Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the functions based on their axis of symmetry (from smallest to largest).

f(x) g(x) h(x)
f(x) = -2(x − 4)2 + 2 g(x) = 5x2 − 10x + 7 graph of negative 1 times the quantity of x plus 2 squared, plus 2

First multiply inside the brackets:

-.5 x -1/4 = 0.125

Now multiply by 12%

0.125 x 0.12 = 0.015

answer: 0.015

Answer:

0.015

Step-by-step explanation:

Answer:

So first we need to determine what the exponential growth function would look like.  Exponential growth functions look like [tex]P(t) = P_0*e^{r*t}[/tex] and in our case [tex]P_0[/tex] would be the initial population which is 5.68 million.  R is the next variable that we need to fill out which is the rate of change which in our case is 2.99% or 0.0299.

This is how our function should look now [tex]P(t)=5.68*e^{0.0299*t}[/tex]

Moving onto part b, we need to estimate the population of the city in 2018 which 6 years from 2012 and we plug that into t and solve.

[tex]P(t)=5.68*e^{0.0299*6}[/tex]

[tex]P(t)=5.68*e^{0.1794}[/tex]

[tex]P(t) = 5.68*1.1965[/tex]

[tex]P(t) = 6.796\ million[/tex]

Moving onto part c, we need to find when the population of the city will be 11 million which will be done by setting P(t) to 10 million and solving for t.

[tex]10 = 5.68*e^{0.0299*t}[/tex]

[tex]\frac{10}{5.68} = \frac{5.68*e^{0.0299*t}}{5.68}[/tex]

[tex]1.76056=e^{0.0299*t}[/tex]

[tex]ln(1.76056)=ln(e^{0.0299*t})[/tex]

[tex]\frac{0.5656}{0.0299}=\frac{0.0299*t}{0.0299}[/tex]

[tex]18.9175\ years = t[/tex]

Moving onto part d, we need to find the doubling time.  This will be similar to the previous part but we will be finding the time it takes to double our population.  So instead of putting 10 million for P(t) we put 5.68* 2 in there which is 11.36.

[tex]11.36= 5.68*e^{0.0299*t}[/tex]

[tex]\frac{11.36}{5.68} = \frac{5.68*e^{0.0299*t}}{5.68}[/tex]

[tex]2=e^{0.0299*t}[/tex]

[tex]ln(2)=ln(e^{0.0299*t})[/tex]

[tex]\frac{0.693}{0.0299}=\frac{0.0299*t}{0.0299}[/tex]

[tex]23.182\ years = t[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

the answer should be 1/11

Step-by-step explanation:

p(blue first) = 3/12

p(yellow second) = 4/11

so p = 3/12 x 4/11

1/11 is your probability

Given :

48°

90°{boxed like shape}

{sum of angles of triangle}

~Tulpe⚘

Answer:

x = 42°

Step-by-step explanation:

Given that,

→ A = 48°

→ B = 90°

→ C = x

Formula we use,

→ A + B + C = 180°

Let's solve for the value of missing angle,

→ A + B + C = 180°

→ 48° + 90° + x = 180°

→ 138° + x = 180°

→ x = 180° - 138°

→ [ x = 42° ]

Hence, value of missing angle is 42°.

Answer:

d

Step-by-step explanation:

The balance point, or average value of those numbers, would be 4.75 or 4 and 3/4

Answer:

17 ?

Step-by-step explanation:

Here's the way to solve ↓

First Identify the sides given:

Now, use the area of rectangular prism formula:

2(Length * Width + Height *  Length + Height * Width)

Solve:

Answer:

1

Step-by-step explanation:

Given a quadratic equation ax² + bx + c = 0, plug the coefficients into the expression b² - 4ac to see what results:

5² - 4(-2 × -3)

Answer:

41,546

Step-by-step explanation:

13,728+12,399+15419=41,546

Answer:

182

Step-by-step explanation:

the formula for the circumference is equal to 2 × pi × r

pi = 3.14

r = 29

hence,

C = 2 × pi × 29

C = 182 inches

Answer:

Multiplication is the process of multiplying. The total cost of the boxes of two types is $90.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of the first box is $12, which has 8 pounds of milk chocolate and 4 pounds of dark chocolate.

The cost of the second box is $15, which has 5 pounds of milk chocolate and 10 pounds of dark chocolate.

Therefore, if we buy the 5 boxes of the first type and 2 boxes of the second type, then the amount of two chocolate that Tim needs will be fulfilled.

The cost of 5 boxes of the first type is $60 ($12 ×5), while the cost of 2 boxes of the second type is $30 ($15×2), therefore, the total cost of the boxes of two types is $90.

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Answer: 480 sq ft

Step-by-step explanation:

for two rectangles on right do 8*16 =128*2 = 256

the rectangle on the right is also 128

total of all rectangles is 384 ft

now for the triangles

formula: 1/2 b*h

1/2 * 16*6 = 48

multiply that by 2 for both triangles

you have 96

add that to total and you get

480 sq ft

Answer:

Step-by-step explanation:

The hypotenuse of the triangles is the length of the rectangles so the length of the rectangles is 16 ft. The width of the rectangles is 8 ft. There are 3 rectangles so the surface area of them is:

(16*8)*3 = 384[tex]ft^{2}[/tex]

The area of a triangle is base times height divided by two. Here, the height of the two triangles is 6 ft and the base is 16 ft. So, the area of the two triangles is:

[tex]\frac{6*16*2}{2}[/tex] = 16*6 = 96  [tex]ft^2[/tex]

Add the two areas together to get the surface area.

384[tex]ft^2[/tex] + 96[tex]ft^2\\[/tex] = 480[tex]ft^2[/tex]

Hence, the surface area of the triangular prism is 480[tex]ft^2[/tex]

Please mark me as brainliest and hope this helps!!!

Answer:

Option A

Step-by-step explanation:

95% confidence interval is obtained using the following formula

COnfidence interval lower bound = mean - critical value * sigma/sq rt n

and upper bound = mean + critical value*sigma/sq rt n

Thus margin of error = critical value*sigma/rt n

varies indirectly as n provided others are remaining the same.

Hence lower sample indicates higher margin of error

Out of 4 options given we find that I option has maximum margin of error as 21%

Hence option A is most likely coming from a small sample

Answer:

187.5 m^3

Step-by-step explanation:

2 to 5 is 2(2.5)

2.5^2 = 6.25

6.25(30) = 187.5

Step-by-step explanation:

1.5 times 1.5 when doing so u need to round it to the tenths place

Answer:

31.4

Step-by-step explanation:

To find circumference, the formula is A=pi*r^2. The radius is 1/2 the diameter. The radius of the donut is 3.5. 3.5^2 is 12.25. Pi is approximately 3.14, so 12.25*3.14 is 38.465. The donut hole takes away from the circumference, so we have to subtract the circumference of the donut hole from the donut. 1.5^2 is 2.25, and 2.25*3.14 is 7.065. 38.465-7.065 is 31.4. The circumference of the circle is 31.4.

Hope this helps!

[tex]~~~~~~|x -1| =3\\\\\implies x-1 = 3~~~~~~~ \text{or}~~~~~~~ x -1 = -3\\\\\implies x = 3+1~~~~~~~\text{or}~~~~~~~~ x = -3 +1\\\\\implies x = 4~~~~~~~~~~~~ \text{or}~~~~~~~~~ x = -2\\\\\text{Solution set:}~ \{-2,4\}[/tex]

first case

[tex]|x-1|=3\\\\x-1=3\\\\x=4[/tex]

second case

[tex]-|x-1|=3\\\\-x+1=3\\\\-x=2\\\\x=-2[/tex]

The solutions are {-2, 4}

Answer:

2. 11x - 10

3. -8 + 11x - 2

5. -8 + 6x + 5x -2

Step-by-step explanation:

To find the equivalent expressions, find the solution to the expression -2(4 - 3x) + (5x - 2). All expressions that are within the solving process or have the same solution are equal to the given expression.

-2(4 - 3x) + (5x - 2)

-2(4 - 3x) + 5x - 2

-8 + 6x + 5x - 2

-8 + 11x - 2

11x - 10

In this case, the equivalent expressions were within the solving process. From this, we can see that the equivalent expressions are 11x - 10, -8 + 11x - 2, and -8 + 6x + 5x - 2. Aka choices 2, 3, and 5.

hope this helps!

Answer:

Step-by-step explanation:

A cube has a surface area of 60 in2. Find the volume in in3.

60 : 6 = 10 in²

√10 = 3,162277660168379

3,162277660168379³ =

99,99999999999996

round

100in³

The angle the 14 foot long wire must make with the gound is approximately 51 degrees.

A right angle triangle is a triangle that has one of its sides as 90 degrees. The situation forms two right angle triangle.

Using cosine law,

17² = 14² + 22² - 2 × 14 × 22 cos C

289 - 196 - 484 = -616 cos C

-391 = -616 cos C

divide both sides by -616

cos C = -391  / -616

cos C = 0.63474025974

C = cos⁻¹ 0.63474025974

C = 50.59929658

C = 51 degrees.

Therefore, the angle the 14 foot long wire must make with the gound is approximately 51 degrees.

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Answer:

50.6

Step-by-step explanation:

yes

Answer:

0.83

Step-by-step explanation:

Probability (E) :

⇒ Outcomes having a result of E / Total no. of outcomes

===============================================================

Solving :

⇒ Outcomes (not E) = 6 - 1 = 5

⇒ Total outcomes = 6

⇒ P (not 3) = 5/6

⇒ P (not 3) = 0.83

Answer:

0.8 or 8/10

Step-by-step explanation:

1/10 can be converted to decimal form as 0.1.

70/100 can be converted to decimal form as 0.7

0.1 + 0.7 = 0.8

Another way is making use of a common denominator:

Common denominator --> 100

1/10 --> mutiply numerator and denominator by 10 --> 10/100

10/100 +70/100 = 80/100 = 8/10 = 0.8

Answer:

See below

Step-by-step explanation:

.3   and  .30   are the same number   they are     =

0.3 = 0.30

Answer:

$29.75

Step-by-step explanation:

15% of 35 is 5.25 so subtract 5.25 from 35 and you get 29.75.

Answer:

$29.75

Step-by-step explanation:

this is the new price after the % minused <;

The length of the straw will be 9.89949 inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula

[tex]X^2=l^2+b^2+h^2[/tex]

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 5 inch , b= 8 inch , h= 3 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

[tex]X^2+l^2+b^2+h^2[/tex]

[tex]X^2=5^2+8^2+3^2[/tex]

[tex]X^2=25+64+9[/tex]

[tex]X^2=98[/tex]

[tex]X=\sqrt{98}[/tex]

X= 9.89949 (in radical form)

Hence, the length of the straw will be  9.89949 inches.

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Answer:

12+y+x+x+x+12+y+x = 24+2y+4x; which is A

Step-by-step explanation:

Answer:

middle a little to the left and done

Step-by-step explanation: