Each of the four lines shown here has equation y = mx + b. For which line is it true that
m > 0 and b < 0?

Answer:

5 books must be read in 1 month for the total charges from each club to be equal.

Step-by-step explanation:

Monthly Charges of ABC club = 40$

Per book read charges of ABC club = 2$

amount of book read = x

Total charges of ABC club = 40 + 2x

Monthly Charges of Easy book club = 40$

Per book read charges of Easy Book club = 3$

Total charges of Easy book club = 35 + 3x

To calculate how many books must be read in 1 month for the total charges from each club to be equal,

Total charges of ABC club =  Total charges of Easy book club

40 + 2x = 35 + 3x

40 - 35 = 3x -2x

5 = x

x = 5

Therefore, 5 books must be read in 1 month for the total charges from each club to be equal.

[tex] \frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour} [/tex]

[tex] \frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour} [/tex]

The boat will travel 6.75 or

[tex]6 \frac{3}{4} [/tex]

miles in 1/2 hour.

[tex]\\Rewrite \ in \ form.\\\\(7x)^2 - (6y)^2\\\\\\\\Use \ difference \ of \ squares \  rule.\\\\(7x  + 6y) (7x - 6y)\\\\\\Therefore, \ you \ get \fbox{(7x+6y)&(7x-6y)}.[/tex]

Answer:

  f(x) = -4/3x² -2/3x +10

Step-by-step explanation:

The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.

___

Or, you can determine it yourself.

The equation can be written in the form ...

   f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts

for some value of "a"

For x = 0, this must match the y-intercept.

  f(0) = a(0 +3)(0 -5/2) = 10

  -15/2·a = 10

  a = -20/15 = -4/3

So, the function can be written as ...

  f(x) = (-4/3)(x +3)(x -5/2)

or

  f(x) = -4/3x² -2/3x +10

-2/3( 2x^2 + x - 15) is the answer.

From the given x-intercepts, 2 factors of the equation will be (x + 3) and

(2x - 5):- So we can write:

At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10  where a is a constant.

a * -15 = 10

a = -2/3  so the function is  (-2/3)(x  + 3)(2x - 5)

= -2/3( 2x^2 + x - 15).

the answer is A :)))))))))))))))))

Answer:

I am pretty sure it is Rhombus or a sideway rectangle but since they dont say more than givin I would say Rhombus

Step-by-step explanation:

Answer: Your answer is option D. In each family of function,the Parent function is the most basic function in the family

The family function has same highest degree, same shape for graph and consequently.

The correct option is D.

Given:

Identify the function is the most basic function in the family.

Below are the few example of family function.

[tex]y=x^2[/tex]

[tex]y=3x^2[/tex]

The graph for the both the function has same highest degree, same shape for graph and consequently. The parent function is the simplest from a family of function.

Thus, the correct option is D.

Learn more about parent function here:

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Answer:

1 mile a minute.

Step-by-step explanation:

Answer:

i think its B on edge

Answer:

your answer is x=16/11

explanation:

solve for x by simplifying both sides of the equation then isolation the variable.

exact form: 16/11

decimal form: 1.45

mixed number form: 1  5/11

hope this helps

~~bangtanboys7

Answer: [tex]x=\frac{16}{11}[/tex]

Step-by-step explanation:

To solve the equation shown in the problem you must:

- Add the like terms, as following:

[tex]\frac{3}{4}x+2x=\frac{5}{3}+\frac{7}{3}\\ \frac{11}{4}x=4[/tex]

- Multiply both sides by 4.

- Divide both sides of the equation by 11.

Therefore, the result is:

 [tex](4)\frac{11}{4}x=4(4)\\11x=16\\x=\frac{16}{11}[/tex]

Answer:

0.0085 centimeters.

Step-by-step explanation:

85/10000 is equal to 0.0085 centimeters, which is absurdly thin for anything, really.

Answer I think it is c I hope that right I am sorry for late responds

Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.

Answer:

S3 = 39

Step-by-step explanation:

* an = 3(3)^(n-1) is a geometric sequence

* The general rule of the geometric sequence is:

 an = a(r)^(n-1)

Where:

a is the first term

r is the common difference between each consecutive terms

n is the position of the term in the sequence

The rules means:

- a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ........................

