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2 years ago

Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder.

Mathematics

1 answer:

jeka57 [31]2 years ago

7 0

Answer:

Step-by-step explanation:

Let n be unknown divisor and a be the same remainder, then

$63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a$

Subtract a from all equalities:

$63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n$

Subtract them:

$63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n$

The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.

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Monica bought a sweater for $48.00. A week later the sweater went on sale for 25% off the original price. If Monica needed to pa

IRINA_888 [86]

Answer:

A $12.84

Step-by-step explanation:

Sweater was originally $48.00 before tax. $48.00 x 7% tax rate (.07) = $3.36 in tax

So the sweater originally would've cost $48.00 + $3.36 = $51.36

The sale price was 25% off the $48.00. $48.00 x 25% (.25) = $12.00

Then you subtract the $12.00 from the $48.00 to get the new price of $36.00

Now that's before tax, so $36.00 x 7% tax rate (.07) = $2.52 in tax

So the sweater would cost on sale $36.00 + $2.52 = $38.52

To figure out how much she would've saved you subtract the sale price & tax from the original price & tax $51.36 - $38.52 = $12.84

8 0

1 year ago

Find the difference using fraction bars or a paper and pencil. Write your answer in simplest form.

nasty-shy [4]

First, find the lowest common denominator. That is 12. You only have to change 3/4 into 12ths.

3/4 = 9/12

11/12 – 9/12 = 2/12 = 1/6

5 0

2 years ago

Read 2 more answers

Solve x2 + 1/2x +1/16=4/9

kolezko [41]

<u>Answer:</u>

x = 0.417 or x = -0.917

<u>Step-by-step explanation:</u>

We are given the following expression and we are to solve it for the variable x:

$x ^2 + \frac { 1 } { 2 } x + \frac { 1 } { 1 6 } = \frac { 4 } { 9 }$

We will find the least common multiple of 2. 6 and 9:

$x^2 \times 144 +\frac{1}{2}x \times 144 +\frac{1}{16} \times 144 = \frac{4}{9} \times 144$

Simplifying it to get:

$144x^2+72x+9=64$

$144x^2+72x+9-64=0$

$144x^2+72x-55=0$

Using the quadratic formula to solve for x:

$x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}$

$x=\frac{-72 \pm\sqrt{72^2-4(144)(-55)} }{2a}$

$x=\frac{5}{12}$ or $0.417$

$x=-\frac{11}{12}$ or $-0.917$

3 0

3 years ago

Does anyone know how to do this?

Elanso [62]

~Shoto Todoroki here~

Answer:

( n − 2 ) × 180

Step-by-step explanation:

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

hope this helps :))

5 0

2 years ago

Find the volume and area for the objects shown and answer Question

klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of the given solids.

$\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2$

$\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\$

$\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}$

$\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}$

$SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}$

6 0

2 years ago