Christopher drove 199.5 miles in 3.5 hours. If he drove at a constant speed, how far did he drive in one hour? *

Answer:

x-intercept: (13/3, 0)

y-intercept: (0, -13)

Step-by-step explanation:

y+1 = 3x-12

y= 3x-13

For y-intercept:

y= 3(0) -13

y=-13

For x-intercept:

0=3x-13

3x=13

x=13/3

The intercepts of the line will be,

x-intercept: (13/3, 0)

y-intercept: (0, -13)

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

Given that y+1=3(x - 4). The x-intercept and y-intercept will be calculated as,

y+1 = 3x-12

y= 3x-13

For y-intercept:

y= 3(0) -13

y=-13

For x-intercept:

0=3x-13

3x=13

x=13/3

Therefore, the x-intercept is (13/3, 0) and the y-intercept is (0, -13).

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Answer:

The largest possible number is 28.

Step-by-step explanation:

Sophie has to choose seven different numbers whose mean is 7, this means that the sum of the numbers is 49. (since the mean is the sum of them all divided by 7 and if we want the mean to be 7, then the sum would need to be 49).

We are asked what is the largest possible number she could choose, so therefore, the other six numbers should be non-zero and the smallest ones so she would have to choose the numbers from 1 to 6 first.

Let's see how much they sum up: [tex]1+2+3+4+5+6=21[/tex]

So now, she needs one more number to sum up to 21 and that will give her 49 in total, this number is 28 (since 28 + 21 =49).

Thus, 28 is the largest number she could choose because if she chose any other greater number the mean would be bigger than 49.

Answer:

(x - 4)

Step-by-step explanation:

Given

x² + 2x - 24

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (+ 2)

The factors are + 6 and - 4, since

6 × - 4 = - 24 and 6 - 4 = + 2, thus

x² + 2x - 24 = (x + 6)(x - 4) ← in factored form

Thus the other factor is (x - 4)

The solution is Option D.

The equation x² + 2x - 24 = 0 has the factors as ( x + 6 ) and ( x - 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² + 2x - 24 = 0   equation (1)

The equation can be factorized as

x² + 6x - 4x - 24 = 0

Taking x as the common factor , we get

x ( x + 6 ) - 4 ( x + 6 ) = 0

So , the equation will be

( x + 6 ) ( x - 4 ) = 0

Therefore , the factors of x are -6 and 4

Hence , the factors of the equations are ( x + 6 ) and ( x - 4 )

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Answer:

Step-by-step explanation:

Given the intensity, or loudness, of a sound  measured in decibels (dB), according to the equation [tex]I (dB)= 10log(\frac{I}{Io} )[/tex] where;

I is the intensity of a given sound and

[tex]Io[/tex] is the threshold of hearing intensity

To get I(dB) when [tex]I=10^{32} Io[/tex]

We will substitute the value of I = [tex]I=10^{32} Io[/tex] into the equation above to have;

[tex]I (dB)= 10log(\frac{10^{32}Io }{Io} )\\I(dB)=10log10^{32}\\ I(dB)=32*10log10\\[/tex]

Since log10 = 1;

[tex]I(dB)=32*10(1)\\I(dB)=320[/tex]

The intensity in decibel is 320 decibel

Answer:

Its D or 80

Step-by-step explanation:

I=10^8 (I subscript 0) can be written as I/I subscript 0, and you can plug that right into the log to get 80.

First you graph "y = 2x +2." You shade in the region below it, because it's y "LESS THAN" and you keep the line solid (not dotted) because it's "equal to" 2x+2 too.

Complete question is:An orange is shot up into the air with a catapult. The function h given by h(t) = 15 + 60t - 16t² models the orange’s height, in feet, t seconds after it was launched.

Select all the true statements about the situation.

Options:

1. The domain of function h only contains values greater than or equal to 0.

2. The orange is at the same height 1 second after launch and 2 seconds after launch.

3. After 3 seconds, the orange has hit the ground.

4. The orange is 15 feet above the ground when it is launched.

5. The value t = 10 does not belong to the domain of h.

Answer:

Option 1 - True

Option 2 - False

Option 3 - False

Option 4 - True

Option 5 - True

Step-by-step explanation:

Looking at the options,

-The domain is the x or t value and it is time. Now, time can only be positive or greater than or equal to zero i.e. t ≥ 0. Thus, option 1 is true.

