what is the slope of the line described by the equation below? Y=-x+8

Answer:

x = 96

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

48 = 1/2 ( x)

Multiply by 2

96 = x

Answer:

[tex]\boxed{x=96}[/tex]

Step-by-step explanation:

Apply the inscribed angle theorem, where the measure of an inscribed angle is half the measure of the intercepted arc.

[tex]48=\frac{1}{2}x[/tex]

Multiply both sides by 2.

[tex]48(2)=\frac{1}{2}x(2)[/tex]

[tex]96=x[/tex]

Answer:

100r^4 + 400r^3 + 600r^2 + 400r + 100

Step-by-step explanation:

Expanding ( r + 1 )^4 gives :-

r^4 + 4r^3 + 6r^2 + 4r + 1

So multiplying 100 with r^4 + 4r^3 + 6r^2 + 4r + 1 gives :-

100r^4 + 400r^3 + 600r^2 + 400r + 100

Answer:

D

Step-by-step explanation:

an inverse function is a function that reverses another function for ex. if f(x)=y and g(y)=x.

Answer:

A and C

Step-by-step explanation:

Answer:

Interval notation is

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Solutions:

[tex]\left(-\infty, -5\right)[/tex]

[tex]\left(0,1)[/tex]

Step-by-step explanation:

[tex]x^3 + 4x^2 - 5x < 0[/tex]

In this inequality, luckly we can easily factor it.

[tex]x^3 + 4x^2 - 5x[/tex]

[tex]x(x^2+4x-5)[/tex]

[tex]x(x-1)(x+5)[/tex]

So we have

[tex]x(x-1)(x+5)<0[/tex]

In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.

Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:

The first step to complete the table is the x value where the factor will be equal to zero.

       [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]                                                                        0

[tex]x-1[/tex]                                                                                                    0        

[tex]x+5[/tex]                      0

Then, just consider the signal:

  [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]    -                -                       -                   0               +                 +             +

[tex]x-1[/tex]  -             -                      -                   -               -                  0             +

[tex]x+5[/tex]  -             0                     +                   +                +               +              +

[tex]x(x-1)(x+5)[/tex]    -     0       +     0      -      0     +

When [tex]x(x-1)(x+5)<0[/tex] ?

It happens when [tex]x<-5[/tex]     and when [tex]0<x<1[/tex]

The solution is

[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Answer:

1. x>20   2. x≤1     3.x<4     4.x>9      5.x≥-13

Answer:

x > 4

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

You have to substitute x = 2, into the equation of y :

[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]

[tex]let \: x = 2[/tex]

[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]

[tex]y = 48 - 20 + 8 - 3[/tex]

[tex]y = 33[/tex]

Answer:

LL

Step-by-step explanation:

We have two right triangles

The two legs are congruent

We can use the LL congruence theorem

Answer:

You would basically expand all the equations!

1. 7(4z+8b) is equal to 28z+56b.

2. 8(2x+3^2) is equal to 16x+72

3. 4(r+r+r+r) is equal to 4r+4r+4r+4r

4. 9(3+8x) is equal to 27+72x

5. 4^2(3+6f) is equal to 48+96t

6. (t+t+t)/4 is equal to t/4+t/4+t/4

7. 2(4s^3+2) is equal to 8s^3+4

8. 30(3x+4) is equal to 90x+120

9. 6(5a+9b) is equal to 30a+54b

10. 9(3x+5^4) is equal to 27x+5625

11. 7(c+c+c) is equal to 7c+7c+7c

12. 9(2+7f) is equal to 18+63f

13. 7^5(4g-8d) is equal to 67228g-134456d

Step-by-step explanation:

Hey there! I'm happy to help!

Let's represent everybody with variables. Raina is R, Justin is J, and Cho is C. Let's write down this information as a system of equations.

R+J+C=79            (they all have 79 total dollars in their wallets combined)

R=J-5                    (Raina has five less than Justin.)

C= 2J                        (Cho has twice that of Justin)

Since we know what R and C equal, we can plug in their values in terms of J into the first equation to solve for J.

J-5+J+2J=79

We combine like terms.

4J-5=79

We add 5 to both sides.

4J=84

We divide both sides by 4.

J=21

This means that Justin has $21. If Raina has 5 less, she has $16 and since Cho has twice that of Justin he has $42. These added up equal 79.

I hope that this helps! Have a wonderful day!

Answer:

x=2

Step-by-step explanation:

[tex]f(x)=\frac{x^2-4}{x^2-12x+20}[/tex]

Factor the numerator and denominator:

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

We can remove (x-2) from the function:

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

(x-2) is a removable discontinuity.

The x-value of x-2 is x=2.

Step-by-step explanation:

3500 × 10/100

rs. 350 is the discount

and to find the amnt the customer should pay subtract 350 from 3500

which is,

3150 Rupees

Answer:

.006

:)

Step-by-step explanation:

8 servings can David make with the current amount of spice.

Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

The rice-to-spice ratio = 15:1

The 75 grams of rice in one serving will require

⇒75/15

⇒5 gram of spice.

