Which equation represent a line that is parallel to the y-axis and passes through the point (4,3)?

y = 2x + 1 is the equation of a line that passes through (1,3) and (4,9)

Solution:

Given that we have to write the equation of a line that passes through (1,3) and (4,9)

Let us first find the slope of line

The slope of line is given as:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here the given points are (1,3) and (4,9)

[tex](x_1, y_1) = (1, 3)\\\\(x_2, y_2) = (4, 9)[/tex]

Substituting the values in formula, we get,

[tex]m = \frac{9-3}{4-1}\\\\m = \frac{6}{3} = 2[/tex]

Thus slope of line is 2

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope and "c" is the y - intercept

To find the y intercept, substitute (x, y) = (1, 3) and m = 2 in eqn 1

3 = 2(1) + c

c = 1

Thus the equation of line is:

Substitute c = 1 and m = 2 in eqn 1

y = 2x + 1

Thus equation of line is found

16+18  = 34

40 - 34 = 6

He needs to sell 6 more candy bars.

Answer:

8 hour.

Step-by-step explanation:

because for it takes 1 hour for 55 miles .

so,

here, divide the 440/55 =8 hours.

explanation,

it takes 1 hour to complete the 55 miles and here we have to complete the 440 miles.

so, above we divide the 440 miles by 55 miles for hour. result =8 hour

to verify the answer.

you can multifly by 8 * 55 and result=440miles. because it is directily propotional.

for another to verify the answer.

dived the 440/8 and result comes=55 miles / hour.becauseit is directly propotional.

Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.

To find the amount of time it will take Steve to get to the Grand Canyon, you can divide the distance he needs to travel (440 miles) by his average rate (55 mph). This will give you the time it takes in hours:

Time = Distance / Rate

So, in this case:

Time = 440 miles / 55 mph = 8 hours

Therefore, it will take Steve approximately 8 hours to drive to the Grand Canyon.

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The best estimate for the sum of 1/8 and 1/6 is 5/24.

The best estimate for the sum of 1/8 and 1/6 is 5/24.

To find the sum of fractions, we need to find a common denominator, which is the least common multiple of the denominators. In this case, the LCM of 8 and 6 is 24.

Thus, we can rewrite 1/8 as 3/24 and 1/6 as 4/24.

Adding 3/24 and 4/24 gives us a total of 7/24, which can be simplified to 5/24.

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The best estimate for the sum of 1/8 and 1/6 is 1/4. Thus, the closest estimate is Option A.

To determine the best estimate for the sum of 1/8 and 1/6, we can use approximate fractions that are easier to work with. 1/8 is approximately equal to 0.125 and 1/6 is approximately equal to 0.167. Adding these decimal values together gives us:

0.125 + 0.167 ≈ 0.292

Given this, we can conclude that the sum will be closer to 1/4 than to 1/2 or 1. So, the best estimate for the given sum is Option A.

Complete question:

​What is the best estimate for this sum?

1/8+1/6

A. The sum will be close to 1/4.

B. The sum will be close to 1/2.

C. The sum will be close to 1.

Answer:

The expression that represents the sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]

Step-by-step explanation:

Given that the sum of b and [tex]5x^2[/tex]

To find the expression that represents the sum of b and [tex]5x^2[/tex] :

The sum of b and [tex]5x^2[/tex] can be written as [tex]b+5x^2[/tex]

Therefore The sum of b and [tex]5x^2[/tex] is [tex]b+5x^2[/tex]

The expression that represents the sum of b and [tex]5x^2[/tex] is  [tex]b+5x^2[/tex]

Answer:

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

Step-by-step explanation:

Vertex Form Of The Parabola

The equation of a parabola can be expressed in either standard or vertex form. The standard form is

[tex]y=ax^2+bx+c[/tex]

and the vertex form is

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

Where (h,k) it the vertex of the parabola

Transforming one into the other form is easily achieved by applying simple algebra .

