Mr Edwards buys 2 new knobs for each of his kitchen cabinets. How many knobs does he buy?

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).

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:

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:

B

Step-by-step explanation:

In the picture above

Hope this helps.

Answer:

Step-by-step explanation:

1. animals - rabbit

2. plants - moss, flowers etc .

3. fungi - mushroom

4. protista - giant kelp

5. eubacteria - thermus

6. archaebacteria - euryarchaeota

Answer:

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

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:

To find the y-intercept of a line you need to first put it into the equation y=mx+b

x+3y=14 (minus x from each side)

3y=-x+14 (divide both sides by 3)

y=-1/3x+14/3

Your y-intercept is the b in the formula above, so your y-intercept would be 14/3

Hope this helps ;)

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: 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.

Answer:

Option B is correct.

Step-by-step explanation:

Paul was asked to use the elmination to find the solution to the system of linear equations

What are the missing steps in his work below?

So, the step missing is multiplying equation 1 by 2 i.e

So, Option B is correct.

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.

The measure of angle y in the heptagon is 145 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

To find the measure of angle y in a heptagon, we can use the formula for the sum of the interior angles of a polygon, which is:

Sum of interior angles = (n-2) x 180 degrees

where n is the number of sides of the polygon.

For a septagon (a polygon with seven sides), we can substitute n=7 into the formula:

Sum of interior angles = (7-2) x 180 degrees = 5 x 180 degrees = 900 degrees

We can now find the value of angle y by adding up the measures of all the given angles and subtracting the sum from the total sum of the interior angles:

y = 900 - (129 + 116 + 120 + 130 + 135 + 125) = 145 degrees

Therefore, the measure of angle y in the Heptagon is 145 degrees.

Read more on regular polygon here:

brainly.com/question/20911145

#SPJ7

Complete question:

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 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

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

#LearnwithBrainly

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.

https://brainly.com/question/14824020

#SPJ6

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:

  (c)  10 cm, 9 cm, 9 cm

Step-by-step explanation:

You want to identify the set of side lengths that can form a triangle.

The triangle inequality requires a + b > c, for any assignment of a, b, c to side lengths. In effect, the sum of the two shortest sides must exceed the length of the longest side.

  6+6 = 12 < 15 . . . . not a triangle

  6+7 = 13 . . . . . . . . not greater; not a triangle

  9+9 = 18 > 10 . . . . forms a triangle

  4+8 = 12 < 14 . . . . not a triangle

The set of sides that will make a triangle is {10 cm, 9 cm, 9 cm}.

__

Additional comment

The semiperimeter (half the sum of side lengths) is always greater than any side length in a triangle. For example, if the perimeter is 20, the longest side must be less than 10.

By applying the Triangle Inequality Theorem, we find the only set of sides that could make a valid triangle is 10 cm, 9 cm, 9 cm.

The question is asking to identify which set of given lengths could make a valid triangle. To answer this question, it's important to remember the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this concept to each option.

Therefore, the only set of lengths that could make a valid triangle is 10 cm, 9 cm, 9 cm.

https://brainly.com/question/1163433

#SPJ11

Answer:

u = 40° , v = 40° and x = 100°

Step-by-step explanation:

i) from the rule of triangle we know that the sum of all three angles = 180°

ii) 100° + 40° + y = 180°. Therefore y = 40°. where y is the angle adjacent to v.

iii) from theorem on parallel lines we can say that u = y =40°

iv) from the properties of parallel lines we get v = 40° as interior alternate angles are equal.

v) again from the properties of parallel lines we get u = 40°

vi) using the triangle property as in i) we can see that u + v + x =180° therefore 40° + 40° + x = 180°. Therefore x = 100°.

vii) Therefore u = 40° , v = 40° and x = 100°

Answer:

25422

Step-by-step explanation:

Answer:

6x+9

Step-by-step explanation:

add like terms

5x+x=6x

7+2=9

5x+7+x+2=6x+9

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:

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:

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 :)

Answer:

Step-by-step explanation:

| - 425 |=425

| - 720 |=720

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

Answer:

6

Step-by-step explanation:

20-8=12

12÷2=6

6x6=36

Answer:

Step-by-step explanation:

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:

see attached work shown