highest common factor of a² + ab and ab + b²​

Answer:

Ob

Step-by-step explanation:

took class

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

The expression can be used to represent this situation is 12°C - 12°C. option A

This is the degree of hotness or coldness of a particular place or person at a period of time.

Expression to represent the situation;

Original temperature = Temperature at 12:00 midni-ght + (Temperature at 6:00am)

= 12°C + (-12°C)

= 12°C - 12°C

Therefore, the expression can be used to represent this situation is 12°C - 12°C.

Complete question:

From 12:00 midni-ght to 6:00am, the

temperature decreased by 12°C. If the original temperature was 12°C, which expression can be used to represent this situation?

A. 12-12

B. 12 + 12

C. 12- (-12)

D. -12 + (-12)

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Answer: (a) To find the absolute maximum miles per gallon, we need to find the maximum value of M(x). We can do this by finding the vertex of the parabola represented by M(x).

The x-coordinate of the vertex is given by:

x = -b / (2a)

where a = -0.015 and b = 1.32 in our case. Plugging in these values, we get:

x = -1.32 / (2(-0.015)) = 44

So the maximum miles per gallon occurs at a speed of 44 miles per hour.

To find the value of M(x) at this speed, we plug in x = 44:

M(44) = -0.015(44)^2 + 1.32(44) - 7.4 ≈ 32.36

Therefore, the absolute maximum miles per gallon is approximately 32.36, and it occurs at a speed of 44 miles per hour.

(b) To find the absolute minimum miles per gallon, we need to find the minimum value of M(x). We can do this by noting that the coefficient of the x^2 term is negative, which means that the parabola opens downward and has a maximum, so there is no absolute minimum.

We can also confirm this by finding the x-coordinate of the vertex, which we already calculated in part (a) to be x = 44. This means that the parabola has a minimum value of M(44), which we found to be approximately 32.36. However, this is not an absolute minimum, as there are values of M(x) that are smaller than 32.36 for other values of x. Therefore, there is no absolute minimum miles per gallon.

Step-by-step explanation:

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

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Complete question -

Seven times a number in algebraic expression

The true statements are;

1) AB + BC = AC

Length of BC = |6 - 1|

2) ∠JMK = 50°

∠KML = 35°

1) From the given number line interval, we can deduce the interpretation as follows;

AB + BC = AC

Length of BC = 5 units or |6 - 1|

Length of B = 3 Units

2) We can see that ∠JML is an angle triangle. Thus, ∠JML = 85°. Thus;

6x + 2 + 4x + 3 = 85

10x + 5 = 85

10x = 85 - 5

10x = 80

x = 80/10

x = 8°

Thus;

∠JMK = 6(8) + 2

∠JMK = 50°

∠KML = 85° - 50°

∠KML = 35°

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Answer:The picture did not load

Step-by-step explanation:Sorry

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Step-by-step explanation:

Q1.

1. 3×1+2=5

=5/3

2. 3×5+3=18

=18/5

3. 8×4+3=35

=35/4

4. 12×3+2=38

=38/3

5. 10×7+2=72

=72/7

Q2.

1. 1/7 = 7/1 = 7

2. 8/3 = 3/8

3. 9 = 1/9

4. 4 1/3 = 4×3+1 = 13 = 13/3 = 3/13

5.14 2/3 = 14×3+2 = 44 = 44/3 = 3/44

Hope this helps you

Answer:

For A)

when you go from mixed number to improper fraction all you have to do is multiply the denominator (bottom number) with the whole number (the big number on the left) then finally add the numerator (on the top). After you get the answer just write the answer divided the denominator (answer/denominator) to write as improper fraction. Examples is shown below.

For B) all you have to do is switch the fraction. If it a whole number then just assume that it is divided by 1, and for mixed fraction just solve it like A then switch the fraction. Examples shown below.

Step-by-step explanation:

For A)

1. 1 (2/3) -> multiply 3 with 1 then add the 2. So, (3 x 1) +2 = 5 then write as improper fraction which is 5/3

2. 3 (3/5) -> (5 x 3) + 3 = 18 -> 18/3

and so on...

