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Evgen [1.6K]
3 years ago
13

Refer to this question below Thank You.

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0
Let's solve this problem using substitution.  Given that x-y=8, x = 8 + y.
(Then x^2 = 64 + 16y + y^2)
This other equation is (x-2)^2 + (y-1)^2 = 25.

Easier to substitute 8 + y for x in (x-2)^2:

(8 + y - 2)^2 + (y-1)^2 = 25

(6 + y)^2 + (y-1)^2 = 25
36 + 12y + y^2 + y^2 - 2y + 1 = 25

Re-writing this in descending powers of y:

2y^2 + 10y + 36 + 1 = 25

Then 2y^2 + 10y - 12 = 0

Reduce by division by 2:  y^2 + 5y - 6 = 0   =   (y+3)(y+2) = 0

Then y=-3 and y=-2.       From each of these we get x:  x = 8 + y

So x = 8 - 3 = 5 and x = 8 - 2 = 6.       There are common solutions.  

Try (5, -3) and (6, -2).  Do these points satisfy both of the given equations?  If they do, you've shown that we have common solutions.
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Cindy and Giovanni plan to make spaghetti sauce. Cindy needs 4 and three-fourths pounds of tomatoes for her recipe. Giovanni nee
Flauer [41]

(4 3/4) + (5 3/4) = (4 + 5) + (3/4 + 3/4)

= 9 + 2×(3/4)

= 9 + 3/2

= 10 1/2 . . . . pounds of tomatoes

7 0
2 years ago
Read 2 more answers
Answer 16., 17., and 18., Text me after you have..!
musickatia [10]
I'm not quite sure how I'd attach a picture of my working so I'll explain the method.

16) I multiplied both 3.5 and 40 by ten so that I could divide them to find the number of servings. 35 divided by 400 is 11 remainder 15. If you then divide the remainder by 10 you get 11 servings and 1.5 ounces left over.

17) if you add up 26, 17, and 37 inches you get 80 inches, or just over 6 feet. Hence, he should buy an 8 foot length rod in order to have as little waste as possible.

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4 0
2 years ago
Solve for x. Please help quick, it’s my last question for my test
Sladkaya [172]

Answer:

x = 9

Step-by-step explanation:

84 + (7x + 5) + (180 - (17x-1)) = 180

84 + 7x + 5 + (181 - 17x) = 180

270 + (-10x) = 180

90 = 10x

x = 9

3 0
2 years ago
Use the identity (x+y)(x^2−xy+y^2)=x^3+y^3 to find the sum of two numbers if the product of the numbers is 28, the sum of the sq
lara31 [8.8K]

Step-by-step explanation:

We have xy = 28, x² + y² = 65 and x³ + y³ = 407.

Since (x + y)(x² - xy + y²) = x³ + y³,

x + y = (x³ + y³)/(x² + y² - xy)

= (407) / [(65) - (28)]

= 407 / 37

= 11.

Hence the sum of the numbers is 11.

4 0
2 years ago
Read 2 more answers
Please help me out! :)
skad [1K]
3x-11=x+23
-x -x
2x-11=23
+11 +11
2x=34
x=17

3(17)-11 17+23
=40 =40

explanation ;
you would equal them because they are congruent . & you substitute x for 17 in each equation to find out the degrees of both of the angles :)

8 0
3 years ago
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