the runner's time to complete the marathon is 45 minutes. The time to complete the last marathon was 49.5 minutes. What is the percent decrease of the time ?

Answer:

-4 ≤ x ≤ 6

Step-by-step explanation:

When we talk of the domain, we are referring to the possible x-values

from the diagram, we can see that we have the x-values at -4 and 6

The dotted line means that -4 and 6 are in the domain

Thus, the two points represent the end and starting point of the domain

Writing this in interval notation, we have the representation as;

-4 ≤ x ≤ 6

Answer:

She has 256 stickers.

Step-by-step explanation:

4 times 64 equals 256

Answer:

se llama agudo el ángulo de 80 grados

Answer:

the second option

Step-by-step explanation:

(5 + i) - (2 + 9i) = 3 — 8i

Answer:

Hello! :) have a good day!

Exact Form:

x = −18/31

Decimal Form:

x = −0.58064516

Answer:

18/5

Step-by-step explanation:

above attached the process

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I hope this helps :)  God bless

Answer:

see explanation

Step-by-step explanation:

Given a quadratic in standard form , y = ax² + bx + c ( a ≠ 0 ), then

The x- coordinate of the vertex, which is also the equation of the axis of symmetry is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = x² + 12x + 32 ← is in standard form

with a = 1, b = 12 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{12}{2}[/tex] = - 6

Substitute x = - 6 into y for corresponding y- coordinate

y = (- 6)² + 12(- 6) + 32 = 36 - 72 + 32 = - 4

Thus

equation of axis of symmetry is x = - 6

vertex = (- 6, - 4 )

To find the y- intercept , let x = 0

y = 0² + 12(0) + 32 = 32 ← y- intercept

The axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.

Important information:

Substitute [tex]x=0[/tex] to find the y-intercept.

[tex]y=(0)^2+12(0)+32[/tex]

[tex]y=32[/tex]

The vertex form of a quadratic function is:

[tex]y=a(x-h)^2+k[/tex]         ...(i)

Where a is constant, (h,k) is vertex and x=h is the axis of symmetry.

Adding and subtracting the square of half of coefficient of x, the given quadratic function can be written as:

[tex]y=x^2+12x+32+6^2-6^2[/tex]

[tex]y=(x^2+12x+6^2)+32-36[/tex]

[tex]y=(x+6)^2-4[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]a=1,h=-6,k=-4[/tex]

Therefore, the axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.

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Answer:

I did this question just the other day. The answer you are looking for is B or the second one.

Step-by-step explanation:

Answer:

[tex]10:02:24\ \text{pm}[/tex]

Step-by-step explanation:

d = Distance to travel = 880 miles

s = Average speed of the car = 65 mph

Time taken to cover the distance is

[tex]t=\dfrac{d}{s}\\\Rightarrow t=\dfrac{880}{65}\\\Rightarrow t=\dfrac{176}{13}\ \text{h}=13.54\ \text{hours}[/tex]

Time the car stopped

[tex]3\times 10+60=90\ \text{minutes}=1.5\ \text{hours}[/tex]

Total time of the journey

[tex]13.54+1.5=15.04\ \text{hours}[/tex]

Converting [tex]0.04\ \text{hours}[/tex] to minutes

[tex]0.04\times 60=2.4[/tex]

So, the total time taken for the journey is [tex]15\ \text{hours and }2\ \text{minutes and }24\text{seconds}[/tex]

Time when they reach their destination

[tex]7:30+15:2.4\approx 10:02:24\ \text{pm}[/tex]

Answer:

Step-by-step explanation:

Given is a table of x, f(x) as below

x             1   3   4   6   7  9  10

f(x)         4   8  6  10  10  12  16

Mid pt      6   7   8  10   11  14

width of

interval    2   1     2   1    2    1

dA1         12   7   16  10  22  14

area = area of all rectangles= 81 sq units.

