Angle relationships and triangles

The equation in slope-intercept form is y = -3/2x + 9. Slope of the equation is - 3/2 and y - intercept is 9.

Calculate the slope (m).

Keep in mind that the slope is determined by dividing the change in y by the change in x. (rise over run).

Find the y-value of the y-intercept by solving (b).

In the formula y=mx+b, swap out m and b with their respective values.

The given equation is -

3x + 2y = 18

divide the equation by 2

3/2x + y = 9

Rearranging the equation -

y = -3/2x + 9

Comparing it with y = mx + c

so slope m = -3/2

and y - intercept = 9

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The value of f(-1) according to the function f(x) given is; 6.

It follows from the task content that the function, f(x) = 2x² + 4.

On this note, to evaluate the value of f(-1), we must substitute -1 for x in the function given as follows;

f(-1) = 2(-1)² + 4

f(-1) = (2×1) +4

f(-1) = 6.

Ultimately, f(-1) = 6.

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If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

We know that when a transversal cuts two parallel lines, then the corresponding angles are equal.

We know that parallel lines never intersect each other. When a third line is perpendicular to one of the parallel lines, then the third line must be perpendicular to another line as well.

To prove if AD is perpendicular to MN, it is also perpendicular to OP

ABN=90o

( Since AD is perpendicular to MN)

BCP=ABN=90o

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The possibility of the outcomes of third coin turn up a head is 2⁹.

Probability:

Probability is the calculated by dividing the favorable outcome by the total number of outcomes.

Given,

Ten coins are tossed simultaneously.

Here we need to find the how many of the outcomes will the third coin turn up a head.

Here we know that,

The third coin must be a head.

So, that means the rest of the coins can be heads or tails.

Therefore, possibility of these can be written as,

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹

different outcomes for the rest of the coins.

Which means the rest of the coins can be either head or tail but the third one is head.

Therefore, the possibility of getting third coin as head is 2⁹.

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Answer:

Volume = 665 cm³

Step-by-step explanation:

We can calculate the volume of a cylinder using the following formula:

[tex]\boxed{\mathrm{Volume = \pi r^2 h}}[/tex],

where:

• r = radius of cylinder

• h = height of the cylinder

In the question, we are told that the diameter of the cylinder is 8.4 cm. Since the diameter is twice of radius:

[tex]\mathrm{radius = 8.4 \div 2}[/tex]

          [tex]= \bf 4.2 \: cm}[/tex]

We are also told that the height of the cylinder is 12.0 cm. Therefore, using this information, as well as the formula above, we can find the volume of the cylinder:

[tex]{\mathrm{Volume = \pi \times (4.2 \mathrm{\: cm})^2 \times 12.0 \mathrm{\: cm}}}[/tex]

            [tex]= \pi \times 17.64 \mathrm{\: cm^} \times 12.0 \mathrm{\: cm}[/tex]

            [tex]\approx \bf 665 \: cm^3[/tex]

Therefore the volume of the cube is 665 cm³.

Answer:

1/2(35-3(2-4)(5-8)

1/2(32(-2(-3))

1/2(32(-6))

1/2(192)

1into192/2

=96

Step-by-step explanation:

Answer:

x-4   IS a factor

Step-by-step explanation:

IF   x-1 is a factor    then putting   x = 1   into the equation will make it =    zero......  it does not

IF x+1  is a factor then putting x = -1   into the equation will result in = 0

     it does not

IF  x -4 is a factor , then puting in x =4 into tthe equation will = 0   it DOES !

Answer: If your rounding to the second spot after the decimal it would be in the hundredths place so in case it would be 2874.29 Although I'm not sure if that's how you wanted it to be done.

Round the number 2,874.2878 to two decimal places will be 2,874.29.

The action of forming anything into a circle. Mathematics. the act of substituting a number with one that is roughly equivalent in value but has fewer digits: To the closest dollar, rounding $27.68 results in $28. a comparable procedure that identifies one of several rules.

