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3 years ago

Find two consecutive even integers such that five times the smaller integer is ten more than three times the larger integer.

Mathematics

1 answer:

quester [9]3 years ago

8 0

5n = 3(n + 2) + 10
5n = 3n + 16
12n = 16
n = 8

8 is smaller integer and 10 is the larger.

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Negative nine is greater than the sum of fifteen and two times a number.

Ugo [173]

Answer:

-9>2x+15

Step-by-step explanation:

6 0

3 years ago

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Determine whether PQ and UV are parallel,

lys-0071 [83]

Answer:

The answer is below

Step-by-step explanation:

The slope of a line (m) is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

Two lines are parallel if they have the same slope and perpendicular if the product of their slope is -1.

$Slope\ of\ PQ=\frac{1-(-2)}{9-(-3)}=\frac{1}{4} \\\\Slope\ of\ UV=\frac{-2-6}{5-3}=-4$

Since the product of their slope is -1, they are perpendicular

$Slope\ of\ PQ=\frac{1-7}{2-(-10)}=-\frac{1}{2} \\\\Slope\ of\ UV=\frac{1-0}{6-4}=\frac{1}{2}$

Since the slope is not the same or product of their slope is not -1, they are neither parallel or perpendicular

$Slope\ of\ PQ=\frac{8-1}{9-1}=\frac{7}{8} \\\\Slope\ of\ UV=\frac{8-1}{2-(-6)}=\frac{7}{8}$

Since the slopes are the same, they are parallel

$Slope\ of\ PQ=\frac{3-0}{9-(-4)}=\frac{3}{4} \\\\Slope\ of\ UV=\frac{6-(-3)}{8-(-4)}=\frac{3}{4}$

Since the slopes are the same, they are parallel

$Slope\ of\ PQ=\frac{1-2}{0-(-9)}=-\frac{1}{9} \\\\Slope\ of\ UV=\frac{-1-8}{-2-(-1)}=9$

Since the product of their slope is -1, they are perpendicular

6 0

3 years ago

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The diameter of a circleis 170inches. The circle has two chords of length 26 inches. What is the distance from each chord to the

vivado [14]

Answer:

Hence the Distance from each other chord to center is 84 inches.

Step-by-step explanation:

Given:

Diameter =170 inches

2 chords with each length =26 inches.

To Find:

Distance of each chord from the circle.

Solution:

Consider a circle with center as O ,

And OA as Radius

(Refer the attachment)

So as chord be BC and DE respectively with each of 26 length

They have both same length so they should located at same distance from center but as mirror images of each other opposite side of the diameter as shown in fig.

Hence we can calculate for one chord as follows:

Radius =diameter/2=170/2=85

r=85 inches.

Let distance from center t o chord be 'x'

Now draw perpendicular to chord BC with F as midpoint for chord and join endpoints of chord to the center which forms triangle OFC as right angled triangle,

By using pythagorus Theorem

$OC^2=FC^2+OF^2$