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saw5 [17]
3 years ago
12

The sides of a rectangle are a number and 4 less than that same numbers. The perimeter is 56. Find the dimensions of the rectang

le. write an algebraic expression or equation to represent the verbal expression.
Mathematics
1 answer:
Rzqust [24]3 years ago
8 0

Answer: find the answer in the explanation.

Step-by-step explanation:

You are given that the sides of a rectangle are a number and 4 less than that same numbers.

Let the length side = L

And width side = L - 4

The dimensions of the rectangle will be

Area = length × width

L × ( L - 4 )

Open the bracket

L^2 - 4L

The verbal expression here,

Perimeter = L + L + W + W

Substitute all the parameters into the formula

56 = L + L + L-4 + L-4

56 = 2L + 2L - 8

56 = 4L - 8

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How much faster does Student B read than Student A?
Romashka-Z-Leto [24]

Answer:

He reads faster by 8 pages.

3 0
3 years ago
I need to know the improper fractions answers for:
zmey [24]

Answer:

Part 1) x=\frac{15}{2}\ units

Part 2) z=\frac{15\sqrt{3}}{2}\ units

Part 3) y= \frac{15\sqrt{3}}{4}\ units

Part 4) b= \frac{45}{4}\ units

Step-by-step explanation:

step 1

Find the value of x

In the large right triangle

cos(60^o)=\frac{x}{15} ----> by CAH (adjacent side divided by the hypotenuse)

Remember that

cos(60^o)=\frac{1}{2}

substitute

\frac{1}{2}=\frac{x}{15}

solve for x

x=\frac{15}{2}\ units ---> improper fraction

step 2

Find the value of z

In the large right triangle

Applying the Pythagorean Theorem

15^2=x^2+z^2

substitute the value of x

15^2=(\frac{15}{2})^2+z^2

solve for z

z^2=15^2-(\frac{15}{2})^2

z^2=225-\frac{225}{4}

z^2=\frac{675}{4}

z=\frac{\sqrt{675}}{2}\ units

simplify

z=\frac{15\sqrt{3}}{2}\ units

step 3

Find the value of y

In the right triangle of the right

sin(30^o)=\frac{y}{z} ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values of y and z

Remember that

sin(30^o)=\frac{1}{2}

so

\frac{1}{2}=y:\frac{15\sqrt{3}}{2}

solve for y

\frac{1}{2}= \frac{2y}{15\sqrt{3}}

y= \frac{15\sqrt{3}}{4}\ units

step 4

Find the value of b

In the right triangle of the right

cos(30^o)=\frac{b}{z} ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values of y and z

Remember that

cos(30^o)=\frac{\sqrt{3}}{2}

so

\frac{\sqrt{3}}{2}=b:\frac{15\sqrt{3}}{2}

solve for y

\frac{\sqrt{3}}{2}= \frac{2b}{15\sqrt{3}}

b= \frac{45}{4}\ units

7 0
3 years ago
Y= -2(x - 1)^2 + 8 the answer
Dahasolnce [82]
Y = (-2x +2)^2 +8
(-2x^2 +4) +8
-2x^2 +12
8 0
3 years ago
A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree using the height (in feet)
alex41 [277]

Answer: The response variable = Volume

and explanatory variable(s) in this study are: Height and Diameter.

Step-by-step explanation:

Important definitions:

  • The explanatory variable is a type of independent variable manipulated by the experimenter for the ongoing experimental study.
  • The response variable is a type of dependent variable which depends on the explanatory values provided by the experimenter.

Given: A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree using the height (in feet) and diameter (in inches) of the trees.

Here, Volume directly depends upon the height and diameter of the tree.

Also, forester ( Experimenter) wants to predict volume by cutting tree that means it is an response variable and it depends on height and diameter , so height and diameter are explanatory variable.

Hence, The response variable = Volume

and explanatory variable(s) in this study are: Height and Diameter.

7 0
3 years ago
Which is the following points is NOT a solution to the inequality y > - x + 3? —a. ( -2,6)b. (5,-1)c. (2,0)d. (0,3)
CaHeK987 [17]

Given -

y > - x + 3

To Find -

The points which is NOT a solution to the inequality

Step-by-Step Explanation -

We will put the value of each in inequality and then see if it satisfies the given condition or not.

a. ( -2,6)

So, x = -2 and y = 6 in y > - x + 3

= 6 > - (-2) + 3

= 6 > 5 (Correct Solution)

b. (5,-1)

So, x = 5 and y = -1 in y > - x + 3

= -1 > -5 + 3

= -1 > -2 (Correct Solution)

c. (2,0)

So, x = 2 and y = 0 in y > - x + 3

= 0 > -2 + 3

= 0 > 1 (Incorrect Solution)

d. (0,3)

So, x = 0 and y = 3 in y > - x + 3

= 3 > -0 + 3

= 3 > 3 (Incorrect Solution)

Final Answer -

The points which is NOT a solution to the inequality =

c. (2,0)

d. (0,3)

3 0
1 year ago
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