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2 years ago

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A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two

congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.

1 answer:

yarga [219]2 years ago

7 0

Answer:

A is TRUE (44 in²*2=88 in²)

B is FALSE x(x-3)=88 (the rectangle) or x(x-3)/2=44 (the triangle)

C is TRUE if x(x-3)=88==>x²-3x-88=0

D is TRUE :

x²-3x-88=0

Δ=9+4*88=361=19²

==>x= 11 or x=-8 (excluded for <0)

E is FALSE for 11*4≠88

Step-by-step explanation:

correct me if i am wrong

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

Within the United States, approximately 11.25% of the population is left-handed. Of the males, 12.6% are left-handed, compared t

GuDViN [60]

Answer:

There is a 45.05% probability that the selected person is a right-handed female.

Step-by-step explanation:

We have these following probabilities

A 50% probability that a person is a male

A 50% probability that a person is a female.

A 12.6% probability that a male is left-handed.

A 9.9% probability that a female is left-handed.

If a person is selected at random, to find the probability that the selected person is a right-handed female, one would compute:

50% are female.

9.9% of the females are left-handed, so 100-9.9 = 90.1% of the females are right handed.

So

$P = 0.5*0.901 = 0.4505$

There is a 45.05% probability that the selected person is a right-handed female.

3 0

2 years ago

The mayor of Gilbert, AZ, randomly selects 300 of its residents for a survey while the mayor of Camp Verde, AZ, randomly selects

Ostrovityanka [42]

I don’t think you wrote it correct but anyway I think the answer to your question is statement number 1

5 0

2 years ago

Read 2 more answers

During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

<u>Interpretation 1:</u> Number of groups if there are 5 students in each

<u>Interpretation 2:</u> Number of students in each group if there are 5 groups

<u>Solving the quotient</u>

$Quotient = \frac{60}{5}$

$Quotient = 12$

<u>For Interpretation 1:</u>

The quotient means: 12 groups

<u>For Interpretation 2:</u>

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

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1 year ago

Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method. Note: interest rate is given as a

inn [45]

Unpaid balance 283.63-60=223.63
Finance charge
223.63*(0.015/12)=3.35
New balance
223.63+3.35+51.36==278.34

5 0

1 year ago