What is the equation of the line in slope-intercept form?

Final answer:

To complete the square for f(x) = x^2 - 6x + 19, we create a perfect square trinomial to rewrite the function as f(x) = (x - 3)^2 + 10, which has a minimum value at the vertex (3, 10).

Explanation:

To complete the square for the quadratic function f(x) = x2 - 6x + 19, we need to form a perfect square trinomial from the x2 and the -6x terms and then adjust the constant term accordingly.

First, we divide the coefficient of the x term, which is -6, by 2, getting -3, and then square it to get 9. We add and subtract this number inside the function to maintain the equality:

f(x) = (x2 - 6x + 9) - 9 + 19

Now, f(x) becomes:

f(x) = (x - 3)2 + 10

Since the coefficient of the x2 term is positive, the parabola opens upward, and the vertex represents the minimum value of the function.

The vertex of the parabola is at (3, 10), so f(3) = 10 is the minimum value of f(x). Therefore, the correct answer is:

D) f(x) = (x - 3)2 + 10 and f(x) has a minimum value f(3) = 10.

The parallel lines are:

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Answer:

-7a-51b

Step-by-step explanation:

-21(a+2b)+14a-9b

-21a-42b+14a-9b

-21a+14a-42b-9b

-7a-42b-9b

-7a-51b

Answer: -7a - 51b

Step-by-step explanation:

see photo for work

Answer:

5

Step-by-step explanation:

Answer:

5 1/2 hours past 7:00 would be 12:30

Step-by-step explanation:

Answer:

12:30 a.m.

Step-by-step explanation:

You can automatically add 5 to the 7, 5 + 7 = 12. Then add 30 to the minuets. 00 + 30 = 30.

So, your answer is 12:30.

Hope this helps!!

Answer

[tex]AP=14[/tex]

Step by Step Explanation

1) Due to the Centroids Theorem we can say that:

AP=2/3AE

AP=2/3*21

∴AP=14

2) Finally, AE =AP+AE

21=14+7 ⇒21=21 True

AP =2PE verifies the Theorem too.

So, the size is 14 .

[tex]AP=14\:u[/tex]

Answer:

perpendicular

Step-by-step explanation:

Convert into y = mx + b form

5y = 6x + 1

y = 6/5x + 1/5

6y = -5x - 4

y = -5/6x - 2/3

Since the y int are different, and the slopes are perpendicular (neg reciprocal), the 2 lines are perpendicular

Answer:

Step-by-step explanation:

Incomplete question.

Answer:

Step-by-step explanation:

22

Answer:

Factored :

2 (5x-3)(x^2+5)

Roots :

[tex]x=\frac{3}{5}  , i\sqrt{5} , -i\sqrt{5} \\[/tex]

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

x = 5

y = 3

6(5) - 3(3)

30 - 9

21

We will subtract 13 from the days of March to find out the days in March Ron will be in Seattle.

Step-by-step explanation:

Given,

Number of days Ron will be in Hawaii = 13 days

Number of days in March = 30 days

As Ron will be in Hawaii for 13 days, the remaining days he will be in Seattle.

So we will subtract 13 from days of March to find out the number of days in March, Ron will be in Seattle.

Number of days in Seattle = Days of March - Number of days in Hawaii

Number of days in Seattle = 30 - 13 = 17 days

We will subtract 13 from the days of March to find out the days in March Ron will be in Seattle.

Keywords: subtraction

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Answer:

x=14.5

Step-by-step explanation:

50.48=-22.02+5x

5x=50.48-(-22.02)

5x=50.48+22.02

5x=72.5

x=72.5/5

x=14.5

Buckets of cement needed is 5 and sand needed is 20

Solution:

Given that Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1 : 4 : 6

cement : sand : gravel = 1 : 4 : 6

Let the cement needed be "1x"

Let the sand needed be "4x"

Let the gravel needed be "6x"

Given that 20 buckets of sand used

4x = 20

x = 5

Thus buckets of cement needed = 1x = 1(5) = 5

Buckets of sand needed = 4x = 4(5) = 20

5 buckets of cement and 20 buckets of sand are needed

Answer:

2:5

Step-by-step explanation:

The ratio of pair of flip flop to pair of sneakers is 4:10 we simplify it to 2:5 by dividing both sides by 2

Answer:

x=1, y=-4. (1, -4).

