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2 years ago

The function f(x) = − x^2+ bx +1 is shown in the graph. What is the value of b?

Mathematics

1 answer:

denis-greek [22]2 years ago

5 0

Answer:

b = 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here ( h, k ) = (2, 5 ) , then

y = a(x - 2)² + 5

to find a substitute any point on the parabola into the equation

using (0, 1 ) then

1 = a(0 - 2)² + 5 ( subtract 5 from both sides )

- 4= a(- 2)²= 4a ( divide both sides by 4 )

- 1 = a

then

y = - ( x - 2)² + 5

= - (x² - 4x + 4) + 5

= - x² + 4x - 4 + 5

= - x² + 4x + 1 ← in the form ax² + bx + c

with b = 4

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the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

RideAnS [48]

Well, first off, let's find what is the slope of BC

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 2}}\quad ,&{{ -3}})\quad 
% (c,d)
C&({{ 10}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2}
\\\\\\
\cfrac{4}{8}\implies \cfrac{1}{2}$

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\
slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}$

now, we know the slope "m" of AB is -2 then, thus

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ a}}\quad ,&{{ 3}})\quad 
% (c,d)
B&({{ 2}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2}
\\\\\\
\cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a
\\\\\\
-1=a$

6 0

3 years ago

Help ASAP Jake took out an interest-free loan of $2,401.56 from the bank to buy a car. He paid the bank $200.13 each month until

Bezzdna [24]

Answer:

Answer: D. Jake paid his loan in 12 months

Step-by-step explanation:

Jake took out an interest-free loan of $2,401.56 from the bank to buy a car.

Since he has to pay no interest for the loan, the monthly payments are totally used to cover the amount of the loan.

He paid the bank $200.13 each month, thus the total months needed to pay the loan is:

$\frac{\$2,401.56 }{\$200.13}=12$

Answer: D. Jake paid his loan in 12 months

6 0

3 years ago

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erma4kov [3.2K]

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7 0

3 years ago

Order the numbers from least to greatest -3,9,0,-11,7,-6

igor_vitrenko [27]

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3 years ago

A variable needs to be eliminated to solve the system of equations below. Choose the

sasho [114]

Step-by-step explanation:

-4x - 2y = 18

+ (4x - 4y = -36)

=> -6y = -18, y = 3

As we added the equations together, we have eliminated x and found y.

Hence the correct answer is "Add to eliminate x".

4 0

3 years ago