Write the quadratic equation y= x^2 -6x + 7 in vertex form

Mrs. Cunningham travels at a speed that is 20mph faster than Mr. Cunningham. Given that Mr. Cunningham has a 165-mile head start, Mrs. Cunningham would need 8.25 hours to cover this distance and catch up with him.

This question can be approached by analysing the relative speeds and the initial advantage Mr. Cunningham had. Mr. Cunningham travels for three hours at 55 mph before Mrs. Cunningham leaves, giving him a 165 mile head start. To determine how long it will take Mrs. Cunningham to overtake Mr. Cunningham, it's necessary to calculate how long it will take her to make up this 165-mile deficit at her faster speed.

Mrs. Cunningham travels 75mph, which is 20mph faster than Mr. Cunningham's speed. Thus, each hour, she closes the distance between them by 20 miles. To find out how many hours it takes her to close the 165 mile distance between them, divide this distance by her relative speed, so: 165miles / 20mph equals 8.25 hours.

Thus, it will take Mrs. Cunningham 8.25 hours to overtake Mr. Cunningham.

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The answer is 7 on e2020.

Answer:

the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]

Step-by-step explanation:

It is given that PQRS is a parallelogram

with sides SR=[tex]4\sqrt{2}[/tex]  and QR = [tex]\sqrt{10}[/tex]

We know that the opposite sides in a parallelogram are equal

so we have

PQ= SR= [tex]4\sqrt{2}[/tex]

PS= QR= [tex]\sqrt{10}[/tex]

Now to find the perimeter of parallelogram we add all the sides

perimeter = [tex]PQ+SR+PS+QR[/tex]

                =[tex]4\sqrt{2} +4\sqrt{2} +\sqrt{10} +\sqrt{10}[/tex] ( plug the values)

                =[tex]8\sqrt{2} +2\sqrt{10}[/tex]

hence the perimeter is [tex]8\sqrt{2} +2\sqrt{10}[/tex]

Answer:

Here, l is the length of the rectangle and w is the width of the rectangle

To Compare the values, you must calculate each given situation.

Area of a rectangle is equal to  length times width.

i.e, [tex]A = l \times w[/tex]

(A)

if l = 8 units and w= 6 units,

then;

[tex]A = l \times w[/tex] = [tex]8 \times 6 = 48 unit^2[/tex]

(B)

if l =7 units  and w = 7 units

[tex]A = l \times w[/tex] = [tex]7 \times 7 = 49 unit^2[/tex]  

Therefore, the Part B would yield a larger area.

If l -7 units and w = 7 units , the area of larger floor is 49 square units.

Answer: B

Step-by-step explanation:

Answer:

B. {3,9,12}

Step-by-step explanation:

test approved

Answer:

B.) $307.60 ; C.) $252 ; B.) $1644

Step-by-step explanation:

1.) Since the employer pays 70% of the premium, this leaves Ms. Everett with 100-70=30% of the cost.

30% = 30/100 = 0.3; this makes her part of the cost

0.3(12304) = 3691.2

She gets paid monthly, so we divide this by 12:

3691.2/12 = 307.6

This means she has $307.60 deducted monthly.

2.) Since the insurance company pays 80% of the costs, this leaves Peter with 100-80 = 20% of the cost.

We take his deductible out of the cost first:

1060-50 = 1010

20% = 20/100 = 0.2; this makes his part of the cost

0.2(1010) = 202+50 = 252, since we have to count the deductible as part of his cost.

3.) The total cost of all visits would be

305(12) = 3660

The insurance company pays 60% of the cost; this means she is left with 100-60 = 40%.  40% = 40/100 = 0.4;

0.4(3660) = 1464

Mattie also pays 12 $15 copays; this adds 12(15) = 180 to this:

1464+180 = $1644

Ms. Everett's monthly deduction for her health insurance premium is $307.60. Peter paid $202 for his nutritional counseling after accounting for the deductible and insurance payment. Mattie paid a total of $1,644 for her chiropractor visits, considering the co-pays and her share of the visit costs after insurance.

1. To determine the amount deducted from Ms. Everett's paycheck for her health insurance premium, we calculate 30% of the total annual premium (since her employer pays 70%) and then divide by 12 to get the monthly deduction.