Our function is

[tex]y=x^2-12x+40[/tex]

Completing squares, we have

[tex]y=x^2-12x+36+40-36[/tex]

Reducing

[tex]\boxed{y=(x-6)^2+4 }[/tex]

The vertex of the parabola is the point (6,4)

Final answer:

To convert the quadratic equation y = x^2 - 12x + 40 into vertex form, the completing the square method is employed, resulting in y = (x - 6)^2 + 4, showing the vertex at (6, 4).

Explanation:

Converting a Quadratic Equation to Vertex Form

The question asks how to convert the quadratic equation y = x2 - 12x + 40 into its vertex form. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation into vertex form, we'll use completing the square method.

This shows the quadratic equation in vertex form with the vertex at (6, 4).

The currently rented double-occupancy apartments are 38 apartments.

Step-by-step explanation:

An apartment has rented x apartments with two occupants and 16 apartments with one occupant and the total occupants were 92, these can be written in the equation as

[tex]2x+16=92[/tex]

To find the number of double occupancy apartments that are rented, we need to solve the equation and find the value of x.

[tex]2x+16=92[/tex]

Subtracting 16 from both sides of the equation,

[tex]\begin{aligned}&2 x=92-16\\&2 x=76\end{aligned}[/tex]

Dividing both sides by 2, we get,

[tex]\begin{aligned}\frac{2 x}{2} &=\frac{76}{2} \\x &=38\end{aligned}[/tex]

Thus, there are 38 double-occupancy apartments are currently rented.

The correct answer is that there are 38 double-occupancy apartments currently rented.

To solve the problem, we start with the given equation that represents the total number of occupants in the apartment building:

[tex]\[ 2x + 16 = 92 \][/tex]

This equation takes into account that each double-occupancy apartment (x) houses two occupants, and there are also 16 single-occupancy apartments. We want to find the value of x, which represents the number of double-occupancy apartments.

First, we subtract 16 from both sides of the equation to isolate the term with x:

[tex]\[ 2x + 16 - 16 = 92 - 16 \][/tex]

[tex]\[ 2x = 76 \][/tex]

Next, we divide both sides of the equation by 2 to solve for x:

[tex]\[ \frac{2x}{2} = \frac{76}{2} \][/tex]

[tex]\[ x = 38 \][/tex]

Therefore, there are 38 double-occupancy apartments currently rented in the building. This matches the correct answer provided at the beginning.

Answer:

It is 6+w, z=1, and 2x^4-y

Step-by-step explanation:

The expressions which are polynomials are;

A polynomial by definition is an expression which is composed of variables, constants and exponents, which are combined using the mathematical operations including addition, subtraction, multiplication and division.

On this note, all of expressions are polynomials.

Read more on polynomials;

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Answer:

Y(x+2) (x+6)

Step-by-step explanation:

Answer:

2,360

Step-by-step explanation:

18% of 2,000 is 360

(0.18)*(2,000)=360

2,000 + 360 = 2,360

Answer: I=2000 + 0.18 T

Step-by-step explanation:

Answer:

The answer = 6

Step-by-step explanation:

Given expression:

[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]

To evaluate the  given expression, when [tex]c=14[/tex] and [tex]d=3[/tex]

Solution:

We have:

[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]

Plugging in [tex]c=14[/tex] and [tex]d=3[/tex] in the given expression, to evaluate.

⇒ [tex]\frac{14}{2}-3+\frac{6}{3}[/tex]

Evaluating:

⇒ [tex]7-3+2[/tex]

⇒ 6 (Answer)

Answer:

hmm 6

Step-by-step explanation:

Answer:

undefined, stays on x so straight vertical - vertical line is undef slope

Answer: The slope is undefined  

Step-by-step explanation:

The slope of a line is calculated using the formula :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = -7

[tex]x_{2}[/tex] = -7

[tex]y_{1}[/tex] = -7

[tex]y_{2}[/tex] = 1

Substituting the values into the formula , we have :

m = [tex]\frac{1-(-7)}{-7-(-7)}[/tex]

m = [tex]\frac{8}{0}[/tex]

m = undefined

Answer:

-1

Step-by-step explanation:

It’s just simple don’t worry just look I won’t make you need the explanation god bless :)

y=2x-0.5

Step-by-step explanation:

Given the expression of Δy in terms of Δx as;

Δy=4/2 Δx

Given y=2.5 and x =1.5 then substituting in the equation above will give;

y-2.5=2(x-1.5)

y-2.5=2x-3

y=2x-3+2.5

y=2x-0.5

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Keywords : formula, expresss

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To write a formula that expresses y in terms of x, we can use the equation y = mx + b. Substitute the given values of x and y into the equation and solve for m and b. The final formula is y = 1.67x + 1.25.

