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2 years ago

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Mala ran 30 laps in week one and will increase the number of laps she runs by 2 each week. Coby runs 16 laps in week one and wil

l increase the number of laps he runs by 5 each week. Assuming the pattern shown in this table continues, in how many weeks will Coby be running more laps each week than Mala?

1 answer:

matrenka [14]2 years ago

7 0

The equations are 30+2x and 16+5x. i plug random numbers into x until you fint the correct answer. the answer is 5.

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a photo collage consists of seven equal sized square photo arranged in a row to form a rectangle if the total area of the colleg

Keith_Richards [23]

Answer:

Step-by-step explanation:

I have attached a written explanation to help :).

Let's say each side of the square = $x$

If we put 7 squares in a row to make the rectangle,

length of the rectangle = $7x$

Area of a rectangle = length multiplied by width

Area of rectangle = $7x$ multiplied by $x$ = $7x^2$

We are also told that the total area = 567

So $7x^2 = 567$

Now solve for $x$ .

Divide both sides by 7.

$\frac{7x^2}{7} = \frac{567}{7}$

$x^2 = 81$

Then square root both sides to find $x$

$x = \sqrt{81}$ = 9

Finally, the question asks to find the length of the collage which we said was $7x$ and we know $x = 9$

Length of collage = $7x = 7$ multiplied by $9$ = ?

7 0

2 years ago

Prove algebraically that the recurring decimal 0.472 can be written as<br> 17<br> 36

Katen [24]

Given:

The recurring decimal is $0.47\overline{2}$ .

To prove:

Algebraically that the recurring decimal $0.47\overline{2}$ can be written as $\dfrac{17}{36}$ .

Proof:

Let,

$x=0.47\overline{2}$

$x=0.472222...$

Multiply both sides by 100.

$100x=47.2222...$ ...(i)

Multiply both sides by 10.

$1000x=472.2222...$ ...(ii)

Subtract (i) from (ii).

$1000x-100x=472.2222...-47.2222...$

$900x=425$

Divide both sides by 900.

$x=\dfrac{425}{900}$

$x=\dfrac{17}{36}$

So, $0.47\overline{2}=\dfrac{17}{36}$ .

Hence proved.

8 0

2 years ago

What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot

ExtremeBDS [4]

Answer:

$18\sqrt2$

Step-by-step explanation:

To simplify:

$2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }$

First of all, let us write 18 and 162 as product of prime factors:

$18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}$

The pairs are underlined as above.

While taking roots, only one of the numbers from the pairs will be chosen.

Now, taking square roots.

$\sqrt{18} =3 \sqrt2$

$162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2$

So, the given expression becomes:

$2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}$

So, the answer is:

$18\sqrt2$ or 18 StartRoot 2 EndRoot

7 0

2 years ago

What do the differences between the points (as shown on the graph) represent? On a coordinate plane, point B is at (2, 7) and po

raketka [301]

Answer:

StartFraction 7 over 2 EndFraction can be used to find the unit rate if one divides 7 by 2 and compares the result to 1

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

B(2, 7) and D(4, 14)

substitute the values

$m=\frac{14-7}{4-2}$

$m=\frac{7}{2}$

The unit rate is

$m=\frac{3.5}{1}$

therefore

StartFraction 7 over 2 EndFraction can be used to find the unit rate if one divides 7 by 2 and compares the result to 1

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2 years ago

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A pair of sunglasses is on sale for $26. The original price of the sunglasses was $40. What percent of the original price is the

GarryVolchara [31]

If the glasses were origanum 40, and were on sale for 26,we minus them from eachother to find out how much money was saved. So 40-26= 14, if $14 was saved we put 14 over the original price and times it buy 100 14/40x100= 35% So 35% was saved. 100-35= 65. Therefore 65% of the original price was paid and 35% was saved.

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2 years ago

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