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3 years ago

In XYZ, XY=XZ Find the length of XY of XYZ if XY=2a, YZ=3a+1, andXZ=5a-12

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

5 0

Answer: XY = 8

Step-by-step explanation:

The diagram of the triangle XYZ is shown in the attached photo.

XY=XZ. This means that two sides of the triangle are equal. Two angles are also equal. It means that the triangle XYZ is an isosceles triangle.

Since XY=XZ, then

2a = 5a - 12

Subtracting 2a from both sides of the equation,

2a - 5a = 5a - 12 - 5a

-3a = -12

a = -12/-3

a = 4

Therefore, the length of XY is 2a = 2×4 = 8

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3 years ago

The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the

Leona [35]

Answer:

The first number is 16

The second number is 6

The third number is 64

Step-by-step explanation:

The information from the word problem are;

The count of the numbers in the sum = 3 numbers

The value of the sum of the three numbers = 86

The value of the third number = 4 × The value of the first number

The value of the first number = 10 + The value of the second

Let 'x' represent the first number, let 'y' represent the second number and let 'z' represent the third number, we have;

x + y + z = 86...(1)

z = 4 × x...(2)

x = y + 10...(3)

From equation (3), we get;

x = y + 10

∴ y = x - 10...(4)

Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;

x + y + z = 86

z = 4 × x = 4·x

y = x - 10

∴ x + y + z = x + (x - 10) + 4·x = 86

x + (x - 10) + 4·x = x + x - 10 + 4·x = 6·x - 10 = 86

6·x = 86 + 10 = 96

∴ x = 96/6 = 16

x = 16

From equation (2), we get;

z = 4 × x

∴ z = 4 × 16 = 64

z = 64

From equation (4), we get

y = x - 10

∴ y = 16 - 10 = 6

y = 6

Therefore; x = 16, y = 6, and z = 64

The numbers are 16, 6, and 64

8 0

3 years ago

Can you explain how to do this correctly?

iVinArrow [24]

8/x-7=7/2
16=7(x-7) cross multiply
16=7x-49
-7x=-49-16
-7x=-65 divides each side by -7
-7x/7=-65/7
X=65/7
Alternative form
X=92/7
Which is 1st options in your questions.

Hope this helps!

7 0

3 years ago

Would be the value of x

gladu [14]

Answer:

for the perimeter to be made into a equation it would take the equation

2(3x - 5) + 2(2x + 1)

And for the perimeter to equal 42 x would have to equal 5

Step-by-step explanation:

so first of all we have to find our equation to equal 42:

2(3x - 5) + 2(2x + 1) = 42

you then multiply 2 for both parentheses:

(3x * 2) + (-5 * 2) + (2x * 2) + (1 * 2) = 42

so its now:

6x -10 + 4x + 2 = 42

now your going to add variables to variables and numbers to numbers:

(6x + 4x) + ( -10 + 2) = 42

to get:

10x + (-8) = 42

Now your going to add 8 to both sides:

10x + (-8) = 42

+8 +8

Giving the equation:

10x = 50

now you divide both sides by 10 to get:

10x/ 10 = 50/10

x = 5

to solve you put 5 in place of the variable x:

2(3*5 - 5) + 2(2*5 + 1)

2(15 - 5) + 2(10 + 1)

20 + 22 = 42

So x equals 5 if the perimeter equaled 42

4 0

3 years ago

−6 < x + 1 ≤ 1 is what kind of linear inequality.

Darya [45]

-6 < x + 1 ≤ 1
-1 -1 -1
-7 < x ≤ 0
-7 < x or x ≤ 0
x > -7 or x ≤ 0

3 0

3 years ago