To write a formula that expresses y in terms of x, we need to determine the relationship between y and x. In this case, we know that when x = 1.5, y = 2.5. So we can start with the equation y = mx + b, where m is the slope and b is the y-intercept.

Using the given values, we can substitute x = 1.5 and y = 2.5 into the equation y = mx + b: 2.5 = 1.5m + b. Now we can solve for m and b by using the given values and algebraic manipulation.

By rearranging the equation and substituting the values of x and y, we can determine the formula that expresses y in terms of x. The final formula will be y = 1.67x + 1.25.

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To make 'n' the independent variable, solve the equation 3m - 2n = 12 by isolating n to obtain n = (3/2)m - 6.

To rearrange the equation 3m - 2n = 12 so that n is the independent variable, you'll want to solve for n. Here's how you do it step by step:

This way, n is now expressed as a function of m, making n the independent variable in the equation.

Answer:

210 people are there at the fair

Step-by-step explanation:

Let the total number of people at the fair = X

People under 16 years old        = 70% of X = 0.7 X

People remaining                       = Total number of people - Under 16 years

                                                    = X - 0.7X = 0.3X

The number of teachers             = 1/3 of People remaining = 1/3 of 0.3X

Since there are 21 teachers

                            1/3 of 0.3X       =  21

                              1/3 x 0.3X       =  21        

                                     0.1X         =   21  

Divide both sides by the coefficient of X            

                                    0.1X/0.1     =   21/0.1

                                               X     =  210

That is 210 people are there at the fair

Answer:

530.05

Step-by-step explanation:

you add 448 and 1.75 together, which is 449.75, then you add 449.75 and 80.3 together, which adds up to 80.3 hope this helps :)

Answer:

Step-by-step explanation:

| - 425 |=425

| - 720 |=720

Beacause 720>425=>| - 720 |>| - 425 |

Nia's backpack after 30% off represents 70% of the original backpack cost. Setting up a ratio of 70/100 = 14/X, we can solve for the original price, X. Patrick will pay $20 if he does not have a 30% off coupon.

This problem can be solved using a bit of Percentage Calculations. We know that after a 30% discount, Nia's backpack cost $14. This means that $14 represents 70% of the original backpack cost (100% - 30%). So to find out the 100%, or the full price, we need to determine what number 70% is 14 of. We can set up a ratio to find the original cost (X).

The steps are:

So, the backpack would cost Patrick $20 without a 30% off coupon.

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Answer:b

Step-by-step explanation:

Answer:

Subtraction then Division

Step-by-step explanation:

Right on Edg

Answer:

Step-by-step explanation:

Student who don't play sports =  24 - 10 = 14

the ratio of students who play sports to those who do not = 10 : 14 = 5:7

Step-by-step explanation:

10:24

5:12

is can be you answer

The height of lighthouse is 52.2 yards

Solution:

Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the  ground and the top of the lighthouse is 41 degree

The diagram is attached below

Consider a right angled triangle ABC

AB is the height of the lighthouse

BC is the distance between the base of a lighthouse and Photographer

As per given, BC = 60 yards

Angle between the ground and the top of the lighthouse is 41 degree

Angle ACB = 41 degree

To find: height of lighthouse i.e AB = ?