The decimal number is given below.

⇒ 2,874.2878

Round 2,874.2878 to two decimal places.

If the third place after the decimal is more than 5, then the second place after the decimal will be increased by one.

In the third place after the decimal is 7, then the number 8 is increased by one that is 9.

Round the number 2,874.2878 to two decimal places will be 2,874.29.

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Using the distance formula, the distance between the pair of points R(-2,3)  and S(3,15) is 13 units

Given,

The points = R(-2,3)  and S(3,15)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}-(y_{2} -y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(3--2)^{2}+(15-3)^{2} }[/tex]

[tex]=\sqrt{5^{2}+12^{2} }\\ =\sqrt{25+144}\\ =\sqrt{169}[/tex]

=13 units

Hence, using the distance formula, the distance between the pair of points R(-2,3)  and S(3,15) is 13 units

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Answer:

-23.4

Step-by-step explanation:

-0.0468 ÷ 0.002 = -23.4 (A negative divided by a negative is a positive!)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

A

Step-by-step explanation:

The line travels through the plane and its intersection point is labeled C

The geometric mean of a and b [tex]=\sqrt{a*b}[/tex] then the geometric mean of 8 and 18 is 12.

In Mathematics, the Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.

The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate.

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the result.

Geometric mean of a and b [tex]=\sqrt{a*b}[/tex]

Geometric mean of 8 and 18 [tex]$=\sqrt{8*18}[/tex]

a = 8 , b = 18  

= √144

= 12

The geometric mean of 8 and 18 is 12.

Therefore, the correct answer is option D. 12.

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The statement "angles 4 and 6 are alternate interior angles" is true

Given,

The statement " Angles 4 and 6 are alternate interior angles"

Here,

∠4 and ∠6 are lie opposite sides of the the transversal and both are nonadjacent interior angles .

So, ∠4 and ∠6 are alternate interior angles

Hence, the statement "angles 4 and 6 are alternate interior angles" is true.

The complete question is:

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

Angles 4 and 6 are alternate interior angles.

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Answer:

b. Solve the inequality. Show all your work.

Step-by-step explanation:

The geometrical representation of y=3 as an equation in

a) one variable is y = 3

b) in two variables is 0x + y = 3.

Based on the information illustrated, the geometrical representation of y=3 as an equation in one variable is y = 3.

Also, the geometrical representation of y=3 as an equation in two variables is:

y = 3.

0x + y = 3

0x + y - 3 = 0

Therefore, y = 3.

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Jorge's drawing of the triangle is greater than the first drawing.

Scales are ratios between two lengths, herein we find an example of scales, defined as ratios of real length to reduced length from drawings. In a nutshell, we have a case of augmentation scales. Mathematically speaking, each scale is represented by the corresponding formulas:

x / y = 30            (1)

x / z = 10             (2)

By (1) and (2) we find the relationship between the two lengths of the two drawings:

30 · y = 10 · z

z = 3 · y

Jorge's drawing of the triangle is greater than the first drawing.

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Evaluate each finite geometric series.

1/5 + 1/10 + 1/20 + 1/40 + 1/80=0.3875

What is the sum of a finite geometric series?

Given:

a=1/5

r=5/10 = 1/2

n=5

[tex]S_n=\frac{a(1-r^{n} )}{1-r} \\\\S_5=\frac{\frac{1}{5}(1-(\frac{1}{2}))^{5} }{1-\frac{1}{2} } \\\\S_5=\frac{1}{5} (\frac{31}{32} *\frac{2}{1}) \\\\S_5=\frac{1}{5} (\frac{31}{16} )\\\\S_5=0.3875[/tex]

What is a finite geometric series?

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The payment she gets after 22 hours of working is $187.

According to the statement

We have to find that the total amount she earned.

So, For this purpose, we know that the

Straight-time pay is the total amount of money you earn in a given pay period.

From the given information:

Sally Barrett, a banjo player for a local band, earns $8.50 per hour.What is her straight-time pay for a week in which she worked 22 hours?

