Put the following equation of a line into slope-intercept form, simplifying all
fractions.
9x – 15y = 135

Answer:

horizontal expansion factor of 2

2^x =2(2)=4

2^4=2×2×2×2= 16

Answer:

In 2025, t=30. so D=418*30+6000 = 18540

Answer:

The endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].

Step-by-step explanation:

A parabola with vertex at point [tex]C(x, y) = (h,k)[/tex] and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

[tex](x-h)^{2} = 4\cdot p \cdot (y-k)[/tex] (1)

Where:

[tex]y[/tex] - Independent variable.

[tex]x[/tex] - Dependent variable.

[tex]p[/tex] - Distance from vertex to the focus.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex.

The coordinates of the focus are represented by:

[tex]F(x,y) = (h, k+p)[/tex] (2)

The latus rectum is a line segment parallel to the x-axis which contains the focus. If we know that [tex]h = 2[/tex], [tex]k = -2[/tex] and [tex]p = -5[/tex], then the latus rectum is between the following endpoints:

By (2):

[tex]F(x,y) = (2, -2-5)[/tex]

[tex]F(x,y) = (2,-7)[/tex]

By (1):

[tex](x-2)^{2} = -20\cdot (-7+2)[/tex]

[tex](x-2)^{2} = 100[/tex]

[tex]x - 2 = \pm 10[/tex]

There are two solutions:

[tex]x_{1} = 2 + 10[/tex]

[tex]x_{1} = 12[/tex]

[tex]x_{2} = 2-10[/tex]

[tex]x_{2} = -8[/tex]

Hence, the endpoints of the latus rectum are [tex](12, -7)[/tex] and [tex](-8, -7)[/tex].

Answer: x = 2

Step-by-step explanation:

P-----------------------T----------------------Q

         (3x-3)                   (5x-7)

Since T is the midpoint we know that PT and TQ are equal

Just solve the equation: 3x-3 = 5x-7

[tex]3x-3 = 5x-7[/tex]

now move the x to one side

[tex]-3 = 2x-7[/tex] (I subtracted the 3x)

then get the 2x by itself

[tex]4=2x[/tex]

lastly, divide by 2 to get x by itself

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

Answer:

[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]

[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]

(negative in the exponent means reciprocal of the fraction)

x= [tex]\frac{1}{250}[/tex]

Brainliest please

Answer:

0.6

Step-by-step explanation:

In this question, the | symbol means "given", so we can phrase the question as "Find the probability that a student watches more than one hour of TV given that they are in the 6th period class"

Next, because there is a 100% chance that the student is in the 6th period class, we can disregard the results of the 3rd period class.

Given that the student is in the 6th period class, there are 15 total students (as 9+6=15 = the sum of the yes and no answers for 6th period) and 9 students that said yes. Therefore, there is a 9/15 = 3/5 = 0.6 probability that a student watches more than 1 hour of TV given that they are in the 6th period class

Answer:

it should be 8.333333%

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]R(x)=\frac{x+3}{x-5} \geq 0\\R(x)=0,gives~x+3=0,x=-3\\R(x)>0 ,if~both~numerator ~and~denominator~are~of~same~sign.\\let~x+3>0,x>-3\\and~x-5>0,x>5\\combining \\x>5\\\\again~let~x+3<0,x<-3\\x-5<0,x<5\\combining\\x<-3\\Hence~R(x)\geq 0\\if ~x \in ~[- \infty,-3]U(5,\infty)[/tex]

Answer:

15

Step-by-step explanation:

3/8 = 9

9÷3= 3

the remainder of 3/8 is 5/8 so

5x3=15

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.

A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...

  f = a² +b² -c²

and interpreted as follows:

(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)

Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.

__

The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.

Answer:

a) 0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.

b) The expected number of at-bats until the next home run is 6.25.

Step-by-step explanation:

For each at bat, there are two possible outcomes. Either it is a home run, or it is not. The probability of an at bat resulting in a home run is independent of any other at-bat, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that Barry Bonds hits a home run on any given at-bat is 0.16

This means that [tex]p = 0.16[/tex]

Part A: What is the probability that the next home run will be on his fifth at-bat?

