b^2 - 4ac for each equation

(a) [tex]y = 9x^2 + 6x + 4[/tex]

a= 9 , b = 6 and c=4

[tex]b^2-4ac= 6^2 - 4(9)(4) = -108[/tex]

determinant not equal to 0

(b) [tex]y = 6x^2 – 12x – 6[/tex]

a= 6 , b = -12 and c=-6

[tex]b^2-4ac= (-12)^2 - 4(6)(-6) = 288[/tex]

determinant not equal to 0

(c) [tex]y = 3x^2 + 7x + 5[/tex]

a= 3 , b = 7 and c=5

[tex]b^2-4ac= (7)^2 - 4(3)(5) = -11[/tex]

determinant not equal to 0

(d) [tex]y = 2x^2 + 8x + 8[/tex]

a= 2 , b = 8 and c=8

[tex]b^2-4ac= (8)^2 - 4(2)(8) = 0[/tex]

determinant equal to 0. So there is only one real solution.

Answer:

It's D. on EtDtGtE

Step-by-step explanation:

Answer: [tex]398.5750[/tex]

Step-by-step explanation:

It is important to remember that the fourth digit after the decimal point is in the ten-thousandth place.

Then, given the  following number:

[tex]398.574986215[/tex]

You can follow these steps in order ti round it to the nearest ten-thousandth:

1. You can identify that the digit in the ten-thousandth place is:

[tex]9[/tex]

2. Identify the digit to the right of [tex]9[/tex]. This is:

[tex]8[/tex]

3. Since:

 [tex]8>5[/tex]

 You must round up. Increase the digit [tex]9[/tex] by 1. (Notice that [tex]9+1=10[/tex], then the digit to the left of  [tex]9[/tex] increases by 1 too). Then:

[tex]398.5750[/tex]

Answer:

-18  

Step-by-step explanation:

f(x) = x² - 3x -10

f(-10) = (-10)² – 3(-10) – 10

f(-10) = 100 + 30 - 10

f(-10) = 120

f(-5) = (-5)² – 3(-5) – 10

f(-5) = 25 + 15 - 10

f(-5) = 30

=====

The average rate of change is the slope m of the straight line joining the two points.

m = (y₂ - y₁)/(x₂ - x₁)

m = (30 - 120)/(-5 – (-10))

m = -90/(-5+10)

m = -90/5

m = -18

Answer:

Given : scale factor(k) = [tex]\frac{3}{4}[/tex]

Labelled the given diagram as A, B , C and D

Also, From the given quadrilateral  figure:

The coordinates are;

A=(-8, 4).

B=(-4, -4),

C=(0, -8) and

D=(4, -4)

The rule of dilation with scale factor k and centered at origin is given by;

[tex](x, y) \rightarrow (kx, ky)[/tex]

or

[tex](x, y) \rightarrow (\frac{3}{4}x, \frac{3}{4}y)[/tex]

Then, the coordinates of the dilated given figures are;

[tex]A(-8, 4) \rightarrow (\frac{3}{4}(-8), \frac{3}{4}(4)) = A'(-6, 3)[/tex]

[tex]B(-4, -4) \rightarrow (\frac{3}{4}(-4), \frac{3}{4}(-4)) = B'(-3, -3)[/tex]

[tex]C(0, -8) \rightarrow (\frac{3}{4}(0), \frac{3}{4}(-8))=C' (0 , -6)[/tex]

[tex]D(4, -4) \rightarrow (\frac{3}{4}(4), \frac{3}{4}(-4)) = D'(3, -3)[/tex]

You can see the graph given below in the attachment

Answer:

It deducts 1.6 each time so the next one would be 22.5  

Answer:

60,000 i believe :)

Step-by-step explanation:

First, set the x value to be 0:

2(0) + 4y = 28

4y = 28

y = 28/4 = 7

So when x = 0, y = 28/4

Now set the y value as 0:

2x + 4(0) = 28

2x = 28

x = 14

So when x = 14, y = 0

Simply plot these two values:

(0, 7) and (14 , 0)

And join them up, an attatched image shows this graph.

Answer:

y = -1/2 + 7

Step-by-step explanation:

You have to isolate y so...

2x + 4y = 28 is the original problem. Then subtract 2x on both sides. After you subtract 2x, you have to divide 4 to both sides. Then after you divide 4 to both sides, it'll be y = -2/4 + 7. After that, simplify -2/4, and you'll get y = -1/2 + 7 as your answer.

Answer:

15

Step-by-step explanation:

you have to divide 975/65=$15 per person

Answer:

none of the solutions

Step-by-step explanation:

if k(x) = 2x-3x

We can substitute x=9 to find k(9)

k(9) = 2(9) -3(9)

      = 18 -27

      = -9

[tex]\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}[/tex]

To estimate the length of each rope, the division sentence 30 ÷ 3 = 10 can be used, suggesting that each jump rope would be approximately 10 feet long using compatible numbers.

The student's question involves dividing a rope into equal lengths to create jump ropes.

To estimate the length of each jump rope using compatible numbers for the division sentence, we can round 29.8 feet to a number that is easier to divide by 3, such as 30 feet.

