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3 years ago

Jose is 7 years older than Kori. In 4 years the sum of their ages will be 75. How old is Jose now?

Mathematics

1 answer:

Licemer1 [7]3 years ago

4 0

Answer:

Step-by-step explanation:

Koris current age = x

Josephs current age = 7 + x

Koris age after four years = x + 4

Josephs age after four years = 7 + 4 + x = 11 + x

In 4 years the sum of their ages will be 75.

So, (x + 4) + (11 + x) = 75

= 2x + 15 = 75

2x = 75 - 15

x = 60/2 = 30

Therefore koris current age = 30

Josephs current age = 30 + 7 = 37

Hope this helps . Have a nice day!

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Use the number line to represent. -4 1/2 + 3 1/4. what is the sum?

dlinn [17]

Answer:

$\displaystyle A+B=-\frac{5}{4}$

Step-by-step explanation:

The Number Line

Let's call

$\displaystyle A=-4\frac{1}{2}$

$\displaystyle B=+3\frac{1}{4}$

Both numbers are given as mixed fractions. Let's convert them to improper fractions:

$\displaystyle A=-4\frac{1}{2}=-(4+\frac{1}{2})=-\frac{8+1}{2}=-\frac{9}{2}$

$\displaystyle B=3\frac{1}{4}=3+\frac{1}{4}=\frac{12+1}{4}=\frac{13}{4}$

The decimal values are A = -9/2=-4.5, B=13/4 = 3.25

Now represent the points in the number line. See the image below

Finally, calculate their sum:

$\displaystyle A+B=-\frac{9}{2}+\frac{13}{4}$

$\displaystyle A+B=-\frac{18}{4}+\frac{13}{4}=\frac{-18+13}{4}$

$\boxed{\displaystyle A+B=-\frac{5}{4}}$

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3 years ago

find the equation of a line parallel to y-5x=10 that passes through the point (3,10). answer in slope intercept form

vichka [17]

The answer is: y=-5x+25

5 0

4 years ago

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How do you solve u=xk-y for x

Lynna [10]

u-y = xk

(u-y)÷k = x

This is the answer.

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write an equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

dimaraw [331]

The equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is $y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

<h3>Solution:</h3>

Given that we have to write equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4)

Let us first find the slope of given line AB

The slope "m" of the line is given as:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here the given points are A(-2,2) and B(5,4)

$\text {Here } x_{1}=-2 ; y_{1}=2 ; x_{2}=5 ; y_{2}=4$

$m=\frac{4-2}{5-(-2)}=\frac{2}{7}$

Thus the slope of line with given points is $\frac{2}{7}$

We know that product of slopes of given line and slope of line perpendicular to given line is always -1

$\begin{array}{l}{\text {slope of given line } \times \text { slope of perpendicular bisector }=-1} \\\\ {\frac{2}{7} \times \text { slope of perpendicular bisector }=-1} \\ \\{\text {slope of perpendicular bisector }=\frac{-7}{2}}\end{array}$

The perpendicular bisector will run through the midpoint of the given points

So let us find the midpoint of A(-2,2) and B(5,4)

The midpoint formula for given two points is given as:

$\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { midpoint } \mathrm{m}(x, y) \text { is given as }$

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Substituting the given points A(-2,2) and B(5,4)

$m(x, y)=\left(\frac{-2+5}{2}, \frac{2+4}{2}\right)=\left(\frac{3}{2}, 3\right)$

Now let us find the equation of perpendicular bisector in point slope form

The perpendicular bisector passes through points (3/2, 3) and slope -7/2

The point slope form is given as:

$y - y_1 = m(x - x_1)$

$\text { Substitute } \mathrm{m}=\frac{-7}{2} \text { and }\left(x_{1}, y_{1}\right)=\left(\frac{3}{2}, 3\right)$

$y - 3 = \frac{-7}{2}(x - \frac{3}{2})\\\\y - 3 = \frac{-7x}{2}+ \frac{21}{4}$

Thus the equation in point-slope form for the perpendicular bisector of the segment with endpoints at A(-2,2) and B(5,4) is found out

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4 years ago

A roller coaster starts from a desk at an elevation of 20 feet above the ground on the first Hill and corn 78 ft and then it dro

AlekseyPX

Answer:

6 ft above ground.

Step-by-step explanation:

The roller coaster starts from an elevation of +20 feet from the ground.

Now, it first corns 78 ft, then drops 85 ft.

So, the final elevation will be (20 + 78 - 85) = 13 feet above the ground on the second hill.

Again, it climbs 103 ft. and drops 110 ft. and finally his elevation will be = 13 + 103 - 110 = 6 ft above ground. (Answer)

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4 years ago