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The two triangles shown are congruent: ΔABC ≅ ΔXYZ. Based on this information, which of the following is a true statement?

Solution :

It is given in the question that Ben goes to the zoo by walking and then he walks down to the city park. He moves several blocks while walking from his home to the zoo and then to the city park.

The figure is provided below.

So from the picture, the least number of blocks that Ben had walked from his home to the city park can be found out by counting the number of blocks he moved.

So the least number of blocks will be = 19

Step-by-step explanation:

Per year it goes up by $180

What about in 5years?

180×5=900

1400+900=2300

=$2300

Answer:

$2,120

Step-by-step explanation:

180 times 4 = 720

1,400 + 720 = 2,120

Year 1: $1,400 a month

Year 2: $1, 580 a month

Year 3: $1,760 a month

Year 4: $1,940 a month

Year 5: $2,120 a month

Answer:

A. & B. are the corect answers

Step-by-step explanation:

Answer:

A and B

x is [tex]\frac{1}{3}[/tex] of y

AND

y is [tex]\frac{3}{4}[/tex] of (x+y)

Step-by-step explanation:

x:y is 1:3

=>  y is bigger than x

=>  y is 3x bigger than x

=>  y = 3 lots of x

=>  [tex]y =[/tex] [tex]3x[/tex]

=>  [tex]\frac{y}{3}[/tex] [tex]= x[/tex]

=>  [tex]\frac{1}{3} y[/tex] [tex]= x[/tex]

So x is [tex]\frac{1}{3}[/tex] of y

y is [tex]\frac{3}{4}[/tex] of (x+y)

If x = 1 and y = 3 (substitute in values)

=>  3 is [tex]\frac{3}{4}[/tex] of (4)

=>  3 is [tex]\frac{3}{4}[/tex](4)

=>  3 is ([tex]\frac{3}{4}[/tex]x4)

=>  3 = 3

Therefore, y is [tex]\frac{3}{4}[/tex] of (x+y) is true

So the answers are:

x is [tex]\frac{1}{3}[/tex] of y

AND

y is [tex]\frac{3}{4}[/tex] of (x+y)

Answer:

-5

Step-by-step explanation:

When rotating a point (x,y) 270 degrees counterclockwise, the new coordinates become (y, -x).

Answer:

(4, -5)

Step-by-step explanation:

Seeing as the coordinates of P are (5, 4) and it's a 270 degrees rotation, the transformation rule is:

[tex](x,y)[/tex] turns into [tex](y, -x)[/tex].

Thus, (5, 4) turns into (4, -5)

Answer:

x = ±√(y/25 + 4)

Step-by-step explanation:

Given the expression;

y = 25x² - 100

We are to make x the subject of the formula;

-25x² = -y - 100

25x²= y + 100

x² = y/25 + 100/25

x²= y/25 + 4

x = ±√(y/25 + 4)

This give the value of x

Given:

The compound inequality is:

[tex]3<x+3<6[/tex]

To find:

The solution for x.

Solution:

We have,

[tex]3<x+3<6[/tex]

To solve the inequality, we need to isolate the variable x.

Subtracting 3 from each side, we get

[tex]3-3<x+3-3<6-3[/tex]

[tex]0<x<3[/tex]

The solution for x is [tex]0<x<3[/tex]. Therefore, the correct option is C.

Answer:

-1,-6

Step-by-step explanation:

The reflection of point P=(-1,6) across the x-axis is the point (-1,-6).

In mathematics, reflection is a transformation that flips a shape, point, or object over a line, plane, or point. Reflection is also known as flipping, mirroring, or symmetry.

In two-dimensional geometry, the most common type of reflection is a mirror reflection, which involves flipping a shape or point over a line (known as the line of reflection) to create a mirror image. The line of reflection acts as a mirror, and the shape or point is reflected in the mirror as if it were a real reflection.

To find the reflection of the point P=(-1,6) across the x-axis, we can use the following formula:

Rx-axis(P) = (x, -y)

where x is the x-coordinate of P, and y is the y-coordinate of P.

In this case, the x-coordinate of P is -1, and the y-coordinate of P is 6. Therefore, the reflection of P across the x-axis, Rx-axis(P), is:

Rx-axis(P) = (-1, -6)

So the reflection of point P=(-1,6) across the x-axis is the point (-1,-6).

To know more about reflection follow

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Answer:

12 inches

Step-by-step explanation:

Answer: 68.5 pounds

Step-by-step explanation:

he grew 1.5 inches, or 6/4 inches, a total of 6 1/4 inches. 6*(3/4) = 4.5.

If he gained 4.5 pounds, then he would be 64 + 4.5 = 68.5 pounds

Answer:

68.5 pounds

Step-by-step explanation:

hope this helps you!

Answer:

what

Step-by-step explanation:

Answer:

I really wanted to help you but the code is an error when I tried to put the link insorry.

Answer:

70 mb

Step-by-step explanation:

264 picture = 528 mb

35 pictures = ?

Solve for one picture:

Variable x = mb per 1 picture

264/528 = 1/x

Cross multiply:

264 × x = 528 × 1

264x = 528

x = 528 ÷ 264

x = 2

Each picture takes up 2 mb.

Multiply the number of pictures per 2 mb:

35 pictures × 2 mb

70 mb total

Answer:

(0,0), (10,6) (15,9)

Step-by-step explanation:

Answer:

Origin(0,0)

First point(2.5,1.5)

2nd point (5,3)

3rd point(10,6)

Step-by-step explanation:

Answer:

x/4+13

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 because the circumference is the diameter x pi. Since the circumference is 3.14, and 3.14 divided by 3.14 is 1, then the diameter is 1.

Answer: I think it's The Third Point Unsure

The solution is, the right answer is :

Group 1: (5, 61); Group 2: (15, 73); Group 3: (25, 79)

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Minutes studying(x) 0 , 5 , 10 , 10 , 15 , 20 , 25 , 30 , 30

Test score(y)            68, 61, 54, 64, 73, 76, 80, 79, 85

The median of x is 15 (The middle value)

Median of y would be 73 (The middle value)

So group 2 would be (15,73)

Here is the sequence 'x' without median 0 , 5 , 10 , 10, 15

The median would be 10.

Here is the sequence 'y' without median 54, 61, 64, 68, 73

The median is 61.

Hence,

So group 1 will be (5, 61).

73, 76, 79, 80, 85 median of 'y' would be 79

15 , 20 , 25 , 30 , 30 median of 'x' would be 25

so group 3 would be (25 , 79)

Therefore the right answer is :

Group 1: (5, 61); Group 2: (15, 73); Group 3: (25, 79)

To learn more on median click:

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Answer:

9z^2+4x+1

Step-by-step explanation:

Remove parentheses.

7{x}^{2}+4x-1+2{x}^{2}+2

7x  

2

+4x−1+2x  

2

+2

2 Collect like terms.

(7{x}^{2}+2{x}^{2})+4x+(-1+2)

(7x  

2

+2x  

2

)+4x+(−1+2)

3 Simplify.

9{x}^{2}+4x+1

9x  

2

+4x+1

Answer:

The slope is 1/8.

Step-by-step explanation:

So basically, when we are trying to find slope, we think of the change of y over the change of x. And so the change of y between those two points would be 4-2 which is 2. And the change of x would be 32-16, which is 16. Because slope is y/x, therefore the slope is 2/16, which is also 1/8 simplified. I hope this helps!

Answer:

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

The given series is an illustration of an arithmetic series, where the sum of first 10 terms of the series is -160.

Given

[tex]2 + (-2) + (-6) + (-10) +.......[/tex]

First, we calculate the common difference of the series

[tex]d = T_2 - T_1[/tex]

[tex]d = -2 -2[/tex]

[tex]d = -4[/tex]

The sum of the first nth term of an arithmetic series is:

[tex]S_n = \frac n2(2a + (n - 1)d)[/tex]

Where:

[tex]n = 10[/tex] ---- i.e. sum of 10 terms

[tex]a = 2[/tex] --- the first term

[tex]d = -4[/tex] --- the common difference

So, we have:

[tex]S_{10} = \frac{10}{2}(2 \times 2 + (10 - 1) \times -4)[/tex]

[tex]S_{10} = 5(4 + 9 \times -4)[/tex]

[tex]S_{10} = 5(-32)[/tex]

[tex]S_{10} = -160[/tex]

Hence, the sum of 10 terms of the series is -160.

Read more about arithmetic series at:

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Answer:

hope it helps.

Answer:

(x2 +2x+1)+(y2+4y)=31+1

(x+1)2 +(y2+4y)=32

(x+1)2 +(y2+4y+4)=32+4

(x+1)2 +(y+2)2=36

The equation can be written in the form (x-p)2 +(y-q)2=r2

so it represents a circle with the radius r=6  and the center (-1,-2)

Step-by-step explanation:

Answer:

6 units is the amswer

Step-by-step explanation:

here you gooo

Answer:

djajahshshsk manually sjss

Answer:the third one

Step-by-step explanation:

Answer: 3/4 hour

Step-by-step explanation: You can add 1/4 at a time to get to the 3 2/4.

Answer:

Not sure how to answer this.

Step-by-step explanation:

Answer:

5 inches

Step-by-step explanation:

if its under that than, that's just disappointing

Answer:

[tex] \alpha = 108\degree, \: \beta = 72\degree [/tex]

Step-by-step explanation:

α and β are Supplementary (given)

[tex] \therefore \alpha + \beta = 180\degree.... (1)[/tex]

It is given that:

[tex] \alpha= \frac{3}{2} \beta[/tex]

Plugging the value of α in equation (1), we find:

[tex] \frac{3}{2} \beta + \beta = 180\degree[/tex]

[tex]\therefore \frac{3+2}{2} \beta = 180\degree[/tex]

[tex]\therefore \frac{5}{2} \beta = 180\degree[/tex]

[tex]\therefore \beta = 180\degree\times \frac{2}{5}[/tex]

[tex]\therefore \beta = 72\degree[/tex]

[tex]\implies \alpha= \frac{3}{2} \times 72\degree= 108\degree [/tex]

So,

[tex] \alpha = 108\degree, \: \beta = 72\degree [/tex]

Answer:

last one

Step-by-step explanation:

Answer: D. 3/2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Slope is change in y / change in x

In the graph there is an interception at 0,1 and 2,4

So the change in x is 2 and the change in y is 3

so 3/2

And it's positive since it's going top right.