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2 years ago

Shawnda spent $259.20 on a scooter. This was 80% of her budget for a new scooter. How much was the total budget?

Mathematics

1 answer:

just olya [345]2 years ago

7 0

X * 0,8 = 259,2 <=>

x = 258,2/0,8 <=>

x = 322,75

The total budget was 322,75$

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If y= x+3/6-x, what is the value of y when x =7i?

djverab [1.8K]

Answer:

Option (2)

Step-by-step explanation:

Given : y = $\frac{x+3}{6-x}$

If x = 7i

y = $\frac{7i+3}{6-7i}$

By simplifying denominator of the given rational expression,

y = $\frac{7i+3}{6-7i}\times \frac{6+7i}{6+7i}$

y = $\frac{(7i+3)(6+7i)}{6^2-(7i)^2}$

y = $\frac{7i(6+7i)+3(6+7i)}{36-49i^2}$

y = $\frac{42i+49i^2+18+21i}{36+49}$ [Since, i² = (-1)]

y = $\frac{63i-49+18}{85}$

y = $\frac{63i-31}{85}$

y = $-\frac{31}{85}+\frac{63}{85}i$

Therefore, Option (2) is the correct option.

3 0

2 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

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3 years ago

Witch fraction has the same value as 2 3/3

saul85 [17]

Answer: Technically, it would be 9/3, but you can simplify that to 3.

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2 years ago

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How to simplify 30/72

Natali [406]

5/12 is the simplified fraction for 30/72 by using the GCD or HCF method. 5/12 is simplified fraction for 30/72 by using the prime fractorization method.

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2 years ago

A line of best fit predicts that when x equals 28, y will equal 27.255, but y actually equals 26. What is the residual in this c

zlopas [31]

Answer:

C) -1.255

Step-by-step explanation:

We are tasked to solve for the residual value given that when x equals 29, y will be equals to 27.255. But, when it is tested, y actual value is 26. The formula in solving residual is shown below:

Residual value = Observed value - predicted value

Residual value = 26 - 27.255

Residual values = -1.255

The answer is -1.255 for residual value.

5 0

2 years ago