- At t = 1 second;

h = 15 + 60(1) - 16(1)²

h = 15 + 60 - 16 = 59 ft

Also, at t = 2 seconds;

h = 15 + 60(2) - 16(2)²

h = 15 + 120 - 64 = 71 ft

So,value of h is not the same at t = 1 and t = 2. Thus, option 2 is not true.

- The orange will hit the ground when h(t) = 0.

However, at t = 3;

h(t) = 15 + 60(3) - 16(3)²

h(t) = 51 ft

h(t) is not equal to zero at t = 3, so option 3 is false

- when the orange is launched it is at time t = 0.

Thus,

h(0) = 15 + 60(0) - 16(0)²

h(0) = 15 ft

So option 4 is true.

- At t=10, h(t) = 15 + 60(10) - 16(10)²

h(10) = -985

This means the orange would be below ground level and thus doesn't belong to the domain of h, so option 5 is true.

Answer:

1 true 4 true and 5 true the rest are false

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, you need to graph all given points in the table, that way you will be able to determine the end behavior.

Remember, the end behavior of a function is the behavior of f(x) as x approaches to positive infinity and negative infinity.

So, based in the graph, we can say that as x approaches to positive infinity, f(x) approaches to negative infinity, and as x approaches to negative infinity, f(x) approaches to negative inifinity. In other words, in either case, f(x) always approaches to negative infinity.

Therefore, the right answer is the last choice.

Answer:

As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞

Step-by-step explanation:

Just took the test!!!

Answer:

Step-by-step explanation:

6 - 2x = 5x - 9x + 10  {add the like terms}

6 - 2x = - 4x + 10        {add (-6) to both side}

6 - 2x - 6 = - 4x + 10 - 6

-2x = - 4x + 4         {add 4x to both sides}

-2x + 4x = -4x + 4 + 4x

2x = 4           {divide both sides by 2}

2x/2x = 4/2

x = 2

Answer:

Step-by-step explanation:

prime: 3 5 7 11 13

P(notprime) = (12-5)/ 12 = 7/12

Answer:

30

Step-by-step explanation:

The LCM of 2,3,5 is the result of multiplying all prime factors the greatest number of times they occur in either number. The LCM of 2,3,5 is 2⋅3⋅5 = 30

Answer:

30

Step-by-step explanation:

Its that easy. I got the answer from online.

Answer:

Answer:

301.4

Step-by-step explanation:

Volume of a cylinder=pi*[tex]r^{2}[/tex]*h.  Assuming you want 3.14 for pi, we can substitue the 4m for r, 6 for h and 3.14 for pi.

V=3.14*[tex]4^{2}[/tex]*6

V=301.44

Since you want to round to nearest tenths, the answer is 301.4

The volume of the cylinder with the given value of radius and height to the nearest tenth place is 301.4 cubic meters.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

We substitute our values into the expression above.

V = π × r² × h

V = 3.14 × (4m)² × 6m

V = 3.14 × 16m² × 6m

V = 301.4m³

The volume of the cylinder with the given value of radius and height to the nearest tenth place is 301.4 cubic meters.

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Answer:

2.275%

Step-by-step explanation:

The first thing to do here is to calculate the z-score

Mathematically;

z-score = (x-mean)/SD

from the question, x = 12,300 hours , mean = 11,500 hours while Standard deviation(SD) = 400 hours

Plugging the values we have;

z-score = (12,300-11,500)/400 = 800/400 = 2

Now, we want to calculate P(z ≤ 2)

This is so because we are calculating within a particular value

To calculate this, we use the z-score table.

Mathematically;

P(z ≤ 2) = 1 - P(z > 2) = 1 - 0.97725 = 0.02275

To percentage = 2.275%

Answer:

Neither

Step-by-step explanation:

Both equations are x=10

C, D, and E are most likely to be right. Its either all of them, one of them, or two of them. A is impossible to use in the equation and if you use b, you get 45.5.

Answer:

Step-by-step explanation:

Price of one pound of apples = $1.49

∴Price of 2 and 1/2 pound of apples = [tex]2\frac{1}{2}[/tex] × [tex]1.49[/tex]

                                                            = 2.5 × 1.49

                                                            = 3.725

                                                            = $ 3.73

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Answer:

$3.73

Step-by-step explanation:

Answer:

A =78.5

Step-by-step explanation:

We need the radius to find the area of a circle

r = d/2 = 10/2 =5

The area of a circle is given by

A = pi r^2

A = 3.14 (5)^2

A =3.14 (25)

A =78.5

Answer:

(5x+2)(2x-3)

Step-by-step explanation:

this is the answer

These questions are some teacher's hairbrained idea that we can keep the students current on algebra while learning geometry.  While there are many ways to combine algebra and geometry, this way is awful.

Triangle angles add to 180 degrees. Geometry done.

Equation that models ...:

2x + 5 + 3x + 7 + 2x = 180

Solving,

7x + 12 = 180

7x = 168

x = 168/7 = 24

Answer: x=24

A=2x+5=2(24)+5= 53°

B = 3x+7 = 3(24) + 7 = 79°

C = 2x = 48°

Answer: A=53°, B=79°, C=48°

Answer:

17/40

17 over 40

Answer:

see below

Step-by-step explanation:

P( yellow) = number of yellow sections / total sections

                 = 4/20

                   1/5

                  20%

Answer:

a.

4 out of 20

1/5

or 20%

b.  The probability may not be as much as the other colors on the wheel depending on how many colors and how many sections of each. You have a 20% chance out of all colors to get the color yellow.

Answer:

1. 10.64

2. 6.45

Step-by-step explanation:

Hope this helps and can u mark me brainliest?

Answer:

= 99/32

Step-by-step explanation:

2 3/4 1 1/8

= 11/4 * 9/8

= 99/32

Answer:

no it is not.

Step-by-step explanation:

%increase = 40% while %loss = about 28.6%

Answer:

1.45

Step-by-step explanation:

1. divide both sides of the equation by 20 to get rid of the 2o on the right side

[tex]\frac{29}{20}[/tex]= p x [tex]\frac{20}{20}[/tex]

now u end up with 1.45=p

hope it helped

Answer:

We have to questions here where we need to find the distance from the origin to each given point.

The formula for distance is

[tex]s=\sqrt{x^{2}+y^{2} }[/tex]

[tex]s_{(3,4)}=\sqrt{3^{2}+4^{2} } =\sqrt{9+16}=\sqrt{25}\\ s_{(3,4)}=5[/tex]

Therefore, the value s that yields the coordinate (3,4) is 5 units.

[tex]s_{(9,1)}=\sqrt{9^{2}+1^{2} } =\sqrt{81+1}=\sqrt{82}\\ s_{(9,1)} \approx 9.05[/tex]

Therefore, the value s that yields the coordinate (9,1) is 9.05 units, approximately.

The values of s that yield the coordinates (3.4) and (9,1) are: 5 and 9.1, respectively

The coordinates are given as:

(3,4) and (9,1)

The single value that yields the coordinates is calculated as:

[tex]s = \sqrt{x^2 + y^2}[/tex]

For (3,4), we have:

[tex]s = \sqrt{3^2 + 4^2} = 4[/tex]

For (9,1), we have:

[tex]s = \sqrt{9^2 + 1^2} = 9.1[/tex]

Hence, the values of s that yield the coordinates (3.4) and (9,1) are: 5 and 9.1, respectively

Read more about coordinates at:

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The answer is the last one: k = 5

Hope I helped and good luck!

Answer:

57

Step-by-step explanation:

Firstly, we will need to calculate what x is.

To calculate this, the important property of the parallelogram to use is that adjacent angles are supplementary.

This means A and B are supplementary while B and C are also supplementary

what we are trying to say is that they add up to be 180

Thus,

5x + 18 + 3x -6 = 180

8x +12 = 180

8x = 180-12

8x = 168

x = 168/8

x = 21

Thus, the measure of angle B is 3x-6 = 3(21) -6 = 63-6 = 57

Now, another important property of parallelograms is that opposite angles are equal. This means that angle B= C = 57

Answer:

Tyson had the better deal

Step-by-step explanation:

We simply want to know who paid less for the ticket.

Tyson bought 8 tickets for the members of his basketball team and it cost it $168 in total.

The cost of each ticket is therefore:

168 / 8 = $21

He paid $21 for each ticket.

The parent bought her son's ticket for $24.

Therefore, Tyson had the better deal because he paid $3 less than the woman.