David's inventory of 40 gram of spice is enough for

40 g/(5 g/serving) = 8 servings

Hence, 8 servings can David make with the current amount of spice.

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Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

the width of the rectangle is 24 centimeters and the length is 31 centimeters.

Step-by-step explanation:

We first have to write an equation for this, but let's just recall that the area of a rectangle is equal to the length times the width. A=L×W.

A is the area

L is the length

W is the width.

So, for our equation we can start out by putting that 744= ? times ?.

So, we are given that the length is 7 more than the width. We are going to have to translate that to represent the length.

We need a variable. Let's use the letter "W," the width of the rectangle.

W=W.

The length is 7 more than the width, so it is L=W+7.

Length represents the W+7

Width represents W.

Now, we can complete our equation.

744=W(W+7).

Simplify the expression.

744=[tex]W^{2}[/tex]+7W.

Alright, you may be thinking on how we are going to solve this problem. This equation correlates with quadratic functions.

Let's complete the square.

In a quadratic function, the standard from is y=[tex]ax^{2} +bx+c[/tex].

We need to find the c value.

We can do this by applying a formula. The formula states that c= b/2 and the whole thing squared. In other words, [tex](\frac{b}{2} )^{2}[/tex].

In this case, the b value is 7.

square 7, which is 49 and square 2 which is 4.

Now, the c value is 49/4.

We have now just created a perfect square trinomial.

Not only do we add 49/4 to W squared plus 7W, we also add 49/4 to 744.

744 plus 49/4 is 756/25.

Now, we have [tex]W^{2}+7w+\frac{49}{4} = 756.25[/tex]

Change W squared plus 7w plus 49/4 to a binomial squared.

Just take the square root of the a value, W, and 49/4 for c. the square root of W squared is W. the square root of 49/4 is 7/2.

Those values are to the power of 2.

In other words, [tex](W+\frac{7}{2})^{2} =756.25[/tex]

To isolate for W, take the square root of both sides.The square root of W plus 7/2 squared is just W+7/2. The square root of 756.25 is 27.5

There are two solutions for W because square roots be positive or negative, but we are dealing with positive since negative doesn't make sense with the context of the problem.

We have [tex]W+3.5 or \frac{7}{2}=27.5[/tex]

Isolate for W by subtracting both sides by 3.5 You get to W=24.

Therefore, the width of the rectangle is 24 centimeters.

Alright, we found the width. We now need to find the length. The problem stated that the rectangle was 7 more than the width. So, 24+7=31. Therefore, the length of the rectangle is 31 centimeters.

L=31cm

W=24cm.

I hope this was helpful! I wish you have an amazing day!

Answer:

y=10000 at rate 0.12 or 12%

x=8500 at rate 0.14 0r 14 %

Step-by-step explanation:

x+y=18500   ⇒ x=18500-y

0.14x+0.12y=2390 ( solve by substitution)

0.14(18500-y)+0.12y=2390

2590-0.14y+0.12y=2390

-0.02y=2390-2590

-0.02y=-200

y=-200/0.02

y=10000 at rate 0.12

x=18500-y

x=18500-10000=8500

x=8500 at rate 0.14

check : 0.14(8500)+0.12(10000)=2390 ( correct)

Answer:

Amount invested at 14% = 8500

Amount invested at 12% =  10000

Step-by-step explanation:

Assume money was invested for one year.

18500 at 14% = 18500*0.14 = 2590

18500 at 12% = 18500*0.12 = 2220

actual interest earned = 2390

Let

x = ratio of money invested at 14%

1-x = ratio of money invested at 12%

Then

18500*x * 0.14 + 18500 * (1-x)*0.12 = 2390

0.14x - 0.12x = 2390/18500-0.12

0.02x = 0.1291892-0.12 = 0.0091892

x = 0.0091892/0.02 = 0.4594595

Amount invested in 14% = 18500 * x = 8500

Amount invested in 12% = 18500 * (1-x) = 10000

Answer:

Gender and Residence of Students

a) What is the probability that a student is female and lives in a dorm?  

= 58.33%

b) What is the probability that a student is female given that she lives in a dorm?

= 21%

Step-by-step explanation:

a) Data and Calculations:

Gender and Residence of Students  

                                           Males   Females Total

Apartment off campus         50        90        140

Dorm room                          150       210       360

With Parent(s)                      100        50        150

Sorority/ Fraternity House 200      150        350

Total                                    500     500      1,000

a) Probability that a student is female and lives in a dorm:

= number of females who live in a dorm divided by total number of students who live in a dorm * 100

= 210/360 * 100

= 58.33%

b) Probability that a student is female given that she lives in a dorm

= number of female students who live in a dorm divided by the total number of students * 100

= 210/1,000 * 100

= 21%

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:

[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]

The value of 86º in radians is:

[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]

[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]

Then, the cosine of 86º is:

[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]

[tex]\cos 86^{\circ} \approx 0.06976[/tex]

The cosine of 86º is approximately 0.06976.

Answer:

One solution, z=-5

Step-by-step explanation:

First, We simplify the right side.

