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dlinn [17]
3 years ago
8

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8.

Mathematics
1 answer:
AlladinOne [14]3 years ago
8 0

Answer:

(1,6) & (7,0)

Step-by-step explanation:

y = -x + 7

y = -0.5(x - 3)² + 8

To solve the system, solve these two equations simultaneously

-x + 7 = -0.5(x - 3)² + 8

-x + 7 = -0.5(x² - 6x + 9) + 8

-x + 7 = -0.5x² + 3x - 4.5 + 8

0.5x² - 4x + 3.5 = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1, 7

y = -1 + 7 = 6

y = -7 + 7 = 0

(1,6) (7,0)

Since the system has two distinct solutions, the line and the curve meet at two distinct poibts9: (1,6) & (7,0)

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(Picture) MULTIPLYING MONOMIALS AND BINOMIALS
motikmotik

Answer:

Second option: 81y^4 - 16x^2, the difference of squares

Step-by-step explanation:

(9y^2-4x)(9y^2+4x) is a special product named difference of squares, then we can apply this formula:

(a-b)(a+b)=a^2-b^2, with a=9y^2 and b=4x, then:

(9y^2-4x)(9y^2+4x)=(9y^2)^2 - (4x)^2

(9y^2-4x)(9y^2+4x)=(9)^2 (y^2)^2 - (4)^2 (x)^2

(9y^2-4x)(9y^2+4x)=81y^(2*2) - 16x^2

(9y^2-4x)(9y^2+4x)=81y^4 - 16x^2


7 0
3 years ago
Find the difference between 7 1/2 and 2 3/4
NNADVOKAT [17]

Answer:

4\frac{3}{4} or 4.75

Step-by-step explanation:

first we're going to convert the number into improper fractions.

7\frac{1}{2}= \frac{15}{2} and 2\frac{3}{4}= \frac{11}{4}

For subtracting it is suitable to adjust both fractions to an equal denominator, so we're going to multiply \frac{15}{2}x2, it'll equal the same number.

So now we have \frac{30}{4}-\frac{11}{4}, 30-11= 19.

\frac{19}4} simplified is, 4\frac{3}{4}.

As you can see I also added 4.75 as an answer, that's if the answer must be a decimal.

I hope this helps you!

3 0
3 years ago
Rudy has been paying an annual homeowners insurance premium of $1,106.30 ($0.37 per $100 of value) since
Luden [163]

Answer:

c. $1,291.30

Step-by-step explanation:

Calculation what will his new annual homeowners insurance premium be

Insurance premium= [$1,106.30+ ($0.37/ $100*$50,000)]

Insurance premium=$1,106.30+$185

Insurance premium=$1,291.30

Therefore what his new annual homeowners insurance premium will be is $1,291.30

5 0
3 years ago
Can someone plz help me with this one problem pls I really need to get to and 85 !!
leonid [27]

Answer:

I think it’s  28.3

Step-by-step explanation:

Sorry If I’m wrong

4 0
3 years ago
Read 2 more answers
What is an algebraic equation for four times a number y is sixteen
Len [333]

4y=16

y is the variable. If you were to solve the equation you would write the equation as 4(4)=16.

3 0
3 years ago
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