Calculate the slope of the line that goes through the points (-15,70) and (5,10)

The function rule of the line is, f(x)=2/3x-2

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (0,-2) and, (3,0)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+2)/(x-0)=(0+2)/(3-0)

=>3y+6=2x

=>y=2/3x-2

Let, y= f(x)

So, the required function rule of the line is f(x)=2/3x-2

Hence, the required  function rule of the line is, f(x)=2/3x-2

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Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.  

In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].

We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].  

Using Pythagorean theorem in triangle JLM we will get,

[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]

[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]

[tex]LM=\sqrt{64-25}[/tex]

[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]

Now let us find length of side KL.

[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]  

[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]

[tex]KL=\sqrt{169-25}[/tex]

[tex]KL=\sqrt{144}=12[/tex]

Now let us find length of KM by adding lengths of KL and LM.

[tex]KM=12+6.24=18.24[/tex]

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

[tex]KM^{2}=JK^{2}+JM^{2}[/tex]  

[tex]18.24^{2}=13^{2}+8^{2}[/tex]

[tex]18.24^{2}=169+64[/tex]

[tex]18.24^{2}=233[/tex]

Upon taking square root of both sides of equation we will get,

[tex]18.24\neq 15.264337522473748[/tex]

[tex]18.2\neq 15.3[/tex]  

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.    

Answer:

I just took the test it is C

To solve this system of equations using the elimination method, we multiply one or both equations so that the coefficients of either x or y are the same or additive inverses. Then, we subtract one equation from the other to eliminate one variable. Finally, we solve for the remaining variable by substituting the value of the other variable.

To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations so that the coefficients of either x or y are the same or additive inverses. In this case, we can multiply the first equation by 3 and the second equation by 2:

12x + 6y = 54

4x + 6y = 30

Next, we subtract the second equation from the first:

(12x + 6y) - (4x + 6y) = 54 - 30

8x = 24

Divide both sides by 8 to solve for x:

x = 3

To find the value of y, substitute the value of x into either of the original equations:

4(3) + 2y = 18

12 + 2y = 18

2y = 18 - 12

2y = 6

y = 6/2

y = 3

Answer:

The arrow should start at zero

Step-by-step explanation:

Because if it star any where else  it  would be incomplete

Answer: $112.5

Step-by-step explanation:

Given : The equation [tex]y=0.25x+50[/tex] models the cost y of renting a car if the car is driven x miles according to the model .

To find the cost for renting a car if you plan to drive 250 miles, we substitute x= 250 in the given equation , we get

[tex]y=0.25(250)+50\\\\\Rightarrow\ y=62.5+50\\\\\Rightarrow\ y=112.5[/tex]

Hence, the cost for renting a car if you plan to drive 250 miles = $112.5

Thus , the best estimate of the cost for renting a car if you plan to drive 250 miles = $112.5

Answer:

The diagonals intersect each other

Step-by-step explanation:

One of the distinguishing features of triangles is the congruency of the diagonals. The diagonals are bisected into two. Each perpendicular bisector gives a segment of the diagonal that is equal to the other.

6(d+1) -2d=54

 distribute the 6

6d+6 -2d=54

 subtract 2d from 6d

4d+6 =54

subtract 6 from each side

4d=48

divide both sides by 4 to get d

d=48/4

d=12

multiply the cost by 1.10 ( 10% plus cost price)

35.96 *1.10 = 39.556 rounded to $39.56

Answer:

In standard equation format, the condition can be written as [tex]V=5x+12[/tex].

Step-by-step explanation:

The capacity of the bathtub is 32 gallons.

The water already in the tub is 12 gallon.

It takes 5 minutes for the tub to be filled.

Let x be the flow rate of water through tap, in gallon per minutes.

Now, the water filled in the tank in 5 minutes will be [tex]5x[/tex] gallons.

So, in equation, the given condition can be written as,

[tex]V=5x+12\\32=5x+12[/tex]

here V represents the volume of the bathtub.

Therefore, in standard equation format, the condition can be written as [tex]V=5x+12[/tex].

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The standard equation for the volume of water in the bathtub at time t is V(t) = 12 + 4t, indicating the tub starts with 12 gallons and fills at a rate of 4 gallons per minute.

To write a standard equation for filling a bathtub, we need to find the rate at which the tub fills. Since the tub starts with 12 gallons and ends up holding 32 gallons, it needs an additional 20 gallons to be filled. If it takes 5 minutes to fill these 20 gallons, then the fill rate is 20 gallons per 5 minutes.

The equation for the volume V of water in the tub at any given time t (in minutes) is:

V(t) = 12 + r × t

where r is the rate of filling the tub. We already calculated r to be 4 gallons per minute (20 gallons/5 minutes). Therefore, the equation becomes:

V(t) = 12 + 4t

This equation represents the amount of water in the bathtub at any given time t, assuming it starts with 12 gallons and fills at a rate of 4 gallons a minute.

Final answer:

To calculate the account balance at the end of the first year for an investment of $8,000 at 7% per year, the formula for simple interest is used. After applying the formula, the final account balance is determined to be $8,560.

Explanation:

The retiree invests $8,000 in a savings plan that pays 7% per year. To find out what the account balance will be at the end of the first year, we can use the formula for simple interest because it is only for one year. The formula is:

Final amount = Principal amount (1 + (Interest rate * Time))

Let's calculate:

Now, substituting the values into the formula:

Final amount = $8,000 (1 + (0.07 * 1))

Final amount = $8,000 (1 + 0.07)

Final amount = $8,000 (1.07)

Final amount = $8,560

So, the account balance at the end of the first year will be $8,560.

Answer:

m= 19

Step-by-step explanation:

In a linear function the rate of change of y-variable respect x-variable must be constant. In mathematical terms:

Δy/Δx = constant

Given two points of the function: (x1, y1) and (x2, y2), Δy = (y2 -y1) and Δx = (x2 -x1).  So,

Δy/Δx = (11 -27)/(12-10) = -8

(m -27)/(11-10) = -8

(m -27) = -8*(11-10)

m = -8 + 27

m = 19

Final answer:

The number that satisfies the original equation is -4.

Explanation:

A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.

To solve this, we set up the equation -9x - 12 = 8 - 4x.

Solving for 'x' involves simple algebraic steps.

First, add 9x to both sides to get the variable terms on one side:

Next, subtract 8 from both sides to isolate the variable term:

Finally, divide both sides by 5 to find 'x':

The number that satisfies the original equation is -4.