A triangle has dimensions 5, 9, and 12. A similar triangle is drawn with a scale
factor of 1.2. What are the dimensions of the new triangle?


The answer?

Answer:

96 m

Step-by-step explanation:

It is given that the two overlapping triangles are similar in the figure.

The landowner wishes to find the distance across the pond. The distance is d.

From the figure, since the two triangles are similar, therefore we can write :

[tex]$\frac{d}{(24+40)}=\frac{60}{40}$[/tex]

[tex]$\frac{d}{64}=\frac{60}{40}$[/tex]

[tex]$d = \frac{60}{40} \times 64$[/tex]

[tex]$d = \frac{6}{4} \times 64$[/tex]

d = 6 x 16

  = 96 m

Therefore, the distance across the pond is d = 96 m

Answer:

Area of a square garden = 2, 500 m².

Length of the side of the garden =  √2,500 = 50 m.

Width of the path = 2.5 m.

Path is inside the garden.

Width of the garden that is inside (enclosed) by the path:

        50 - 2 * 2.5 = 45 m.

Length of the garden inside by the path :  = 45 m.

So the area of garden inside the path = 45 * 45 m²

     = 2, 025 m².

Area of the path = 2, 500 - 2, 025  

    = 475 m².

Cost of laying the path = Rs 25 /m² * 475 m²

   = Rs 11, 875.

Step-by-step explanation:

92, 110, 128, 146, 164, 182. ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]92,110,128,146,164,182 \\ ➵ \: 92 + 18 = 110 \\ ➵ \: 110 + 18 = 128 \\ ➵ \: 128 + 18 = 146 \\ ➵146 + 18 = 164 \\ ➵ \: 164 + 18 = 182[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

y=3x

Step-by-step explanation:

Answer:

The half-life of this radioactive substance is of 8.6 months.

Step-by-step explanation:

Exponential decay of an amount:

The equation that models an amount after t units of time, subject to exponential decay, is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A radioactive substance decays to 30% of its original mass in 15 months.

This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]

[tex](1-r)^{15} = 0.3[/tex]

[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]

[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]

[tex]1 - r = 0.9229[/tex]

So

[tex]A(t) = A(0)(0.9229)^t[/tex]

Determine the half-life of this radioactive substance to the nearest tenth.

This is t for which A(t) = 0.5A(0). So

[tex]A(t) = A(0)(0.9229)^t[/tex]

[tex]0.5A(0) = A(0)(0.9229)^t[/tex]

[tex](0.9229)^t = 0.5[/tex]

[tex]\log{(0.9229)^t} = \log{0.5}[/tex]

[tex]t\log{0.9229} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]

[tex]t = 8.6[/tex]

The half-life of this radioactive substance is of 8.6 months.

Answer:

Chi-Square and Linearization ... A random sample of 315 subjects is selected and represented in the table below. ... claim that aerobic walking and cholesterol levels are related.

Answer:

((y + 2) ^ 2)/25 - ((x - 3) ^ 2)/4 = 1 O A. ( (3, - 2 plus/minus sqrt(21)) B. (3, - 2 plus/minus sqrt(29)) O B. O c. D . (3 plus/minus sqrt(21), - 2); (3 plus/minus sqrt(29), - 2)

The foci of the hyperbola will be (3, -2 + √29) and (3, -2 - √29). Then the correct option is B.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The hyperbolic equation is given as,

(y - k)² /a² - (x - h)² /b² = 1

Then the foci of the hyperbola are given as,

(h, k + c) and (h, k - c)

The equation of the hyperbola is given below.

(y + 2)² /25 - (x - 3)² / 4 = 1

Compare the equations, then we have

(h, k) = (3, -2)

a² = 25

b² = 4

Then the value of 'c' is given as,

c² = a² + b²

c² = 25 + 4

c² = 29

c = √29

Then the foci of the hyperbola will be (3, -2 + √29) and (3, -2 - √29). Then the correct option is B.

More about the hyperbola link is given below.

https://brainly.com/question/12919612

#SPJ2

Answer:

y = 5/4x - 14

Step-by-step explanation:

Given:

Passes through (8, -4)

Slope (m) = 5/4

Slope-intercept equation:

y - y1 = m(x - x1)

y - (-4) = 5/4(x - 8)

y + 4 = 5/4x - 10

y = 5/4x - 14

Answer:

The radian :

[tex] \frac{2\pi}{3} [/tex]

Area = π × ( radius )^2

Area = π × ( 18 )^2

Area = π × 324

Area = 324 π mm^2

Answer:

Approximately 169

Step-by-step explanation:

Set up as fractions and use cross multiplilcation to solve for the unknown.

These are our fractions from the information we are given; the winners represent the numerators (and x is the unknown, becuase we don't yet know how many winners there will be with 50000 participants). Note that the denominator on the first fraction is (1476 + 5) because we want it to represent TOTAL amount of particpants in the ratio:

[tex]\frac{5}{1481} = \frac{x}{50000}[/tex]

Now cross multiply by multiplying numerators and denominators that are ACROSS from each other, so 5 * 50000 and 1481 * x; now we have:

250000 = 1481x

Now to isolate x (to know its value) we need to divide both sides by 1481, and we are left with:

168.8 = x

But I rounded up to 169.

Answer:

(a) (0, 2)

(b) (3, 26)

Step-by-step explanation:

y = 8x + 2

(a) x = 0, y = 8(0) + 2 = 2

(b) x = 3, y = 8(3) + 2 = 24 + 2 = 26

Answer:

2x+3

f(-2)=:2x+3

2(-2)+3

-4+3

= -1

Answer:

32.5%

Step-by-step explanation:

Answer:

32.5

Step-by-step explanation:

divided by 100 to get percentage

Answer:

10

Step-by-step explanation:

subtract lower quartile (10) from upper quartile (20)

Answer:

The area of the canvas must be 30 feet.

Step-by-step explanation:

Answer:

235.619 is my answer since I have done V = (pi) radius squared and height/3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the bank loans the borrower

hope it help

what is the question?? because this equation is false?

Answer:

x = 33

y = 5

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

y = 12

12 = 1/5 x 60

12= 12

y = 9

9 = 1/5 x 45

9 = 9

and so on and it always results to one fifth

Answer: I thin it’s Opposite of 2

Step-by-step explanation:

Answer:

The distance between A and D

Step-by-step explanation:

when it is |-2| (in the box) it changes to 2

Answer:

[tex]p' = 0.22[/tex]

Step-by-step explanation:

Given

[tex]p = \frac{78}{100}[/tex]

Required

Probability that a [tex]customer[/tex] does [tex]not[/tex] live [tex]within[/tex] [tex]50[/tex] miles

To do this, we make use of complement rule;

Which states that:

[tex]p + p' = 1[/tex]

Make p' the subject

[tex]p' = 1 - p[/tex]

So, we have:

[tex]p' = 1 - \frac{78}{100}[/tex]

Express fraction as decimal

[tex]p' = 1 - 0.78[/tex]

[tex]p' = 0.22[/tex]

Answer:

y = 5 sin (2x) + 4

Step-by-step explanation:

this is sines function,

the amplitude is [9 - (-1)]/2 = 10/2 = 5

the period is 2πx/π = 2x

the x-axis of actual function is at y = 4

so, the function is :

y = 5 sin (2x) + 4

Answer:

5

Step-by-step explanation:

-75 divided (-15) = 5

Answer:

84in

Step-by-step explanation:

84in

Answer:

The sentence

"The Number of Chem textbooks sold is 86 less than the number of History textbooks"

This seems to be the confusing part.

Now look at it this way...

'If CHM text is 86 less than History text... It also means that History Text is 86 More than CHM'

This expression can be written as

Let History Text be "H"

Let CHM text be "C"

C - 86 = H

or

C=H + 86.......1

First line of this question is interpreted thus

H + C = 326.......2

From eqn 1... C=H+86

Substitute into Eqn 2

H + C=326

H + (H+86)=326

H+H=326-86

2H=240

H=240/2

H=120.

C=H+86

C=120+86

C=206.

This answer is correct... Why?

The key statement says .. The Number of CHM sold is 86 less than History...

Also interpreted as

The Number of CHM – 86 = History

206 - 86 =120.

Have a great day!!!

Answer:

The first term is 8

The common ratio is 2, because the ratio of 8:16 is 1:2 and the ratio of 16:32 is 1:2

Step-by-step explanation:

Answer:

The common ratio of the following geometric sequence is x2 everytime.