For B)

1. 3/7 -> 7/3

3. 9 which is 9/1 -> 1/9

5. 14 (1/3) -> (3 x 14) + 1 = 43 -> 43/3 -> 3/34

Answer:

  C.  C = $10 +$5h

Step-by-step explanation:

The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.

The cost is ...

   cost = admission fee + hourly charge

The hourly charge is the product of the cost per hour ($5) and the number of hours (h).

  C = $10 +$5h

The ranking from the lowest to highest APR for the given companies is A, B, D, C.

The correct option is b.

To rank the companies from the lowest to highest Annual Percentage Rate (APR) based on a $600 loan amount, we need to calculate the APR for each company. The formula to calculate APR is APR = (Fees / Loan Amount) * (365 / Terms of Loan).

Let's calculate the APR for each company:

For Company A:

APR_A = ($60 / $600) x (365 / 18) = 0.1 x 20.28 = 2.028%

For Company B:

APR_B = ($80 / $600) x (365 / 12) = 0.1333 x 30.42 = 4.054%

For Company C:

APR_C = ($90 / $600) x (365 / 10) = 0.15 x 36.5 = 5.475%

For Company D:

APR_D = ($110 / $600) x (365 / 14) = 0.1833 x 26.07 = 4.79%

Now, we can rank the companies from the lowest to highest APR:

Company A - APR: 2.028%

Company B - APR: 4.054%

Company D - APR: 4.79%

Company C - APR: 5.475%

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Answer:

it it B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer= (2,6)

">" means greater than..

y-x >-3 so in this case you would plug in y= 6, and x=2

6-2=4 and 4 is greater than -3. :)

The other answers give negative numbers of -3, and -4 which aren't greater than -3.

The whole number that can be substituted for z is 1.

To order these numbers from least to greatest, we need to first find a value for x that makes the expressions comparable.

1/x can be rewritten as 0.01/x

80% can be written as 0.8

So, the list becomes:

0.01/x, x/3, 0.8

To compare 0.01/x and x/3, we can cross-multiply and simplify:

0.01/x < x/3

0.01*3 < x^2

0.03 < x^2

x > sqrt(0.03)

Since x has to be a whole number, the smallest possible value for x is 1.

So, substituting x = 1, the list becomes:

0.01, 1/3, 0.8

Ordering these from least to greatest, we get:

0.01, 0.8, 1/3

Therefore, the whole number that can be substituted for z is 1.

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The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Answer:

option A is the effect on the graph

Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

\(\frac{154}{200} =0.77\)

\(1-0.77=0.23\)

\(\sqrt{\frac{(0.77)(0.23)}{200} }\)=0.049

0.77±0.049< 0.819, 0.721

Answer:

Animals help pollinate flowers by eating them and depositing the seeds in different areas.

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

b bro and u get a good day too

Answer:

Pretty sure its C  >:]

Explanation:

    It's the third option because if you put a piece of paper in the corner its a lil more than 90 degrees, so it wouldn't be B (there's a little more white space left). And it obviously wouldn't be A because that's self explanatory, lol.

    And you can't make a perfect square in the inside of the angle so that's another way to tell.

Extra:

I hope you have an amazing day too,, you seem very nice ^-^   good luck on your schoolwork today :]

Answer:

Statements:                                                 Reasons:

1) ∠2 and ∠4 are vertical angles               given

2) limes m and n intersect at P                    definition of vertical angles

3) ∠3 and ∠4 are linear pair                       definition of linear pair

4) ∠2 and ∠3 are linear pair                       definition of linear pair

5) m∠3 + m∠4 =180                                     angle addition postulate

6) m∠2 + m∠3 =180                                     angle addition postulate

7) m∠2 + m∠3 = m∠3 + m∠4                   substitution property

8) m∠2 = m∠4                                             subtraction property

9) ∠2 ≅ ∠4                                                 definition of congruent(≅) angles

This is what I got those other answers didn’t work for me

Answer:

the median is increased from 7 to 7.5

114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

Answer:

3:20

Step-by-step explanation:

6000:40,000

find HCF (2000)

divide both sides by 2000

3:20

Answer:

Rotation

Step-by-step explanation:

Answer:

rotation

Step-by-step explanation:

Answer:

A b and c

Step-by-step explanation:

D might be true but i am not sure