We know that,

[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]

Here Base is BC and perpendicular is AB

[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]

Substituting the values,

[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]

Thus the height of lighthouse is 52.2 yards

Answer:

52.2

Step-by-step explanation:

It was correct on my assignment

Answer:

well i need to see the graph

Step-by-step explanation:

Both forms are equivalent, just different ways to write the same thing

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

Explanation:

Use the slope formula first

The points we plug in are (x1,y1) = (-3,4) and (x2,y2) = (6,1)

m = (y2-y1)/(x2-x1)

m = (1-4)/(6-(-3))

m = (1-4)/(6+3)

m = (-3)/(9)

m = -1/3

The slope of the line is -1/3

Use one of the points, say the point (x,y) = (-3,4) and the slope we just found with y = mx+b. The goal is to solve for b

y = mx+b

4 = (-1/3)*(-3) + b

4 = 1 + b

4-1 = b

3 = b

b = 3

We have m = -1/3 as the slope and b = 3 as the y intercept

Therefore, the equation in slope intercept form is y = (-1/3)x + 3

In standard form, Ax+By = C, this is is equivalent to x+3y = 9 after we multiply both sides by 3, then add x to both sides.

Answer:

Option D.

Jenn's answer is not correct. She got it substituting [tex]c=4[/tex] into the equation and solving for "x".

Step-by-step explanation:

Given the following equation:

[tex]\frac{1}{2}(2x + 4) = 3x-c[/tex]

Since you need that [tex]x=4[/tex], you hace to substitute that value into the equation:

[tex]\frac{1}{2}(2(4) + 4) = 3(4)-c[/tex]

Now you need to solve for "c":

[tex]\frac{1}{2}(8 + 4) = 12-c\\\\\frac{12}{2}= 12-c\\\\6=12-c\\\\c+6=12\\\\c=12-6\\\\c=6[/tex]

Therefore for a  a value of [tex]c=6[/tex], you get [tex]x=4[/tex]

Then, the you can identify that the correct answer is the one given in the Option D.

Jenn made a mistake, because she substituted [tex]c=4[/tex] into the equation and then solve for "x":

[tex]\frac{1}{2}(2x + 4) = 3x-(4)\\\\x+2=3x-4\\\\2+4=3x-x\\\\6=2x\\\\\frac{6}{2}=x\\\\x=3[/tex]

To determine the value of c when x equals 4 in the given equation, substitute x with 4 and solve for c. The resulting value of c is approximately 11.9167.

To find the value of c for which x = 4 in the equation 1 / (2x + 4) = 3x - c, we start by substituting x with 4:

1 / (2×4 + 4) = 3×4 - c
1 / (8 + 4) = 12 - c
1 / 12 = 12 - c

Now we solve for c:

1 / 12 = 12 - c
c = 12 - 1 / 12
c = 12 - 0.0833

Finally, we find the value of c:

c = 11.9167

Therefore, for x = 4, the value of c is approximately 11.9167.

Answer:

none of above because the correct equation is y= -3x+90

Answer:

e

[tex]d = e {}^{2} - 21 [/tex]

Answer:

e

Step-by-step explanation:

d = e {}^{2}  - 21

Answer:

Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?

Step-by-step explanation:

Water tank A has a capacity of 250 gallons and is 77% full. Water Tank B is 68% full. The ratio of the capacity of tank A to tank B is 5 : 14. What is the capacity of tank B?

Step-by-step explanation:

Hi! I am a little confused because in this question they would normally ask for the equation of the line but if you are wondering what the slope is, it says in the information that the slope is 2. I will solve for the line equation anyway though.

A line has this form: y=mx+b.

For this question they will want us to give the answer with x and y as variables (letters) and m and b (the slope and y-intercept respectivly) with numerical values.

First, we can put in the point into the equation. The point given is (14,33) so the x value is 14 and they y value is 33.

y=mx+b

33=m(14)+b

We know the slope is 2 (from the given information) so we can substitute that in for m.

33=(2)(14)+b

Solving for b, the Y-intercept, we get b=5.

Perhaps your question was "what is the Y-intercept" and then this would be the answer.

Finally, the final equation for the line is:

y=2x+5

Hope this helps!

Answer:

Step-by-step explanation:

Hey there) We do it like this:

[tex]6\times 3\times 4+3\times 3\times 2=90[/tex]

Hope, this helps. Have a nice day :)