Find the y-intercept and the axis of symmetry of f(x) = ax2 – 6ax +2.
The y-intercept is
and the axis of symmetry is x=

Answer:

[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\cos(x)\tan(x)=\cos(x)[/tex]

On the interval [0, 2π).

First, we can subtract cos(x) from both sides:

[tex]\cos(x)\tan(x)-\cos(x)=0[/tex]

Factor:

[tex]\cos(x)\left(\tan(x)-1\right)=0[/tex]

Zero Product Property:

[tex]\cos(x)=0\text{ or } \tan(x)-1=0[/tex]

Solve for each case:

[tex]\cos(x)=0\text{ or }\tan(x)=1[/tex]

Using the unit circle:

[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{5\pi}{4}, \frac{3\pi}{2}\right\}[/tex]

However, since tangent isn't defined for π/2 and 3π/2, we remove them from our solutions. Hence:

[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]

Answer:

[tex]9.5 \sqrt{?} [/tex]

Answer:

#1: x=8, #2: x=21, #3: x=9

Step-by-step explanation:

So, to solve each of these x's, we need to do two things:

Find the scale factor

Then scale for x.

So lets start off with the first one.

We have a side value fo 3.

In the scaled version, we have the same side with a value of 6.

To find the scale, divide the 6 by 3:

6/3

=

2

So our scale is 2.

Next, lets look at our value on the traingle we know, and solve for the unkown x. We know that on the orginal traingle, its 4. For the version thats 2 times bigger, its x

So to solve this, multiply the 4 by 2:

4*2

=

8

This is your x value for the first question.

Next we have the side value 12 for the trapezoid. For the one next to it, the trapezoid has the same side with a value of 18.

To find the scale, lets divide 18 by 12.

18/12

=

1.5

That is our scale factor.

In these trapezoids, the bottom value is orginally 14.

In the scaled version, which we know is 1.5 times bigger, we have x.

To solve for x, lets multiply the 14 by 1,5:

14*1.5

=

21

So we know our x is 21 for the second answer.

Finally we have the third question.

This one is opposite to the last ones, where the smaller value has the missing x value.

Here our top side value is 20.

On the scaled version it is 15.

Lets divide 15 by 20, instead of what we normally do. Which would have been 20 by 15:

15/20

=

.75

Now, with this scale factor, our x will be smaller than the known value. Looking at the side length, the orginal value is 12.

On the scaled side length that is 0.75 times as big, its x

So lets multiply 12 by 0.75:

12*0.75

=

9

So this is your last x value, for your third answer!

This might seem long and tedious, but its actually a simple way of thinking about it, and you may find that you can quickly do this in your head, instead of a shorter, more complex way.

Hope this helps!

Answer:

The null hypothesis is [tex]H_0: \mu = 13[/tex]

Step-by-step explanation:

Before a high-school football game the footballs were inflated to p = 13 psi (pounds per square inch).

This means that, as we are going to test the inflation levels before and after the game, we test at the null hypothesis that it is of 13 psi, that is:

[tex]H_0: \mu = 13[/tex]

Answer:

[tex]g(2) = 3[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]g(2)[/tex]

To solve this, we make use of:

[tex]g(x) = |7 - x^2|[/tex]

Because [tex]x \le 2[/tex]

i.e. [tex]2 \le 2[/tex]

So, we have:

[tex]g(2) = |7 - 2^2|[/tex]

[tex]g(2) = |7 - 4|[/tex]

[tex]g(2) = |3|[/tex]

Remove absolute brackets

[tex]g(2) = 3[/tex]

9514 1404 393

Answer:

  4) -ln(2)/3

  5) x = 9

  6) x = 2

  7) x = -6

Step-by-step explanation:

4) e^(-3x) = 2 . . . . given

  -3x = ln(2) . . . . . take the natural log

  x = -ln(2)/3 . . . . divide by the coefficient of x

__

5) ln(3x -5) = ln(11) +ln(2)

