What is the highest common factor (HCF) of 9 and 15?

Answer:

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Step-by-step explanation:

We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:

cos(C) =  a2 + b2 − c22ab

cos(A) =  b2 + c2 − a22bc

cos(B) =  c2 + a2 − b22ca

Answer:

Law of cosines, two sides and the included angle known

Step-by-step explanation:

double check that the question is exactly the same to make sure you get the question correct

"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."

Answer:

(B)21+3a

Step-by-step explanation:

An expression is said to be distributive when:

[tex](a+b)c=a \cdot c+b \cdot c[/tex]

Given the algebraic expression: (7 + a)3

Applying the distributive property

[tex](7 + a)3 = 7 \cdot 3+a \cdot 3\\=21+3a[/tex]

An equivalent expression is 21+3a.

The correct option is B

Answer:

answer is b). y = 100+ 0.05x

Step-by-step explanation:

Answer:

a)16      (2*2*2*2= 16)

b)16  (-4*-4-16)(-+-=+)

c)500 (5*5*5=125        125*4=500)

d)0.49  (0.7*07)

e)480  (4^=16     9^=81  121^0=1          16+81 -1 =96     96*5=480)

f)5^2  or 25 (a^m/ a^n=a^m-n)

g) 11^14 (reason same as the f one)

h)8.20

i) 4(-4*16=64)

j)900

Answer:

JL = 32

Step-by-step explanation:

We are told in the above question that:

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

From the attached diagram, we can see that

JL : JK = JK: JM

Therefore,

JL/ JK = JK /JM

Where JL = Unknown

JK = 24

JM = 18

JL/ 24 = 24/18

Cross Multiply

24 × 24 = JL × 18

Divide both sides by 18

JL = (24 × 24) /18

JL = 576/18

JL = 32

Answer:

  -63

Step-by-step explanation:

Compare ...

  f(x) = x^2 -3x +18

to the standard form ...

  f(x) = ax^2 +bx +c

and you will see that ...

  a = 1, b = -3, c = 18.

__

The value of the discriminant is ...

  d = b^2 -4ac

  d = (-3)^2 -4(1)(18) = 9 -72 = -63

The discriminant is -63.

Answer:

The answer is d

Step-by-step explanation:

The place value of the 8 is 8/1000 or 0.008 or 8 thousandths in 4.328.

The place value of a digit is determined by the position of the digit relative to the decimal point. In a number with a decimal point, the digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractions.

here, we have,

Each place to the right of the decimal point represents a fraction that is one-tenth the size of the place to its left. For example, the hundredth place is one-tenth the size of the tenth place, the thousandth place is one-tenth the size of the hundredth place, and so on.

In the number 4.328, 8 is in the thousandth place, which is the third place to the right of the decimal point.

Thus, the place value of the 8 is 0.008, or 8 thousandths.

Learn more about the place value strategy here:

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Answer:

18x - 63y.

Step-by-step explanation:

9(2x-7y)

= 9 * 2x - 9 * 7y

= 18x - 63y

Hope this helps!

Answer:

Step-by-step explanation:

Distribute (multiply) the 9 to both the 2x and -7y

You get: 18x -63y        

This is because 9 times 2x is 18x. Furthermore, 9 times -7y is equal to             -63y

There isn't an obvious question to this problem but with the given we can assume what is to be asked. I think we are to find the total cost of a certain poultry seasoning. The poultry seasoning would have a total weight of 4+2=6 ounces. The total cost will then have to be 4(4) + 2(3) = 22 dollars. 

Answer:

D. 6

Step-by-step explanation:

Got it correct on edg2020

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Step-by-step explanation:

From the given information,  

The population mean SAT critical reading score is

[tex]\mu = 495[/tex]

The population standard deviation is

[tex]\sigma = 118[/tex]

You choose an SRS of 100 students and average their SAT Critical Reading score.

[tex]n = 100[/tex]

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean  SAT critical reading score.

[tex]\bar{x} = \mu = 495[/tex]

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Answer:

Step-by-step explanation:

graph attached

Answer:

graph y

Step-by-step explanation:

Hey there! :)

Answer:

C) 74 units.

Step-by-step explanation:

MT is congruent to KT because the diagonals of a quadrilateral bisect each other. Therefore:

8y + 18 = 12y - 10

Subtract 8y from both sides:

18 = 4y - 10

Add 10 to both sides:

28 = 4y

Divide both sides by 4:

28/4 = 4y/4

y = 7 units. Plug this into the equation for MT:

8(7) + 18 = 74 units.

Answer:

74

Step-by-step explanation:

Set up the equations

8y + 18 = 12y -10

Combine like terms

28 = 4y

Divide each side by 4

y=7

Plug in the value of y in the equation of 8y + 18 since that's the value for MT

8(7) + 18 = 74

Hope this helps!

Answer:

6root(2)/25

Step-by-step explanation:

5^-2 = 1/25

3(root(8)) = 6(root(2))

so you get 6(root(2))(1/25)

= 6(root(2))/25

The required simplified value of the given expression is 0.34 or  6√2 / 25.

Given that,
Expression to simply ios given,
5⁻² x 3√8

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Simplification =>
= 5⁻² x 3√8
= 1/ 5⁻² x 3 x 2 √2
= 6√2 / 25
= 0.34

Thus, the required simplified value of the given expression is 0.34 or  6√2 / 25.

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Answer:

101.58 in

Step-by-step explanation:

The ramp r is the hypotenuse of a right triangle with the ground and 28 in height being the legs.

The angle of elevation 16° is the angle inside the triangle opposite the 28 in height.

Using the sine ratio in the right triangle, then

sin16° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{28}{r}[/tex] ( multiply both sides by r )

r × sin16° = 28 ( divide both sides by sin16° )

r = [tex]\frac{28}{sin16}[/tex] ≈ 101.58 in

Answer:

The 3rd answer

Step-by-step explanation:

Answer:

a. A/B = 7/3

b. (p,q) = (4,0)

c. (p,q) = (0,2)

Step-by-step explanation:

We have the line as:

21x-6y-15 = 0

The general form of the equation of a straight line is;

y = mx + c

Where m is the slope and c is the y -intercept

writing the above in this manner, we have

6y = 21x -15

Now let’s divide through by 6;

y = 21x/6 -15/6

y = 7x/3 -5/3

Since in the general equation of a straight line, the coefficient of x is the slope, this means that our slope is 7/3 which makes A = 7 and B = 3

Considering the equation;

3x + 6y = 12

Expressing in the general form, we have

6y = 12-3x

divide through by 6

y = 12/6 -3x/6

y = 2-0.5x

Now we want to find the x intercept. At the x-intercept, the value of y = 0

Thus 0 = 2-0.5x

0.5x = 2

x = 2/0.5 = 4

so (p,q) = (4,0)

For the y intercept

y = 2-0.5x

Obviously the y intercept here is 2, so the coordinates of the y-intercept here is (0,2) = (p,q)

Answer: 2.4 UNITS

Step-by-step explanation:

The sine rule :

Sine A / a = Sine B / b = Sine C / c

From the diagram attached :

QR = s = 2.4 ; QS =r = 3.1 ; RS =q =?

We need to find the angle RQS

using Sine rule :

Sine R / r = Sine S / s

Sin 80° / 3.1 = sin S / 2.4

0.9848077 / 3.1 = sin S / 2.4

Sin S × 3.1 = 0.9848077 × 2.4

Sin S = 2.3635386 / 3.1

Sin S = 0.7624318

S = Sin^-1(0.7624318)

S = 49.67°

Therefore, form using ;

A + B + C = 180° ( SUM of angles in a triangle)

SQR = 180° - (QRS + QSR)

= 180° - ( 80 + 49.67)° = 50.33°

Q = 50.33°

THEREFORE,

Sine Q / q = Sin S / s

Sin 50.33° / q = Sin 49.67° / 2.4

0.7697339 / q = 0.7623295 / 2.4

0.7623295q = 0.7697339 × 2.4

q = 1.84736136 / 0.7623295

q = 2.4233108

q = Segment RS = 2.4units

Answer:

B) 2.5 is the right answer

Step-by-step explanation:

i got 100%

Answer:

  [tex]\textbf{A. }4\sqrt{6}[/tex]

Step-by-step explanation:

The hypotenuse of the isosceles right triangle is √2 times the length of one leg, so is 6√2.

