how do you find the GCF in a math problem?

Answer:

New cars sold = 20,

Used cars sold = 25

Cars serviced = 290

Step-by-step explanation:

In a month they sold fifteen less used cars than twice the number of new cars.

Lets say 'x' number of new cars were sold, then:

The number of used car sold is:

[tex]2\times x-15=2x-15[/tex]

In the same month they serviced fifty more than twelve times the number of new cars sold. So the number of cars serviced is:

[tex]12\times x+50=12x+50[/tex]

Altogether they sold or serviced 335 cars, so the sum of all the cars sold and serviced should be 335:

[tex]x+(2x-15)+(12x+15)=335[/tex]

Solving for 'x' we get:

[tex]x+2x+12x-15+50=335[/tex]

[tex]15x+35=335[/tex]

[tex]15x=335-35=300[/tex]

[tex]x=\frac{300}{15}=20[/tex]

Therefore, the number of new cars sold in that month is 20.

Number of used car sold [tex]=2x-15=2\times 20-15=40-15=25[/tex]

Number of cars serviced [tex]=12\times x+50=12\times20+50=240+50=290[/tex]

We can also cross check by summing them up:

[tex]290+25+20=335[/tex]

Subtract.

1 - 3/8 = 5/8

Think of a cube with side lengths of 10.

The volume of the cube will be L*W*H = 10*10*10 = 1000

This volume of 1000 is what we consider a perfect cube.

Answer: yes

10*10*10=[tex]10^{3}[/tex]

10*10*10=1,000

1,000 is a perfect cube, because 10^3 is 1,000.

I hope this helps :)

hello again

17-1/49 is your correct answer thank you and have a great day please mark me as brainliest if can

Answer:

Expression which represents “seventeen more than one-fourth y” is:

[tex]\dfrac{1}{4}y+17[/tex]

Step-by-step explanation:

We have to find a expression which represents

“seventeen more than one-fourth y”

one-fourth y= [tex]\dfrac{1}{4}y[/tex]

So, seventeen more than one-fourth y= [tex]\dfrac{1}{4}y+17[/tex]

Hence, expression which represents “seventeen more than one-fourth y” is:

[tex]\dfrac{1}{4}y+17[/tex]

Answer:

TRUE

Step-by-step explanation:

Lateral area of cone is given by: πrl

where r is the radius and l is the slant height

Here r=r and l=2h

Hence, lateral area of cone A= π×r×2h

                                            =  2πrh

Lateral area of cylinder is given by: 2πrh

where r is the radius and h is the height

Lateral area of cylinder B=2πrh

Clearly, both the lateral areas are equal

Hence, the statement that:The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is:

True

x + 8y = 0

x - intercept when y = 0:

x + 8(0) = 0

x + 0 = 0

x = 0

y - intercept when x = 0:

0 + 8y = 0

8y = 0    |:8

y = 0

Answer:

The x-intercept is 0

The y-intercept is 0

B. The equation of this line is x = 3.

E. This graph is not a function because the value x = 3 is assigned to more than one y-value.

Remark

The formula for a discriminate is b² - 4*a*c

a = 2

b = 1

c = - 3

So the discriminate =

D =  (1)² - 4*2*(-3)

D = 1 - - 24

D = 25

Answer:

Option D is the correct answer.

Explanation:

 The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function.

We need to find f(x)

Checking each options.

a) f(x) = [tex]2^x[/tex]

    For (0,1)

              f(0) = [tex]2^0=1[/tex]

    For (1,5)

              f(1) =  [tex]2^1=2[/tex], given that f(1) = 5, so option A is wrong.

b) f(x) = [tex]3^x[/tex]

   For (0,1)

              f(0) = [tex]3^0=1[/tex]

    For (1,5)

              f(1) =  [tex]2^1=3[/tex], given that f(1) = 5, so option B is wrong.

c) f(x) = [tex]4^x[/tex]

   For (0,1)

              f(0) = [tex]4^0=1[/tex]

    For (1,5)

              f(1) =  [tex]4^1=4[/tex], given that f(1) = 5, so option C is wrong.

d) f(x) = [tex]5^x[/tex]

   For (0,1)

              f(0) = [tex]5^0=1[/tex]

    For (1,5)

              f(1) =  [tex]5^1=5[/tex]

   For (2,25)

               f(2) =  [tex]5^2=25[/tex]

  For (3,125)

               f(3) =  [tex]5^3=125[/tex]

 So all values are satisfied Option D is the correct answer.

Answer:

B) Isosceles

Step-by-step explanation:

The given triangle has vertices at A(-1,2), B(4,2) and C(3,-1).

We must first determine the length of the sides of the triangle, before we can classify it.

We apply the distance formula to find length of the sides.

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

[tex]\Rightarrow |AB|=\sqrt{(4+1)^2+(2-2)^2}[/tex]

[tex]\Rightarrow |AB|=\sqrt{5^2+(0)^2}[/tex]

[tex]\Rightarrow |AB|=\sqrt{25}[/tex]

[tex]\Rightarrow |AB|=5 units[/tex].

The length of side BC

[tex]|BC|=\sqrt{(3-4)^2+(-1-2)^2}[/tex]

[tex]\Rightarrow |BC|=\sqrt{(-1)^2+(-3)^2}[/tex]

[tex]\Rightarrow |BC|=\sqrt{1+9}[/tex]

[tex]\Rightarrow |BC|=\sqrt{10}[/tex]

The length of side AC

[tex]|AC|=\sqrt{(3--1)^2+(-1-2)^2}[/tex]

We simplify to obtain;

[tex]|AC|=\sqrt{(3+1)^2+(-3)^2}[/tex]

[tex]\Rightarrow |AC|=\sqrt{(4)^2+(-3)^2}[/tex]

[tex]|AC|=\sqrt{16+9}[/tex]

[tex]|AC|=\sqrt{25}[/tex]

[tex]|AC|=5\:units[/tex]

Since [tex]|AC|=5\:units=|AB|[/tex], the given triangle is an isosceles triangle.

The correct answer is

Answer:

B) isosceles

Step-by-step explanation:

The two equations are vertical angles, which mean they are equal.

Set each equation to equal each other and solve for x.

3x-3 = 6(x-10)

Simplify the right side:

3x-3 = 6x-60

Subtract 3x from each side:

-3 = 3x - 60

Add 60 to each side:

57 = 3x

Divide both sides by 3:

x = 57 / 3

x = 19

the slope is 0 over 1 and the y-intercept is 3

Solution :

Given, the equation [tex]y=-2x[/tex].

To graph the equation on the coordinate plane, we first need to derive the different points of the equation  [tex]y=-2x[/tex],

[tex]at\:\;x=0\Rightarrow y= -2(0)=0\\\\at\:\;x=1\Rightarrow y= -2(1)=-2\\\\at\:\;x=2\Rightarrow y= -2(2)=-4\\\\at\:\;x=3\Rightarrow y= -2(3)=-6\\\\at\:\;x=-1\Rightarrow y= -2(-1)=2\\\\at\:\;x=-2\Rightarrow y= -2(-2)=4\\\\at\:\;x=-3\Rightarrow y= -2(-3)=6[/tex]

The graph plotted using these points is shown in the figure,

The formula of a midpoint:

[tex]\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have

[tex]A(-2,\ 5),\ B(3,\ -3)[/tex]

Substitute:

[tex]\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\\dfrac{5+(-3)}{2}=\dfrac{2}{2}=1[/tex]

Answer: (0.5, 1).

Answer:

The midpoint of AB is (0.5,1).

Step-by-step explanation:

From the given graph it is clear that the vertices of the triangle ABC are A(-2,5), B(3,-3) and C(-4,-1).

If end points of a line segment are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the midpoint of that segment is

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

We need to find the midpoint of AB.

[tex]Midpoint=(\frac{-2+3}{2},\frac{5+(-3)}{2})[/tex]

[tex]Midpoint=(\frac{1}{2},\frac{5-3}{2})[/tex]

On further simplification we get

[tex]Midpoint=(\frac{1}{2},\frac{2}{2})[/tex]

[tex]Midpoint=(0.5,1)[/tex]

Therefore the midpoint of AB is (0.5,1).

Answer:

A 1/1,000,000

Step-by-step explanation:

Answer:

He did not add 13 to 26.

Step-by-step explanation:

Given : Step 1: x − 13 = 26  

           Step 2: x = 26 − 13  

           Step 3: x = 39

To Find: Which statement best explains why Step 2 is incorrect in Colton’s solution?

Solution:

Correct steps

Step 1:[tex]x- 13 = 26[/tex]

Step 2:[tex]x = 26+13[/tex]

Step 3:[tex]x = 39[/tex]

So, this concludes that He did not add 13 to 26 in step 2

So, Option C is correct.

Hence He did not add 13 to 26.

Answer:

he did not add 13 to 26

Step-by-step explanation:

Therefore, the best and most correct answer among the choices provided by the question is the fourth choice "15 - 2x ≥ 4y". I hope my answer has come to your help.

Answer:

Step-by-step explanation: B) 2x - 15 ≥ 4y is the correct answer

i think the answer might be 3

The answer is  3. Have a great day!

Answer:

The value of f(-3) is 1.

Step-by-step explanation:

Given expression,

[tex]f(a)=-2a^2-5a+4----------(1)[/tex]

For finding the value of f(-3),

Put a = - 3 in equation (1),

We get,

[tex]f(-3)=-2(-3)^2-5(-3)+4[/tex]

[tex]=-2(9)+15+4[/tex]

[tex]=-18+19[/tex]

[tex]=1[/tex]

Hence, the value of f(-3) is 1 for the given function.