  3x -5 = 11·2 . . . . . take antilogs

  3x = 27 . . . . . . . . add 5

  x = 9 . . . . . . . . . . divide by 3

__

6) log4(x -1) +log4(x +2) = 1

  (x -1)(x +2) = 4 . . . . . take antilogs

  x^2 +x -2 = 4 . . . . . . eliminate parentheses

  x^2 +x +1/4 = 6 1/4 . . . add 2 1/4 to complete the square

  (x +0.5)^2 = 6.25 . . . . write as a square

  x +0.5 = ±2.5 . . . . . . . take the square root

  x = -0.5 ± 2.5 = {-3, +2} . . . . . . x = -3 is an extraneous solution

  x = 2

__

7) 8^x = 4^(x -3)

  2^(3x) = 2^(2(x -3)) . . . . write using a common base of 2

  3x = 2(x -3) . . . . . . . . . . take logarithms base 2

  x = -6 . . . . . . . . . . . . . . .subtract 2x

Answer:

$165.8 ;

$223.83 ;

Henry would pay less for the tablet on the website.

Step-by-step explanation:

Given :

Regular price = $829

On website :

80% discount off the regular price :

(100 - 80)% * regular price

20% * 829

0.2 * $829 = $165.8

At store :

70% off regular price :

(100 - 70)% * 829

0.3 * 829

= $248.7

10% off sale price :

(100 - 10)% * $248.7

0.9 * 248.7

= $223.83

Henry would pay less for the tablet on the website.

Answer:

4.692 to 7.308

Step-by-step explanation:

Given :

n1 = 25 ; n2 = 20 ;

Mean x1 = $12 ; mean x2 = $6

Standard deviation, s1 = 3 ; s2 = 1

Confidence interval :

(x1 - x2) ± t*√(s1²/n1) + (s2²/n2)

x1 - x2 = (12 - 6) = 6

√(s1²/n1) + (s2²/n2) = √(3²/25) + (1²/20) = 0.640

Degree of freedom :

((s1²/n1) + (s2²/n2))² / (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1

Numerator = 0.1681

Denominator = 0.0054 + 0.0001315 = 0.0055315

Degree of freedom = 0.1681 / 0.0055315 = 30.38 = 30

Tcritical at 0.05, df = 30 = 2.042272

Hence ;

6 ± 2.042272(0.640)

6 ± 1.30705408

Lower boundary = 6 - 1.30705408 = 4.69294592

Upper boundary = 6 + 1.30705408 = 7.30705408

(4.693 ; 7.307)

Answer:

6.25 hours

Step-by-step explanation:

30.5 - 24.25 = 6.25 hrs.

Answer: the third option (3/6 > 5/12)

Step-by-step explanation:

process of elimination:

option one is incorrect because 1/2 = 3/6 (not 1/2 > 3/6)

option two is incorrect because again, 1/2 = 3/6

option four is incorrect because 3/6 > 5/12

Answer:

https://rr.noordstar.me/83819a0f

Answer: B

Step-by-step explanation:

I didn't waste time looking at if the data was Symmetric or skewed, because A, C and D are all false statements:

A - If it's skewed Mean wouldn't be used

C - If it's Symmetric IQR wouldn't be used

D - If it's skewed Standard Deviation wouldn't be used

Answer:

Constant Force F= ?

A= 5m/s²

M=9kg

According to the Question

A

[tex] \alpha [/tex]

1/m

A=F/m

So F=ma

F=5×9

F=45N

we look for m using the formula A=F/m

m=F/A

where A=3

F=45

M=?

So M=45/3

M=15kg

Answer:

Each person should pay $6.00

Step-by-step explanation:

First, add everyone's cost

8 + 4 + 7 + 5 =  24

Then, divide by 4

24 ÷ 4 = 6

Lastly, have a great day! :)

Answer:

A the answer is a because i was just working on that rn

Step-by-step explanation:

Answer:

48 ounces.

Step-by-step explanation:

:) have a good rest of your day.

Answer:

Step-by-step explanation:

Chanclas

Answer:

$110.94

Step-by-step explanation:

221.88 divided by 2 is 110.94

Answer:

The proportion of people who were caught after being on the 1010 Most Wanted list would be 40.81%.

Step-by-step explanation:

Since the FBI wants to determine the effectiveness of their 1010 Most Wanted list, and to do so, they need to find out the fraction of people who appear on the list that are actually caught, supposing a sample of 517517 suspected criminals is drawn, and of these people, 211211 were captured, to estimate the proportion of people who were caught after being on the 1010 Most Wanted list using this data, the following calculation must be performed:

517,517 = 100

211,211 = X

211,211 x 100 / 517,517 = X

21,121,100 / 517,517 = X

40.81 = X

Therefore, the proportion of people who were caught after being on the 1010 Most Wanted list would be 40.81%.

