4x(a-b)+3(b-a) factorise

Answer:

"If the line has a slope that is not 0, then the the line is not horizontal".

Step-by-step explanation:

The contrapositive of "If p then q" is "If not q then not p".

p=a line is horizontal

not p= a line that is not horizontal

q=the line has a slope equal to zero

not q=the line has a slope that is not zero

The equivalent statement in contrapositive form is therefore:

"If the line has a slope that is not 0, then the the line is not horizontal".

Answer:

Step-by-step explanation:

The answer is attached. I hope this helps answer your question!

Answer:

m∠QRS = 49°

Step-by-step explanation:

Complementary angles are angles that add up to 90°. So m∠ABC + m∠QRS = 90°. When you simplify you get 41° + m∠QRS = 90°. So m∠QRS = 49°.

Answer:

[tex](f-g)(x)=x^2-4x-21[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=x^2-3x-28\text{ and } g(x)=x-7[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

Substitute:

[tex]=(x^2-3x-28)-(x-7)[/tex]

Distribute:

[tex]=x^2-3x-28-x+7[/tex]

Rearrange:

[tex]=(x^2)+(-3x-x)+(-28+7)[/tex]

Hence:

[tex](f-g)(x)=x^2-4x-21[/tex]

Answer:

18 L

Step-by-step explanation:

a = 36,864 * (1/2)^(11)

a = 18

36 L of water will be left after 11 days

GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number .

Constituting an GP according to the question

36,864 , 18432 , 9216 , ...........

In order to find nth term  of an GP, formula used will be :

a(n) = a (r^(n-1))

considering above GP ,

a(n) = ? water left after 11 days

a = 36864

r= 18432 /36864 = 1/2

n = 11

a(n) = 36864 ((1/2)^(11-1))

  a(n) =   36

Hence 36 L of water will be left after 11 days

Learn more about GP:

https://brainly.com/question/4853032?referrer=searchResults

#SPJ2

Answer: 42 -(-6)= 48

Step-by-step explanation:

a negative - a negative will always equal a positive

:)

Answer:

lx-3l

Step-by-step explanation:

negative in the abs means moving to the right

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

Explanation:

We start with the parent function y = |x|

Shifting it 3 units to the right will make the equation y = |x-3| and that's the equation of the green curve shown.

The x-3 is because each input is 3 units smaller than it used to be. Imagine the xy axis moved 3 units to the left while the V shaped graph stayed fixed in place. It would give the illusion the V shape moved while the xy axis stay fixed.

The graph doesn't shift up or down, so k = 0

The value of 'a' stays the same at a = 1.

9514 1404 393

Answer:

  D.  32 square units

Step-by-step explanation:

At 40% scale, the length is ...

  (20 units)×40% = 8 units

and the width is ...

  (10 units)×40% = 4 units

The area is the product of length and width, so is ...

  A = (8 units)(4 units) = 32 square units

solution//

= 4(m-3) = 24

= 4m-12 = 24

= 4-12+12 = 24+12

= 4m = 36

= 4m = 36

4 4

= m = 9

Step-by-step explanation:

Thank you

[tex]\sf\purple{The\:value\:of\:m\:is\:9.}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]4 \: (m - 3) = 24 \\ ⇝4 \: m - 12 = 24 \\ ⇝4 \: m = 24 + 12 \\ ⇝4 \: m = 36 \\ ⇝m = \frac{36}{4} \\ ⇝m = 9[/tex]

To verify:-

[tex]4(m - 3) = 24 \\ ⇝4(9 - 3) = 24 \\ ⇝4 \times 6 = 24 \\ ⇝24 = 24 \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Answer:

let the number of adult tickets = x

Then the number of student tickets = 3x

Total tickets x+3x = 416

4x = 416

x = 416/4

x = 104

Therefore the number of adult tickets sold is 104

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hi there!

We are given the points (-1,2) and (3,3) and we need to find the slope.

