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3 years ago

The sum of two numbers is 59 and the difference is 15 . what are the numbers?

1 answer:

5 0

Write a system of equation based on the number
For an instance, the two numbers are a and b.
"The sum of two numbers is 59" can be written as follows.
⇒ a + b = 59 (first equation)
"The difference is 15" can be written as follows.
⇒ a - b = 15 (second equation)

Solve the system of equation by elimination/substitution method.
First, eliminate b to find the value of a.
a + b = 59
a - b = 15
--------------- + (add)
2a = 74
a = 74/2
a = 37

Second, substitute 37 as a in one of the equations
a + b = 59
37 + b = 59
b = 59 - 37
b = 22

The numbers are 37 and 22

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PLS ANSWER WILL GIVE 10 PTS

Whitepunk [10]

<h3>Answer: b) 18 cm </h3>

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Work Shown:

Since the parallelogram has perpendicular diagonals, this means that we're dealing with a rhombus. A rhombus has all four sides equal to one another.

One diagonal is bisected, or cut in half, to form the smaller pieces of length (150/x) + 10 and x-10. Set these two expressions equal to each other and solve for x

(150/x) + 10 = x-10

1500/x = x-10-10

1500/x = x-20

1500 = x(x-20)

1500 = x^2-20x

0 = x^2-20x-1500

x^2-20x-1500 = 0

(x-50)(x+30) = 0

x-50 = 0 or x+30 = 0

x = 50 or x = -30

We'll ignore the negative x value as it leads to a negative length which doesn't make sense.

If x = 50, then

x-10 = 50-10 = 40
(150/x)+10 = (150/50)+10 = 30+10 = 40

Each piece of this diagonal is 40 cm long.

The two smaller pieces combine to 40+40 = 80, which is the length of one of the diagonals. If this was the shorter diagonal, then 80 would be listed as part of the answer choices. However, 80 is not one of the answers.

-------------

Note how the two diagonals of the rhombus cut the figure into four right triangles.

Each right triangle has one known leg to be 40 and an unknown leg of y. The hypotenuse is 164/4 = 41 since we divide the perimeter by the four equal sides of the rhombus.

We'll use the pythagorean theorem to find the value of y

a^2 + b^2 = c^2

40^2 + y^2 = 41^2

1600 + y^2 = 1681

y^2 = 1681-1600

y^2 = 81

y = sqrt(81)

y = 9

This represents half of the other diagonal, so the full length of this other diagonal is 2*9 = 18 cm.

7 0

3 years ago

Read 2 more answers

PLEASE HELP its math

xxMikexx [17]

Answer:

y = 3x + 6

Step-by-step explanation:

We are given a line.

We know this line is parallel to the line y=3x+2, and passes through (1, 9).
We want find the equation of this line.

Parallel lines have the same slopes.

So, let's find the slope of y=3x+2.

The line is written the format y=mx+b, where m is the slope and b is the value of y at the y intercept.

As 3 is in the place of where m (the slope) is, the slope of the line is 3.

It is also the slope of the line parallel to it.

We should write the equation of the line parallel y=3x+2 in slope-intercept form as well, however, before we do that, we can write the line in point-slope form, and then convert it to slope-intercept form.

Point-slope form is given as $y-y_1=m(x-x_1)$ , where m is the slope and $(x_1,y_1)$ is a point.

We can substitute 3 as m in the formula, as we know that is the slope of the line

$y-y_1=3(x-x_1)$

Recall that we were given the point (1, 9), which also belongs to (it passes through) the line.

Therefore, we can use its values in the formula.

Substitute 1 as $x_1$ and 9 as $y_1$ .

y - 9 = 3(x-1)

We can now convert the equation into slope intercept form.

Notice how y is by itself in slope-intercept form; this means we'll need to solve the equation for y.

Start by distributing 3 to both x and -1.

y - 9 = 3x - 3

Now add 9 to both sides.

y = 3x + 6

5 0

1 year ago

I need help with question 13 pleaseee im struggling

Sergio039 [100]

You could create a equation such below:

y= 50x+20

Next, put 12 in both y=50x+20 and y=15x+80

Then, y=50x+20=50 · 12+ 20=600+20= 620

y=15x+80=15 · 12+ 80=180+80= 260

Compare these two, it's clearly that the second one is cheaper

Answer: The camera in the second store is cheaper.

4 0

3 years ago

Some cones are mathematically similar. Two of the cones have radii in the ratio 2:3. Write down the ratio of their masses.

xenn [34]

Answer:

8:27.

Step-by-step explanation:

The ratio of their masses will be equal to the ratio of their volumes, assuming they are both of the same uniform density.

So it will be 2^3:3^3

= 8:27.

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2 years ago

Given: ∠D and ∠B are right angles DC || AB Prove: △ADC ≅ △CBA

raketka [301]

Since angle CDA + angle ABC = 180 then DC is Parallel to AB by transversal of parallel line theorem c-pattern for co-interior angles. to help visualize it draw it

4 0

3 years ago