90x=120y What is the ratio of x : y?

Answer:

The y-intercept is -1

The x-intercept is 4.5

Step-by-step explanation:

We have the following equation:

f(x) = log(2x+1) - 1

The y intercept is the value of f(x) when x is equal to 0, so replacing x by 0 and solving for f(x), we get:

f(0) = log(2*0 + 1 ) -1

f(0) = log(1) - 1

f(0) = 0 - 1 = -1

Additionally, the x-intercept is the value of x when f(x) is equal to 0. So, replacing f(x) by 0 and solving for x, we get:

[tex]0 = log(2x + 1) - 1\\1 = log(2x + 1)\\10^1=10^{log(2x + 1)}\\10 = 2x + 1\\10 - 1 = 2x\\4.5 = x[/tex]

Answer: -64

Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64

Answer:

-64

Step-by-step explanation:

-4 • -4 • -4

-4*-4 = 16

16*-4

-64

Answer:

Step-by-step explanation:

I. If discriminant >0 then the quadratic equation has the roots x1 and x2 and

a) x1 and x2 are real numbers

b) x1≠x2

II.  If  discriminant =0 , then x1=x2 and is a real number

III. If discriminant < 0 the equation has complex roots , x1=a+bi ,

x2=a-bi ,  where i=V-1

Answer: B. There are 2 real roots.

Step-by-step explanation:

Edge 2023

Answer:

The solutions are the roots of the quadratic. They are found where the graph crosses the x-axis.

Step-by-step explanation:

Hey there! :)

Answer:

m= -2/3.

Step-by-step explanation:

A perpendicular line has a slope that is the negative reciprocal of the original. Therefore:

Begin by converting this equation into slope-intercept form:

(y = mx + b)

2y - 3x = 8

Add 3x to both sides:

2y = 3x + 8

Divide both sides by 2:

y = 3/2x + 4

Find the negative reciprocal of 3/2:

3/2 --> -2/3. This is the slope of the perpendicular line.

Answer:

4 x (4 + 3)

Step-by-step explanation:

This is 4 x (4 + 3) = 4 x 7 = 28

and this is 16 + 12 as well

hope this helps

Step-by-step explanation:

Hey there! I'm happy to help!

PART A

Let's break down each terms in the expression to find the factors that make it up and see the greatest thing they all have in common

To break up the numbers, we keep on dividing it until there are only prime numbers left.

TERM #1

Three is a prime number, so there is no need to split it up.

3pf²= 3·p·f·f              

TERM #2

We have a negative coefficient here. First, let's ignore the negative sign and find all of the factors, which are just 7 and 3. One of them has to be negative and one has to be positive for it to be negative. It could be either way, and when comparing to other, we might want one to be negative or positive to match another part of the expression to find the greatest common factor. So, we will use the plus or minus sign ±, knowing that one must be positive and one must be negative.

-21p²2f= ±7·±3 (must be opposite operations) ·p·p·f

TERM #3

6pf= 2·3·p·f

TERM #4

Since 42 is made up of 3 prime factors (2,3,7), one of them or all three must be negative, because two negatives would make it positive. We will use the plus-minus sign again on all three because it could be just one is negative or all three are, but we don't know. We can use these later to find the greatest common factor when matching.

-42p²= ±2·±3·±7·p·p

Now, let's pull out all of our factors and see the greatest thing all four terms have in common

TERM 1: 3·p·f·f  

TERM 2: ±7·±3·p·p·f     (7 and 3 must end up opposite signs)

TERM 3: 2·3·p·f

TERM 4: ±2·±3·±7·p·p   (one or three of the coefficients will be negative)

Let's first look at the numbers they share. All of them have a three. We will rewrite Term 2 as -7·3·p·p·f afterwards because 3 must be positive to match. With term four, the 3 has to positive so not all three can be negative, so that means that either the 2 or 7 has to be negative, but in the end we they will make a -14 so it does not matter which one because.

Now, with variables. All of them have one p, so we will keep this.

Almost all had an f except the fourth, so this cannot be part of the GCF.

