Factor completely 16x8 − 1. (4x4 − 1)(4x4 1) (2x2 − 1)(2x2 1)(4x4 1) (2x2 − 1)(2x2 1)(2x2 1)(2x2 1) (2x2 − 1)(2x2 1)(4x4 − 1).

Using proportions, it is found that the sales tax is of 8%.

A proportion is a fraction of a total amount.

In this problem, he buys a shirt for $32.00, then the second at 35% off, hence the price of the second shirt is:

P = (1 - 0.35) x 200 = 0.65 x 20 = $13.

The total price of the shirts is:

T = $32.00 + $13.00 = $45.00.

Hence, he pays $3.60 in taxes, and the sales tax is given by:

Tax = (3.6/45) x 100% = 8%.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

[tex]\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}[/tex]

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

[tex]\displaystyle \large{0=\sqrt{(x+3)(x+2)}}[/tex]

Solve for x, square both sides:—

[tex]\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}[/tex]

Simply solve a quadratic equation:—

[tex]\displaystyle \large{x=-3,-2}[/tex]

Therefore, x-intercepts are:—

[tex]\displaystyle \large{\boxed{x=-3,-2}}[/tex]

__________________________________________________________

Finding y-intercept

Let x = 0.

[tex]\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}[/tex]

Therefore, y-intercept is:—

[tex]\displaystyle \large{\boxed{\sqrt{6}}}[/tex]

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

Answer:

60

Step-by-step explanation:

D

The sum of the angle measures is 180 degrees

  -->[tex](3x + 28)+(5x + 52) +(2x -10) = 180\\10x + 70 = 180\\10x = 110\\x = 11[/tex]

Since x= 11, angle c = 2(11) - 10= 12

Hope that helps!

Answer:

The picture is too blurry to see, so let me explain how you find the answer for yourself...

Step-by-step explanation:

Basically, time is the y-axis (up and down), and # of rebounds is the x-axis (left and right). The question asks for rebounds made in 15 minutes, so first find the 15 mark on the left of the graph. Trace that line across the graph to the right (use ur finger if you have to) until you hit a dot. Trace the line that the dot is on down to the bottom of the graph. The number you hit will be your answer (# of rebounds).

~Hope this helps :)

Answer:

  (h)  ST, ∠S, ∠R

Step-by-step explanation:

In general the Law of Sines is applicable when you have two angles and a side. The solution of the triangle will be unique if the given side is opposite the largest angle.

These conditions are met in choice h.

  x/sin(S) = ST/sin(R)

  x = sin(S)·ST/sin(R) = sin(34°)·7/sin(92°)

  x ≈ 3.917

__

Additional comment

Here's why the other choices don't work.

  (f) These values would require sin(R) = 15.3/8.1×sin(38°) ≈ 1.163. No angle has a sine of this value, so no triangle can be formed with these values.

  (g) The given angle is between the given sides, so the Law of Cosines is needed for solving the triangle.

  (j) Three angles are given, but no sides are given. The lengths of the sides, including x, cannot be determined.

Answer:

2/7

Step-by-step explanation:

This is a direct proportionality qn

Answer:

x=3.5

Step-by-step explanation:

In one minute 3.5 pancakes are eaten, and the variable is constant

121 = 55%

121 / 11 = 5%

11 = 5%

11 * 20 = 100%

220 = 100%

220 students in 7th grade

[tex]\\ \rm\rightarrowtail 4^{x+1}=5^{-x}[/tex]

[tex]\\ \rm\rightarrowtail ln4^{x+1}=ln5^{-x}[/tex]

[tex]\\ \rm\rightarrowtail (x+1)ln4=-xln5[/tex]

[tex]\\ \rm\rightarrowtail xln4+ln4=-xln5[/tex]

[tex]\\ \rm\rightarrowtail xln4+xln5=-ln4[/tex]

[tex]\\ \rm\rightarrowtail x(ln4+ln5)=-ln4[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-ln4}{ln4+ln5}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-ln4}{ln20}[/tex]

Option F is correct

Answer:

1. factored form is - 5/2, 3, 2 solutions 2. - 1/2 , -5 2 solutions 3. -2, 3 2 solutions 4. -2 , 5, 2 solutions

Step-by-step explanation:

Question 1:

  [tex]2x^{2} -x-15=0\\(2x+5)(x-3)=0[/tex]

   Solutions are x = -5/2 and 3

Question 2:

  [tex]2x^2+11x =-5\\2x^2 + 11x +5 = 0\\(2x+1)(x+5)= 0[/tex]

   Solutions are x = -1/2 and x =-5

Question 3:

 [tex]x^2-x-6=0\\(x-3)(x+2)=0[/tex]

  Solutions are x = 3 and -2

Question 4

  [tex]x^{2} -3x-10 = 0\\(x-5)(x+2)=0[/tex]

  Solutions are x = 5 and x = -2

Answer:

1. Quadratic, 2nd degree

2. Constant, no degree

3. Cubic, 3rd degree

4. Linear, 1st degree

Answer:

7

Step-by-step explanation:

any number greater than 3 but it has to be less than 9

When it comes to right triangles, there's one extremely important equation that you'll have to use almost every single time you come across one: the Pythagorean Theorem.

[tex]a^{2} + b^{2} = c^{2}[/tex]... Does that equation ring any bells? This equation is utilized to solve for any of the sides of a right triangle, given that you know the values of two of the sides. in a right triangle, there are three sides - one of which is known as a hypotenuse (the longest side of a right triangle). Variables a and b represent the lengths of the non-hypotenuse sides (basically, the two smaller sides, the ones that form a right angle). There's no special rule to which side is designated a and which is designated b, so don't worry about trying to figure out which side should be labeled which. Variable c represents the length of the hypotenuse.