0 on his next 4(P(X = 0) when n = 4)

Home run on his 5th at-bat, with 0.16 probability. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.16)^{0}.(0.84)^{4} = 0.49787136 [/tex]

0.49787136 *0.16 = 0.0797.

0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.

Part B: What is the expected number of at-bats until the next home run?

The expected number of trials for n successes is given by:

[tex]E = \frac{n}{p}[/tex]

In this question, [tex]n = 1, p = 0.16[/tex]. So

[tex]E = \frac{1}{0.16} = 6.25[/tex]

The expected number of at-bats until the next home run is 6.25.

Answer:

Option B.

Step-by-step explanation:

3 points are collinear if we can draw a line that connects the points.

And we know that any 2 or 3 points are always coplanar because we can find a plane such that the 2 or 3 points belong to it.

In the image we can see that B, A, and E are at the same y-value, thus these points are collinear, then the points define a line, and these are 3 points, thus we know that are coplanar.

Then points A, B, and E are collinear and coplanar.

The correct option is B.

Answer:

x=2    x=-1

Step-by-step explanation:

f(x) = x^2 - X - 2

0= x^2 -x-2

Factor

0 =(x-2)(x+1)

Using the zero product property

x-2 =0   x+1 =0

x=2    x=-1

Answer:

x=2, -1

Step-by-step explanation:

Hi there!

We want to find the zeros of this function: f(x)=x²-x-2

The zeros are the values of x that will make f(x)=0

So that means in order to find the zeros, set f(x) as 0

In that case,

x²-x-2=0

Now let's solve the quadratic equation

We can do it by factoring

-x is the sum of two numbers, while -2 is the product of those two same numbers

Now think: which two numbers add up to -1, but multiply to get -2?

Those numbers are -2 and 1

Now factor the polynomial by FOIL:

(x-2)(x+1)=0

Split and solve

x-2=0

x=2

x+1=0

x=-1

The zeros are x=2, -1

Hope this helps!

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

Explanation:

Since f(x) is linear, this means f(x) = mx+b

Let's plug in x = 6

[tex]f(x) = mx+b\\f(6) = m*6+b\\f(6) = 6m+b[/tex]

Repeat for x = 2

[tex]f(x) = mx+b\\f(2) = m*2+b\\f(2) = 2m+b[/tex]

Now subtract the two function outputs

[tex]f(6)-f(2) = (6m+b)-(2m+b)\\f(6)-f(2) = 6m+b-2m-b\\f(6)-f(2) = 4m\\[/tex]

The b terms cancel out which is very handy.

Set this equal to 12, since f(6)-f(2) = 12, and solve for m

[tex]f(6)-f(2) = 12\\4m = 12\\m = 12/4\\m = 3\\[/tex]

So the slope of f(x) is m = 3

-------------------------------------------------------------------------

Next, plug in x = 12

[tex]f(x) = mx+b\\f(12) = m*12+b\\f(12) = 12m+b[/tex]

We can then say:

[tex]f(12)-f(2) = (12m+b)-(2m+b)\\f(12)-f(2) = 12m+b-2m-b\\f(12)-f(2) = 10m\\[/tex]

Lastly, we plug in m = 3

[tex]f(12)-f(2) = 10m\\f(12)-f(2) = 10*3\\f(12)-f(2) = 30\\[/tex]

Answer:

The population is the population of 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

Step-by-step explanation:

Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.

Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.

Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.

The population is all 3521 people who made credit card purchases.

The sample is the 172 people who returned the survey form.

Answer:

B is the right statement

Answer:

add the answer choices

Step-by-step explanation:

It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.

Answer:

10,-4

Step-by-step explanation:

not sure where the options are but if you were to solve this equation first bring everything to one side.

x^2 - 6x - 40 = 0

factor it

(x-10)(x+4) = 0

set each part to 0

x-10 = 0 and x+4 = 0

solutions are 10 and -4

Answer:

B. 3.39 m

Step-by-step explanation:

r² = A/π

= 36/3.14

= 11.465

r = √11.465 = 3.39

Answer:

21

Step-by-step explanation:

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

The number of people who bought the more expensive ticket is 21.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Let the number of people be X so we can form the following expression given below:-

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

Therefore the number of people who bought the more expensive ticket is 21.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

That's a question about exponentiation.

