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3 years ago

I need the answer in a fraction if possible

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

7 0

Answer:

12 ft 9 5/6 inches

Step-by-step explanation:

We can use proportions to solve this. Put the height of the object over the shadow. Change the height of the object to inches

Alonzo

5 ft 11 inches = 5 ft *12 inches/ft + 11 inches = 60 inches + 11 inches = 71 inches

2 ft shadow = 2* 12 inches/ ft = 24 inches

Basketball goal

4 ft 4 inches = 4 ft *12 inches/ft + 4 inches = 48inches + 4 inches = 52 inches

Alonzo Basketball

71 inches x inches tall

------------ = --------------------

24 inches 52 inches

Using cross products

71*52 = 24*x

Divide each side by 24

71*52/24 = 24x/24

923/6 =x

Lets change this to a mixed number

6 goes into 923 153 times with 5 left over

153 5/6 inches

Now we need to change inches to feet

How many time does 12 go into 153 12 times (12*12 =144 with 9 left over)

12 ft 9 5/6 inches

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Select the correct answer.

Ierofanga [76]

Answer:

$19.2x+96$ units

Step-by-step explanation:

The perimeter of a square is 4 times the length of one side.

The length of the sides of a square is given by the expression $4.8x+24$

To find the perimeter, we multiply this expression by 4.

$Perimeter=4(4.8x+24)$

We expand to obtain:

$Perimeter=4*4.8x+4*24$

This simplifies to:

$Perimeter=19.2x+96$

7 0

3 years ago

a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the l

GrogVix [38]

Answer:

$\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}$

Step-by-step explanation:

The equation of a line:

$y=mx+b$

We have

$m=\dfrac{2}{3}$

substitute:

$y=\dfrac{2}{3}x+b$

The formula of a distance between a point and a line:

General form of a line:

$Ax+By+C=0$

Point:

$(x_0,\ y_0)$

Distance:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}$

Convert the equation:

$y=\dfrac{2}{3}x+b$ |subtract $y$ from both sides

$\dfrac{2}{3}x-y+b=0$ |multiply both sides by 3

$2x-3y+3b=0\to A=2,\ B=-3,\ C=3b$

Coordinates of the point:

$(0,\ 0)\to x_0=0,\ y_0=0$

substitute:

$d=4$

$4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}$

$4=\dfrac{|3b|}{\sqrt{13}}\qquad|$ |multiply both sides by $\sqrt{13}$

$4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}$ |divide both sides by 3

$b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}$

Finally:

$y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}$

4 0

3 years ago

(2A) Find f(2x + 4) for f(x) = 1 - x2

Aleksandr-060686 [28]

Answer:

f(2x + 4) = -4x² - 16x - 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Terms/Coefficients
Expanding (FOIL)

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 1 - x²

Step 2: Evaluate

Substitute in x [Function f(x)]: f(2x + 4) = 1 - (2x + 4)²
Expand [FOIL]: f(2x + 4) = 1 - (4x² + 16x + 16)
(Parenthesis) Distribute negative: f(2x + 4) = 1 - 4x² - 16x - 16
Combine like terms: f(2x + 4) = -4x² -16x - 15

8 0

2 years ago

on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solv

Cloud [144]

Although the concept here is physics, the solution is technically just algebra. You have two situations that are related to each other which can be expressed in equation form. Actually, the equation is already given which is 7/12 w= 13 5/12. So, basically, all you have to do is solve for w.

Let's simplify 13 5/12 first into an improper fraction.You do this by multiplying the denominator with the whole number and adding to it the numerator. This will be your new numerator, The denominator would still be 12. So, this is equal to (12*13 + 5)/12 = 161/2. Then,

(7/12) w = 161/12

By cross multiplication,

7*12*w = 161*12
w = 161/7 = 23

Therefore, w = 23 pounds which is the weight of the object on Earth.

8 0

3 years ago

Find the following (Show your work) 1) 20% of 5 2) 35% of 50 2) 71% of 22

seropon [69]

Answer:

Step-by-step explanation:

1. 1

2. 17.5

3. 15.62

8 0

3 years ago