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3 years ago

Simplify the expression -4x2(3x − 7).

1 answer:

8 0

-4*2(3x-7)
-8(3x-7)
8 times 4 is 24 so it would be negative 24
so 3 times 16.3=48.9 then you add 7 which rounds it off it 56
so x is 16.3 thats how you get this expession
-24x +56

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The table represents a linear function f(x) in the equation represents a function g(x):

Juli2301 [7.4K]

A: Looking at the last two rows of the table of f(x), the slope is simply (3-0)/(1-0) = 3, while the slope of g(x) is the coefficient of the variable x, which is 7.

B. y-int is the y value when x = 0. f(x) has a y-int of 0, which g(x) is 2. The latter has a greater y-int.

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3 years ago

A multivitamin tablet contains 16.5 . How much vitamins c does a bottle of 30 tablets contain? Write your answer in grams?

AURORKA [14]

Multiply 16.5 by 30

16.5x30=495

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3 years ago

Part 4: Use the information provided to write the vertex formula of each parabola.

sergey [27]

Answer: 1. x = (y - 2)² + 8

$\bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1$

3. y = 2(x +9)² + 7

<u>Step-by-step explanation:</u>

Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h

(h, k) is the vertex
point of vertex is midpoint of focus and directrix: $\dfrac{focus+directrix}{2}$

$\bullet\quad a=\dfrac{1}{4p}$

p is the distance from the vertex to the focus

$focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1$

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

$focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}$

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

$\bold{x=-\dfrac{1}{2}(y-10)^2}+1$

***************************************************************************************

$focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)$

Now let's find the a-value:

$p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2$

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

4 0

3 years ago

3m - 12 =18<br> Step by step

9966 [12]

Answer:

3m=18+12

3m=30

divide both sides by 3

m=10

6 0

4 years ago

Read 2 more answers

The length of a rectangle is 5 more than the width. The perimeter is 120. What is the length, width, and area? Please HELP

Ad libitum [116K]

Answer:

l = 32.5 units, w= 27.5 units, A = 893.75 units²

Step-by-step explanation:

width is w

length is l = 5+w

P = 2( l+w) , substitute l for 5+w

P = 2(5+w+w)

P = 2(5+2w)

P = 10 +4w

P = 120

10 +4w = 120

4w = 120-10

4w = 110

w= 110/4

w= 27.5 units

l = 5+w = 5+ 27.5 = 32.5 units

A = l*w = 27.5 * 32.5 = 893.75 units ²

5 0

3 years ago