Now, how can we apply the Pythagorean Theorem to this question? We are given the values of the two legs of the triangle, 1 m and [tex]\sqrt{15}[/tex] m. Since we are prompted to solve for the length of the hypotenuse, we will use the Pythagorean Theorem and solve for c, the variable for the length of the hypotenuse.

[tex]c^{2} = a^{2} + b^{2}[/tex]

c = [tex]\sqrt{a^{2} + b^{2} }[/tex]

(We square root both sides in order to isolate c. Now, let's plug in the values we were given. As we learned earlier, it doesn't matter which leg is a or b)
c = [tex]\sqrt{1^{2} + \sqrt{15}^{2} }[/tex]

c = [tex]\sqrt{1 + 15}[/tex]

c = [tex]\sqrt{16}[/tex]

c = 4 (m)

The length of the hypotenuse is 4 meters.

And we're done! Though I wrote a lot, the equation is fairly simple and will come extremely handy any time you're faced with questions like these. If you have any questions about anything I wrote here or you need clarification on anything, let me know!

- breezy ツ

Answer: No, this is false

Step-by-step explanation:

    Difference of [tex]\frac{1}{5}[/tex] and [tex]\frac{1}{10}[/tex],

[tex]\frac{1}{5}[/tex] - [tex]\frac{1}{10}[/tex] = [tex]\frac{2}{10}[/tex] -  [tex]\frac{1}{10}[/tex]  =  [tex]\frac{1}{10}[/tex]

   [tex]\frac{1}{2}[/tex] is equal to [tex]\frac{5}{10}[/tex]. Since 1 is closer to 0 than it is to 5, the answer is no, this is false.

Answer:

No

Step-by-step explanation:

To find the area Use B x H = A

so 7 x 9 = 63

The percentage of actual yield is 60.66%.

The percentage of a number is the hundredth part of that number.

Given that the total yield is 872.7 grams and the actual yield is 529.4 grams.

The percentage is calculated by the formula given below.

[tex]Percentage\; of\; Yield = \dfrac {Actual \;Yield }{ Total\; Yield}\times 100[/tex]

Substituting the values, we get the percentage,

[tex]Yield \;\% = \dfrac {529.4}{872.7}\times 100[/tex]

[tex]Yeils\;\%=60.66\;\%[/tex]

Hence we can conclude that the percentage of actual yield is 60.66%.

To know more about the percentage, follow the link given below.

https://brainly.com/question/8011401.

Answer:

-270 is the smallest negative possible angle.

Step-by-step explanation:

Cotrrminal Angle have been period of 360 degrees.

Since we won't it to be negative, we subtract 360.

[tex]90 - 360 = - 270[/tex]

We can keep going infinitely if we want to.

[tex] - 270 - 360 = - 630[/tex]

Or so on...

Answer:

  695 revolutions

Step-by-step explanation:

Finding the number of revolutions is basically a units conversion problem. You want to translate miles to revolutions. We can do this by way of feet and inches. The circumference of the wheel is pi times the diameter.

  1 mi = (1 mi) × (5280 ft)/(1 mi) × (12 in)/(1 ft) / (29π in)/(1 rev)

  = (1·5280·12·1)/(1·1·29π) = (63360/(29π)) rev ≈ 695.45 rev

About 695 revolutions will be needed to make the bike travel 1 mile.

Answer:

[tex] \frac{2x - 2}{3} - \frac{3x - 6}{4} = 1 \\ \frac{8x - 8 - 9x + 18}{12} = 1 \\ - x + 10 = 12 \\ - x = 12 - 10 \\ x = - 2[/tex]

A poll worker analyzing the ages of voters found that  [tex]\mu =65[/tex]     [tex]\sigma=5[/tex] the possible voter age at Zx=1.14 will be around 71.

It is given that

[tex]\rm Mean\ \mu=65[/tex]

[tex]\rm standard \ deviation \ \sigma =5[/tex]

[tex]\rm X= Ages\ of \ the \ workers[/tex]

From the Z-score concept, we know that

[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]x=\sigma Z+\mu[/tex]

putting the values

[tex]X=5\times 1.14+65=70.7[/tex]

Thus A poll worker analyzing the ages of voters found that  [tex]\mu =65[/tex]     [tex]\sigma=5[/tex] the possible voter age at Zx=1.14 will be around 71.

To know more about the Z-score concept follow

https://brainly.com/question/14777840

Answer:

11

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] of 88

= [tex]\frac{88}{8}[/tex]

= 11

The polynomial is a binomial

The coefficients are the invested amounts

From the question, we have the following parameters that can be used in our computation:

Polynomial expression = 400x^8 + 600x^6

The above has two terms

So, it can be classified as a binomial

From the question, we have:

investing $400 for 8 years and $600 for 6 years

This means that the coefficients are the invested amounts

Read more about polynomial at

https://brainly.com/question/7693326

#SPJ1

Answer:

6) 1 over 12

7) 10 over 12

8)9 over 12

6.

[tex]\tt \dfrac{1}{6}\times \dfrac{2}{2}=\dfrac{2}{12}[/tex]

7.

[tex]\tt \dfrac{5}{6}\times \dfrac{2}{2}=\dfrac{10}{12}[/tex]

8.

[tex]\tt \dfrac{3}{4}\times \dfrac{3}{3}=\dfrac{9}{12}[/tex]

Answer:

sheesh this is big

Step-by-step explanation:

aight for the conver to meters

1)2

2)7

3)6.5

4)4

5)0.40

convert to litres

sorry my class just ended ill answer the rest in like 5 minutes

So

Now

These are correct