Total annual premium: $12,304
Employer's share (70%): $12,304 × 0.70 = $8,612.80
Ms. Everett's share (30%): $12,304 × 0.30 = $3,691.20
Monthly deduction: $3,691.20 / 12 = $307.60

2. To find out how much Peter paid for his nutritional counseling, we subtract the $50 deductible from the total cost and then calculate 20% of the remaining amount (since the insurance pays 80%).

Total cost of counseling: $1,060
Deductible: $50
Amount after deductible: $1,060 - $50 = $1,010
Peter's share (20%): $1,010 × 0.20 = $202

3. To determine the total amount Mattie paid for her chiropractor visits, we multiply the co-pay by the number of visits and add to it the total amount of her share for the visits after insurance contribution.

Cost per visit: $305
Insurance pays (60%): $305 × 0.60 = $183
Mattie's share per visit (40%): $305 × 0.40 = $122
Co-pay per visit: $15
Total co-pay: $15 × 12 = $180
Total Mattie's share for visits: $122 × 12 = $1,464
Total amount Mattie paid: $1,464 + $180 = $1,644

To find JL, we simply add the lengths of JK and KL together which gives us 22 units.

If K is the midpoint of JL, it means that JK is equal in length to KL.

Thus, we can set up the equation 5x + 1 (for JK) equal to 7x - 3 (for KL) since these expressions represent the lengths of JK and KL respectively.

Solving the equation 5x + 1 = 7x - 3 for x, we find that x = 2. Substituting x back into the expression for either JK or KL yields the length of one segment, which in this case is 11 units for both JK and KL.

Answer:

The area of the clock face is [tex]79\ m^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=5\ m[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(5^{2})=78.5\ m^{2}[/tex]

Round to the nearest square meter

[tex]78.5\ m^{2}=79\ m^{2}[/tex]

Answer: 39,075 is the answer

Step-by-step explanation:

Answer:

[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for x and y of a 45-45-90 degree triangle.}[/tex]

[tex]\large\underline{\textsf{What is a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \textsf{Triangle?}}[/tex]

[tex]\textsf{A 45}^{\circ} \textsf{- 45}^{\circ} \textsf{- 90}^{\circ} \ \textsf{triangle is a special right triangle with legs that are congruent.}[/tex]

[tex]\textsf{These kinds of Triangles are considered "Special Right Triangles" as first they're}[/tex]

[tex]\textsf{Right Triangles, and secondly they have special side lengths that can be figured}[/tex]

[tex]\textsf{out with only one side length given.}[/tex]

[tex]\underline{\textsf{What are the Ratios between the sides?}}[/tex]

[tex]\tt Leg : Leg : Hypotenuse[/tex]

[tex]\tt x : x : x \sqrt2[/tex]

[tex]\textsf{If we are given a leg, the other leg will equal the same since these kinds of triangles}[/tex]

[tex]\textsf{have 2 equal sides, which are considered \underline{Isosceles Triangles}. Given that 4 is one}[/tex]

[tex]\textsf{leg, this means that the other leg is 4, and the Hypotenuse is 4} \tt \sqrt 2. \ \textsf{The}[/tex]

[tex]\textsf{Hypotenuse is always multiplied by} \ \tt \sqrt 2 \ \textsf{to equal the sum of the legs. Finding}[/tex]

[tex]\textsf{the legs are different however, as we need to divide the Hypotenuse by} \ \tt \sqrt2.[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{We are given the Hypotenuse, and a 45}^{\circ} \ \textsf{angle to show that it's a 45}^{\circ}\textsf{- 45}^{\circ} \textsf{- 90}^{\circ}[/tex]

[tex]\textsf{triangle. Let's divide the Hypotenuse by} \ \tt \sqrt 2 \ \textsf{to find the value of x and y. Remember}[/tex]

[tex]\textsf{that the legs are equal to each other.}[/tex]

[tex]\tt \frac{Hypotenuse}{\sqrt2} = Leg.[/tex]

[tex]\tt \frac{4 \sqrt{\not2}}{\sqrt{\not{2}}} = x \ and \ y.[/tex]

[tex]\large\boxed{\tt x \ and \ y = 4}[/tex]

Answer: There is one outlier, indicating very few books were checked out on that day.

Step-by-step explanation:

The given data of he number of books checked out from a library during the first two weeks of the month:

36, 39, 40, 42, 45, 2, 38, 41, 37, 38, 35, 37, 35, 38

Here , all the data value are near to each other except one i.e. 2.