Distribute -5, -5z-5=-2z+10

Now add +2z to both sides, −3z−5=10

Add 5 to both sides, now the equation stands as -3z=15

We can simplify this by dividing -3 to both sides, z=-5.

Now we know there is only one solution to this equation!

Answer: 23 cans of soda/4 people.

or (23/4) cans of soda per person.

Step-by-step explanation:

So we have the rate:

46 cans of soda/ 8 people

First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:

46/2 = 23

8/2 = 4

Then the rate can be:

23 cans of soda/4 people.

Now 23 is a prime number, so we can not simplify it furthermore

You probably want the unsigned area, which means you don't compute the integral

[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]

but rather, the integral of the absolute value,

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]

[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]

Answer:

B. -3x

Step-by-step explanation:

A term is defined as either a constant or a variable with a coefficient.

-3 is incorrect because there is no constant -3 in the expression.

-3x is correct because there is a -3x in the expression

(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.

-7 is incorrect because it has to be distributed.

Answer:

5x 10 ^-5

Step-by-step explanation:

UHM that would be

NaN × [tex]10^{0}[/tex]

I hope this helps!

so my reasoning...  Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.  

Answer:

Hello some parts of your question is missing below is the missing part

suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows:

Least Squares Linear Regression of Height

Predictor

Variables    Coefficient    Std Error T P

Constant    20.2833    8.70520 2.33    0.0223

DadsHt 0.67499 0.12495    5.40    0.0002

R² 0.2673 Mean Square Error (MSE) 23.9235

Adjusted R² 0.2581    Standard Deviation 4.9000

Answer : We expect most of the sampled heights to fall within 9.8 inches of their least squares predicted values.

Step-by-step explanation:

standard deviation is the statistical measurement of the level at which a dataset disperses from its mean value

interpreting the standard deviation in this problem ,

given that the standard deviation is 4.9 inches, it simply means that the dataset heights will be either +4.9 inches or -4.9 inches away from the mean value. this means that most of the sampled Dad/'s height will fall within 9.8 inches of their least squares predicted values

Answer:

$22

Step-by-step explanation:

Let Vincent = v, Francis= f

Equations to reflect given:

and  

Replacing f with v+8:

Now finding f:

Francis gets $22

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.

Then, for the parent function, we get:

[tex]1 = 2\pi f_1[/tex]

or solving for [tex]f_1[/tex]:

[tex]f_1=\frac{1}{2\pi }[/tex]

At the same way, for f(x), we get:

[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]

But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:

[tex]f_2=2f_1[/tex]

It means that the frequency of f(x) is two times the frequency of the parent function.

Answer:

It is a geometrical progression

Step-by-step explanation:

Geometric progressions have a constant number that they are multiplied by

To find that number you divide the 2nd term by the 1st term and also the 4th term by the 3rd term. ie,

[tex]\frac{-40}{20} = \frac{-10}{5} \\[/tex]

[tex]-2 = -2[/tex]

since they are both equal it is a G.P

Because they have a constant ratio.

Answer:

Geometric progression.

Step-by-step explanation:

I suppose you mean this equation:

5, -10, 20, -40, ...

For a geometric progression, an n^th term is given by:

[tex]a_{n}[/tex] = [tex]a_{n - 1}[/tex] × r

Where a is the first time, n is the term and r is the common ratio.

The common ratio here is -2 .

For instance to check the forth term;

[tex]a_{4}[/tex] = [tex]5_{4 - 1}[/tex] × -2  = 20 × -2 = -40

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

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Answer:

Step-by-step explanation:

1. The Hamilton method has you compute the number represented by each board member (total population/# members). Using this factor, the number of board members for each district are computed. This raw value is rounded down.

Because this total does not allocate all board members, the remaining members of the board are allocated to the districts based on the size of the fraction that was truncated when rounding down. Allocations start with the largest fraction and work down until all board members have been allocated.

The attached spreadsheet implements this algorithm using a "threshold" that is adjusted to a value between 0 and 1, signifying the cutoff point between a fraction value that gets an additional member and one that doesn't. (Often, that threshold can be set at 0.5, equivalent to rounding the raw board member value to the nearest integer.)

The resulting allocations are ...

  Town A: 2

  Town B: 2

  Town C: 6

  Town D: 12

__

2. The second attachment shows the result after the population move. The allocations of board members are identical.

__

3. The "factor" (persons per board member) is about 4500, so we don't expect a move of 900 people to make any difference in the allocation. These results make complete sense.

__

4. Of course each town will consider its own interest at the expense of everyone else, so they may or may not consider the results fair. The towns have population ratio of about 9 : 9 : 25 : 56, so the ratios 2 : 2 : 6 : 12 are quite in line. Even in the second year, when the ratios are closer to 9 : 10 : 26 : 56, the changes are small enough that the allocation of board members still makes sense. The results are fair.

_____

Comment on "fair"

The reason there are different methods of allocation is that each seeks to rectify some perceived flaw in one or more of the others. The reason there is not a general agreement on the method to be used is that some benefit more from one method than from another. "Fair" is in the eye of the beholder. I believe in this case it would be very difficult to justify any other allocations than the ones computed here.