Using the slope formula, find the slope of the line through the given points.
(9,4) and (6,7)

Answer: about 0.41

Step-by-step explanation:

Use calculator

[tex]arcsin=sin^{-1}x\\\\\boxed{sin^{-1}(0.4) = 0.41151684}[/tex]

Answer:

Step-by-step explanation:

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Wa, wǒ xǐhuān chī hěnduō shíwù, yīnwèi wǒ xǐhuān bìng xǐhuān tā.

Answer:

5 is not divisible by 3 and 9 .

The area of the farm in acres is 864 acres.

An acre is equal to​ 43,560 square​ feet, and there are 5280 feet in a mile.

Therefore,

1 mile = 5280 feet's

The farm has the shape of a rectangle measuring 0.9 miles by 1.5​ miles. Therefore, let's convert to feet's

1 mile = 5280 feet's

0.9 miles = ?

cross multiply

length = 0.9 × 5280 = 4752 feet

1 mile = 5280 feet's

1.5 miles = ?

width = 1.5 × 5280 = 7920 feet's

Hence,

area of the farm = 4752 × 7920

area of the farm = 37635840

Therefore, the area of the farm in acres can be calculated as follows:

43560 ft = 1 acre

37635840 ft = ?

cross multiply

area of farm = 37635840 / 43560

area of the farm = 864 acres.

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The value of x in the angles is 20

The angles are given as

4x - 12 and 7x - 28

These angles are same side interior angles

So, we have

4x - 12 + 7x - 28 = 180

Collect the like terms

So, we have

4x + 7x  - 12 - 28 = 180

Evaluate the like terms

So, we have

11x  = 220

Divide both sides by 11

x= 20

Hence, the value of x in the angles is 20

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Answer:

USE AIR MATH!!

Step-by-step explanation:

hope that helps

The inequality shown by a number line which describes that 12 is to the right of -2 is; 12 > -2.

It follows from the task content that the inequality which represents the number line as described in the task content is to be determined

On this note, it follows that since, numbers are arranged from left to right in increasing order on the number line, then;

Since 12 is to the right of -2, the inequality which represents the situation is; 12 > -2.

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A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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

Explanation:

The given sequence is 5, 12, 33, 96, 285, ...

The sequence of increases is: 7, 21, 63, 189

Then notice,

Assuming this pattern keeps up, the next increment will be 189*3 = 567

We add this increment to the last term of the original sequence

285+567 = 852

The sequence is now 5, 12, 33, 96, 285, 852, ...

Answer:

41

Step-by-step explanation:

because if m=-4 that means (-4)2+6(-4)+9=41

Answer:

Step-by-step explanation:

Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100.

The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending

the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

Answer:

Step-by-step explanation:

This article is about the basic inequality {\displaystyle z\leq x+y}{\displaystyle z\leq x+y}. For other inequalities associated with triangles, see List of triangle inequalities.

Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows a case where z is much less than the sum x + y of the other two sides, and the bottom example shows a case where the side z is only slightly less than x + y.

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that

{\displaystyle z\leq x+y,}z\leq x+y,

with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):

{\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}\|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,

Answer:

2

Step-by-step explanation:

Take 92 and divide by 3

3*30 = 90

92-90 = 2

There are 2 donuts left over

We're given:

If the shop sold " [tex]9\dfrac{9}{10}[/tex]  times as much milk chocolate as white chocolate", we must multiply [tex]9\dfrac{9}{10}[/tex] by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply [tex]9\dfrac{9}{10}[/tex] by 9 ounces:

[tex]9\dfrac{9}{10}\times9[/tex]

Convert the fraction into an improper fraction:

[tex]=\dfrac{99}{10}\times9[/tex]

Multiply:

[tex]=\dfrac{891}{10}[/tex]

The shop sold [tex]\dfrac{891}{10}[/tex] ounces of milk chocolate.

