The function f is given by f(x) = (x + 3)^2 - 1.
1) Write the coordinates of the vertex of the graph of f.
2) Does the graph open up or down? How do you know?

Answers

Answer 1

Answer:

the coordinate of the vertex is going to be (-3,-1) and it's concave up

Step-by-step explanation:

1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)

2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up

In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive


Related Questions

Sam runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?

Answers

Answer:

4.8

Step-by-step explanation:

6/55= ~0.109

0.109*44=4.8

Help again please
A stack of 400 pieces of paper is 1.800 inches tall.
A. Derion guesses that each piece of paper is 0.015 inches thick. Explain how you know that Derion’s answer is not correct.

B. Compute the thickness of each piece of paper. Show your reasoning.

Answers

Think the answer may of be A.

Solve this system of equations, then determine what y equals.
x + 5y= 7
2x + 4y = -4
A y=-18
B y=3
C y=8
D y=-8

Answers

2+2=4 and 4+4=8 and 8+8=16

[tex]x+5y = 7~~~....(i)\\\\\\2x+4y = -4~~~.....(ii)\\\\\\\text{Multiply equation (i) by 2,}\\\\\\2x+10y = 14~~~.....(iii)\\\\\\(iii) - (ii):\\\\2x+10y-2x-4y = 14-(-4)\\\\\implies 6y = 14+4\\\\\implies 6y = 18\\\\\implies y = \dfrac{18}6\\\\\implies y = 3[/tex]

Mateus recorded the number of miles driven and the amount
of gasoline used in the table below.
Gas Mileage
Distance Gas Usage
(in miles) (in gallons)
105
5
210
10
315
15
420
20
At this rate, what is the maximum miles that can be driven
with 12 gallons of gasoline?
A) 220 miles
B) 236 miles
C) 252 miles
D) 262.5 miles

Answers

Answer:

C. 252 miles.

Step-by-step explanation:

Since we already know how many miles is driven for 10 gallons of gas, we only need to find 2.

Since 105 miles runs on 5 gallons, divide 105 by 5 to find out how many miles runs on 1 gallon.

105/5=21

Then, multiply that by 2 to find out how many miles run on 2 gallons of gas.

21x2=42.

Finally, add 42 to 210 to get the amount of miles that runs on 12 gallons of gas.

210+42=252

**PLEASE HELP ASAP**

Ben is concerned that he is not reading enough. He decides to record how many pages he reads each day for the month of April, and he makes a box plot of the data. Then he repeats the process for the month of June. His 2 plots are shown below.

Answers

In June he read 0 to 45 pages per day
In April he reads 10 to 90 pages per day

What is the answer to X=7-3y And 2x-4y=-6



I need it

Answers

Answer:

x = − 3 y + 7

Step-by-step explanation:

Reorder  7  and  − 3

A medication with an initial concentration of 1. 5 milligrams per liter is administered to a
patient, and the decay rate of the drug is 10% per hour. Which equation can be used to model
the concentration, C, of the drug in the patient’s body as a function of time, t, in hours since the
drug was administered?

Answers

Answer: Exponential decay model:

y

=

x

(

1

r

)

t

, half life of tablet is about

2

hours and after

t

=

3

hours , remaining drug on patient's system is

42.875

mg.

Step-by-step explanation: Initial drug

x

=

125

mg ; rate of decay

r

=

30

100

=

0.3

gm/hour

Exponential model:

y

=

x

(

1

r

)

t

=

125

(

1

0.3

)

t

=

125

0.7

t

Half life:

y

=

125

2

=

62.5

mg

62.5

=

125

0.7

t

or

0.7

t

=

1

2

. Taking logarithm on both sides we get ,

t

log

(

0.7

)

=

log

(

0.5

)

t

=

log

(

0.5

)

log

(

0.7

)

1.94

(

2

d

p

)

hour

The half life of tablet is about

2

hours.

After

t

=

3

hours , remaining drug on patient's system is

y

=

125

0.7

t

=

125

0.7

3

=

42.875

mg [Ans]

Find x, given the slope is -2. (x,-6) (-6,10)

Answers

Answer:

x= 2

Step-by-step explanation:

[tex]\boxed{slope = \frac{y _{1} - y_2}{x_1 - x_2} }[/tex]

Substitute known values into the formula:

[tex] - 2 = \frac{ - 6 - 10}{x - ( - 6)} [/tex]

[tex] - 2 = \frac{ - 16}{x + 6} [/tex]

-2(x +6)= -16

Divide both sides by -2:

x +6= -16 ÷(-2)

x +6= 8

Subtract both sides by 6:

x= 8 -6

x= 2

What expression is equal to 4/8

Answers

The value of 12/24 is equals to 0.5.

Answer:

The value of 12/24 is equals to 0.5. Hence, this fraction is equivalent to 4/8.

Step-by-step explanation:

im not sure tho. hope u get it right.

What is the slope of the line through (2, -1) and (-2, -3)?

Answers

[tex]\text{Given that,}\\\\\\(x_1,y_1) = (2,-1)~~\text{and}~~ (x_2,y_2) = (-2,-3)\\\\\\\text{Slope,}~ m =\dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{-3+1}{-2-2} = \dfrac{-2}{-4} = \dfrac 12[/tex]

Answer:

Step-by-step explanation:

Using slope formula:

(y2-y1)/(x2-x1)

(-3 + 1) / (-2-2)

-2/-4

slope: 1/2

3. Avery noticed that of the apples in a basket are red. There are 45 red apples in the basket.
(a) Represent the situation with an equation. Use a for the variable.
(b) Solve the equation in Part (a). Show your work.
(c) What does the solution of the equation represent in the situation?

Answers

Answer:

Step-by-step explanation:

Something missing in "noticed that of the apples."  Perhaps "that 40% of . . .?"

But I'll try to answer, using an example:  

Avery noticed that 30% of the apples in a basket are red. There are 45 red apples in the basket.

To find the total number of apples, X:

(0.30)X = 45

X = 150 apples total.  45, or 45/150, is 0.3 0r 30%.

Can someone please take the time out of their day and help me with this question

Answers

Answer:

76, 76 104

Step-by-step explanation:

Angle 3 is vertical so it is congruent to Angle 2.

Angle 6 is corresponding, so it is congruent to Angle 2.

Angle 8 is linear to Angle 6, so they add to 180

Answer:

see explanation

Step-by-step explanation:

(a)

∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 3 and ∠ 6 are corresponding angles and are congruent , then

∠ 6 = 76°

(c)

∠ 2 and ∠ 8 are same- side exterior angles and sum to 180° , that is

∠ 8 + 76° = 180° ( subtract 76° from both sides )

∠ 8 = 104°

will mark brainleist pls help

Answers

Step-by-step explanation:

Angle c + angle d = 180° ( linear pair)

given,

angle c = 5x + 9

angle d = 5x - 6

now,

5x + 9 + 5x - 6 = 180

10x + 3 = 180

10x = 180 - 3 = 177

10x = 177

x = 177/10 = 17.7

so,

angle C = 5x + 9 = 5(17.7) + 9 = 97.50°

angle D = 5x - 6 = 5(17.7) - 6 = 82.50°

Hope this answer helps you dear! take care!.

Write an absolute value inequality to represent the situation.
What is the range of the number for calories in the chicken.

The menu at Jeanne's favorite restaurant states that the roasted chicken with vegetables entree typically contains 480 Calories. Based on the size of the chicken, the actual number of Calories in the entree can vary by as many as 40 Calories from this amount.​

Answers

Answer:

|x-480|<=40

Step-by-step explanation:

The absolute distance on the number-line from x to 480 has to be 40.

|x-val| <= error-margin

|x-480| <= 40

Carson rides his bike for 30 mins each day he rides a total of 12 miles every 3 days how many days will it take to ride a total of 80 miles

Answers

Answer:

20 days

Step-by-step explanation:

If he rides 12 miles every 3 days, then he rides 4 miles in one day. Divide 80 / 4 and you get 20 days.

The chess clubs at school decides to give $400 to a charity at Christmas time. If the chess club raised $1,000 fund raising. What percent of the fund raiser did they donate to charity

Answers

Answer: 40%

Step-by-step explanation:

To find the percent, divide the amount donated by the full amount of money raised. 400/1000 = 0.4.

Now to make this into a percentage, multiply the answer by 100. 0.4 * 100 = 40.

Percent of the fund raiser did they donate to charity 40%

What is percentage ?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.

To find the percent,

divide the amount donated by the full amount of money raised. 400/1000 = 0.4.

Now to make this into a percentage,

multiply the answer by 100.  0.4 * 100 = 40.

To learn more about the percentage here:

https://brainly.com/question/29224972

#SPJ7

Plz help. I need this by tomorrow or I’ll get detention.

Answers

[tex]\dfrac{6+ \sqrt{27}}{4-\sqrt3} \\\\\\=\dfrac{\left(6+\sqrt{27}\right)\left(4+\sqrt 3 \right)}{\left(4-\sqrt 3\right) \left(4+\sqrt 3\right)}\\\\\\=\dfrac{24+6\sqrt 3+4\sqrt{27}+\sqrt{27\cdot 3}}{4^2 - \left(\sqrt 3 \right)^2}\\\\\\=\dfrac{24+6\sqrt3+4\sqrt{9\cdot 3} +\sqrt{81}}{16-3}\\\\\\=\dfrac{24+6\sqrt 3 +12\sqrt 3 + 9 }{13}\\\\\\=\dfrac{33+18\sqrt 3}{13}\\\\\\\text{Hence, r = 33 and s = 18}[/tex]

46 degrees and x

X =

Answers

Answer:

136° that's 90 plus 46.........

Answer:

x = 136°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 90° + 46° = 136°

Solve the equation. Please

Answers

Answer:

y=3

Step-by-step explanation:

1/4 = 3/12

The property of 12x2-7=6-2x2+2

Answers

12x2-7=6-2x2+2
14x^2-15=0
a=14 , b =0 , c=-15
0^2-4x14x(-15) =
840

Adrian purchases a book for $9.86 and a poster for $3.49. If she gives the cashier
$15.00, how much change should she receive? (Don't worry about taxes!)

Answers

She receives $1.65 cents

Write an exponential function to model each situation. Find each amount after the

specified time.


A population of 1,236,000 grows 1.3% per year for 10 years

Answers

The formula would be y = 1,236,000(1.3)^t

After 10 years, the population would grow to become 17,039,309.59 people. You can round up to 17,039,310 people if the question asks to round to the nearest person.

Will mark brainliest if you can resolve this problem ( 2 possible answers, NO LINKS OR ANSWERS WITHOUT EXPLANATION)
I can give u the permission of drawing the boxplot by:
- saving the picture or screenshot it ( it's better to screenshot it (Windows+ Logo+Shift+s) )
- drawing the answer on the screenshot Windows
- save the picture (Ctrl+s)
- and finally send it to brainly
(P.s: many people (those who are good at I.T) will argue with the procedure of doing the answer. But many people don't. So I gave the procedure step-by-step to you to show me the working) Thx
Here's the picture:

Answers

Answer:

Hopefully this is what you are looking for.

Step-by-step explanation:

Hope this helps!

Complete the table if x & y vary inversely

Answers

Answer:

(. ❛ ᴗ ❛.)(. ❛ ᴗ ❛.)(. ❛ ᴗ ❛.)(. ❛ ᴗ ❛.)(. ❛ ᴗ ❛.)

1
A line has a slope of -2 and a y-intercept of -2.

What is the x-intercept of the line?
A -4
B -1
C 1
D 4

Answers

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 and c = - 2 , then

y = - 2x - 2 ← is the equation of the line

To find the x- intercept let y = 0 in the equation and solve for x , that is

- 2x - 2 = 0 ( add 2 to both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

The x- intercept is - 1 → B

Kate took out a subsidized Stafford loan worth $9,710 to pay for college. The interest rate on the loan was 5. 9%, compounded monthly. It took Kate 5 years to pay off the loan after graduation. What portion of the total amount she paid represented the interest? a. $11,236. 22 b. $9,710. 00 c. $1,526. 22 d. $2,942. 37.

Answers

Answer:

the answer is 10,0000

Step-by-step explanation:

PLEASE NO LINKS AND NO NEGATIVITY

Answers

Answer: 4 - 2g

Explanation: The order of operations is distributive property so think of it as
(1/2 • 8) - (1/2 • 4g) Also just think of dodging 8 and 4 by two since 1/2 in a number format is .5 and 8 mutuales by .5 is 4 and 4 is 2.

Hope this helps!

Need help now pls on HS geometry

Answers

Answer:

b

Step-by-step explanation:

RT is a perpendicular bisector of QS , then

Δ QRS is isosceles with 2 congruent legs , that is

QR = SR

7x - 22 = 4x + 5 ( subtract 4x from both sides )

3x - 22 = 5 ( add 22 to both sides )

3x = 27 ( divide both sides by 3 )

x = 9

Then

RS = 4x + 5 = 4(9) + 5 = 36 + 5 = 41

Please show work!! I'll give you brainliest

10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?

Answers

Answer:

b=34.2m

Step-by-step explanation:

equation for area of parallelogram

a=b×h

in which b is the base(length) and h is the height

[tex]690.84 = b \times 20.2[/tex]

[tex]b = \frac{690.84}{20.2} [/tex]

b=34.2m

what is ur favorite character from boondocks mine is Riley freeman and also Huey freeman

Answers

Answer:lol

Step-by-step explanation:

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After two weeks, the subjects were surveyed by technicians to determine their level of allergic symptoms.Which of the following would benefit this experiment the most?This experiment should be double blind. Neither the subject nor the technician should know which group is receiving the new medication and which is receiving the placebo. This method would control for the placebo effect and prevent any effect on the response.This experiment should be single blind. The subjects do not know which treatment they are receiving to control for the placebo effect, but the technicians need to know which group received which treatment.This experiment should be single blind. The subjects know which treatment they are receiving but the technicians do not know which group received which treatment, so the response being measured is not affected.This experiment should not use blinding. 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