The formula for slope calculated from two points is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points

since we have two points, we can substitute them into the formula, but let's label their values to avoid any confusion

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

[tex]y_{1}[/tex]=2

[tex]x_{2}[/tex]=3

[tex]y_{2}[/tex]=3

now substitute into the formula (m is the slope); remember: we have a negative number in this, so we'll be subtracting a negative.

m=[tex]\frac{3-2}{3--1}[/tex]

simplify

m=[tex]\frac{3-2}{3+1}[/tex]

m=[tex]\frac{1}{4}[/tex]

so B is your answer

Hope this helps! :)

Answer:

Step-by-step explanation:

a)

The mean for ground floor is 20.67

The mean for balcony is 15.8

b)

the difference between the means is ground floor - balcony

20.67 - 15.8 = 4.87

You can talk about it yourself for part c

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

[tex]-3y=-4x+5[/tex] and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

[tex]y=\frac{4}{3}x-\frac{5}{3}[/tex] So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

[tex]y-5=-\frac{3}{4}(x-3)[/tex]* and

[tex]y-5=-\frac{3}{4}x+\frac{9}{4}[/tex] and

[tex]y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}[/tex] so

[tex]y=-\frac{3}{4}x+\frac{29}{4}[/tex]** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

Answer:

150

Step-by-step explanation:

35÷7=5 therefore each 5 apples is equal to 1 orange

Answer:

150

Step-by-step explanation:

we're gonna compare ratios. if the initial ratio is 35/7, then we will need to make a similar one for this question. with apples on top, we'll write 'x/30' and cross multiply and solve to get 150

Answer:

7,982 ft

Step-by-step explanation:

c = πd

25077 = πd

Divide both sides by π

25077/π = d

d = 7,982 ft

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

I think the 25077 number in the question might be a typo

Just divide the correct number by 3.14 to get the diameter.

Answer:

32

Step-by-step explanation:

we substitute the values first

5 * (the absolute value of )-5) + 7

absolute value means neither the positive or negative value, so no signs before that number (the one your taking the absolute value of)

5*5+7

5*5 = 25

25+7 = 32

done!

Answer:

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

Step-by-step explanation:

First we have to find the sample mean and the sample standard deviation.

We have 15 measurements. Using a calculator, the mean is [tex]\overline{x} = 3.79[/tex] and the standard deviation is of [tex]s = 0.97[/tex].

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

T interval

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 = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{0.97}{\sqrt{15}} = 0.54[/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 3.79 - 0.54 = 3.25 hours

The upper end of the interval is the sample mean added to M. So it is 3.79 + 0.54 = 4.33 hours

A 95% prediction interval for the drying time for the next trial of the paint is between 3.25 and 4.33 hours.

t-3.2 ≤ 7.5

"at most" means less than or equal to

Answer:

MBI, MBV, ABV, ABI, MPI, MPV, APV, API

Answer:

[tex](a)\ \sec^2(\theta) = 82[/tex]

[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]

[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]

[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = 9[/tex]

Required

Solve (a) to (d)

Using tan formula, we have:

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

This gives:

[tex]\frac{Opposite}{Adjacent} = 9[/tex]

Rewrite as:

[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]

Using a unit ratio;

[tex]Opposite = 9; Adjacent = 1[/tex]

Using Pythagoras theorem, we have:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]

[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]

[tex]Hypotenuse^2 = 81 + 1[/tex]

[tex]Hypotenuse^2 = 82[/tex]

Take square roots of both sides

[tex]Hypotenuse =\sqrt{82}[/tex]

So, we have:

[tex]Opposite = 9; Adjacent = 1[/tex]

[tex]Hypotenuse =\sqrt{82}[/tex]

Solving (a):

[tex]\sec^2(\theta)[/tex]

This is calculated as:

[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

Where:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]

So:

[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]

[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]

[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]

[tex]\sec^2(\theta) = 82[/tex]

Solving (b):

[tex]\cot(\theta)[/tex]

This is calculated as:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

Where:

[tex]\tan(\theta) = 9[/tex] ---- given

So:

[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]

[tex]\cot(\theta) = \frac{1}{9}[/tex]

Solving (c):

[tex]\cot(\frac{\pi}{2} - \theta)[/tex]

In trigonometry:

[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]

Hence:

[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]

Solving (d):

[tex]\csc^2(\theta)[/tex]

This is calculated as:

[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]

[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]

Where:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]

So:

[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]

[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]

[tex]\csc^2(\theta) = \frac{82}{81}[/tex]

Hope this help!!!

Have a nice day!!!

Answer:

0.281 = 28.1% probability a given player averaged less than 190.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

A bowling leagues mean score is 197 with a standard deviation of 12.

This means that [tex]\mu = 197, \sigma = 12[/tex]

What is the probability a given player averaged less than 190?

This is the p-value of Z when X = 190.

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

[tex]Z = \frac{190 - 197}{12}[/tex]

[tex]Z = -0.58[/tex]

[tex]Z = -0.58[/tex] has a p-value of 0.281.

0.281 = 28.1% probability a given player averaged less than 190.

Answer:

4

Step-by-step explanation:

i think thats not my answer

Answer:c

Step-by-step explanation:

c