The converse, the inverse, and the contrapositive of the statement

"If the figure is square, then the figure is a quadrilateral." is given below.

We have,

The statement: "If the figure is square, then the figure is a quadrilateral."

Converse:

The converse of the statement switches the "if" and "then" parts of the original statement.

Converse: If the figure is a quadrilateral, then the figure is square.

Inverse:

The inverse of the statement negates both the "if" and "then" parts of the original statement.

Inverse: If the figure is not square, then the figure is not a quadrilateral.

Contrapositive:

The contrapositive of the statement also switches the "if" and "then" parts and negates both of them.

Contrapositive: If the figure is not a quadrilateral, then the figure is not square.

Thus,

Converse: If the figure is a quadrilateral, then the figure is square.

Inverse: If the figure is not square, then the figure is not a quadrilateral.

Contrapositive: If the figure is not a quadrilateral, then the figure is not square.

Learn more about converse, inverse, and contrapositive here:

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okay so you just plug in the x and ys. x is the first number, y is the second. then you just do them all out

So we know that an ordered pair looks like (x,y), right? For this inequality, we're supposed to plug in the values of x and y. If it isn't true, then the inequality does not represent the ordered pair.

First option: (0,1)

[tex]2x + 3y \geq -1[/tex] --> [tex]2(0) + 3(1) \geq -1[/tex] --> [tex]5 \geq -1[/tex]

So this option is correct.

Second option: (-2,1)

[tex]2x + 3y \geq -1 --> 2(-2) + 3(1) \geq -1[/tex]

--> [tex]-4 + 3 \geq -1 --> -1 \geq -1[/tex]

This is also correct.

Third option: (-6,0)

[tex]2(-6) + 3(0) \geq -1 --> -12 \geq -1[/tex]

This is not true, so this option is not correct.

Fourth option: (0,-1)

[tex]2(0) + 3(-1) \geq -1 --> -3 \geq -1[/tex]

This is not correct.

Fifth option: (2,-1)

[tex]2(2) + 3(-1) \geq -1 --> 4 - 3 \geq -1[/tex]

This is correct.

To solve this problem we will directly use the formula:

[tex]h=\frac{1}{2}gt^2[/tex]..........Equation 1

where symbols have their usual meanings.

Here g=32.2 ft/s^2 and h=108 feet

Therefore, from Equation 1 we will get:

[tex]t=\sqrt{\frac{2h}{g}}[/tex]....Equation 2

Plugging in the values in Equation 2 we get:

[tex]t=\sqrt{\frac{2\times 108}{32.2}}\approx 2.59[/tex] seconds.

Therefore, the amount of time it would have taken the rock to fall is 2.59 seconds.

Answer:

$28 per pair is not a good estimate.

Step-by-step explanation:

Let x represent cost of each pair with tax.

We have been given that a case of 24 pairs of the same kind of sport shoes cost a little more than $800.

The cost of 24 pairs would be [tex]24x[/tex].

[tex]24x>800[/tex]

[tex]\frac{24x}{24}>\frac{800}{24}[/tex]

[tex]x>33.33[/tex]

Since the cost of each pair is greater than $33.33, therefore, $28 is not a good estimate.

f(a,b) = 2(a+b)

f(2,3) = 2(2+3)

f(2,3) = 2(5)

f(2,3) = 10

Step 1: Add 3 to both sides.

2x-3+3=7+3

2x=10

Step 2: Divide both sides by 2.

2x/2=10/2

x=5

Standard Form 2x-10=0

Factorization 2(x -5)=0

Solution x=10/2=5

zm= a+b/a, for a

Switch sides to have a on left side

a+b/a=zm

Now multiply both sides by a

A+b= zm(a)

A+b= ama

Now subtract azm both sides

A+b-azm=0

Subtract b both sides

A-azm= -b

Factor out a from ask

A(1 -zm)= -b

Divide each term by 1 - zm to get

A= - b/1-zm

a line through the point (0, 6 )

to find a point on the line, choose any value of x , substitute into the equation and solve for y

x = 0 : 0 + 4y = 24 ( divide both sides by 4 )

y = [tex]\frac{24}{4}[/tex] = 6

hence line goes through (0, 6 )

The correct graph that represents the equation 2x + 4y = 24 is option A, which shows a line through the points (0, 6) and (12, 0).

The equation 2x + 4y = 24 can be rearranged to y = -0.5x + 6. This means that the equation represents a linear function with a slope of -0.5 and a y-intercept of 6.

Option A, which shows a line through the points (0, 6) and (12, 0), is the correct graph since it satisfies the equation. The slope is -0.5 and the y-intercept is 6.

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