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3 years ago

Solve (1,21),(2,6);y=a(x+1)^2 +k

Mathematics

1 answer:

slamgirl [31]3 years ago

5 0

Put the coordinates of the points (1, 21) and (2, 6) to the equation of the function:

$y=a(x+1)^2+k\\\\(1,\ 21)\\\\21=a(1+1)^2+k\\21=a(2)^2+k\\21=4a+k\qquad\text{subtract 4a from both sides}\\21-4a=k\qquad(*)\\\\(2,\ 6)\\\\6=a(2+1)^2+k\\6=a(3)^2+k\\6=9a+k\qquad(**)$

Substitute (*) to (**):

$6=9a+(21-4a)\\6=9a+21-4a\\6=5a+21\qquad\text{subtract 21 from both sides}\\-15=5a\qquad\text{divide both sides by 5}\\-3=a\to\boxed{a=-3}$

Put the value of a to (*):

$k=21-4(-3)\\k=21+12\\\boxed{k=33}$

Answer:

$y=-3(x+1)^2+33$

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Two angles form a linear pair the Measure of one angle is 2.6 times the measure of the other angle find the measure of each angl

Sedaia [141]

Answer:

The measures of the angles are 50° and 130°

Step-by-step explanation:

Let

x ----> the measure of one angle

y ----> the measure of the other angle

we know that

If two angles form a linear pair , then their sum is equal to 180 degrees

$x+y=180$ -----> equation A

$x=2.6y$ ----> equation B

substitute equation B in equation A

$2.6y+y=180$

solve for y

$3.6y=180$

$y=50^o$

Find the value of x

$x=2.6(50)=130^o$

The measures of the angles are 50° and 130°

3 0

3 years ago

What number is 76.8% of 42.5

Law Incorporation [45]

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 42.5 is 100% - because it's the output value of the task. 
2. We assume, that x is the value we are looking for. 
3. If 42.5 is 100%, so we can write it down as 42.5=100%. 
4. We know, that x is 76.8% of the output value, so we can write it down as x=76.8%. 
5. Now we have two simple equations:
1) 42.5=100%
2) x=76.8%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
42.5/x=100%/76.8%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 76.8% of 42.5

42.5/x=100/76.8
(42.5/x)*x=(100/76.8)*x - we multiply both sides of the equation by x
42.5=1.30208333333*x - we divide both sides of the equation by (1.30208333333) to get x
42.5/1.30208333333=x 
32.64=x 
x=32.64

now we have: 
76.8% of 42.5=32.64

6 0

4 years ago

If y is directly proportional with x and y=24 when x=6. What is the value of y when x=48

Thepotemich [5.8K]

Answer:

192

Step-by-step explanation:

Multiply 48 by 24, then divide by 6

7 0

3 years ago

Keisha will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an a

Mazyrski [523]

650 miles has to driven before the plans cost the same

When the two plans cost the same, the cost is $ 137.5

Solution:

Given that, Keisha can choose one of two plans

Let "n" be the number of miles driven

For Keisha 1st Plan:

The first plan has an initial fee of $40 and costs an additional $0.15 per mile driven

Therefore,

Cost of plan 1 = 40 + (0.15)n

For Keisha 2nd plan:

The second plan has an initial fee of $53 and costs an additional $0.13 per mile driven

Cost of plan 2 = 53 + (0.13)n

To find out the number of miles where the two plans cost the same set the two expressions equal to each other and solve for n

40 + 0.15n = 53 + 0.13n

0.15n - 0.13n = 53 - 40

0.02n = 13

n = 650

Thus 650 miles has to driven before the plans cost the same

Substitute 650 in any one of equations

40 + 0.15n = 40 + (0.15)(650) = 40 + 97.5 = 137.5

When the two plans cost the same, the cost is $ 137.5

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3 years ago

What is the value of m?

Sliva [168]

Answer:

4) M=5

Step-by-step explanation:

When multiplying exponents, you add them. When raising an exponent to another power, you multiply them.

(x^5*x²)³=(x^7)³=x^21

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3 years ago