Find the slope of the line

The area of triangle ABC when Angle B=120°, AB= 6, BC = 10 is 25.980 square unit.

As per the question statement, we are supposed to find out the area of triangle ABC in which angle B=120°, AB= 6, BC = 10.

Lets find out AC for which we should know about Cosine formula

i.e., [tex]AC^{2} =AB^{2} +BC^{2} -2(AB)(BC)cos(B)\\AC^{2} =6^{2} +10^{2} -2*6*10cos120\\AC^{2}= 36+100-120*(-0.5)\\AC^{2}=196\\AC=\sqrt{196} =14[/tex]

Hence We have measures of all three sides of the triangle ABC.

Now we use the Heron's formula for calculating the area of triangle ABC.

We need semi perimeter i.e., [tex]s=\frac{AB+BC+AC}{2}[/tex]

[tex]s=\frac{30}{2} =15[/tex]

Now Area is given by,

[tex]area=\sqrt{s(s-AB)(s-BC)(s-AC)} \\area=\sqrt{15(15-6)(15-10)(15-14)} \\area=\sqrt{15*9*5*1} \\area=\sqrt{675} \\area = 25.980 unit^{2}[/tex]

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A difference quotient that best approximates the instantaneous rate of change of g at x=2.5 is; -3

We can define the average rate of change of a function g(x) in an interval [a, b] as:

r = [g(b) - g(a)]/(b - a)

Particularly, if we want to find an approximation of the rate of change for a particular value x', we can choose:

a < x' < b

Such that a and b are really close to x'.

Then if we want to find the instantaneous rate of change of g at x = 2.5, we need to find values of a and b really close to 2.5.

Looking at the graph, we can choose:

a = 2

b = 3

(are the two closer ones to 2.5)

Then the rate of change can be written as:

f'(x) = g(3) - g(2)]/(3 - 2)

f'(x) = (1 - 4)/1

f'(x) = -3

Thus, we can conclude that a good approximation of the instantaneous rate of change is -3.

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Answer: It is m<U = 60 and m<V = 120 (x = 20)

Step-by-step explanation:

1. We know that these 2 angles are supplementary, which means both adds up to 180 degrees.

2. So first, we do this:
             3x + 2(m<U) = 180
          2a. We do this to find m<U

3. We can also notice that 3x is m<U, so substituting m<U with 3x makes sense. 3x + 2(3x) = 180

4. We then simplify:
3x + 6x = 180
9x = 180

5. We will then divide:
x = 20

6. With the new found info, we substitute x with 20:
m<U = 3(20)
m<V = 2(3(20))

7. Doing the math, it becomes:
m<U = 60
m<V = 120

(i) You can add both up if you want to make sure, but it is correct

The probability that the bolt will be inserted in 19 minutes or less is 0.8413.

It should be noted that the probability will be illustrated as:

P(X < x) = P[z < (x - u/sd)]

where

x = number

u = mean

SD = standard deviation

Therefore given the numbers, this will be:

P(x < 19) = P(z < (19 - 15)/4)

= P(z < 4/4) = P(z < 1)

= 0.8413

Therefore, the probability that the bolt will be inserted in 19 minutes or less is 0.8413.

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The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less?

There is no relationship between the number of movies and the number of sleep hours.

It is always a thing of importance to show data by the use of a scatter plot. The scatter plot must always have two axes. The vertical (y axis ) and the horizontal (x axis). It is always common to plot the independent variable on the x axis and the dependent variable on the y axis.

The scatter plot thus represented shows how one variable is related to another. In this case, we are trying to obtain how the number of sleep  hours tend to be related with the number of movies and this has been shown on the scatter plot that is shown in the question above.

It is clear from the statements in the question that the line of best fit would show that as the number of movies remained constant, the number of sleep hours decreased. This now implies that there is no relationship between the number of movies and the number of sleep hours.

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Answer:Answer:

The measurement of the angle is 60

Step-by-step explanation:

The two blue lines are straight and parallel lines. The sum of the angles on a straight line is 180 degrees. Angle 5 and angle 6 are on a straight line. Therefore

Angle 5 + angle 6 = 180

If angle 5 is 120 degrees, then

Angle 6 = 180 - 120 = 60 degrees.

The best interpretation of the number 8.6 according to the task content is; The completion time of the reaction.

It follows from the task content that the number 8.6 as given in the task content can be agreed to be the completion time of the reaction.

This follows from the fact that, at time, s = 8.6, amount in moles, m of the reactants remaining becomes, 0 in which case, the reaction is complete.

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Answer:

0.6

Step-by-step explanation:

Answer: 20%

Step-by-step explanation: If you look at it like 100 then think of 20% of 100.

20% or 2.

Answer: d)

-10 + 15 = 5

Answer:

D. 5

Step-by-step explanation:

-10 + 15 Can be rewritten as 15-10

15-10=5

The answer is 5.

Hope this helps!

Please mark as brainliest if correct!