Therefore, the division sentence would be 30 ÷ 3 = 10. So, each jump rope would be approximately 10 feet long.

This is an estimate that allows us to perform calculations quickly in our head or on paper, and it is very close to the exact answer.

Final answer:

To estimate the length of each rope from a total length of 29.8 feet when the rope is divided into 3 parts, compatible numbers are used, rounding 29.8 to 30, and the division sentence is 30 ÷ 3, resulting in each estimated rope being about 10 feet long.

Explanation:

To estimate the length of each rope when a 29.8-foot long rope is cut into 3 equal parts, we could use compatible numbers for easier division in our head. Compatible numbers are numbers that are close to the actual numbers and make it easy to do mental arithmetic. We could round 29.8 feet to 30 feet because 30 is divisible by 3. Here's the division sentence using compatible numbers:

30 feet ÷ 3 = 10 feet

Thus, each rope would be approximately 10 feet long. This process is similar to converting units where the scale factor may be omitted at the end when it is 1, as in converting 3.55 m to 355 cm.

Answer:

Step-by-step explanation: Thew figures are similar becasue 5/15 equals 3/9. They bothe equal one third. This shows that they are bhoth orportionate to eachoither. The ratios of the lengths of their corresponding sides are equal.

Answer: Hello mate!

our set of numbers is 6, 2, 3, 2, 4, and 1.

the two extremes of the set are the lower and bigger numbers, so in this case are 1 and 6, so the range of the values in the set is {1,6} and the distance between these points is 6 - 1 = 5.

this means that all the numbers in our set are in the range between 1 and 6.

The values of x and y for the Isosceles triangle are 90° and 43° respect.

By observation, the triangle ∆ABC is an Isosceles triangle with the markings on both legs of the triangle so the base angles are equal,

angle C = angle B = 47°.

Since the line AD bisects the angle A, then line AD is perpendicular to the base BC and so angle x is a right angle

x = 90°

Considering the right triangle ∆ADB can evaluate for y as follows;

x + y + angle B = 180° {sum of interior angles of a triangle}

y + 90 + 47 = 180

y + 137 = 180

y = 180 - 137

y = 43°.

Therefore, the values of the x is equal to 90° and that of y is 43° for the Isosceles triangle ∆ABC.

Answer:

No

Yes

Yes

No

Step-by-step explanation:

X's repeat

X's don't repeat

X's don't repeat

X Values repeat

Answer:

C

Step-by-step explanation:

I am assuming the top and bottom are closed.

Surface are = area of the curved side + 2 * area of the top

=  9* 14 * π + 2 * π * 7^2

= 126π + 98π

= 224π ft^2

Answer:

224

Step-by-step explanation:

<, > - opened circle

≤, ≥ - closed circle

<, ≤ - draw line to left

>, ≥ - draw line to right

Answer in the attachment.

<,> - dotted line

≤, ≥ - solid line

<, ≤ - shadow to left

>, ≥ - shadow to right

x = -6 - its a vertical line

Answer:

5(b - 3)(b + 1)

Step-by-step explanation:

take out a common factor of 5

= 5(b² - 2b - 3)

to factor the quadratic consider the factors of - 3 which sum to - 2

These are - 3 and + 1, thus

= 5(b - 3)(b + 1)

Answer:

See below. The solutions are x=-1/3 and y=-4/3

Step-by-step explanation:

[tex]\frac{1}{2}\log_2 y-\log_4 x = 1\\\frac{1}{2}\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\\frac{1}{2}\log_2y = log_44x\\\frac{1}{2}\frac{\log_4y}{\log_4 2}=\log_4 4x\\\log_4y=\log_44x\\4^{\log_4y}=4^{\log_44x}\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -\frac{1}{3}, y=-\frac{4}{3}[/tex]

Answer:

I) B = 20 m², h = 4 m are NOT possible dimensions for the area of the base and the height of the prism.

Step-by-step explanation:

Given that the triangular prism has a volume = 240 m³, we can use the formula for the volume of a triangular prism to check the given answers for possible dimensions.  V = Bh, where B = the area of the base and h = height of the prism.  In this case, we simply need to multiply each of the given dimensions together to see if they equal 240 m³:

F) B = 48 m², h = 5 m:  v = 48 x 5 = 240 m³ (possible)

G) B = 24 m², h = 10 m; v = 24 x 10 = 240 m³ (possible)

H) B = 12 m², h = 20 m: v = 12 x 24 = 240 m³ (possible)

I) B = 20 m², h = 4 m: v = 20 x 4 = 80 m³ (NOT possible)

Answer:

The correct answer is D.

Step-by-step explanation:

p + 7 = ≤ 50

because I did it for the ECA 3 Exam. :>

The inequality which helps to find the possible values for x will be x + 7 ≤ 50.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Total budget = $50

Ticket cost = $7

Total spent ≤ total budget

x + 7 ≤ 50

x ≤ 43

Hence "The inequality which helps to find the possible values for x will be x + 7 ≤ 50".

For more about inequality,

brainly.com/question/20383699

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