Solve for y in terms of x

6x+3/2y=16

Answer: g(x) = -(x - 6)² + 4

Step-by-step explanation:

g(x) = -x² + 12x - 32

g(x) = -(x² - 12x) - 32

g(x) = -(x² - 2 × x × 6 + 6² - 6²) - 32

g(x) = -[ (x - 6)² - 36 ] - 32

g(x) = -(x - 6)² + 36 - 32

g(x) = -(x - 6)² + 4

Here, (6,4) is vertex.

QP=24 cm

RS=11.25 cm

QS=18.75 cm

Explanation:

Given that TQ bisects <RTP

[tex]therefore <QTP=<QTR\\[/tex](1)

consider ΔRQS and ΔRPT

QS||PT,RP and RT are transversals

[tex]<SQT=<QTP[/tex](alternate angles)(2)

comparing (1) and (2)

[tex]<SQT=<STQ[/tex] and triangle SQT is isocelus

Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle)

Therefore <RQS=<RPT(corresponding angles)

<RSQ=<RTP(corresponding angles)

therefore by AA criterion for similarity

ΔRQS~ΔRPT

According to the property of similar triangles

[tex]RQ/RP=RS/RT=QS/PT[/tex][tex]9/RP=X/30=QS/50\\9/RP=X/30=(30-X)/50\\X/30=(30-X)/50\\50X=30(30-X)\\50X=900-30X\\50X+30X=900\\80X=900\\X=900/80=11.25\\RS=11.25 cm\\QS=30-X=30-11.25\\QS=18.75 cm\\9/RP=X/30\\9/RP=11.25/30\\9*30/11.25=RP\\RP=24 cm[/tex]

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 is 30

Step-by-step explanation:

1.5 of X = 30

1.5*X = 30

X = 30/1.5

= 20

Answer:

20

Step by step explanation:

30/1.5

=20

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:

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:

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:

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

Answer:

320

Step-by-step explanation:

87 1/2% (same as 87.5%) " of " the total jackets " is" 280

let j represent the total jackets

turn ur percent to a decimal....87.5% = 0.875

" of " means multiply , " is " means equals

0.875j = 280

j = 280 / 0.875

j = 320 <====== ur answer

Final answer:

The workers at the clothing factory were expected to make a total of 320 jackets for the week, as 280 jackets represented 87.5% of their weekly target.

Explanation:

To find the total number of jackets the workers were expected to make for the week, we'll set up a proportion where 87.5% corresponds to the 280 jackets they had made by Thursday. We know that 87.5% can also be expressed as the fraction 7/8. Therefore, if 7/8 of the total is 280 jackets, we need to divide 280 by 7 and then multiply by 8 to find the total number of jackets.

First, calculate the number of jackets corresponding to 1/8 of the total:

280 jackets
7 (parts) = 40 jackets

Next, multiply the value of 1/8 of the total by 8 to get the full 100%:

40 jackets
8 (parts) = 320 jackets

So, the workers were expected to make a total of 320 jackets for the week.

Answer:

I would use cubic meters :)

Step-by-step explanation:

Final answer:

The capacity of a backyard pool is commonly measured in gallons in the United States, or liters and kiloliters in countries using the metric system, due to the large volume of water pools can hold.

Explanation:

When considering the capacity of a backyard pool, we're dealing with a fairly large volume of water that needs to be measured. In the United States, the most common unit of measure for this purpose would be gallons, as it is a large unit for capacity suitable for measuring significant amounts of liquid like the volume of water in a swimming pool. Elsewhere, where the metric system is more common, one would likely use liters or kiloliters to quantify the capacity of a backyard pool.

For example, a typical backyard pool may contain about 15,000 gallons of water, which is significantly larger than quantities we would measure in smaller units such as milliliters or ounces. When discussing such large volumes, it's essential to use a unit of measure that appropriately represents the size of the container or space, hence gallons or liters are most suitable for the situation.

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).

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:

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:

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

Answer:

Step-by-step explanation:

| - 425 |=425

| - 720 |=720

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

Answer:

B

Step-by-step explanation:

In the picture above

Hope this helps.

16+18  = 34

40 - 34 = 6

He needs to sell 6 more candy bars.

Answer:

i) [0,4)

ii) [-2,-10]

iii) (-6,-4)

Step-by-step explanation:

i) the interval notation shown in the figure for the first option is [0,4) . Square bracket is used when an end value is included in the range as indicated by the black circle and a normal bracket is used to indicate when the end value is not included in the range as indicated by the white circle.

ii) the interval notation for the second option is given as [-2, 10].

iii) the interval notation for the third option is given by (-6, -4)

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 :)

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:

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:

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:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have two points (1, -4) and (-2, 5).

Substitute:

[tex]m=\dfrac{5-(-4)}{-2-1}=\dfrac{5+4}{-3}=\dfrac{9}{-3}=-3[/tex]

Substitute the value of a slope and the coordinates of the point (1, -4) to the equation of a line:

[tex]-4=-3(1)+b[/tex]

[tex]-4=-3+b[/tex]            add 3 to both sides

[tex]-4+3=-3+3+b[/tex]

[tex]-1=b\to b=-1[/tex]

Finally:

[tex]y=-3x-1[/tex]

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:

e

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

Answer:

e

Step-by-step explanation:

d = e {}^{2}  - 21

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]

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

Learn More

Linear equations:https://brainly.com/question/8738418

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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Answer:

West Painting can paint, on average, 1 7/8 rooms per gallon of paint

Complete statement and question:

At West painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job Will take. If they average painting 3/4 of a room with 2/5 of a gallon of paint, then they can paint, on average ______ rooms per gallon.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of paint needed to paint 3/4 of a room = 2/5 of a gallon

2. They can paint, on average how many rooms per gallon?

Let's use the Rule of Three Simple to answer this question, this way:

Paint                 Rooms

2/5 gallon          3/4

1 gallon               x

x = Number of rooms on average painted with one gallon of paint

x * 2/5 = 3/4 * 1

x = 3/4 / 2/5

x = 3/4 * 5/2 = 15/8 = 1 7/8

West Painting can paint, on average, 1 7/8 rooms per gallon of paint

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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