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3 years ago

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a rectangular photograph has an area of 104 square inches. if the width of the photograph is 5 inches less than its hight, find

the dimensions

1 answer:

Umnica [9.8K]3 years ago

5 0

Height is 13 inches. width is 8 inches. dimensions is 42 inches

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Two consecutive even integers have a product that is 1848. What are the integers?

yKpoI14uk [10]

Factors of 1848=1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924, 1848 X(x+2)=1848 X^2+2x=1848 X^2+2-1848=0 (X+44)(x-42)=0 X+44=0 X=-44 X-42=0 X=42 So x=-44,42

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3 years ago

A popcorn cup is in the shape of a cone

Serggg [28]

Answer: u multiply all those number that’s what the pi stands for I’m pretty sure

Step-by-step explanation:

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3 years ago

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)?

olga2289 [7]

Step $1$

<u>Find the slope of the given line</u>

Let

$A(-3,2)\ B(2,-1)$

slope mAB is equal to

$mAB=\frac{(y2-y1)}{(x2-x1)} \\ \\ mAB=\frac{(-1-2)}{(2+3)} \\ \\ mAB=-\frac{3}{5}$

Step $2$

<u>Find the slope of the line that is perpendicular to the given line</u>

Let

CD ------> the line that is perpendicular to the given line

we know that

If two lines are perpendicular, then the product of their slopes is equal to $-1$

so

$mAB*mCD=-1\\ mAB=-\frac{3}{5} \\ mCD=-\frac{1}{mAB} \\ mCD=\frac{5}{3}$

Step $3$

<u>Find the equation of the line with mCD and the point (3,0)</u>

we know that

the equation of the line in the form point-slope is equal to

$y-y1=m(x-x1)\\\\ y-0=\frac{5}{3} *(x-3)\\\\ y=\frac{5}{3} x-5$

Multiply by $3$ both sides

$3y=5x-15$

$5x-3y=15$

therefore

the answer is

the equation of the line that is perpendicular to the given line is the equation $5x-3y=15$

4 0

3 years ago

Read 2 more answers

a business has recently made some upgrades to their shop that cost them $1,200. Normally, this business has a running cost of $5

DedPeter [7]

Answer:

9.23 hours to recover the money spent.

Step-by-step explanation:

50+80=130

130x 9=1170

130x9.23=1200

5 0

3 years ago

2х5y-3z-=14<br> x-2y+=-12<br> -x+ Зу-2z =13

lukranit [14]

Answer:

x = -34/3, y = 1/3, and z = -35/3

Step-by-step explanation:

2х+5y-3z-=14 <u>let's call this </u><u>equation 1.</u>

x-2y=-12 <u>let's call this </u><u>equation 2.</u>

-x+Зу-2z =13 <u>let's call this </u><u>equation 3.</u>

<u>USING </u><u>EQUATION 1</u><u> AND </u><u>EQUATION 3</u><u>.</u>

2х+5y-3z-=14 (EQUATION 1)

-x+Зу-2z =13 (EQUATION 3)

<u>LET'S GET RID OF </u><u>z</u><u>, BY MAKING THE COEFFICIENT OF </u><u>z</u><u> IN THE TWO EQUATION THE SAME. WE WILL MULTIPLY </u><u>EQUATION 1</u><u> BY </u><u>2</u><u> AND </u><u>EQUATION 3</u><u> BY </u><u>3</u><u>.</u>

2х+5y-3z-=14 (EQUATION 1) * 2

-x+Зу-2z =13 (EQUATION 3) * 3

4х+10y-6z-=28 <u>let's call this </u><u>equation 4.</u>

-3x+9у-6z =39 <u>let's call this </u><u>equation 5.</u>

<u>TO GET RID OF </u><u>z</u><u>, WE WILL HAVE TO SUBTRACT </u><u>EQUATION 5</u><u> FROM </u><u>EQUATION 4</u><u> PLEASE TAKE NOTE OF THE SIGNS (-) (+).</u>

4х+10y-6z-=28 (EQUATION 4)

- (-3x+9у-6z =39) (EQUATION 5)

(4x - 3x) + ((+10y) - (+9y)) + ((-6z) - (-6z)) = (28 - 39)

x + y + 0 = -11

x + y = -11 <u>let's call this </u><u>equation 6.</u>

<u>USING </u><u>EQUATION 2</u><u> AND </u><u>EQUATION 6</u><u>, LET'S FIND </u><u>x</u><u> AND </u><u>y</u><u>.</u>

x-2y=-12 (EQUATION 2)

x + y = -11 (EQUATION 6)

<u>x</u><u> has the same coefficient in both equations, which is </u><u>1</u><u>. Let's get rid of </u><u>x</u><u> so we can find the value of </u><u>y</u><u>.</u>

<u>We will subtract </u><u>equation 6</u><u> from </u><u>equation 2</u><u>. Take note of the signs.</u>

x-2y=-12 (EQUATION 2)

- (x + y = -11) (EQUATION 6)

(x - x) + ((-2y) - (+y)) = ((-12) - (-11))

0 + -3y = -1

-3y = -1

<u>Divide both sides by </u><u>-3</u><u>.</u>

-3y/-3 = -1/-3

y = 1/3

<u>LET'S SUBSTITUTE THE VALUE OF </u><u>y</u><u> INTO</u><u> EQUATION 2</u><u> TO GET THE VALUE OF </u><u>x</u><u>.</u>

x-2y=-12 (EQUATION 2)

x-2(1/3)=-12

x -2/3 = -12

<u>Add </u><u>2/3</u><u> to both sides.</u>

x -2/3 + (2/3) = -12 + (2/3)

x + 0 = -34/3

x = -34/3

<u>LET'S SUBSTITUTE THE VALUES OF </u><u>x</u><u> and </u><u>y</u><u> INTO</u><u> EQUATION 1</u><u> TO GET THE VALUE OF </u><u>z</u><u>.</u>

2х+5y-3z-=14 (EQUATION 1)

2(-34/3)+5(1/3)-3z-=14

-68/3 + 5/3 - 3z = 14

-21 - 3z = 14

<u>Add </u><u>21</u><u> to both sides.</u>

-21 + (21) - 3z = 14 + (21)

0 - 3z = 35

-3z = 35

<u>Divide both sides by </u><u>-3</u><u>.</u>

-3z/-3 = 35/-3

z = -35/3 <em>or</em>

Therefore, x = -34/3, y = 1/3, and z = -35/3

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6 0

3 years ago