The hypotenuse of the 30°-60°-90° right triangle is 2/√3 times the length of the longer leg.

  [tex]x=\dfrac{2}{\sqrt{3}}\cdot 6\sqrt{2}\\\\=\dfrac{(2\sqrt{3})(6\sqrt{2})}{3}\quad\text{rationalize the denominator}\\\\\boxed{x=4\sqrt{6}}[/tex]

Answer:

No.

Step-by-step explanation:

Let's first and try to isolate x.

-2x < 5

(Divide by -2)

x > -5/2 ( < changes to > b/c it was divided by a negative)

x > -2.5

Since x is all values greater than -2.5, -6 is not within those bounds.

Thus, -6 is not a solution to the inequality.

Hope that helps!

Answer:

He will have 13 packages containing 3 pairs of headphones and 1 music player each.

Step-by-step explanation:

He has 39 pairs of headphones and 13 music players.

He wants to sell both set of items in identical packages.

To do this he has to divide them in such a way that the same number of both set of objects are in every box.

Let us find the ratio of the pairs of headphones to music players:

39 : 13 = 3 : 1

Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.

So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer: the answer is A

Step-by-step explanation:

Answer:

(0, 6)

Step-by-step explanation:

The solution is the point of intersection of the lines.

(0, 6)

Answer:

16/64 i think

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Total Marks = 64

Correct = 48

Incorrect = 64-48

=> 16

Fraction of Incorrect Answers:

=> [tex]\frac{16}{64}[/tex]

In simplest form:

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

Answer:

Step-by-step explanation:

[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]

Answer:

its G(2)

Step-by-step explanation:

Gg

Answer:

17.5 kg of water.

Step-by-step explanation:

The amount of alcohol in the 15% solution = 20*0.15 =  3kg.

If 3 kg is equivalent to 8% solution

then 100%  is  3*100 / 8 = 37.5 kg.

So the amount of water to be added to make 8% solution = 37.5 - 20

= 17.5 kg.

Answer:

y = (x-.5)^2 -12.25

Step-by-step explanation:

first, find the vertex

x from (x,y) = -b/2a

ax^2-bx - c

1x^2-1x -12

-1/2(-1) = -1/-2 - 1/2

(1/2,y) then use x value to find y value

y = 1/2^2 - 1/2 - 12

y = .25 -.5 - 12    = -12.25

(.5,-12.25) input values into this formula:

y = a(x-h)^2 + k where h = x-value and k = y-value. use same a value = 1

y = (x-.5)^2 -12.25

Answer:

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

[tex](u-2)+(n-2)=40[/tex]

[tex]u+n-4=40[/tex]

[tex]u+n=44[/tex]

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

[tex]u+2=3(n+2)[/tex]

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

[tex]u=44-n[/tex]

We can substitute this into the second equation.

[tex](44-n)+2=3(n+2)[/tex]

[tex]46-n=3n+6[/tex]

[tex]40=4n[/tex]

[tex]n=10[/tex]

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

Answer:B

Step-by-step explanation:

Answer: B is the correct choice

Step-by-step explanation:

The values are essentially the same. You need to recognize how the symbols in the expressions match up with the symbols on the graph.

The open circle on the right end of the parabola means the function is less than (not including) 2 so <2 for that part.

The solid circle at the left of the line means f(x) includes all the values to the right are greater than or equal to 2 so ≥2 for that part.