Answer:

x = 4

Step-by-step explanation:

4x-5 = 2x+3

subtract 2 x from each side and add 5 to each side

2x = 8

x = 4

Answer: In 1 hour , it will waste = 1.25ml

Step-by-step explanation:

Volume of water  wasted by the tap in 9 Hours = 11,250 ml

Since  it drips in equal quantity,

In 1 hr , it will drip=  1 x 11,250 / 9 = 1,250 ml

But  1000 ml = 1 Liter

1250 ml = 1250ml x 1Liter / 1000ml= 1.25L

Answer:im lonely

Step-by-step explanation:

Answer:

-99

Step-by-step explanation:

1/100 is positive, and -99 is negative, so 1/100 is greater

Answer:

8 students

Step-by-step explanation:

17 ÷ 2  1/8 = 8

Answer:

40%

Step-by-step explanation:

assuming all the money in the purse is from babysitting then (32/80)*100= 40%.

in other words, 32 is 40% of 80

Answer:

89.6

Step-by-step explanation:

Answer:

The distance between two points ( -1,1) and (2,-4) is:

[tex]d=\sqrt{34}[/tex]  or d = 5.8 units.

Step-by-step explanation:

Given the points

Finding the distance between (-1, 1) and (2, -4) using the formula

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

substitute (x₁, y₁) =  (-1, 1)   and  (x₂, y₂) = (2, -4)

   [tex]=\sqrt{\left(2-\left(-1\right)\right)^2+\left(-4-1\right)^2}[/tex]

   [tex]=\sqrt{\left(2+1\right)^2+\left(-4-1\right)^2}[/tex]

   [tex]=\sqrt{3^2+5^2}[/tex]

   [tex]=\sqrt{9+25}[/tex]

   [tex]=\sqrt{34}[/tex]  units

or

[tex]d = 5.8[/tex] units

Therefore, the distance between two points ( -1,1) and (2,-4) is:

[tex]d=\sqrt{34}[/tex]  or d = 5.8 units.

Answer

what is 2 increased by 5 times a number = 10

Step-by-step explanation:

Answer:

The number:

1: 7

2: 12

3: 17

4: 22

5: 27

6: 32

7: 37

8: 42

9: 47

10: 52

The increase for each number will be 5.

Step-by-step explanation:

The measure of the missing angle is 119 degrees.

Explanation:

This is because this angle is a supplementary angle, which means that two angles put together equal 180 degrees. Since we already know the measure of one angle (61 degrees), we can subtract it from 180 degrees. We could figure this out by doing 180-61, which would get us the measure of the missing angle, 119 degrees.

Answer:

0.5

Step-by-step explanation:

total tiles = 12

green tiles = 6

so : 6/12 = 0.5

Answer:

5 watts

Step-by-step explanation:

power (measured in watts) is joules per second, or J/s

J = 20

s = 4

J/s = 5

Answer:

one solutions

Step-by-step explanation:

Beacause at the end of the solution the value of x

will be the solution

Answer:

1080

Step-by-step explanation:

1/2*base area*h

Answer:

a = 55

Step-by-step explanation:

By exterior angle theorem:

a+10 + 44 = 2a

a= 55

Here's the proof:

Consider the same figure shown

say a+10 = x and 44 = y

Thus the remainng angle is 180 - x-y

and the exterior angle is 180- ( 180 - x- y) = x+y

Thus proved

Answer:

Step-by-step explanation:

When [tex]5\frac{2}{3}[/tex]  is divided by 4 then the result will be [tex]\frac{17}{12}[/tex] in fraction form.

We have to divide the mixed fraction [tex]5\frac{2}{3}[/tex]  by 4.

Let us convert the mixed fraction to improper fraction.

[tex]5\frac{2}{3}[/tex] = [tex]\frac{17}{3}[/tex]

Now divide the fraction [tex]\frac{17}{3}[/tex] by a whole number 4.

[tex]\frac{\frac{17}{3}}{4}[/tex]

When a fraction is divided by a whole number then the fractions denominator is multiplied with the whole number.

[tex]\frac{17}{3 \times 4}[/tex]

Simplifying further:

[tex]\frac{17}{12}[/tex]

Hence, when [tex]5\frac{2}{3}[/tex]  is divided by 4 then the result will be [tex]\frac{17}{12}[/tex].

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Answer:

-5/3

Step-by-step explanation: rise over run it goes down -5 and goes across 3