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anygoal [31]
3 years ago
15

The sum of two numbers is 65 and the difference is 13.what are the numbers?

Mathematics
1 answer:
Karolina [17]3 years ago
3 0

Answer: 26 and 39

Step-by-step explanation:

Let the numbers be x and y . Also , let us take x as the larger number.

From the first statement :

x + y = 65 ...................... equation 1

From the second statement :

x - y = 13 ....................... equation 2

Solving the system of linear equation by elimination method. Let us eliminate y first , then we need to add the two equations to eliminate y , the equation then becomes

2x = 78

x =39

substitute x = 39 into equation 1 , that is

39 + y = 65

y = 65 - 39

y = 26

Therefore , the numbers are 26 and 39

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Samuel purchased 2 1/2lb of nuts for $10.50.
aalyn [17]

Answer:

22.05

Step-by-step explanation:

21/2 has 5 halves

10.5 divided by 5= 2.1

2.1= 1/2 2.1 x 10 = 21

2.1 / 2 = 1.05

21 + 1.05= 22.05

6 0
2 years ago
Read 2 more answers
Give two points with integer coordinates that have a slope of 10/7 between them
Fittoniya [83]

Answer:

(0,0) and (7,10)

Step-by-step explanation:

recall that the slope - intercept  form of a linear equation can be given as

y = mx + b

where m = slope and b = y intercept

in our case, we are given that slope, m = 10/7, hence our equation becomes

y = (10/7) x + b

since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.

We pick b = 0, hence the equation simplifies to:

y = (10/7) x  ----- eq 1

we can see immediately that if x = 0, y must also = 0

proof if x = 0:

y = (10/7)(0) =0

since 0 is an integer, then (0,0) must be the first point.

we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:

y = (10/7) x 7

y = 10

hence (7,10) is the second point.

7 0
3 years ago
Which of the following is a scaled copy of figure A.
bonufazy [111]

Answer:

D

Step-by-step explanation:

D is 2x bigger than A, therefore is a scaled copy.

7 0
2 years ago
Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4
Alik [6]

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

(x-h)^2+(y-k)^2=r^2

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

8 0
3 years ago
Describe how to determine which side of the boundary line should be shaded
iogann1982 [59]
Hello Bri,

If you are talking about a boundary line on a coordinate plane, the best way to determine which side to shade is to start by selecting a coordinate point (x, y) that is not on the line.

Then, substitute those values into your inequality. Simplify the inequality. If the resulting statement is true, then shade the side with your point. If the resulting statement is false, then shade the other side.

Testing a point like this shows the side of the inequality that is the solution and needs to be shaded.

Good luck!
8 0
3 years ago
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