complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15

Answers

Answer 1

[tex] - {x}^{2} - 4x + 15 \\ = - {x}^{2} - 4x - 4 + 15 + 4 \\ = - ( {x}^{2} + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^{2}}_{ \leqslant 0} + 19 \\ \Rightarrow - {(x + 2)}^{2} + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2

[/tex]


Related Questions

Please help. I think I know the answer but I am not 100 percent sure.

Answers

Answer:   105°

Step-by-step explanation:

∠U and ∠S are supplementary angles, so

∠U + ∠S = 180°

 x  +  75° = 180°

 x            = 105°

Answer:

x = 105 degrees.

Step-by-step explanation:

RS is parallel to  TU so x + 75 = 180

x = 105 degrees.

As its is isosceles y is also = 105 degrees.

If the outside temperature ranges from -5 degrees c to 40 degrees c, find the range in degrees fahrenheit.

Answers

Answer: -109

Step-by-step explanation:

if you make celcius into fahrenheit,

-5 degrees becomes 23 degrees

40 degrees becomes 104 degrees

-5 + 104 = -109

Answer:

Step-by-step explanation:

(1CQ) Write the repeating decimal as a fraction .51

Answers

Answer: Your answer is 17/33! Hope this helps. If you need anymore help let me know!

For this case we must indicate the representation in the form of a fraction of the following decimal number:

0.51 periodic number

Option A:

[tex]\frac {17} {100} = 0.17[/tex]

Option B:

[tex]\frac {51} {100} = 0.51[/tex]

Option C:

[tex]\frac {17} {33} = 0.51515151[/tex]

Option D:

[tex]\frac {51} {33} = 1.5454[/tex]

So, the correct option is C

Answer:

Option C

The function below has been transformed from f(x) = x2. Describe the transformation. h(x) = 4x2 + 12

Answers

Answer:

vertically expanded by a factor of 4then, translated upward 12 units

Step-by-step explanation:

If f(x) = x² and g(x) = 4x² = 4f(x), the function g(x) represents a vertical expansion of f(x) by a factor of 4.

If h(x) = g(x) +12, the function h(x) represents a translation of g(x) by 12 units upward.

Together, these transformations on f(x) are ...

vertical expansion by a factor of 4translation upward by 12 units

_____

Please be aware that there are alternate transformations that will do the same thing:

  h(x) = 4(f(x) +3) . . . . is a translation upward by 3, then a vertical expansion by a factor of 4

  h(x) = f(2x) +12 . . . . is horizontal compression of f(x) by a factor of 2, then a translation upward by 12.

Which of the following shows the correct order of the numbers below?

First who answers will get brainlyest

Answers

Answer:

c)

Step-by-step explanation:

if you look at option c it would be correct because 0.75 (3/4) is bigger than 0.7. Then 11/12 is a bigger proportion then 0.75. there for your answer is correct.

Final answer:

The correct order of the numbers given when converted to decimals for easy comparison is 0.7, 3/4 and 11/12, which corresponds to option b: 0.7 < 3/4 < 11/12.

Explanation:

This is a question about comparing and ordering fractions and decimals. To answer this, we first need to convert all the numbers into the same format. We can convert the fractions 11/12 and 3/4 into decimals for easier comparison.

First, to convert 11/12 to a decimal, you'll do the division to find approximately 0.9167. Secondly, 3/4 can be converted to a decimal by performing 3 divided by 4, which equals 0.75. Now, we can easily compare these decimals to 0.7.

From this, we can see that 0.7 is less than 0.75 (3/4) and both 0.7 and 0.75 are less than 0.9167 (11/12). So the correct order of the numbers from least to greatest would be 0.7 < 3/4 < 11/12.

So the correct option is b. 0.7 < 3/4 < 11/12.

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A college football stadium holds 45,000 fans. In a random sample of 30 fans, 26 were wearing the colors of the home team. Predict the number of fans who are wearing the colors of the home team.

Answers

Answer:

38,999

Step-by-step explanation:

In your sample you have 26 out of 30. I like to get that number into a percentage, so you do 26 divided by 30

26/30 = .8666

Then you take your total amount of fans, 45,000 and multiply it by your percentage wearing team colors.

45,000 x .8666 = 38,999.97

Since you can't have .97 of a person, your round it down to 38,999.

Mr. Fox took 3,648 pieces of candy and divided it into treat bags of 14 pieces of candy each. How many treat bags was he able to make with the candy?

Answers

The answer to this question is 260

3 /(6x4 x7x7 x1(6 would be 11 because the power of 3x11 would be 33 leaving it to the power of 11

David and Tonya each cut a cylinder in half. The cross-section that results from David's cut is a rectangle. The cross-section that results from Tonya's cut is a circle.

Answers

Answer:

Tonya cut the cylinder vertically and David cut it diagonally.

Final answer:

David’s cut along the length of his cylinder resulted in a rectangular cross-section, while Tonya’s perpendicular cut resulted in a circular cross-section. This illustrates principles of geometric cross-sections and plane intersections with solids.

Explanation:

In the problem described, David and Tonya are each cutting a cylinder, a geometric shape. The cuts they make, and the cross-sections they create, depend on the orientation of their cuts in relation to the shape of the cylinder.

When David cuts the cylinder, his cross-section result is a rectangle. This implies that he made a longitudinal cut along the length of the cylinder, essentially splitting it from top to bottom.

When Tonya cuts her cylinder, the cross-section is a circle. This means she made a cross-sectional cut perpendicular to the length of the cylinder, slicing it into two equal half cylinders.

This problem illustrates the principles of geometric cross-sections and plane intersections with solids, which are part of the broader field of study in geometry.

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We have 7 sandwiches. Everyone ate 1/4 sandwich for a snack. How many people had sandwiches

Answers

7 divided by 1/4 equals 7 times the reciprocal of 1/4, which is 4
7 divided by 1/4 equals 7x4=28
28 people had sandwiches.

By dividing the 7 sandwiches into quarters, 28 quarters are available, allowing for 28 people to have 1/4 sandwich each.

The student has asked: "We have 7 sandwiches.

Everyone ate 1/4 sandwich for a snack.

To find out how many people can have sandwiches, we first need to understand how much of a sandwich each person gets.

Since each person ate 1/4 of a sandwich, we can take the total number of sandwiches (7) and divide them into quarters, giving us [tex]7 * 4 = 28[/tex] quarters of sandwiches.

Since each person eats one quarter, 28 people can have sandwiches.

James thought of a number and divided it by 9.

What can he do to get back his original number?

A) multiply by 9.
B) add 9.
C) divide by 9 again.
D) subtract 9.

Answers

The correct answer is A.

Example: 36 divided by 9= 4 and 4 x 9 = 36

Example: 72 divided by 9= 8 and 8 x 9 = 72

Hope this helps.

To get back the original number after dividing by 9, one should multiply the result by 9, because multiplication and division are inverse operations.

The student's question asks: James thought of a number and divided it by 9. What can he do to get back his original number? The correct answer is (A) multiply by 9. When a number is divided by 9 to undo this operation one must multiply it by 9. This is because multiplication is the inverse operation of division. Therefore, if James wants to obtain his original number back, he should take the result he got after dividing by 9 and multiply it by 9.

In circle O, the measure of ∠ROW is 110°. What is the measure of arc RAW?

Answers

Answer:

250°

Step-by-step explanation:

We know that a circle has a total of 360°.

Now we know that ∠ROW is 110° and that Arc RAW has the same End points as ∠ROW.

We can safely assume that arc RAW will be the difference of ∠ROW and 360°.

So we then get:

360° - 110° = 250°

This means that Arc RAW will be 250°

Which system of linear inequalities is graphed?

Answers

Both lines are dotted so no equation should include equal to in it.

The shaded area is on the left side .

The correct answer would be y>2x+1 and x+y = -2

The 3rd answer is correct.

Answer:

y>2x+1 and x+y < -2 represent the graph line.

Step-by-step explanation:

Given : graph .

To find : Which system of linear inequalities is graphed

Solution : We have given graph with two line both lines are dotted line and shaded down.

Equation of line form  : y = mx + b.

Where, m = slope ,  b= y intercept.

Line x+y < -2 less than sign for shaded down and y intercept -2.

and y>2x+1.

Therefore, y>2x+1 and x+y < -2 represent the graph line.

Which expression is equivalent to sqr 400i8j4k6

Answers

I have attached the correct answer. Brainliest will be much appreciated!

Which expression can you use to find the slope of the line containing the points -3, 2 and 7 , -1

Answers

Use the formula y1-y2/ x1-x2. 2+1/-3-7= 3/-10

Fill in the blank to make the the equation true

__________ x 9/5 = -27

Answers

Answer:

-15

Step-by-step explanation:

Multiply the whole equation by the inverse of the multiplier of the blank. Then you get ...

___ × 1 = (-27)×(5/9) = -15

The blank filled with -15 will make the equation true.

We could represent the blank as a variable o make solving the equation easier.
Let’s make the variable x.
Our equation is now x9/5=-27
Now, divide both sides by 9/5 to isolate x.
(Hint, the decimal form of 9/5 is 1.8, so simply divide -27 by 1.8)
-27/1.8=-15
X=-15
Hope this helps!

Before she went on a diet, Jenna's waist measured 32.45 inches.After the diet, it measured 26.97 inches.How many inches did Jenna lose?

Answers

Answer:

5.48

Step-by-step explanation:

32.45 - 26.97 = 5.48

Answer:

Jenna lost 5,48

Step-by-step explanation:

Before the diet Jenna's waist measured 32.45 inches.

After the  diet Jenna's waist measured 26.97 inches.

To get the difference between the two measures,  we have to discount the new measure from the previous one.

So,  difference is  26.97 inches-32.45 inches= -5,48. It is negative because she lost inches.

Suppose x is any positive number. Circle 1 has a center at (−2, 7) and a radius of 8x. Circle 2 has a center at (−3, 0) and a radius of 5x. Why is Circle 1 similar to Circle 2?Circle 1 and Circle 2 have the same area, and Circle 1 has a radius 0.625 times longer than Circle 2.Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6.Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 0.625.Circle 1 and Circle 2 have the same circumference, and Circle 1 has a radius 1.6 times the length of Circle 2's radius.

Answers

Answer:

The correct answer is "Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6"

Step-by-step explanation:

We can tell this because first they identify the movement properly. When going from (-3, 0) to (-2, 7), we move to the right one and up 7.

Also, we know there is a scale factor of 1.6, because when we look at the radius of each circle, we can divide and find that factor.

8x/5x = 1.6

The length of the side of square a is twice the length of the side of square b. What is the ratio of the area of square a to the area of square b

Answers

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

As you can tell, the ratio of the lengths is 2 : 1 (the length of a is twice the length of b)

The ratio for area would be the squared version of the length ratio

2^2 = 4

1^1 = 1

The ratio for area is 4 : 1

Hope This Helps You!

Good Luck (:

Have A Great Day ^-^

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In last year, San Diego basketball team won 32 games, and lost 8 games. What percent of the games were won?

Answers

Answer:

80%

Step-by-step explanation:

The total amount of games last year was 40.

32 + 8 = 40

question says the percent of games were won which means 32/40

In percentage, it means 80%

Please help me out.............

Answers

Since the sides are equal the angels have to be equal too

5x-20=2x+37

3x=57

X=19

Please help if possible.............

Answers

Answer:

y = 16

Step-by-step explanation:

The opposite angles of a parallelogram are congruent, hence

10y - 29 = 7y + 19 ( subtract 7y from both sides )

3y - 29 = 19 ( add 29 to both sides )

3y = 48 ( divide both sides by 3 )

y = 16

Use the x-intercept method to find all real solutions of the equation.
x^3-11x^2+31x-21=0

Answers

Answer:

c. [tex]x=1,3,\:or\:7[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3-11x^2+31x-21=0[/tex]

To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.

The corresponding function is;

[tex]f(x)=x^3-11x^2+31x-21[/tex]

From the graph the x-intercepts are

(1,0),(3,0) and (7,0).

Therefore the real solutions are

[tex]x=1,3,\:or\:7[/tex]

Answer:

C. is the answer

Step-by-step explanation:

If the apy of a saving account is 2.8% and if the principal in the savings account is $2600 for an entire year, what will be the balance of the savings account after all the interest is paid for the year

Answers

Answer:

[tex]\$2,672.80[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ year\\ P=\$2,600\\r=0.028[/tex]

substitute in the formula above

[tex]A=\$2,600(1+0.028*1)=\$2,672.80[/tex]

What is the least common multiple (LCM) of 3 and 7?

Answers

it is 21 :)))))))))))))))

let's find the least common multiple (LCM) of 3 and 7 is 21.

List the multiples of each number.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...

Multiples of 7: 7, 14, 21, 28, 35, 42, ...

identify the common multiples.

The common multiples of 3 and 7 are the numbers that appear in both lists. In this case, the number 21 is the smallest positive integer that appears in both lists Determine the LCM.

the LCM of 3 and 7 is 21.

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An amusement park ride has cars that move around a circular track at the rate of 16 revolutions in 20 seconds. To the nearest hundredth, the angular velocity of the cars is radians per second.

Answers

Answer:

[tex]5.03\frac{rad}{sec}[/tex]

Step-by-step explanation:

To find the angular velocity divide the revolutions by the time

so

[tex]\frac{16}{20}=0.8\frac{rev}{sec}[/tex]

Remember that

[tex]1\ rev=2\pi \ rad[/tex]

Convert rev/sec to rad/sec

[tex]0.8\frac{rev}{sec}=0.8*(2\pi)=1.6 \pi\frac{rad}{sec}[/tex]

assume [tex]\pi=3.1416[/tex]

[tex]1.6(3.1416)=5.03\frac{rad}{sec}[/tex]

Answer:

5.03

Step-by-step explanation:

Find the surface area of the figure

Answers

Answer:

[tex]\large\boxed{S.A.=1,119\ in^2}[/tex]

Step-by-step explanation:

We have:

two triangles with base b = 17in and height h = 7in

two rectangles with length l = 17in and width w = 10in

two rectangles with length l =11in and width w = 10in

one rectangle with length l = 8in and width w = 11in

one rectangle with length l = 15in and width w = 11in

one rectangle with length l = 17in and width w = 11in

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

Calculate:

[tex]A_\triangle=\dfrac{(17)(7)}{2}=59.5\ in^2\\\\A_1=(17)(10)=170\ in^2\\\\A_2=(11)(10)=110\ in^2\\\\A_3=(8)(11)=88\ in^2\\\\A_4=(15)(11)=165\ in^2\\\\A_5=(17)(11)=187\ in^2[/tex]

The Surface Area:

[tex]S.A.=2A_triangle+2A_1+2A_2+A_3+A_4+A_5[/tex]

Substitute:

[tex]S.A.=2(59.5)+2(170)+2(110)+88+165+187=1,119\ in^2[/tex]

A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)=0.19. They have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S∩LC) ?


0.35


0.03


0.02


0.83

Answers

Answer:

P (S∩LC) = 0.03

Step-by-step explanation:

We are given that the probability that someone is a smoker is P(S)=0.19 and the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158.

Given the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.158 = P(S∩LC) / 0.19

P (S∩LC) = 0.158 × 0.19 = 0.03

HELP CHECK MY ANSWERS, TY!
The graph shows the vertical position of a ball attached to a spring oscillating between a low point and a high point as a function of time.



Select all statements that describe the graph.

Answers

Answer:

That is correct

Step-by-step explanation:

When doing the math you can find that b and d are correct

Answer:

Step-by-step explanation:

Here all the statement describing the graph.

1- the cycle of the graph is 2 second.

2- mid-line of the graph is at y=0

3- amplitude is 24 i.e 12 unit + 12 unit

4- ball is traveling 24 cm in 1 sec. I.e. 12 unit in 0.5 sec and another 12 units in 0.5 sec.

HELP PLEASE!
Find the exact values of cos and sin for the angle measure. 180 degrees

Answers

Answer:

[tex]\large\boxed{\sin180^o=0\ and\ \cos180^o=-1}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\sin(2\theta)=2\sin\theta\cos\theta\\\\\cos(2\theta)=\cos^2\theta-\sin^2\theta\\\\180^o=2(90^o)\\\\\sin90^o=1\\\\\cos90^o=0\\===================\\\\\sin180^o=\sin(2\cdot90^o)=2\sin90^o\cos90^o=2(1)(0)=0\\\\\cos180^o=\cos(2\cdot90^o)=\cos^290^o-\sin^290^o=0^2-1^2=-1[/tex]

A. concave dodecagon

B. Concave hexagon

C. Convex hexagon

D. Convex dodecagon

Answers

Answer:

bro whats the question

Step-by-step explanation:

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