Step-by-step explanation:

y=-7x+3

y=-x-3

-------------

-7x+3=-x-3

-7x-(-x)+3=-3

-7x+x=-3-3

-6x=-6

6x=6

x=6/6

x=1

y=-1-3=-4

Answer:

Step-by-step explanation:

We are given that IE bisects <KID

Using this, we can say that <EID is congruent to <EIK by the definition of an angle bisector.

We are also given that <IED is congruent to <IEK.

Since these two angles are congruent, we can say that <IDE is congruent to <IKE. This is proven with the 3rd angle theorem.

Since the two base angles are congruent, the triangle is isosceles by the definition of an isosceles triangle.

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.  

% Decrease = Decrease ÷ Original Number × 100

If your answer is a negative number then this is a percentage increase.

Thus, the answer is a 86.7% (rounded) increase.

Final answer:

The sale of KIDZ sneakers increased by $1.3 billion, representing an 86.7% increase when rounded to the nearest tenth of a percent.

Explanation:

To find the percent of increase for the sale of KIDZ sneakers, we subtract the original amount ($1.5 billion) from the new amount ($2.8 billion) and then divide by the original amount. The difference between the two values is $2.8 billion - $1.5 billion = $1.3 billion. To calculate the percentage increase, we divide $1.3 billion by $1.5 billion, which gives us approximately 0.8667. To get the percentage, we then multiply by 100, resulting in an 86.67% increase. Finally, rounding to the nearest tenth of a percent, we get an increase of 86.7%.

210 / x = 15

--> 210/15 = x

--> x = 14

True options:

1. The vertex of the function is at (1,–25).

5. The graph is negative on the entire interval –4 < x < 6.

Step-by-step explanation:

Part of the graph of the function f(x) = (x + 4)(x – 6) is shown in attached diagram.

This graph intesects the x-axis at points (-4,0) and (6,0). So, the x-coordinate of the vertex is \dfrac{-4+6}{2}=\dfrac{2}{2}=1

The y-coordinate of the vertex is

y=(1+4)(1-6)=5\cdot (-5)=-25

Hence, the vertex is ar the point (1,-25) - frist option is true, second option is false.

For all x<1 the graph is decreasing, for all x>1 the graph is increasing. So, third option is false.

The graph is positive (placed above the x-axis) for all x<-4 or x>6. This means fourth option is false.

The graph is negative (placed below the x-axis) for all -4<x<6. This means fifth option is true.

hope this helps homie

Answer:

Step-by-step explanation:

consecutive numbers are one right after the other...

ur 3 consecutive numbers are :

x and x + 1 and x + 2.....and they total 84

x + x + 1 + x + 2 = 84.....combine like terms

3x + 3 = 84

3x = 84 - 3

3x = 81

3x = 81/3

x = 27

x + 1 = 27 + 1 = 28

x + 2 = 27 + 2= 29

so your 3 numbers are 27,28,29 with the lowest being 27

Answer: 24

Step-by-step explanation: This problem states that the sum of 3 consecutive numbers is 84 and it asks us to find the smallest number.

3 consecutive numbers can be represented as follows.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

Since the sum of our 3 consecutive numbers is 84, our equation will read X + X + 1 + X + 2 = 84.

Simplifying on the left we get 3x + 3 = 84.

Subtracting 3 from both sides, we have 3x = 81.

Now we can divide both sides by 3 to get x = 27.

This means that 27 will be the smallest number.

Answer:

It will measure 75 millimetres on the plan.

Step-by-step explanation:

Given:

Scale on the plan = 1:100

Length of the fence =  7,500 mm

To find:

how many millimetres will it measure on the plan

Solution:

As the ratio on the plan is 1: 100, the for 7500 the ratio will

x : 7500

Now by cross multiplication we get

[tex]7500 \times 1 = x \times 100[/tex]

[tex]7500 = 100x[/tex]

[tex]x =\frac{ 7500}{100}[/tex]

x = 75

Final answer:

The fence will measure 75 millimeters on the plan.

Explanation:

To find out how many millimetres a fence that is 7,500 mm long in reality would measure on a plan with a scale of 1:100, you would convert the actual size to the scale size. You do this by dividing the actual size by the scale factor.

Here is the calculation for this scale conversion:

The fence would measure 75 mm on the plan.

Long-term purchase on a credit card better than taking out a loan when interest rate is 0% or very lower than loan, or any other benefits

We can use a credit card for long term purchases if there is a 0% interest rate on purchase is allowing you to pay off your shopping with no additional cost for an introductory period. Or some of the credit cards may offer interest-free purchases for 3 to 6 months others can run for as long as 12 to 14 months. An interest-free period could be considered long-term if it lasts between 12 and 14 months or more.

We could benefit from one of these cards if you are making a large purchase and need more breathing room to pay it off without any interest. This is especially useful if you have a high spending period such as an overseas holiday coming up.

A long  term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.

In order to understand that what is more beneficial for us a long term purchase or taking out a loan we have to see the interest rates of the both the schemes.

If the interest  rate of loan is higher than the interest rate offered by credit card then we must go for long term purchase on credit card and the amount can be paid later .

Also credit cards often offer other benefits too. These options can also be seen as a determining parameters of whether to take loan or a long term purchase on credit card is beneficial.

Also we can have a look at the period of interest free purchase offered by the credit card.

Depending upon the credit card and its usage they can vary from three months to one year with multiple other benefits which promote the use of credit card.

so we can conclude that

A long  term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.

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376 people visited the nature center in September.

Step-by-step explanation:

Given,

Number of visitors in December = 94 people

This number is one quarter of the number of people in September.

One quarter = [tex]\frac{1}{4}[/tex]

Let,

x represent the number of visitors in September.

[tex]\frac{1}{4}x=94[/tex]

Multiplying both sides by 4

[tex]4*\frac{1}{4}x=94*4\\x=376\\[/tex]

376 people visited the nature center in September.

Keywords: fraction, multiplication

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Answer:

Looking at the example Alana will walk. 15.23 miles in two days

step-by-step explanation:

Looking at the example and using place value system

8.63 + 6.60= 15.23 miles

Sum = 14 ones + 8 tenths + 6 hundredths

= 4 ones + 2 tenths + 3 hundredths

= 1 ten + 4 ones + 2 tenths + 3 hundredths

Alana walks 12.3 miles in two days.

In the given problem, Alana walks 6.6 miles on the first day.

To find the total distance she walks in two days, we perform a multi-digit addition.

We start by adding the ones place, which gives us 14 ones. Moving to the tenths place, we add 8 tenths to the existing sum.

In the hundredths place, we have 6 hundredths. This gives us a total of 14 ones, 8 tenths, and 6 hundredths.

Next, we simplify this into a mixed decimal, resulting in 4 ones, 2 tenths, and 3 hundredths.

Converting to place value, this becomes 1 ten, 4 ones, 2 tenths, and 3 hundredths.

Therefore, Alana walks a total of 12.3 miles in two days.

This process involves careful consideration of place value and addition to accurately determine the distance covered over the two-day period.

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complete question should be:

Look at the example problem. Suppose Alana walks 6.6 miles the next day. Complete the steps below to find the number of miles she walks in two days.                                                                                                  

Alana walks ____ miles in 2 days.

Answer: 16

Step-by-step explanation: 80x20=1600

Put the decimal place where it belongs

80% of 20=16

Hope this helps!

To find the number of red skittles in the bag, multiply the total number of skittles by the percentage of red skittles (in decimal form). In this case, there are 16 red skittles in the bag. So, there are 16 red skittles in the bag.

To find the number of red skittles in the bag, we can use the concept of percentages. We know that 20% of the skittles are red, and there are 80 skittles in total. To find the number of red skittles, we multiply 80 by 20% (or 0.20).

80 * 0.20 = 16

So, there are 16 red skittles in the bag.

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Answer: Total cost = Cost of each bottle × Number of bottles

Step-by-step explanation: If each bottle of water Marissa bought cost 0.95cents. This means four bottles will cost = 0.95 + 0.95 + 0.95 + 0.95 = 3.80 cents

This can be written simply as 0.95 × 4 = 3.80 cents

Therefore, a general equation for calculating the total cost of bottle water will be;

Total cost = Cost of each bottle × Number of bottles.

Answer:

6

Step-by-step explanation:

3/5 = 6/10

6/10 / 1/10

6/10 times 10/1

60/10

6

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