So, all the terms have 3p in common. Let's take the 3p out of each term and see what we have left. In term 4 we will combine our ±7 and ±2 to be -14 because one has to be negative.

TERM 1: f·f

TERM 2: -7·p·f

TERM 3: 2·f

TERM 4: -14·p

The way we will write this is we will put 3p outside parentheses and put what is left of all of our terms on the inside of the parentheses.

3p(f·f+-7·p·f+2·f-14·p)

We simplify these new terms.

3p(f²-7pf+2f-14p)

Now we combine like terms.

3p(f²-7pf-14p)

If you used the distributive property to undo the parentheses you could end up with our original expression.

PART B

Completely factoring means the equation is factored enough that you cannot factor anymore. The only things we have left to factor more are the terms inside the parentheses. Although there won't be something common between all of them, one might have pairs with one and not another, and this can still be factored out, and this can be put into (a+b)(a+c). Let's find what we have in common with the three terms in the parentheses.

TERM 1: f·f

TERM 2: -7·p·f

TERM 3: 2· -7·p (I just put 7 as negative and 2 as positive already for matching)

Term 1 and 2 have an f in common.

Terms 2 and 3 have a -7p in common.

So, we see that the f and the -7p are what can be factored out among all of the terms, so let's take it out of all of them and see what is left.

Term 1: f

Term 2: nothing left here

Term 3: 2

So, this means that all we have left is f+2. If we multiply that by f-7p we will have what was in the parentheses in our answer from Part A, and we cannot simplify this any further. This means that our parentheses from Part A= (f-7p)(f+2). This shows that (f-7p) is multiplied by (f+2)

Don't forget the GCF 3p; that's still outside the parentheses!

Therefore, the answer here is 3p(f-7p)(f+2).

Have a wonderful day! :D

Answer:

9

Step-by-step explanation:

Since drainage is to be included in the possible combinations, we can therefore determined the number from the remaining 6 options which can be in combination with drainage

(6 2) = 15 pairs.

Now there are restrictions placed, where we have no pairing of damp roofing with bricklaying or plastering. This removes two pairs, so we are left with 13pairs.

Another restrictions is that students choosing Joinery must also choose Flooring. This gives the three options: joinery, flooring and drained with no pairing with the remaining four pairs this removing another four pair.

So we are left with 9 pairs in total.

Answer:

101

Step-by-step explanation:

We are given that

r(t)=[tex]<t^2,1-t,4t>[/tex]

We have to find the derivative of r(t).a(t) at t=2

a(2)=<7,-3,7> and a'(2)=<3,2,4>

We know that

[tex]\frac{d(uv)}{dx}=u'v+v'u[/tex]

Using the formula

[tex]\frac{d(r(t)\cdot at(t))}{dt}=r'(t)\cdot a(t)+r(t)\cdot a'(t)[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}=<2t,-1,4>\cdot a(t)+<t^2,1-t,4t>\cdot a'(t)[/tex]

Substitute t=2

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot a(2)+<4,-1,8>\cdot a'(2)[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=<4,-1,4>\cdot <7,-3,7>+<4,-1,8>\cdot <3,2,4>[/tex]

[tex]\frac{d(r(t)\cdot at(t))}{dt}_|t=2=28+3+28+12-2+32=101[/tex]

The derivation of the equation will be "101".

Given expression is:

r(t) = 〈t², 1 - t, 4t〉

Let,

a(2) = <7, -3, 7>

a'(2) = <3, 2, 4>

As we know,

→ [tex]\frac{d(uv)}{dx}[/tex] = u'v + v'u

By using the formula, the derivation will be:

→ [tex]\frac{d(r(t).at(t))}{dt}[/tex] = r'(t).a(t) + r(t).a'(t)

                  = <2t, -1, 4>.a(t) + <t², 1 - t, 4t>.a'(t)

By substituting "t = 2", we get

                  =  <4, -1, 4>.a(2) + <4, -1, 8>. a'(2)

                  = <4, -1, 4>.<7, -3, 7> + <4, -1, 8>.<3, 2, 4>

                  = 28 + 3 + 28 + 12 - 2 + 32

                  = 101

Thus the response above is appropriate.

Find out more information about derivatives here:

https://brainly.com/question/22068446

It appears to be a parallelogram. But without actual numerical data, I don't think it's possible to prove this or not. I could be missing something though.

Answer:

[tex]28 . 26cm[/tex]

Step-by-step explanation:

First find the radius

[tex]d = 2r \\ 9 = 2r \\ \frac{9}{2} = \frac{2r}{2} \\ r = 4.5[/tex]

Now find the CIRCUMFERENCE

[tex]c = 2\pi \: r \\ = 2 \times \pi \times 4.5 \\ = 9 \times \pi \\ = 28.26[/tex]

Answer:

The tree was 175 centimeters tall when Vlad moved into the house.

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Step-by-step explanation:

The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:

[tex]H(t) = H(0) + at[/tex]

In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.

He measured it once a year and found that it grew by 26 centimeters each year.

This means that [tex]a = 26[/tex]

So

[tex]H(t) = H(0) + 26t[/tex]

4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?

This means that when t = 4.5, H(t) = 292. We use this to find H(0).

[tex]H(t) = H(0) + 26t[/tex]

[tex]292 = H(0) + 26*4.5[/tex]

[tex]H(0) = 292 - 26*4.5[/tex]

[tex]H(0) = 175[/tex]

The tree was 175 centimeters tall when Vlad moved into the house.

How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

This is t for which H(t) = 357. So

[tex]H(t) = H(0) + 26t[/tex]

[tex]H(t) = 175 + 26t[/tex]

[tex]357 = 175 + 26t[/tex]

[tex]26t = 182[/tex]

[tex]t = \frac{182}{26}[/tex]

[tex]t = 7[/tex]

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Answer:

I feel like you are mistaken on the first question...

6 plus 27 equals 33.

33 equals 100 percent.

What is 6 over 33? 0,18.

What's 27 over 33? 0,82.

Therefore, 19 plus 12 equals 31.

19 divided by 31 equals 0,61.

12 over 31 equals 0,39.

Answer:

  27π/2

Step-by-step explanation:

The differential of volume is the product of a differential of area and the circumference of the revolution of that area about the given axis. The limits of integration in the x-direction are where y=28 crosses the curve, at x=4 and x=7.

   [tex]dV=2\pi(x-4)(y-28)\,dx\\\\dV=2\pi(x-4)(-x^2+11x-28)\,dx=2\pi(-x^3+15x^2-72x+112)\,dx\\\\\displaystyle V=\int_4^7{dV}=2\pi\int_4^7{(-x^3+15x^2-72x+112)}\,dx\\\\=2\pi\left(\dfrac{4^4-7^4}{4}+15\dfrac{7^3-4^3}{3}-72\dfrac{7^2-4^2}{2}+112(7-4)\right)=2\pi\dfrac{27}{4}\\\\\boxed{V=\dfrac{27\pi}{2}}[/tex]

_____

Check

The parabola's vertex is (5.5, 30.25), so its area above the line y=28 is ...

  A = (2/3)(7 -4)(30.25 -28) = 4.5 . . . square units

The centroid of that area lies on the line x=5.5, a distance of 1.5 from the axis of rotation. So, the volume of revolution is ...

  V = 2π(1.5)(4.5) = 27π/2 . . . matches the above

Answer:

The probability that it will take less than 80 minutes

  P(X≤80) = 0.0768        

Step-by-step explanation:

Step(i):-

Given mean of the Population = 92 minutes

Given standard deviation of the Population = 8 minutes

Let 'X' be the random variable in normal distribution

Let 'X' = 80 minutes

[tex]Z = \frac{x-mean}{S.D} = \frac{80 - 92}{8} = -1.5[/tex]

Step(ii):-

The probability that it will take less than 80 minutes

P(X≤80) = P(Z≤-1.5)

            =  0.5 - A(1.5)

            = 0.5 - 0.4232

           =0.0768

Final answer:-

The probability that it will take less than 80 minutes

  P(X≤80) = 0.0768        

Answer:

It's A

Step-by-step explanation:

Trust me i did it in geogebra

Answer:

57.62% probability that a randomly selected adult has an IQ between 89 and 121.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 105, \sigma = 20[/tex]

Find the probability that a randomly selected adult has an IQ between 89 and 121.