∵ an = 3(3)^(n-1)

∴ a = 3 and r = 3

∴ a1 = 3

∴ a2 = 3(3) = 9

∴ a3 = 3(3)² = 27

* S3 = a1 + a2 + a3

∴ S3 = 3 + 9 + 27 = 39

Note:

We can use the rule of the sum:

Sn = a(1 - r^n)/(1 - r)

S3 = 3(1 - 3³)/1 - 3 = 3(1 - 27)/-2 = 3(-26)/-2 =3(13) = 39

Answer:

The correct answer is S₃  = 39

Step-by-step explanation:

It is given that,

aₙ = 3(3)ⁿ⁻¹

To find a₁

a₁ = 3(3)¹⁻¹ = 3(3)°

= 3 * 1 = 3

To find a₂

a₂ = 3(3)²⁻¹ = 3(3)¹

= 3 * 3 = 9

To find a₃

a₃ = 3(3)³⁻¹ = 3(3)²

= 3 * 9 = 27

To find the value of S₃

S₃ = a₁ + a₂ + a₃

 = 3 + 9 + 27 = 39

Therefore the correct answer is S₃  = 39

BCA is 90 degrees, because a tangent line is perpendicular to the raduis line BC.

Final answer:

The measure of angle M is 90 degrees.

Explanation:

The measure of angle M is 90 degrees. To understand why, we can use the fact that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. In this case, line AD is tangent to circle B at point C, so we can draw line AC, which is the radius of the circle, and find the measure of angle M by finding the complement of the angle formed by lines AD and AC. Since the complement of a 90-degree angle is 90 degrees, the measure of angle M is 90 degrees.

Answer:

Step-by-step explanation:

Look at the picture.

A₁ = 2 · 2 = 4

A₂ = 2 · 3 = 6

The area of a rhombus:

A = A₁ + A₂ ⇒ A = 4 + 6 = 10

You can use the formula of an area of a rhombus:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

d₁ = 4, d₂ = 5

Substitute:

[tex]A=\dfrac{(4)(5)}{2}=(2)(5)=10[/tex]

Answer:

10 ft²

Step-by-step explanation:

A = 1/2 (d1) (d2)

A = 1/2 (4) (5)

1/2 x 20

=10 ft²

Answer:   [tex]\bold{\dfrac{11}{18}}[/tex]

Step-by-step explanation:

Think of the products row by row:

11  12  13  14  15  16  - 0 products greater than 6

21 22 23 24 25 26  - 3 products greater than 6

31 32 33 34 35 36  - 4 products greater than 6

41 42 43 44 45 46   - 5 products greater than 6

51 52 53 54 55 56  - 5 products greater than 6

61 62 63 64 65 66  - 5 products greater than 6

[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]

Answer:

11/18.

Step by.step explanation:

There are 36 possible outcomes when 2 dice are rolled.

Outcomes for a product greater than six are:

2,4  2,5  2,6  3,3  3,4  3,5  3,6  4,2  4,3  4,4  4,5  4,6  5.2 ......5.6 , 6.2 .......6.6.

=  22 ways.

required Probability is 22/36 = 11/18 (answer).

20% as a fraction is 1/5

25% is 1/4

40% is 2/5

and 70% is 7/10

Depending on what your fraction is, you can find the answer in the fraction itself-

20%, you can take 20, 5 times to get to 100. Hence 1/5.

25 can go into 100 4 times (1/4)

40 is just 20 twice, so its 2/5.

Take 10 7 times and get 7/10.

Hope this helps a bit :)

Answer:

A) 0.5564; B) 0.8962; C) Choice D. Part​ (a) because the seat performance for a single pilot is more important.

Step-by-step explanation:

For part A,

We will find the z score for each value and then subtract the probabilities for each to give us the area between them.  We use the z score for an individual value:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

Our first X is 130 and our second X is 191.  Our mean, μ, is 136 and our standard deviation, σ, is 28.5:

[tex]z=\frac{130-136}{28.5}=\frac{-6}{28.5}\approx -0.21\\\\z=\frac{191-136}{28.5}=\frac{55}{28.5}\approx 1.93[/tex]

Using a z table, we can see that the area under the curve to the left of z = -0.21 is 0.4168; the area under the curve to the left of z = 1.93 is 0.9732.  This means the area between them is

0.9732-0.4168 = 0.5564.

For part B,

We will find the z score for each value again and subtract them; however, since we have a sample we will use the z score for the mean of a sample:

[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]

Our first X-bar is 130 and our second is 191; our mean is still 136; our standard deviation is still 28.5; and our sample size, n, is 36:

[tex]z=\frac{130-136}{28.5\div \sqrt{36}}=\frac{-6}{28.5\div 6}\approx -1.26\\\\z=\frac{191-136}{28.5\div \sqrt{36}}=\frac{55}{28.5\div 6}\approx 11.58[/tex]

The area under the curve to the left of -1.26 is 0.1038; the area under the curve to the left of 11.58 is 1.00:

1.00-0.1038 = 0.8962

For part C,

We want the probability that each individual pilot will be safe in these seats, so the value in part A is more important.

The probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%. The probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%. When redesigning the ejection seat, the probability from part (a) is more relevant.

To find the probability that a randomly selected pilot's weight is between 130 lb and 191 lb, we need to calculate the z-scores for both weights and find the area under the curve between those two z-scores. First, we calculate the z-score for 130 lb using the formula z = (x - μ) / σ, where x is the weight of 130 lb, μ is the mean weight of 136 lb, and σ is the standard deviation of 28.5 lb. Solving for z, we get z = (130 - 136) / 28.5 = -0.21. Using a z-table or calculator, we find that the area to the left of -0.21 is approximately 0.415. Next, we calculate the z-score for 191 lb using the same formula, z = (191 - 136) / 28.5 = 1.93. Again using a z-table or calculator, we find that the area to the left of 1.93 is approximately 0.973. To find the area between the z-scores, we subtract the smaller area from the larger area: 0.973 - 0.415 = 0.558. Therefore, the probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%.

To find the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb, we need to use the Central Limit Theorem. The sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the mean is still 136 lb and the standard deviation is 28.5 lb divided by the square root of 36, which is 4.75 lb. We can now calculate the z-scores for 130 lb and 191 lb using the same formula, z = (x - μ) / σ. The z-score for 130 lb is (130 - 136) / 4.75 = -1.26, and the z-score for 191 lb is (191 - 136) / 4.75 = 11.58. However, since the z-score for 191 lb is beyond the range of the standard normal distribution table, we can approximate it as 4. This means that we need to find the area under the curve to the left of -1.26 and subtract the area to the left of -4. Using a z-table or calculator, we find that the area to the left of -1.26 is approximately 0.1056, and the area to the left of -4 is approximately 0.000032. Subtracting the smaller area from the larger area, we get 0.1056 - 0.000032 = 0.1056. Therefore, the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%.

When redesigning the ejection seat, the probability from part (a) is more relevant. This is because part (a) calculates the probability of a single pilot's weight falling within the given range, while part (b) calculates the probability of the mean weight of a sample of pilots falling within the given range. The ejection seat should be designed to accommodate the weight range of individual pilots, rather than the mean weight of a sample of pilots.

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Answer:

= 32√3 ft²

Step-by-step explanation:

Area of the trapezoid will be equal to the area of the square and that of the triangle.

Considering the triangle part;

Cos 60 = x/8

x = 8 × sin  60

   = 4

Base of the triangle part = 4 ft

Therefore, top of the trapezoid = 6 ft

Height = 8 × sin 60

            = 8 × √3/2

           = 4 √3

Area of the trapezoid

Area = ((a+b)/2) × h

        = ((6 + 10 )/2 )× 4√3

        = 16/2 × 4√3

        = 32√3 ft²

Answer:

4th option is correct

Step-by-step explanation:

Here in the triangle we have angle = 60

hypotenuse= 8

opposite and adjacent can be solved using trigonometric ratios

cos 60  = [tex]\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}[/tex]

which gives adjacent = 4  on solving

likewise using sine we can find opposite side to the angle which is height of

trapezium.

sin60[tex]\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}[/tex]

therefore height =[tex]4\sqrt{3}[/tex] and adjacent = 4  ft

therefore opposite sides of Trapezium are 10 ft and 6 ft  

Formula for area of Trapezium =[tex]\frac{1}{2}[/tex](sum of parallel sides)x height

=      [tex]\frac{1}{2}[/tex](10+6)x [tex]4\sqrt{3}[/tex]

on solving it ,we get  [tex]32\sqrt{3}[/tex]

Answer:

(4,10) is the solution

Step-by-step explanation:

2x + y = 18

x – y = –6

Using elimination

2x + y = 18

x – y = –6

----------------------

3x    = 12

Dividing each side by 3

3x/3 = 12/3

x =4

Now we can find y

2x+y = 18

2(4) +y =18

8+y = 18

Subtracting 8 from each side

8-8+y = 18-8

y=10

(4,10) is the solution

The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.

To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.

Substituting this in the integral, we get:

∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du

Integrating the above expression, we get:

∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du

To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:

(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C

Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:

∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188

Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.

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Answer:

Area of Large Circle = 380.13

Area of Small Circle = 254.47

Area of Sidewalk = 125.66

Step-by-step explanation:

The side walk is just subtracting the smaller number from the bigger one.