Answer:

3

Step-by-step explanation:

Think of "f(a)" like "y" in this context.   You can set that equal to 11 and solve for a:

f(a) = 3a + 2

11 = 3a + 2

9 = 3a

3 = a

Answer:

[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]

Step-by-step explanation:

Standard form of a quadratic equation:

[tex]\boxed{ax^2+bx+c=0}[/tex]

Question 1

Given:

[tex]x^2+x=20[/tex]

Rearrange to standard form by subtracting 20 from both sides:

[tex]\implies x^2+x -20=20-20[/tex]

[tex]\implies x^2+x -20=0[/tex]

Therefore:

Question 2

Given:

[tex]4x^2-2x=28[/tex]

Rearrange to standard form by subtracting 28 from both sides:

[tex]\implies 4x^2-2x-28=28-28[/tex]

[tex]\implies 4x^2-2x-28=0[/tex]

Therefore:

Question 3

Given:

[tex]5x^2=225[/tex]

Rearrange to standard form by subtracting 225 from both sides:

[tex]\implies 5x^2-225=225-225[/tex]

[tex]\implies 5x^2-225=0[/tex]

Therefore:

Question 4

Given:

[tex]x^2-x=36[/tex]

Rearrange to standard form by subtracting 36 from both sides:

[tex]\implies x^2-x-36=36-36[/tex]

[tex]\implies x^2-x-36=0[/tex]

Therefore:

Question 5

Given:

[tex]3x^2-4=7x[/tex]

Rearrange to standard form by subtracting 7x from both sides:

[tex]\implies 3x^2-4-7x=7x-7x[/tex]

[tex]\implies 3x^2-4-7x=0[/tex]

[tex]\implies 3x^2-7x-4=0[/tex]

Therefore:

Answer:

30x100= 3000

Step-by-step explanation:

If A line of best fit for the data is  B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D.  $2.38.

Given:

B= 0.45m + 1.93.

Where:

m= 1 month (First month)

Hence:

B= 0.45(1) + 1.93

B= 0.45+ 1.93

B=$2.38

Therefore if A line of best fit for the data is  B= 0.45m + 1.93. The value that is the best estimate of the amount of money in the jar at the end of the first month is: D.  $2.38.

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in the equation y= -x-1/2

the slope is -1/1 which can also be shown as -1.

Answers:

f(6) = 4

f ' (6) = 1/6

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

Explanation:

f(6) = 4 since the point (6,4) is on the f(x) curve. This is where the tangent is touching.

The tangent line also goes through (0,3)

Let's find the slope of the line through those two points.

[tex](x_1,y_1) = (6,4) \text{ and } (x_2,y_2) = (0,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{0 - 6}\\\\m = \frac{-1}{-6}\\\\m = \frac{1}{6}\\\\[/tex]

The slope of the tangent line is 1/6. This is the value of f ' (6) because the derivative measures the tangent at the given x value. It's useful to determine the instantaneous rate of change.

Answer:

1440

Step-by-step explanation:

3(4+4)(4+1)(4+2)(4-2)

3*8*5*6*2

1440

Answer:factors

Step-by-step explanation:

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

Answer: 124.12347

Step-by-step explanation:

The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.

It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.

Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.

Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.

Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.

Thus, An = A + [(n-1)*d]

A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)

A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)

A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)

Solving equation (1) and (2), we get d = 5 and A = 10.

Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.

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[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{16 \dfrac{40}{50}}[/tex]

[tex]\mathsf{= \dfrac{16\times50 + 40}{50}}[/tex]

[tex]\mathsf{= \dfrac{800 + 40}{50}}[/tex]

[tex]\mathsf{= \dfrac{840}{50}}[/tex]

[tex]\mathsf{= 840\div50}[/tex]

[tex]\mathsf{= 16.8}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{16.8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

From the question, we are to determine how much water is left in the barrel

From the given information,

"The barrel is filled with 18 gallons of water"

and

"Ryan used 9.7 gallons to water his garden in June"

After this time,

The quantity of water that would be left in the barrel will be 18 gallons - 9.7 gallons

= 8.3 gallons

Then,

3 and one eighth gallons in July

3 and one eighth = 3 1/8 = 3.125 gallons

The quantity of water that would be left is 8.3 gallons - 3.125 gallons

= 5.175 gallons

Hence, the quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

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Answer:

b

Step-by-step explanation:

Step-by-step explanation:

there is no real number solution for the square root of a negative number.

a sqare root multiplied by itself had to deliver exactly the number inside the square root.

so for sqrt(-49), what can be the answer ?

which number multiplied by itself gives -49 ?

it any negative number at that.

because

a × a = a²

and

-a × -a = a² but definitely not -a².

we get a negative number only, when we multiply a positive number with a negative number or vice versa.

the only solution is complex or imaginary (based on the imaginary number i):

i² = -1

i = sqrt(-1)

so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i

but again, no real solution.