Answer:

y = 5

Step-by-step explanation:

A line with a slope of 0 is a horizontal line parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 4, 5 ) with y- coordinate 5 , then

y = 5 ← equation of line

Solution:

[tex]y = \frac{1}{2}[/tex]

Process of Solution:

1. Switch sides.

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

2. Add 1 to both sides.

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

3. Simplify.

[tex]y = \frac{1}{2}[/tex]

Hope this helps!

The linear equation from the given statement is the N + F+11 = 2F.

According to the statement

We have to write the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F.

Then

The number of shirts left = N

The number of the shirts which are folded = F+11

The total number of shirts = 2F

And then

The linear equation becomes :

N + F+11 = 2F

This the linear equation for the given statement.

So, The linear equation from the given statement is the N + F+11 = 2F.

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Answer: the scale factor is 5

Step-by-step explanation:

5 squares on the dilated shape and for the original shape it’s only 1 and the original shape is always going to be the denominator while the numerator is going to be the shape after it’s dilated so it’s 5/1 which equals 5

So THE ANSWER IS 5

the probability of drawing 2 red marbles from the bag will be 0.0455.

Number of Red marbles = 3

Number of blue marbles = 5

Number of green marbles = 4

Total marbles = 3 + 5 + 4 = 12

Probability of drawing 2 red marbles from the bag will be:

P = 3 / 12 × 2 / 11

P = 6 / 132

P = 3 / 66

P = 1 / 22

P = 0.0455

Therefore, the probability of drawing 2 red marbles from the bag will be 0.0455.

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Answer:

6x + 9

3(2x + 3)

please correct me if I'm wrong

Answer:

-0.25

Step-by-step explanation:

1). When beginning, you need to find the least common multiple (lcm), which would be 2.

2). Divide 3 by 2 leaving you with 1.5.

3). Then divide 1.5 by 2 leaving you with -1/4.

4). Convert -1/4 into a decimal.

5). Final answer -0.25.

Answer: -0.25

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}-\frac{3}{4}=\\\\ \frac{1*2}{2*2} -\frac{3}{4} =\\\\\frac{2}{4} -\frac{3}{4}=\\\\ \frac{2-3}{4} =\\\\\frac{-1}{4} =\\\\-\frac{1}{4} =\\\\-0.25[/tex]

Answer: $0.38

Step-by-step explanation:

2.29/8=

0.38167=

0.38167=$0.38

Answer:

1111101001

Step-by-step explanation:

Binary 1001 = 9. « Previous (1000) Next (1010) ».

The simplified form of the algebraic expression is [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Given expression is of the form:

[tex]\frac{3}{5} (\frac{1}{2}p+2r )+2p[/tex]

Now we will use the distributive property to expand the algebraic expression:

[tex]or, (\frac{3}{5} \times\frac{1}{2}p+\frac{3}{5} \times2r) +2p\\\\or,\frac{3}{10}p+\frac{6}{5} r+2p\\ \\or,\frac{3+20}{10} p+\frac{6}{5} r\\\\or,\frac{23}{10} p+\frac{6}{5} r[/tex]

Hence the simplified algebraic expression is  [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .

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According to the question, srs is a simple random sample whose size consists of individuals from the population and chosen in such a way that every set of individuals has an equal chance to be sampled.

What is Stratified random samples?

For stratified random samples, initially classify the population into the groups of similar individuals which is called as “strata”. Later choose simple random samples and combine them to form a full sample.

As per question, srs of [tex]200[/tex] of the [tex]25000[/tex] undergraduate students and the srs of [tex]100[/tex] of the [tex]500[/tex] graduate students. This overall sample is a stratified sample.

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Step-by-step explanation:

(4h⁴)⁴ / (4h^-8)

remember, multiplying exponents means adding them. exponents of exponents means multiplying them.

and dividing exponents means subtracting them.

also, n^-a = 1/(n^a).

let's look at the numerator (top part) first :

(4h⁴)⁴ = 4^1×4 × h^4×4 = 4⁴×h¹⁶

now, for the denominator, the exponent -8 applies only to h. not to 4.

so,

1/(4h^-8) = h⁸/4

and so, the whole expression is then simplified

4⁴×h¹⁶ × h⁸/4 = 4³ × h²⁴

Answer:

It's the third choice:

2/3 j^2/k^4

Step-by-step explanation:

√ [4j^4/9k^8)]

= √(4j^4) / √9k^8

= 2j^2 / 3k^4

= 2/3 j^2/k^4

Answer:

I D K if this even helps at all T B H

Using it's concept, the probability of at least 1 red face upper most is 17/18 = 0.9444 = 94.44%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For each cube, the probability of no red faces is:

Hence the probability of no red faces in anu cube is:

1/6 x 1/2 x 2/3 = 1/18.

Which means that the probability of at least 1 red face is given by:

1 - 1/18 = 17/18 = 0.9444 = 94.44%.

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