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Marina86 [1]
3 years ago
9

Determine the equation of the graph shown y = a(x - h)^2 + k

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
4 0

Answer:

y=-(x+1)^2+4

Step-by-step explanation:

we know that

y=a(x-h)^2+k

Is the equation of a vertical parabola written in vertex form

where

(h,k) is the vertex

a is the leading coefficient

In this problem we have

The vertex is the point (-1,4)

so

(h,k)=(-1,4)

substitute

y=a(x+1)^2+4

Find the value of a

we have the ordered pair (0,3)

substitute the value of x and the value of y in the quadratic equation and solve for a

3=a(0+1)^2+4

3=a+4\\a=3-4\\a=-1

therefore

y=-(x+1)^2+4

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PLEASE HELPPPP ! 16^x=64^x+4
Vladimir [108]

Answer:

x = -12

Step-by-step explanation:

Set logs up on both sides-

log 16^x = log 64^x+4

The variable goes behind because of the exponent log <em>property</em> (exponents are permitted to go behind the log to multiply)-

x * log 16 = x + 4 * log 64

Divide both logs out-

log 64/log 16 = 1.5

Simplify-

x = x+4(1.5)

1.5x + 6 = x

Remove 1.5-

1 - 1.5 = -.5x

Simplify-

-.5x = 6

Divide both sides-

6/-.5x = -12

Hence, the answer would be -12

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4 years ago
What is the slope for (5,7) (-4,-2)
Wewaii [24]

Answer:

Slope = 1

Step-by-step explanation:

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3 years ago
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Determine weather the two expressions are equivelent tell what property is applied if not explain why (35+17)+43 and 35 +(17+43)
madam [21]

Answer:

Associative Property

Step-by-step explanation:

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2 years ago
Use a matrix equation to solve the system of linear equations. left brace Start 2 By 1 Matrix 1st Row 1st Column 2nd Row 1st Col
natali 33 [55]

Answer:

\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

A^{-1} = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = \left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]

A^{-1}= \frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right] = \left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]

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3 years ago
What is the mode? -5 0 -9 0 0 -9
Natalka [10]

The mode for this question is <u>0</u>

<h3>Mode</h3>

In a set of numbers, the mode is the number that occurs most often. In other words, it measures how frequently a particular number occurs within a set of numbers. It is a type of average, like its counterparts, the median and mean.

To find the mode of a set of numbers,

  • List the set of numbers in ascending or descending order, including any duplicates
  • Count the number of times each number in the set of numbers occurs. The number that occurs the highest number of times is the mode of the set of data
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2 years ago
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