Answer:

SA = 56 sq mi

Step-by-step explanation:

SA = area of base + 1/2(perimeter of base)(slant height)

SA = 16 + 1/2(16)(5)

SA = 16 + 8(5)

SA = 16 + 40

Answer:

32 units squared

Step-by-step explanation:

Split up the figure into easy to find area parts. So, theres 2 triangles, and in the middle of those, you can make a square. And that would make the top part a large triangle! Now find the area of these

Large triangle: 1/2 (4)(10) = 20

Smallest triangle: 1/2(2)(2) = 2

Medium triangle: 1/2(6)(2) = 6

Square: 2*2 = 4

Now add them all up! 20+2+6+4 = 32 units squared!

Answer: 2*5^2-12

5 to the 2nd power is 25

2*25-12

2*25=50

50-12=38

the answer is C 38

hope this helps

Answer: [tex]\$29.7[/tex]

Step-by-step explanation:

Given

The trophy has a side of [tex]a=9\ in.[/tex]

Slant height [tex]l=11\ in.[/tex]

Rate  of painting [tex]r=\$\ 0.15/in.^2[/tex]

Lateral surface area of square pyramid is [tex]2al[/tex]

Insert the values

[tex]\Rightarrow 2\times 9\times 11\\\Rightarrow 198\ in.^2[/tex]

Cost of painting

[tex]\Rightarrow 198\times 0.15=\$29.7[/tex]

Answer: The histogram is skewered to the right (right-skewered)

Step-by-step explanation:

The peak veers to the left and the tail is towards the right.

The histogram given is right-skewed.

A histogram is a representation of the distribution of data with intervals.

We have,

Right-skewed and left-skewed are terms used to describe the shape of a data distribution.

A right-skewed (or positively skewed) distribution is one in which the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.

A left-skewed (or negatively skewed) distribution is the opposite of a right-skewed distribution.

In this case, the tail on the left-hand side of the graph is longer or fatter than the tail on the right-hand side.

Now,

We see that the histogram given is right-skewed because the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.

Thus,

The histogram given is right-skewed.

Learn more about histograms here:

https://brainly.com/question/16819077

#SPJ3

Answer:

1.3 liters

Step-by-step explanation:

4 x 150 is 600

4 x 175 is 700

700 + 600 = 1300 milliliters

1300 milliliters = 1.3 liters  

Answer:

1.3 liters

Step-by-step explanation:

So first off, lets find the amount of milileters of lotion there is.

To do this, take 8, and divide it in half:

8/2 = 4. So we know that 4 bottles of lotion each contain 150 militers of lotion.

We know that the other 4 bottles each contain 175 milileters of lotion.

Next, lets multiply the 150 and 175 by the four bottles:

150x4

=

600

175x4

=

700

Now lets add these two values together, to find the total amount of lotion:

700+600

=

1300

Remember, this problem asked for liters of lotion, not milileters. Lets recall that 1000 milileters are equivelent to 1 liter:

1300/1000

=

1.3

This is your answer!

Hope this helps! :)

Answer:

15.3

Step-by-step explanation:

Cos 32 = x/18

Cos 32 = 0.848048096

x/18 = 0.848048096

x = 15.3 (rounded)

Answer:

2/3 pounds of lima beans

Step-by-step explanation:

2 divided by 3 = 2/3 = 2/3

Hope this helps!

Answer:

2/3 pounds (Option B)

Step-by-step explanation:

Using unitary method ,

3 families will receive = 2 pounds of lima beans.

(Dividing both the sides by 3)

⇒ [tex]\frac{3}{3}[/tex]  family will receive = [tex]\frac{2}{3}[/tex] pounds of lima beans

⇒ 1 family will receive = [tex]\frac{2}{3}[/tex] pounds of lima beans.

∴ Each family will receive 2/3 pounds of lima beans.

Answer:

x=12

Step-by-step explanation:

Since the triangles are congruent, you can use either B or D to solve for x.

7x+10=94

7x=94-10

7x=84

x=84÷7

x=12