The area is just Pi*r^2

Answer:

A  379.94 m^2

B 254.34 m^2

C 125.6 m^2

Step-by-step explanation:

A  Area of a circle is given by

A = pi r^2

We know the radius is 11

A = pi 11^2

A = 3.14 (121)

A = 379.94 m^2

B The Area of the orange circle

A = pi r^2

The radius is 9 m

A = pi 9^2

A = 3.14 (81)

A = 254.34 m^2

C  The Area between the circles is the difference between the large circle and the small circle

Ablue-Aorange

379.94-254.34

125.6 m^2

Answer:

log9(11x)

Step-by-step explanation:

log9(11) + log9(x)

We know that loga(b) + loga(c) = loga(b*c)

log9(11*x)

log9(11x)

Final answer:

To rewrite a sum of two logarithms as a single logarithm, combine them using the property that the log of a product equals the sum of the logs. For example, log a + log b becomes log (ab).

Explanation:

To rewrite the sum of two logarithms as a single logarithm, we use the relevant log properties. One of the most important properties of exponents is that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which is log xy = log x + log y. Conversely, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, if you have two logarithms of the same base you're adding, like log a + log b, you can combine them into a single log by multiplying the two arguments to get log (a*b).

An example using numbers could look like this:

log₂(3) + log₂(5) = log₂(3*5) = log₂(15)

Therefore, the sum of two logarithms, log a + log b, can be rewritten as log (ab), which expresses the multiplication of a and b within a single logarithm.

Answer:

Step-by-step explanation:

Line passes through (0,0) and (-1,4) .

Slope = -4

Equation of line is : y - 0 = - 4(x - 0)

                                 y = - 4x

The correct equation to find out how much was spent on the clothes is 50 - c = 16. Solving this, we find that c, the cost of the clothes, is $34.

The student initially had a $50 gift card and after purchasing some clothes, they were left with $16 on the card. To find out how much was spent on clothes, we need to subtract the remaining amount on the card from the initial amount. The correct equation to represent this situation is:

B. 50 - c = 16

We can then solve for c, which represents the cost of the clothes:

50 - 16 = c
34 = c

So, the amount spent on clothes is $34.

Answer:

The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)

Step-by-step explanation:

* Let the hot air balloon  at point A , the soccer fields

  at point B and the football field at point C

∵ The measure of the angle of depression to the

   soccer fields is 20° 15'

∴ The measure of angle B = 20° 15'

∵ The measure of the angle of depression to the

   football field is 62° 30'

∴ The measure of angle C = 62° 30'

∵ The sum of measures of the interior angles of any triangle = 180°

∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'

* The distance between the balloon and the soccer field

  is represented by the side AB of triangle ABC

- Use the sin Rule to find the length of side AB

∵ a/sin(A) = b/sin(B) = c/sin(C)

- a is the side opposite to angle A, b is the side opposite

 to angle B and c is the side opposite to angle C

∵ AB = c ⇒ opposite to angle C

∵ The distance between the two fields = 4 miles

∴ BC = 4 miles

∵ BC = a ⇒ opposite to angle A

∴ 4/sin(97° 15') = c/sin(62° 30')

∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')

∴ c = 3.6 miles

∴ The distance from the balloon to the soccer fields = 3.6 miles

   answer (b)

Answer:

  your choices are correct

Step-by-step explanation:

sin(x +π/2) is a translation of the sine function to the left by π/2 units, which makes it look exactly like the cosine function that you want.

cos(-x) is the same as cos(x), since the cosine function is an even function.

___

sin(x -π/2) will look like -cos(x), not what you want.

The third choice is a reflection across the x-axis of the function you started with. It is not equivalent.

Answer:

5x = 14

Step-by-step explanation:

If 5 yards of fabric is $14 you need an equation that would solve how much 1 yard of fabric costs. You can say 5x = 14 or x = 2.8 which means that one yard of fabric (1x or just x) is $2.80.

Answer: [tex]y==\frac{14}{5}x[/tex]

Step-by-step explanation:

By definition, we know that Direct proportion equation has the following form:

[tex]y=kx[/tex]

Where k is the constant of proportionality.

Then, If 5 yards of fabric cost $14, you can calculate k as following:

[tex]14=k(5)\\k=\frac{14}{5}[/tex]

Therefore substituting the value of k into the first equation, you obtain the following equation:

[tex]y==\frac{14}{5}x[/tex]

Answer:

Geometric

Step-by-step explanation:

Does multiplying the same number with each term give the next term?

If so, then it is Geometric Sequence.

Does adding the same number with each term give the next term?

If so, then it is Arithmetic Sequence.

We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.

It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.

Answer is "Geometric"