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1 year ago

TIME REMAINING

Mathematics

1 answer:

ollegr [7]1 year ago

7 0

Answer:

(b) (x -10)(x +10)

Step-by-step explanation:

The factorization of the difference of squares is a special form:

a² -b² = (a -b)(a +b)

<h3>Application</h3>

Your expression is recognizable as the difference of squares:

x² -100 = x -10²

Using the above form, the factorization is ...

= (x -10)(x +10) . . . . . . . . matches the second choice

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Jack had 4 hours of school. He spent 45 minutes in the library and 12 hour on a science lecture and had a lunch break of 25 minu

andre [41]

Answer:

$\dfrac{10}{4} \ hour$

Step-by-step explanation:

Given that :

Jack had 4 hours of school.

He spent 45 minutes in the library

1/2 hour on a science lecture and;

had a lunch break of 25 minutes

The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.

In order to do that, we will have to convert the minutes into hours,

we all know that; 60 minutes = 1 hour.

Then,

45 minutes = (45/60)hour = 3/4 hour

25/60 minutes = 1/4 hour

Therefore, the amount of time left for the school to get over is:

= $4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})$

= $\dfrac{16-(3+2+1)}{4}$

= $\dfrac{16-6}{4}$

= $\dfrac{10}{4} \ hour$

7 0

2 years ago

What is equivalent to 9 3/4?

Nata [24]

Step-by-step explanation:

We need to say that $9^{3/4}$ is equivalent to what.

We know that, (3)² = 9

So,

$9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}$

We can write $3^{3/2} =3\times 3^{1/2}$

And $3^{1/2}=\sqrt{3}$

So,

$3\times 3^{1/2}=3\sqrt{3}$

So, $9^{3/4}$ is equivalent to $3\sqrt{3}$ .

Hence, this is the required solution.

6 0

2 years ago

PLEASE HELP!!!! IN NEED OF IT

prisoha [69]

Answer:

Below in bold.

Step-by-step explanation:

This is a regular polygon so all sides are congruent, therefore:

The perimeter of the polygon = 6*34 = 204 units.

We can divide the polygon into 6 conguent triangle with height 30 and base 34.

So area of 1 triangle = 1/2*34*30 = 510.

So area of the polygon = 6 * 510 = 3060 unit^2.

Perimeter of the polygon = 6*34 = 204 units.

6 0

2 years ago

You have $7000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want

Arlecino [84]

Answer:

1857.12 square meters

Step-by-step explanation:

Let L be the length of the rectangle and 'W' be the width

Perimeter = $2L + 2W + 2W$

The fencing material costs $30 per meter.

The material for the partitions costs $25 per meter

$cost=30(2L + 2W) +25( 2W)\\60L+60W+50W\\60L +110W$

$7000=60L+110W$

Solve for L

$7000=60L+110W\\7000-110W= 60L\\L=\frac{700}{6} -\frac{11}{6} W$

Area = length times width

$( \frac{700}{6} -\frac{11}{6} W)(W)\\A(W)=\frac{700}{6}W -\frac{11}{6} W^2$

Now take derivative and set it =0

$A(W)=\frac{700}{6}W -\frac{11}{6} W^2\\A'(W)=\frac{700}{6} -\frac{22}{6} W$

set the derivative =0 and solve for W

$0=\frac{700}{6} -\frac{22}{6} W\\\frac{700}{6}=\frac{22}{6} W\\W= 31.8$

So width = 31.8 that gives maximum area

$L=\frac{700}{6} -\frac{11}{6} (31.8)=58.4$

$Area = length \cdot width = 31.8 \cdot 58.4= 1857.12$ square meter

4 0

3 years ago

The length of a rectangle is one more than five times the width. Express the perimeter of the rectangle in

Artemon [7]

Step-by-step explanation:

length = 5×width + 1

perimeter = 2×length + 2×width =

= 2×(5×width + 1) + 2×width =

= 10×width + 2 + 2×width = 12×width + 2

7 0

2 years ago