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Bond [772]
3 years ago
10

The graph of the parabola defined by the equation y=-(x+1)^2+1 is shifted 1 unit to the right, then shifted 5 units down, then r

otated 180 degrees about its vertex. The resulting parabola has zeros at x=a and x=b, where b > a. What is b-a?
Mathematics
2 answers:
Vlad [161]3 years ago
8 0

Answer:

Step-by-step explanation:

45

erica [24]3 years ago
4 0

Answer:

4

Step-by-step explanation:

y = -(x + 1)² + 1

Shift 1 unit to the right:

y = -(x + 1 − 1)² + 1

y = -x² + 1

Shift 5 units down:

y = -x² + 1 − 5

y = -x² − 4

Rotate 180° about the vertex:

y = -(-x²) − 4

y = x² − 4

Find the zeros:

0 = x² − 4

x² = 4

x = -2 or 2

Therefore, a = -2 and b = 2, so b−a = 4.

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dmitriy555 [2]
The variable “x” can be defined as the price of regular gas.
The equation is x = x - (.02)7
x = x - (.02)7
(.02)7 = .14
x = x - .14
 X - X = nothing so it just leaves you with -.14
The answer is that the gas price changed by a total of - 14 cents or -0.14
7 0
3 years ago
A snail sets out on a 3 3/5 -mile journey, traveling at a speed of 2/65 miles per hour. a. How many hours will the journey take?
fiasKO [112]

Answer:a)117 hours b)4.875days.

Step-by-step explanation:

Using the formula

Speed =Distance / Time

Given Distance = 3 3/5 -mile

and Speed=2/65  miles per hour.

Time =Distance / Speed

Time = (3 3/5)/(2/65)

Time =18/5÷2/65

Time =18/5 x 65/2 =117 hours

Now 24 hours =1 day

therefore 117hours =(117hours x 1 day )/ 24 =4.875days.

3 0
3 years ago
Geometry question on finding x.
Dmitrij [34]

Answer:

x =63^o

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

  • \text{ $\overline{MN} $ and $\overline{ML}$ are tangents .}

We know that the tangents are perpendicular to the radius at the point of contact . And here OLMN is a quadrilateral. Also we know that , the angle sum property a triangle is 360° .

<u>According</u><u> to</u><u> question</u><u> </u><u>:</u><u>-</u><u> </u>

\implies x + 117^o + 90^o +90^o = 360^o \\\\\implies x + 297^o = 360^o \\\\\implies x = 360^o - 297^o \\\\\implies x = 63^o

<u>Hence</u><u> the</u><u> </u><u>value</u><u> of</u><u> x</u><u> </u><u>is </u><u>6</u><u>3</u><u>°</u><u> </u><u>.</u>

6 0
3 years ago
Helppppp please very important
VMariaS [17]

The curves cross at coordinates (x, y) = (1, 4). The x-value is said to represent the increase in temperature, while the y-value is said to represent the numbers of visitors and those and who leave early.

The "solution" is the temperature change at which the number of visitors is equal to the number who leave early.

7 0
3 years ago
It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.
vova2212 [387]

Answer:

300%

Step-by-step explanation:

Given

y\ \alpha\ \frac{1}{x^2}

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

y\ = \ \frac{k}{x^2}

Where k is the constant of proportionality

When x decreased by 50%

Y = \frac{k}{(x - 0.5x)^2}

Y = \frac{k}{(0.5x)^2}

Y = \frac{k}{0.25x^2}

Expand

Y = \frac{1}{0.25} * \frac{k}{x^2}

Substitute \frac{k}{x^2} for y

Y = \frac{1}{0.25} * y

Y = 4 * y

Y = 4 y

The percentage change is then calculated as:

\%Change = \frac{Y - y}{y} * 100\%

\%Change = \frac{4y - y}{y} * 100\%

\%Change = \frac{3y}{y} * 100\%

\%Change = 3 * 100\%

\%Change = 300\%

<em>The percentage in y is 300%</em>

7 0
3 years ago
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