Since 2 is very small value as compare to the other data values.

It means 2 is the outlier for the data.

It means only 2 books were checked out on that day, which is much lesser number of books than the other day.

Hence, the statements is true based on the data set :

There is one outlier, indicating very few books were checked out on that day.

To solve the quadratic equation 2x^2-2x-12=0, the quadratic formula is used yielding two solutions, x = 3 and x = -2.

To find the solutions for the quadratic equation 2x^2-2x-12=0, we can use the quadratic formula. The general form of a quadratic equation is ax^2 + bx + c = 0. For the given equation, the coefficients are a = 2, b = -2, and c = -12. Applying the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a), we substitute in our coefficients to get:

x = (2 ± √((-2)^2 - 4(2)(-12))) / (2(2))

x = (2 ± √(4 + 96)) / 4

x = (2 ± √(100)) / 4

x = (2 ± 10) / 4

Thus, the two solutions for x are:

Therefore, the two solutions of the quadratic equation 2x^2-2x-12=0 are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The solutions are x = 3 and x = -2.

To solve the equation 2x^2 - 2x - 12 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

For our equation, a = 2, b = -2, and c = -12. Plugging in these values, we get:

$$x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(2)(-12)}}{2(2)}$$

Calculating the values inside the square root:

$$x = \frac{2 \pm \sqrt{4 + 96}}{4}$$

$$x = \frac{2 \pm \sqrt{100}}{4}$$

$$x = \frac{2 \pm 10}{4}$$

So the two solutions to the equation are:

$$x = \frac{2 + 10}{4}$$

$$x = \frac{12}{4}$$

$$x = 3$$

and

$$x = \frac{2 - 10}{4}$$

$$x = \frac{-8}{4}$$

$$x = -2$$

The answer provides the total number of combinations of ice cream cones based on flavors, cone types, and toppings.

The number of different combinations of ice cream cones that can be created considering different flavors of ice cream, types of cones, and toppings:

i put C and it was correct !

Answer:

  f(0) = -1

Step-by-step explanation:

Any scientific or graphing calculator can help you do this. According to the Order of Operations, the exponent is evaluated first, then the sign is applied:

  f(0) = -2^0 = -(2^0) = -1

The approximate probability is  0.40 .

Random selection refers to how the sample is drawn from the population as a whole, while random assignment refers to how the participants are then assigned to either the experimental or control groups.

Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

According to the question

The table below shows the number of U.S. residents with health insurance in 2015, in thousands, categorized by age group and annual income.

Now,

if a U.S. resident with health insurance who was 35-64 in 2015 is selected at random,

The probability that this resident had an income between $50,000 and $74,999

As

By using formula of probability

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

where

Total outcomes = Total resident had an income between $50,000 and $74,999  = 56,908

Number of favorable outcomes = U.S. resident with health insurance who was 35-64 in 2015 and income between $50,000 and $74,999  

= 7,185 + 14,978

= 22,163

Now,

Putting value in formula

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes ).

Probability of an event P(E) = [tex]\frac{22163}{56908}[/tex]

                                                = 0.389

                                                = 0.40 (approx.)

Hence, the approximate probability is  0.40 .

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Final answer:

The students need 9 more blankets to reach their goal of donating 50 blankets. This is a part-whole problem because we are looking for the unknown number of blankets needed to complete the whole goal.

Explanation:

The student club set a goal of donating 50 blankets to a local shelter, with Ms. Carter’s class and Mr. Moriarti’s class contributing towards this goal. To determine how many more blankets are needed, we need to use addition and subtraction. We add the number of blankets collected by both classes then subtract that total from the goal. Ms. Carter’s class gathered 18 blankets and Mr. Moriarti’s class gathered 23 blankets. The sum of their contributions is 18 blankets + 23 blankets = 41 blankets. The goal is 50 blankets, so we subtract the number collected from the goal: 50 blankets – 41 blankets = 9 blankets. So, the answer is that the students need 9 more blankets to reach their goal of 50.

This is a part-whole problem because the unknown number of blankets that are still needed is part of the whole goal of 50 blankets. The problem does not compare the amounts collected by each class, nor does it compare the number still needed with the number collected; instead, it regards the collected blankets as part of the complete set, which is why we can dismiss the other options.