This is the pvalue of Z when X = 121 subtracted by the pvalue of Z when X = 89. So

X = 121

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{121 - 105}{20}[/tex]

[tex]Z = 0.8[/tex]

[tex]Z = 0.8[/tex] has a pvalue of 0.7881

X = 89

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{89 - 105}{20}[/tex]

[tex]Z = -0.8[/tex]

[tex]Z = -0.8[/tex] has a pvalue of 0.2119

0.7881 - 0.2119 = 0.5762

57.62% probability that a randomly selected adult has an IQ between 89 and 121.

Answer:

  54

Step-by-step explanation:

  [tex](\sqrt{6} + \sqrt{24})^2=(\sqrt{6}+2\sqrt{6})^2\\\\=(3\sqrt{6})^2=(3^2)(6)=\boxed{54}[/tex]

Answer:

D.

Step-by-step explanation:

The graph of a function and its inverse are symmetric with respect with the line y = x.

On each graph you are given, plot the line y = x. If the two functions are symmetric with respect to the line y = x, then the graph does show a function and its inverse.

You will see this is true only for choice D.

Answer: 0.00153

Step-by-step explanation:

Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.

Number of ways of dealing 7 cards from 52 cards = [tex]^{52}C_7[/tex]

Since there are 13 clubs and 13 spades.

Number of ways of getting exactly 4 clubs and 3 spades=[tex]^{13}C_4\times\ ^{13}C_3[/tex]

Now, the probability of being dealt exactly 4 clubs and 3 spades

[tex]=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153[/tex]

Hence,  the probability of being dealt exactly 4 clubs and 3 spades = 0.00153

Answer:  initial cost 26956.00 USD

value after 6 years approx= 21100.00 USD

Step-by-step explanation:

The initial cost is the price of new car , it means t ( time)=0

Substitute t by 0 in our equation and get the initial car's value

v(0)= 26956*0.96^0=26956.00 USD

The value after 6 years:  substitute t by 6

v(6)=26956*0.96^6=21100.00 USD

Answer:

x + 7

Step-by-step explanation:

Answer:

5 + 52.25x

Step-by-step explanation:

flat rate plus cost per pound times number of pounds

5 + 52.25x

Answer:

The correct snswer is

There are three basic methods for solving quadratic equations:factoring, using the quadratic formula, completing the square.

Step-by-step explanation:

hope this works out!!!

Answer:

0

Step-by-step explanation:

0 works, because 4,571.109 ≤ 4,571.1197.

9514 1404 393

Answer:

  any digit will make the sentence true

Step-by-step explanation:

Using 'd' to represent the digit, the sentence can be rewritten ...

  4571.109 +0.01d ≤ 4571.1997

Subtracting the constant on the left gives ...

  0.01d ≤ 0.0907

  d ≤ 9.07

Every single digit is less than 9.07, so any digit will do. (There are 10 right answers.)

Answer:

Unfortunately on this image we are only able to see a portion of the problem, could you send a better photo, and i will solve imidiatly, thank you!!!!!

Step-by-step explanation:

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable X represent the time it takes to wash the dishes.

The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.

The probability density function of X is as follows:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

[tex]P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx[/tex]

                           [tex]=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333[/tex]

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Answer:

B

Step-by-step explanation:

Given

x² + 10x = 15

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = 15 + 25, that is

(x + 5)² = 40 → B

Answer:

[tex]\boxed{ (x + 5)^2 = 40}[/tex]

Step-by-step explanation:

[tex]x^2 + 10x= 15[/tex]

[tex]ax^2 +bx=-c[/tex]

Add [tex](\frac{b}{2} )^2[/tex] on both sides.

[tex](\frac{10}{2} )^2 =5^2 =25[/tex]

[tex]x^2 + 10x+25= 15+25[/tex]

[tex]x^2 + 10x+25= 40[/tex]

Factor left side of the equation.

[tex](x + 5)^2 = 40[/tex]