Then

The amount she get as a rate per hour = $8.50

And

The time for which she works =  22 hours

Then

Pay she get after the work of the 22 hours = $8.50 * 22

Then

Pay she get after the work of the 22 hours = $8.50 * 22

Now multiply these to get the answer

Pay she get after the work of the 22 hours = $187

So, The payment she gets after 22 hours of working is $187.

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There were 29 nickels and 10 dimes in the bank.

We know that:

1 dime = 5 cents

1 nickel = 10 cents.

Also, $ 3.40 = 340 cents

Let the  number of nickels be n and the number of dimes be d.

Now, we are given that:

5 dimes and 2 nickels were taken away.

So, total coins = 46 - 2 - 5 = 46 - 7

Total coins = 39

We get the equation:

n + d = 39

d = 39 - n

Now, we also know that:

5 d + 10 n = 340

d + 2 n = 68

Put the value of d, we get that:

39 - n + 2 n = 68

n = 68 - 39

n = 29

d = 39 - n

d = 39 - 29

d = 10

Therefore, we get that, there were 29 nickels and 10 dimes in the bank.

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The Proportional relationship y = 10x is a good fit for the data.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality,

i.e., y = kx

In which k is the constant of proportionality.

For this problem, foe each value of x, the output is 10 times that, hence the constant is k = 10 and the proportional relationship y = 10x is a good fit for the data.

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Answer:

The Proportional relationship y = 10x is a good fit for the data.

The polynomial function V to represent the volume of a round bale is  V(x) = π(x + 5)²(x + 8).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Let the dimensions of round bale is x+5 feet radius and 3 feet wide.

As we know that round bale is a shape of cylinder in which we will consider wide instead of height.

Volume of Round Bale (V) = πr²w

    V = πr²w = π(x + 5)²[(x + 5) + 3]

V(x) = π(x + 5)²(x + 8)

Hence, we got the polynomial function that represent the volume of round bale is  V(x) = π(x + 5)²(x + 8).

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Answer:

2) y= 4x+17

Step-by-step explanation:

y- y1 = m(x- x1)
y- 5 = 4 (x - (-3))
y-5= 4( x+ 3)
y-5= 4x+ 12
y= 4x+17

Answer:

length=12

width=7

Step-by-step explanation:

I tried random numbers like 6+6+11+11 then tried another one 8+8+13+13. After that I found out the pattern and worked out the answer

Answer:

-0.1

Step-by-step explanation:

-1/100 = -0.01

1/10 = 0.1

-0.01/0.1 = -0.1

Answer:

i didn't understand please write it in a clearer way so I can help

Answer: given clear information about the question

Step-by-step explanation:

What I can advise is, Please look for the "X or Y" carefully, work on it step by step!!

The solution of the equation (2x - 4) (x + 6) = 0  is is x = {2, -6}  (C)

The solutions of an equation means if we substitute these solutions into the variables of the equation, it will lead to the correct equality.

Suppose we have an equation in the form of:

(x - a) (x - b) = 0

This is called a factorization form. The equality will be true if either:

The given equation is:

(2x - 4) (x + 6) = 0

This equality will be correct if:

2x - 4 = 0

⇒ x = 2

or

x + 6 = 0

⇒ x = -6

Hence, the solution is x = {2, -6}  (C)

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Answer:

m

------- <------ fraction bar means divide too

z + u

Hope this helps :)

He typically work each day for 10 hours.

According to the question, the expression can be written as:

The time taken to stretch the fingers = (1/2)t

Similarly, the time taken to smashed toes = (1/5)t

Total time = 7 hours

Now, the final expression can be written as:

(1/2)t + (1/5)t = (7)

(7/10)t = 7

t = 10 hours

Hence, he typically work each day for 10 hours.

What is time and work?

The time and work represents the problems deals with the time either with the individual or the group of the people to complete the piece of work. And the efficiency taken by each individual.

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