Answer:

Kenji is wrong because he does not aply the porperty correctly.

Step-by-step explanation:

A exponetiation has this form:

[tex]\boxed{a^b}[/tex]

a is the base

b is the power or exponent

To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:

[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]

Examples:

Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.

I hope I've helped. ^^

Enjoy your studies! \o/

Answer:

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.9432.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9432\frac{0.16}{\sqrt{7}} = 0.12[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.12 = 2.68 pounds.

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.12 = 2.92 pounds.

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

Answer:

B. 11.5

Step-by-step explanation:

That missing length can be solved via the equation a^2+b^2=c^2, where the hypotenuse is c. We know A and B, which is 7 and 9.

7^2+9^2=130

sqrt 130 is 11.4017543

Here, you kinda have to break the rules of rounding to say that it is B.

There could be a more efficient route for resolving this answer, but this is the method that I was taught.

2 Answers:

z = 1 + i   and   z = -1 - i

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

Explanation:

We want z to be a complex number in the form z = a+bi, where a,b are real numbers and [tex]i = \sqrt{-1}[/tex] is imaginary.

Let's plug that into the equation your teacher gave you

[tex]z^2 = 2i\\\\(a+bi)^2 = 2i\\\\(a+bi)(a+bi) = 2i\\\\a(a+bi)+bi(a+bi) = 2i\\\\a^2+abi+abi+b^2*i^2 = 2i\\\\a^2+2abi+b^2*(-1) = 2i\\\\a^2+2abi-b^2 = 2i\\\\(a^2-b^2)+2abi = 0+2i\\\\[/tex]

You could use the FOIL rule to take a shortcut. I'm deciding to be a bit more wordy to show a further breakdown how everything is multiplying out.

Notice that the real part a^2-b^2 must be 0 so that it matches the real part on the right hand side.

a^2-b^2 = 0

(a-b)(a+b) = 0 .... difference of squares rule

a-b = 0 or a+b = 0

a = b or a = -b

So whatever solution z = a+bi is, it must have either a = b or a = -b.

--------------------------------

If a = b, then the 2abi portion on the left side turns into 2a^2*i

Set this equal to 2i on the right hand side and isolate 'a'

[tex]2a^2*i = 2i\\\\2a^2 = 2\\\\a^2 = 1\\\\a = 1 \text{ or } a = -1\\\\[/tex]

So a = 1 leads to b = 1

Or a = -1 leads to b = -1

Two complex solutions so far are:   z = 1 + i   and   z = -1 - i  based on those two cases above.

--------------------------------

Now consider the case that a = -b

We'll effectively have the same steps as the previous section, but the equation to solve now is [tex]-2a^2*i = 2i\\\\[/tex]

The only difference is that negative is out front. You should find that it leads to a^2 = -1, but this has no solutions because we stated earlier that a,b were real numbers.

So if a = -b, then it concludes with a,b being nonreal numbers. Ultimately we rule out the case that a = -b is possible.

Put another way, note how -2a^2 is always negative which clashes with the idea that the right hand side is positive (ignore the 'i' portions). This contradiction means that no real values of 'a' will make the equation [tex]-2a^2*i = 2i\\\\[/tex] to be true.

--------------------------------

To wrap things up, we only have two solutions and they are  

z = 1 + i   and   z = -1 - i

You can use a tool like WolframAlpha to confirm this.

Answer:

✎There will be 30 Chocolate-Covered raisins in each bag.

✎ And 5 Remaining.

Step-by-step explanation:

Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)

Answer:

The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.

Answer:Around 3 spaces between?

Step-by-step explanation:

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

[tex]180=l(4)(9)[/tex]

or

[tex]180=36l[/tex]

To find the answer, divide by 36.

[tex]\frac{180}{36} =\frac{36l}{36}[/tex]

[tex]5=l[/tex]

Answer:  200 miles

Work Shown:

(1.25 inches)/(250 miles) = (1 inch)/(x miles)

(1.25)/(250) = 1/x

1.25x = 250*1 ..... cross multiplication

1.25x = 250

x = 250/(1.25)

x = 200 miles