A man is four times as old as his daughter.in five years time, the square of his age will exceed the square of his daughter's age by 120 years. find the daughter's age​

Answer:

Step-by-step explanation:

θ = angle of incidence = angle of reflection

You have two similar triangles.

tanθ = 6/4 = h/45

h = 45×6/4 = 67.5 ft

The required height of the building is 67.5 feet.

Johnny uses a mirror placed on level ground to measure the height of a building. Johnny's eyes are 6 feet above the ground and he stands 4 feet away from the mirror. If the mirror is 45 feet away from the building’s base, how tall the building is determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Since the two triangles are similar,
Let the height of the building is x.
The ratio of height and distance from the mirror Jhonny = height and distance of mirror from the building.
6/4=x/45
x = 11.25*6
x = 67.5

Thus, the required height of the building is 67.5 feet.

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9514 1404 393

Answer:

  P'(1, -7)

  Q'(6, -7)

  R'(-3, -10)

Step-by-step explanation:

The relevant transformation is ...

  (x, y) ⇒ (y, x) . . . . . . reflection over y=x

Simply interchange the x- and y-coordinates.

  P'(1, -7)

  Q'(6, -7)

  R'(-3, -10)

Answer:

x<2

Step-by-step explanation:

Hello There!

Our objective for this problem is to isolate the variables

To do so we use inverse operations

x+4<6

subtract 4 from each side

4-4 cancels out

6-4=2

we're left with

x<2

Step-by-step explanation:

It is just like a normal x equation just with an inequality. So for now, just represent the < as and =

so we have x+4=6

subtract 4 from both sides

x+4-4=6-4

x=2

Now we insert the <

x<6

so all values for x are all less than 6

Hope that helps :)

Answer:

120 - 14 = 106

Step-by-step explanation:

7 x 2 = 14

10 x 12 = 120 therefore you,

120 - 14 = 106

The area of the shaded region is 106 m².

We have,

The area of the rectangle:

= length x width

From  the figure,

Bigger rectangle dimensions:

Length = 12 m

Width = 10 m

Smaller rectangle dimensions:

Length = 7 m

Width = 2 m

Now,

The shaded region.

= Area of the bigger rectangle - Area of the smaller rectangle

= 12 x 10 - 7 x 2

= 120 - 14

= 106

Thus,

The area of the shaded region is 106 m².

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Answer:

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Answer:

g(5) - f(1) = 8

g(5) = 11

Step-by-step explanation:

Given:

g(x) = 2x + 1

f(x) = x + 2

Find:

g(5)

g(5) - f(1)

Computation:

g(x) = 2x + 1

g(5) = 2(5) + 1

g(5) = 11

f(x) = x + 2

f(1) = 1 + 2

f(1) = 3

g(5) - f(1) =11 - 3

g(5) - f(1) = 8

Answer:

1/(32^1.4)

Step-by-step explanation:

1/(32^1.4)

Answer:

The coefficients are:

[tex](a)\ 5x[/tex]

[tex](b)\ -4b[/tex]

[tex](c)\ 38bc[/tex]

[tex](d)\ -24b^2c[/tex]

Step-by-step explanation:

Required

The coefficient of a

To get the coefficient, we simply remove a. The remaining terms is the required coefficient

Solving (a):

[tex]Expression = 5ax[/tex]

Remove a

5x:

Hence, the coefficient is 5x

Solving (b):

[tex]Expression = -4ab[/tex]

Remove a

-4b

Hence, the coefficient is -4b

Solving (c):

[tex]Expression = 38abc[/tex]

Remove a

38bc

Hence, the coefficient is 38bc

Solving (d):

[tex]Expression=-24ab^2c[/tex]

Remove a

[tex]-24b^2c[/tex]

Hence, the coefficient is [tex]-24b^2c[/tex]

Answer:

a) x = 1.52

b) s = 1.16

Step-by-step explanation:

We have that:

5 students watched 0 movies.

9 students watched 1 movie.

5 students watched 2 movies.

5 students watched 3 movies.

1 student watched 4 movies.

(a) Find the sample mean x.

Sum divided by the number of students. So

[tex]x = \frac{5*0 + 9*1 + 5*2 + 5*3 + 1*4}{5 + 9 + 5 + 5 + 1} = \frac{38}{25} = 1.52[/tex]

(b) Find the approximate sample standard deviation, s.

Standard deviation of the sample.

Square root of the sum of the squares of the values subtracted from the mean, divided by the sample size subtracted by 1. So

[tex]s = \sqrt{\frac{5*(0-1.52)^2 + 9*(1-1.52)^2 + 5*(2-1.52)^2 + 5*(3-1.52)^2 + 1*(4-1.52)^2}{24}} = \sqrt{\frac{32.24}{24}} = 1.16[/tex]

Answer:

a) V = 35.1 in.^3

b) V = 288 pi in.^3

c) h = 2.7 in.

Step-by-step explanation:

a)

radius of base = 2 in.

height = 8 in.

volume of cone = (1/3)(pi)(r^2)h

V = (1/3)(pi)(2 in.)^2(8 in.)

V = 35.1 in.^3

You are correct.

b)

You must leave the answer in terms of pi, so do not use 3.14 or another approximation for pi.

radius of base = 6 in.

height = 24 in.

volume of cylinder = (pi)(r^2)h

V = (1/3)(pi)(6 in.)^2(24 in.)

V = 288 pi in.^3

c)

volume = 288 pi in.^3

radius = 18 in.

288 pi in.^3 = (1/3)(pi)(18 in)^2 h

288 in. = (1/3)(324)h

288 in. = 108h

h = 2.666 in.

h = 2.7 in.

Answer:

3 1/2

Step-by-step explanation:

That is the largest value.

Answer:

3 1/2 ounces

Step-by-step explanation:

That is the biggest number on the graph.

Answer:

45/64 m²

Step-by-step explanation:

We are given the length and width of the tablecloth (breath = width).

We know that the formula for the area of a rectangle is A = L × W.

Assuming the tablecloth is in the shape of a rectangle (since the problem gives us length and width), we can substitute the length and width into the formula.

The area of the tablecloth is 45/64 m².

Answer:

nonagon

Step-by-step explanation:

The correct name for a 9-sided polygon is nonagon.

Answer:

option c. nonagon

..............

Answer:

B

Step-by-step explanation:

Answer:

Distributive Property

Step-by-step explanation:

This is distributive property because you are distributing the 5 by multiplying it by the variables in the parenthesis.

Answer:

[tex]given \\ heigh(h) = 7m \\ area \: of \: triangle \: (a) = 22m {}^{2} \\ base(b) = x \\ a = \frac{1}{2} \times h \times b \\ \frac{a}{h} = \frac{1}{2} \times b \\ b = 2( \frac{a}{h} ) \\ b = 2( \frac{22m {}^{2} }{7m} ) \\ b = 6.29m \\ base = 6.29m[/tex]

Answer:

V would go to (6,-3), S (4,-2), T (4,2), U (6,6)

Step-by-step explanation:

move each point right 10 points, and down 2 points. :)

Answer:

Fraction form:33/20 money:$1.65

Step-by-step explanation:

$0.2 + $x = %1.36

20 IB + 80 IB = 100 IB

Equation: 0.2*20+x*80=1.36*100

there fore the answer is 33/20

Answer:

33/20

Step-by-step explanation:

Step-by-step explanation:

One interior angle of a triangle = 30⁰ .

The measure of other two are x and y .

We know that the angle sum property of a triangle is 180⁰ .

=> x + y + 30⁰ = 180⁰

=> x + y = 180⁰ - 30⁰.

=> x + y = 150⁰.

Possible solution set of x and y are ,

(1,149) (2,148 ) ...... (148+2) & (149+1)

Basically we are here decreasing y and increasing x to obtain the values .

Hope it helped !

Answer:

I don't understand what the problem is saying... 2124...95...

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A is specific to a single neighborhood

B is specific to a single nursing home

D is specific to only patrons

When looking for a random sample, in this case - the town, you have to consider how to select based on the entire sample.

Answer:

the principal balance at the beginning of June is $22,222.22

Step-by-step explanation:

The computation of the principal balance at the beginning of June is shown below:

Principal balance = Interest paid ÷ (Interest Rate ÷ 12 Months)

= $250 ÷ (13.5% ÷ 12)

= $22,222.22

Hence, the principal balance at the beginning of June is $22,222.22

Answer:

Perimeter = 2*Length + 2*Width

                = 2(10’6”) + 2(14)

                = 21’ + 28’

                = 49’

Step-by-step explanation:

Answer:

Step-by-step explanation:

b

Answer:2.5

Step-by-step explanation: