Mathematics College

What is the axis of symmetry and vertex for the function f(x) = 3(x – 2)2 + 4?
x =

Answers

Answer 1
hello : 
 the axis of symmetry is the line for equation : x = 2
the vertex  is the point :  A (2 , 4)
Answer 2

Answer:

x= 2 vertex: (2,4)

Step-by-step explanation:

just did the assignment

Related Questions

32% of 300 is what number? A.96 B.64 C.32 D.90

Answers

32% = 0.32

300 * 0.32 =96

 Answer is A

Bob's Skate Shop had a profit of $3,563 during the month of August. The company models its profit using P=x^2+10x-12
, where x is the number of skateboards the company sells. How many skateboards did the company sell during the month of August? A. 50 B. 55 C. 60 D. 75

Answers

[tex]x^2+10x-12 =3563 \\ x^2+10x-12 -3563=0 \\ x^2+10x-3575=0 \\ D=b^2-4ac=10^2-4*1*(-3575)=100+14300=14400 \\ x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{-10б \sqrt{14400} }{2}= \frac{-10б 120 }{2} \\ x_1= -65 \ \ \ \O \\ x_2=55[/tex]

The company sold 55 skateboards.

what is the distance between (-5,5) and (2,6) rounding to the nearest hundred

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -5}}\quad ,&{{ 5}})\quad % (c,d) &({{ 2}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[2-(-5)]^2+[6-5]^2}\implies d=\sqrt{(2+5)^2+(6-5)^2} \\\\\\ d=\sqrt{7^2+1^2}\implies d=\sqrt{50}[/tex]

A health clinic has 3 1/2 quarts and 1 gallon of antiseptic wash in inventory.How many fluid ounces of antiseptic wash do they have on hand?

Answers

1 gallon is 128 fluid ounces;
4 quarts make 1 gallon. 

Change the mixed unit volume of antiseptic to just one unit. Which you choose is your choice.

((3 1/2) -4)) quarts = ((7/2)+4)) quarts = (7+8/2) quarts = (15/2) quarts

15/2 quarts = 240 fluid ounces

Answer:

240 fluid ounces

Step-by-step explanation:

A health clinic has [tex]3\frac{1}{2}[/tex] quarts and 1 gallon of antiseptic wash in inventory.

We have to convert the unit of fluid in ounces.

1 quart = 32 ounces

1 gallon = 128 ounces

[tex]3\frac{1}{2}[/tex] quarts = [tex]3\frac{1}{2}[/tex] × 32 = 112 ounces

Total fluid of antiseptic wash = 112 + 128 = 240 fluid ounces

They have 240 fluid ounces of antiseptic wash in hand.

A student club with 30 members need to chose an executive committee. there are five members of the committee and all have equal votes. how many possible sets of members are there for the committee

Answers

17100720 possible combinations

Find the general solution of the given system. dx dt = −6x + 4y dy dt = − 7 4 x + 2y

Answers

I assume the coefficient on [tex]x[/tex] in the second equation is [tex]-\dfrac74[/tex]. The coefficient matrix

[tex]\begin{bmatrix}-6&4\\\\-\frac74&2\end{bmatrix}[/tex]

has eigenvalues given by

[tex]\begin{vmatrix}-6-\lambda&4\\\\-\frac74&2-\lambda\end{vmatrix}=\lambda^2+4\lambda-5=(\lambda+5)(\lambda-1)=0[/tex]

The eigenvalues are thus [tex]\lambda_1=-5[/tex] and [tex]\lambda_2=1[/tex].

For the eigenvalue [tex]\lambda_1[/tex], the corresponding eigenvector [tex]\eta_1[/tex] satisfies

[tex]\begin{bmatrix}-1&4\\\\-\frac74&7\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies\eta_{1,1}=4\eta_{1,2}[/tex]

so that we can choose [tex]\eta_1=\begin{bmatrix}4\\1\end{bmatrix}[/tex].

For [tex]\lamda_2=1[/tex], we have

[tex]\begin{bmatrix}-7&4\\\\-\frac74&1\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies7\eta_{2,1}=4\eta_{2,2}[/tex]

and we can choose [tex]\eta_2=\begin{bmatrix}4\\7\end{bmatrix}[/tex] for the corresponding eigenvector.

Then the general solution to the ODE system is given by

[tex]\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=C_1\begin{bmatrix}4\\1\end{bmatrix}e^{-5t}+\C_2\begin{bmatrix}4\\7\end{bmatrix}e^t[/tex]

Bethany wants to estimate the value of (4.296 x 10^11) x (1.8614 x 10^-14). Which statement about the estimate is true?

A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.

B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.

C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.

D. The number will be less than 1 because when adding the exponents,
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.


Answers

D. The number will be less than 1 because when adding the exponents, 
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.

[tex](4.296 * 10^{11}) * (1.8614 * 10^{-14})= \\ \\ 4.296*1.8614*10^{11+(-14)}=\\\\7.99657*10^{-3}= \\ \\ \cfrac{7.99657}{1000}=\\\\0.00799657 [/tex]

need help with this inequality

Answers

answer is D
|x-4| </ 1

x-4 </ 1
and
x-4 >/ -1

+4 both sides

x </ 5
x >/ 3
this is shown in the graph

Mary is making Magic Marshmellow cake . The recipe calls for 3/4 cup of milk and 2 eggs per serving. The wants to make enough cake for 20 people . How much milk will Mary need?

Answers

[tex]\bf \begin{array}{ccllll} \textit{cups of milk}&serving\\ -----&-----\\ \frac{3}{4}&1\\ x&20 \end{array}\implies \cfrac{\frac{3}{4}}{x}=\cfrac{1}{20}\implies \cfrac{\frac{3}{4}}{\frac{x}{1}}=\cfrac{1}{20} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{1}{20}\implies \cfrac{3}{4x}=\cfrac{1}{20}\implies 3\cdot 20=1\cdot 4x\implies \cfrac{3\cdot 20}{4}=x[/tex]

and surely you know how much that is.

What addition doubles fact can help you find 4+ 3? Explain how you know

Answers

7 because if u add 4 and 3 that's what u end up with

By using the commutative law of addition, the result of the addition would be 7.

What is commutative property of addition?

The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.

For two numbers x and y, we have:

x + y = y + x

Thus, if we take 3 numbers as a,b and c, then:

a + b + c = b + a + c = b + c + a = a + c + b = c + a + b = c + b + a

And so for any amount of numbers.

We have been Given that the expression 4 + 3, we need to determine what addition shows that the statement is true.

We know that the sum of 4 and 3 is 7, we can explain that by using the commutative law of addition as shown;

According to the law, A + B = B+ A

4 + 3 = 3 + 4 = 7

Therefore, By using the commutative law of addition, the result of the addition would be 7.

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) there are exactly 20 students currently enrolled in a class. how many different ways are there to pair up the 20 students, so that each student is paired with one other student

Answers

Assuming that "pair up students" means "divide up all 20 of the students into groups of two," and we regard two pairings as the same if and only if, in each pairing, each student has the same buddy, then I believe that your answer of 20! / [(2!)^10 * (10!)] is correct. (And I also believe that this is the best interpretation of the problem as you've stated it.) 

There are at least two ways to see this (possibly more). 


One way is to note that, first, we have to select 2 students for the first pair; that's C(20, 2) (where by C(20, 2) I mean "20 choose 2"; that is, 20! / (18! * 2!). ) 

Then, for each way of selecting 2 students for the first pair, I have to select 2 of the remaining 18 students for the second pair, so I multiply by C(18, 2). 

Continuing in this manner, I get C(20, 2) * C(18, 2) * ... * C(2, 2). 

But it doesn't matter in this situation the order in which I pick the pairs of students. Since there are 10! different orders in which I could pick the individual pairs, then I want to divide the above by 10!, giving me the answer 

[C(20, 2) * C(18, 2) * ... * C(2, 2)] / 10!. 

This is the same as your answer, because C(n , 2) = n(n - 1) / 2, so we can simplify the above as 

[(20 * 19) / 2 * (18 * 17) / 2 * ... * (2 * 1) / 2] / 10! 
= 20! / [2^10 * 10!] 
= 20! / [(2!)^10 * (10!)]. 



Another way is to reason as follows: 

1. First, arrange the 20 students in a line; there are 20! ways to do this 
2. We can get a pairing by pairing the 1st and 2nd students in line together, the 3rd and 4th students together, etc. 
3. But if I switch the order of the 1st and 2nd student, then this doesn't give a different pairing. I don't want to count both orderings separately, so I divide by 2! 
4. The same argument from step 3 holds for the 3rd and 4th student, the 5th and 6th student, etc., so I need to divide by 2! nine more times 
5. Finally, the particular order in which I selected the ten pairings are unimportant--for example, the following orderings don't produce different pairings: 

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 
3, 4, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 

So I need to further divide by the number of ways I can arrange the ten pairs, which is 10!. 


The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sin⁡t3+5cos⁡t3, where p(t)p(t) is the displacement from the equilibrium position in centimeters, and tt is the time elapsed in seconds. at what time does the weight first reach the equilibrium position?

Answers

Final answer:

To find the time at which the weight first reaches the equilibrium position, set the equation of motion equal to zero and solve for t.

Explanation:

The equation of motion for the weight suspended from the spring is given by p(t) = 2sin(t/3) + 5cos(t/3), where p(t) is the displacement from the equilibrium position in centimeters and t is the time elapsed in seconds. The weight first reaches the equilibrium position when the displacement p(t) equals zero. To find the time at which this occurs, we set the equation equal to zero and solve for t.

2sin(t/3) + 5cos(t/3) = 0

Using trigonometric identities, we can rewrite the equation as:

2sin(t/3) = -5cos(t/3)

Dividing both sides by cos(t/3), we get:

2tan(t/3) = -5

Therefore, to find the time at which the weight first reaches the equilibrium position, we need to solve the equation 2tan(t/3) = -5 for t.

While passing a slower car on the highway, i accelerate uniformly from 12 m/s to 24 m/s in a time of 10.0s. How far do you travel during this time and what is the magnitude of your acceleration

Answers

You say that there is uniform acceleration so:

vf-vi=at  (final velocity minus initial velocity is equal to acceleration times time)

We know vf, vi, and t so we can solve for acceleration:

24-12=a10

12=10a

a=1.2

That is the acceleration, we will need to integrate with respect to time twice...

v=⌠a dt

v=at+vi  , we know a=1.2m/s^2 and vi=12m/s

v=1.2t+12, 

x=⌠1.2t+12 dt

x=1.2t^2/2+12t+xo, we can just let xo=0 for this problem...

x(t)=0.6t^2+12t

Now we know that this acceleration lasts for 10 seconds so the distance traveled in that time is:

x(10)=0.6(10^2)+12(10)

x(10)=60+120

x(10)=180 meters

Describe the two possible ways to use the angle of depression that is outside a right triangle to find the measure of an angle inside the triangle?

Answers

1) The angle of depression is complementary to up angle of the right triangle:

=> Angle of depression = 90° - up angle

=> up angle = 90° - angle of depression

2) The angle of depression is equal to the bottom angle of the right triangle.

=> bottom angle = angle of depression.


Find the product and quotient of 24.6 and 1.2

Answers

Product: 24.6 X 1.2 = 29.52

Quotient: 24.6 / 1.2 = 20.5

The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.

What is product and quotient?

Product is of two or more numbers is the result of multiplying these numbers, and

Quotient of two numbers is the result of division of these numbers.

Now the given numbers are 2.4 and 1.2.

Now for product of these numbers let us multiply these numbers. So we have,

2.4 x 1.2 = 2.88

Hence the product of 2.4 and 1.2 is 2.88

Again for quotient of 2.4 and 1.2, let us divide these numbers. So we have,

2.4 ÷1.2 = 2

Hence the quotient of 2.4 and 1.2 is 2.

Therefore,The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.

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what is 37% of 600? what are the steps.

Answers

37% /100 = .37
.37 x 600 = 222
37% of 600 is 222 
"of" means multiplication
It's asking you to multiply 37% to 600
First, you have to turn 37% into a decimal
To turn a percent into a decimal, you have to divide it by 100, or just simply move the decimal point two places to the left
You get 0.37
Now, multiply 0.37 and 600
0.37*600=222
hope this helps:)

a model train engine is 6 inches long the real train is 42 feet long what is the scale factor

Answers

0.5:42 = 1:84. One foot on the model is equal to 84 feet.

500 is 10 times as much as

Answers

The answer is 50 because 50 times 10 is equal to 500.
50 is the answer!!!!!!!!!!

The hypergeometric distribution is used when samples are taken from an infinite population with replacement.

Answers

The hypergeometric distribution is used when samples are taken from an infinite population with replacement.
The statement is FALSE

The hypergeometric distribution describes the probability of a certain number of successes in samples taken without replacement from a finite population, not an infinite one as stated in the question.

The hypergeometric distribution is a statistical model used to calculate probabilities in experiments where samples are drawn without replacement from a finite population. Unlike the statement presented in the question, the hypergeometric distribution is not used for infinite populations nor for sampling with replacement; that would be the domain of the binomial distribution.

In January 2008, the temperature in parts of Minnesota fell from 46 F degrees to -14 F degrees over a 24 hour period. What was the average temperature change per hour?

Answers

it went from 46 to -14....thats a 60 degree change...in a 24 hr period
60/24 = 2.5 degree drop per hr...so the average temp change is -2.5 degrees per hr

The average temperature change per hour is -2.5 F per hour.

What is temperature?

Temperature is simply an average measure of the kinetic energy for particles of matter.

Here,

at t = 0 hour,   Temp. = 46 F

at t = 24 hours,  Temp. = -14 F

Now, average temp change per hour = (T₂-T₁)/(t₂-t₁)

                                                              = (-14-46)/(24-0)

                                                              = -60/24

                                                              = -2.5 F per hour

Thus, the average temperature change per hour is -2.5 F per hour.

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How many lines of symmetry does the figure have?

0
1
2
3

Answers

only 1
so answer is

1
hope it helps
The figure shown is an arrow. The concept of symmetry is the means of being made up of corresponding parts facing each other or around an axis. To put it more simply, the arrow has to be divided into perfect halves, or pieces to have lines of symmetry. With this information at hand, you must come to the conclusion that the arrow has only 1 line of symmetry. 

What is the constant high temperature at which organisms are able to live in thermal vents and volcanoes? A. 250 degrees Celsius B. 250 degrees Fahrenheit C. 250 degrees Kelvin D. 250 degrees Newton

Answers

I truly believe 250 Celsius because 250 degrees Fahrenheit is extremely hot and I don't believe any living organism can live in that type of heat and the other two answers just don't  make any sense to me. I hope this helps!

Answer:

it is actually 250 degrees Fahrenheit

Step-by-step explanation:


Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. find all points of intersection of the graphs correct to one decimal place. (enter your answers as a comma-separated list. round any decimal answers to one decimal place.)

Answers

The graphs of
f(x) = x⁵ and g(x) = 5x
are shown in the figure below.
The initial plot interval is -2 ≤ x ≤ 2.

In order to determine the points of intersection (to 1 decimal place accuracy) more graphs (shown in accompanying figures) were necessary.
The points of intersection are
x = -1.5, x = 0, and x = 1.5

Answer:
The points of intersection are x = -1.5, 0, and 1.5 (accurate to 1 decimal place)


Final answer:

To compare the functions f(x) = x^5 and g(x) = 5x, graph both functions and find their points of intersection.

Explanation:

To compare the functions f(x) = x^5 and g(x) = 5x, we can graph both functions in several viewing rectangles. By finding the points of intersection of the graphs, we can compare their values at those points.

Start by graphing the function f(x) = x^5 using a graphing calculator or software. This will give us a curve with a steep increase as x gets larger.Next, graph the function g(x) = 5x in the same viewing rectangle as f(x). This will give us a straight line that increases more gradually as x gets larger.Identify the points of intersection between the graphs of f(x) and g(x). These are the x-values at which the two functions have the same y-value. Round these x-values to one decimal place and list them as the points of intersection.

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810. What is the administration fee?

Answers

Answer:

answer = 60

Step-by-step explanation:

It might be option A or D. Mine was D

write in order from least to greatest

Answers

.021, 99/1000, .845 hope this helps

A list of elements from which the sample may be drawn is called a

Answers

A list of elements from which the sample may be drawn is called a "population"

If the following fraction is reduced, what will be the exponent on the p? -5p^5q^4/ 8p^2q^2

A. 5
B.4
C.3
D.2

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ \cfrac{-5p^5q^4}{8p^2q^2}\implies \cfrac{-5p^5q^4p^{-2}q^{-2}}{8}\implies \cfrac{-5p^5p^{-2}q^4q^{-2}}{8} \\\\\\ \cfrac{-5p^{5-2}q^{4-2}}{8}\implies \cfrac{-5\boxed{p^3} q^2}{8}[/tex]

Answer: D. 2

Step-by-step explanation:

What is the future value of a $1,500 investment, earning 10 percent interest
per period, after two periods? (Round your answer to the nearest cent.)

Answers

For 1 period
A=P(1+rt)
A=1500(1+(1*.1))
A=$1650
For 2 periods
A=$1800
The amount of interest earned each time is $150.  
The formula of compound interest is
A=p (1+r)^t
A future value?
P present value 1500
R interest rate 0.1
T two periods 2
A=1,500×(1+0.1)^(2)=> A=1,815

HELP PLZ? You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?

Answers

volume =  l x w x h

area 1 = 3 x 1.5 x 2 = 9 cubic feet

area 2 = 2 x 1.5 x 2 = 6 cubic feet

area 3 = 1.5 x 1 x 2 = 3 cubic feet 


9+6+3 = 18 cubic feet total

Answer:

The volume of Podium is:  18 cubic feet.

Step-by-step explanation:

The volume of Podium is equal to the volume of 3 cuboids of different heights.

We know that a volume of cuboid with length l, width b and height h is given by:

Volume= l×b×h

Hence,

Volume of cuboid numbered as 3 is:

Volume= 1×2×1.5= 3 cubic feet.

Volume of cuboid numbered as 2  is:

Volume=2×2×1.5=6 cubic feet.

Similarly volume of cuboid numbered as 1 is:

Volume= 3×1.5×2=9 cubic feet.

             Hence, the Volume of Podium is:

                          3+6+9=18 cubic feet.

A wheel in this scale drawing is 4 cm wide. The ratio of the drawing is 1:14. How wide is the actual wheel in cm?

Answers

1:14 means that for every 1 cm it is drawn at it is actually 14 cm

 so multiply 4 x 14 = 56

 it is actually 56 cm wide

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