Suzy drove to a hair appointment at 50mph. Her average speed on the return home was 40mph. The return home took 1/4hr longer because of heavy traffic. How far did she travel to her hair appointment?

The coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

Vertex of the parabola is the point of intersection of symmetry axis of the parabola and the parabola itself.

The given equation of parabola is [tex]y=x^2 + 5x + 10[/tex].

To get the coordinates of vertex of this parabola, we have to write the equation of parabola in the standard form.

So, write the equation of parabola in its standard form as,

[tex]y=x^2 + 5x + 10\\y=x^2+2\times \dfrac{5}{2}x+\dfrac{25}{4}-\dfrac{25}{4}+10\\y=(x-\dfrac{5}{2})^2+\dfrac{15}{4}\\(y-\dfrac{15}{4})=(x-\dfrac{5}{2})^2[/tex]

The standard form of parabola is,

[tex]y-b=(x-a)^2[/tex] where (a, b) is the coordinate of the vertex.

So, by comparing the equations, the vertex of the parabola will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

Therefore, the coordinates of the vertex of the given parabola [tex]y=x^2+5x+10[/tex] will be [tex](\dfrac{5}{2},\dfrac{15}{4})[/tex].

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The maximum amount of water that can be used by each house on a daily basis is 100 liters.

From the information given, the gated community consists of 40 houses and requires 500 liters of water everyday for common utilities of the community.

The maximum amount of water that can be used by each house on a daily basis will be:

4500 = 40x + 500

40x = 4500 - 500

40x = 4000

x = 4000/40

x = 100

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Answer:

6

Step-by-step explanation:

When you have a proportion (fraction=fraction), you can crossmultiply to solve. See image.

A graph that uses bars of various heights to represent the frequencies is a Histogram

A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" (or "bucket") the range of values—that is, divide the entire range of values into a series of intervals—and then count how many values fall into each interval.

Therefore, a graph that uses bars of various heights to represent the frequencies is a Histogram

================================

[tex] \large \sf \underline{Question:}[/tex]

A graph that uses bars of various heights to represent the frequencies.

================================

[tex] \large \sf \underline{Answer:}[/tex]

[tex] \qquad \qquad \huge \bold{Option \: A}[/tex]

================================

[tex] \large \sf \underline{Explanation:}[/tex]

A graph that uses bars of various heights to represent the frequencies is called Histogram

A Histogram is typically a statistical schematic diagram which bars are displayed at random with no space interval. The bars of a Histogram are side-by-side, there are no spaces between the bars.

================================

The only value of the angles that could not be the value of the θ is determined as 240⁰.

If sinθ is given as [tex]\frac{\sqrt{3} }{2}[/tex], then the value of θ is determined as follows;

sinθ = √3/2

sinθ = 0.866

θ = sin⁻¹(0.866)

θ = 60⁰

When the angle is translated in radians, θ  = π/3 = 180/3 = 60⁰

thus, θ  = π/3

2(π/3) = 2(60) = 120⁰

using the following formula, we can obtain the rest;

θ = π/3 + 2πk

when k = 1;

θ = π/3 + 2π(1)

θ = 60 + 2(180)

θ = 420⁰

Thus, the only value of the angles that could not be the value of the θ is determined as 240⁰.

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Answer:

3/8  = 12/32 is a proportion

Step-by-step explanation:

2:3 and 9:4 is not a proportion, 10/12 and 20/25 is not a proportion, 4/9 and 17/38 is not a proportion

Answer:

-4585

Step-by-step explanation:

Answer:

To estimate the square root of a number, you're going to use:

Get as close as possible to the number you're trying to square root by finding two perfect square roots that give a close number.

Answer:

2 inches is the height of the box.

Step-by-step explanation:

Answer:

well yes it but it depends on how much each points you will get for each assignment and how much you have, but other than that I am very sure It will! don't lose hope! keep doing your best! only think positive!!!

Answer:

A6n+4

Step-by-step explanation:

Answer:

C. 27

Step-by-step explanation:

27 + 23 = 50

:)

Answer: hii :)

i know this oneeeee ^^ your answer is 27 <3

Step-by-step explanation:

Move all terms not containing x to the right side of the equation.

hopefully this helps you

- Matthew ~

Answer:

GH8 remains 70 and gh remains 10

Step-by-step explanation:

there is no five or more

The volume of the red bird feeder will be equal to V=651.88 cubic inches

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length,width and height of the cube or Cuboid.

It is given that:-

Diameter = 10 inches

Height =  8.3 inches

Volume=?

Since the feeder is cylindrical so the volume will be calculated as:-

[tex]\rm Volume=\dfrac{\pi }{4}d^2H\\\\\\Volume=\dfrac{\pi }{4}(10)^2(8.3)\\\\\[/tex]

V=651.88 cubic inches

Hence volume of the red bird feeder will be equal to V=651.88 cubic inches

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Answer:

1) A

2) A

3) C

Step-by-step explanation:

Answer: B, A, A

Step-by-step explanation:

I'm not 100% sure this is the answer sorry if I'm wrong

Answer:

5.641 = x

Step-by-step explanation:

Work on the right triangle

pythag theorem

9^2 + L^2 = 10^2

L = sqrt 19

then x = 10 - sqrt 19 =5.641

Answer:

2(3x + 4)

Step-by-step explanation:

to solve this equation you can distribute the two throughout the equations

an easy way to see which one is correct is to check the symbols and what they multiply to

the first expression is obviously wrong as it has a negative symbol

we can now look at the second to last ones

the third one is wrong because 4x and 2 multiply to 6x

the last one is wrong because 2 and 8 do not multiply to 8

the answer is the third one

Using translation concepts, it is found that the correct option is given by:

B. The graph of f(x) is shifted three units down from the graph of g(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]g(x) = -4^{5x}[/tex]

The translated function is:

[tex]f(x) = -4^{5x} - 3[/tex]

3 was subtracted from the original function, which means that the translated function was shifted 3 units down, and option B is correct.

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Step-by-step explanation:

[tex] {x}^{2} + 2x - 2 = 0[/tex]

Now Adding three on both sides we get

[tex]{x}^{2} + 2x - 2 + 3 = 0 + 3[/tex]

[tex] {x}^{2} + 2x + 1 = 3[/tex]

[tex] {(x + 1)}^{2} = 3[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The expressions can be arranged as shown below.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

According to the number of terms, the expressions can be arranged as,

Hence, the expressions can be arranged as shown above.

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Answer:

108π

Step-by-step explanation:

volume of a cylinder = πr²h , where r = radius and h = height

given values

==> plugging in given values into formula

V = πr²h

r = 3 , h = 12

V = π(3²)(12)

==> evaluate exponent

V = π(9)(12)

==> multiply 9 and 12

V = 108π

Answer: 490*x + 700y ≤ 4000

It is ≤ as it can either be equal to 4000 per week or less than.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find:

To use:

Given:

The slope of a line is often indicated by the letter m.

It can be calculated by selecting any two points on the line and calculating the rate of change between them.

[tex]\underline{\text{Slope:}}[/tex]

[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Solve.

[tex]\Longrightarrow: \sf{\dfrac{-9-\left(-8\right)}{-9-0}=\dfrac{-1}{-9}=\boxed{\sf{\dfrac{1}{9}}}[/tex]

The slope is 1/9.

Slope-intercept form:

All points (x,y) on the line have m slope and (0,b) y-intercept that satisfy the equation.

The m represents the slope.

The b represents the y-intercept.

The y-intercept is -8.

[tex]\Longrightarrow: \boxed{\sf{y=\dfrac{1}{9}x-8 }}[/tex]

I hope this helps, let me know if you have any questions.

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Answer:

[tex]\frac{6}{14}[/tex]

Step-by-step explanation:

P(A and B) = P(A) × P(B)

~~~~~~~~

P(A) = [tex]\frac{6}{7}[/tex]

P(B) = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

P(A and B) = [tex]\frac{6}{7}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{6}{14}[/tex]

Answer:

3) B. 160

4) D. 72

5) C. 16

Step-by-step explanation:

3) 240 - 80 = 160

4) 12 = w/6

w = 6*12

w = 72

5) 44-28 = 16

Answer:

attached image

Step-by-step explanation:

Formula:

Discount = Regular price x (% / 100)        

you divided by 100 to change it into a decimal

Sale Price = Regular price - Discount

Answer:

Step-by-step explanation:

A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.

The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.

There are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).

  f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).

The function will be negative where it is not positive (except at the zeros)

  f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).

_____

Additional comment

The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...

  f(x) = (x +1)(x^4 -3x^2 -9)

The remaining factor is a quadratic in x^2, which has roots ...

  x = ±√(1.5 ±√11.25)

The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).

Answer:

x = (-1±i√3)/2

Step-by-step explanation:

y = -2x² + 9x - 4

x = (-b±√(b²-4ac))/2a

x = (2±√((-2)²-4(-1)(-4))/2(-2)

x = (2±√(4-16))/-4

x = (2±√-12)/-4

√-12 = √12 x √-1

√12 = √4√3

2i√3

x = (-1±i√3)/2