Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k. The equation is

Answer:

[tex]\large\boxed{D)\ y=\dfrac{1}{5}x+5}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the y-intercept (0, 5) ⇒ b = 5

and the other point (5, 6).

Put the coordinates of the point to the formula of a slope:

[tex]m=\dfrac{6-5}{5-0}=\dfrac{1}{5}[/tex]

Finally we have the equation:

[tex]y=\dfrac{1}{5}x+5[/tex]

Answer:

this is the correct answer 100% correct dont forget to friend request me bye

Step-by-step explanation:

Answer:

Step-by-step explanation:

Is a ≤ b < c are the side lengths of a right triangle, then

[tex]a^2+b^2=c^2[/tex]

A. 6cm, 8cm, 10cm.

Substitute:

[tex]6^2+8^2=10^2\\36+64=100\\100=100\to TRUE[/tex]

B. 12cm, 35cm, 37cm.

Substitute:

[tex]12^2+35^2=37^2\\144+1225=1369\\1369=1369\to TRUE[/tex]

C. 4cm, 6cm, 10cm.

It's not the side lengths of a triangle, because 4 + 6 = 10.

Without looking at it, we will check equality

[tex]4^2+6^2=10^2\\16+36=100\\52=100\to FALSE[/tex]

D. 10cm, 24cm, 26cm.

Substitute:

[tex]10^2+24^2=26^2\\100+576=676\\676=676\to TRUE[/tex]

The measurement that could not represent the side length of a right triangle is  4 cm, 6 cm, 10 cm.

A right triangle is a triangle that consists of three sides. The longest side is the hypotenuse. The other sides are the base and the length. The sum of angles in a triangle is 180 degrees.

According to this theorem, the square of the hypotenuse should be equal to the sum of the square of the other two sides.

The Pythagoras theorem: a² + b² = c²

where:

a = length

b = base

c = hypotenuse

6² + 8² = 10²

36 + 64 = 100

Option B = 12² + 35

= √144 + 1225

= √1369

= 37

Option C = 4² + 6²

16 + 36

= √52

= 7.2

Option D: 10² + 24² = 26²

100 + 576

= √676

= 26

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Answer:

1.2 pounds

Step-by-step explanation:

As mentioned in the question,

14.4 pounds of foods is distributed among 24 dogs.

Therefore, each dog gets: [tex]\frac{14.4 (pounds)}{24} = 0.6 pounds[/tex]

6 dogs eat only 0.4 pounds, so the amount left:  ( 0.6 - 0.4 ) = 0.2 pounds

Hence, the total food left in the bowls of six dogs = 6 * 0.2 = 1.2 pounds

Fine the average rate of change by the difference in N over the difference in T:

3000 - 500 / 4-0 = 2500 / 4 = 625

This means for every 1 T, N = 625.

Now multiply 625 by 8:

625 x 8 = 5000

When T = 8 N = 5,000

The decay rate can be found by dividing -ln(2) by the half life.

Decay rate = -ln(2) / 5715 = -0.00012

[tex] \cos t (\sec t - \cos t) = \sin^2 t [/tex]

[tex] \cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t [/tex]

[tex] \dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t [/tex]

[tex] 1 - \cos^2 t = \sin^2 t [/tex]

Use the identity: [tex] \sin^2 t + \cos^2 t = 1 [/tex] and solve for [tex] \sin^2 t [/tex]. You get: [tex] \sin^2 t = 1 - \cos^2 t [/tex]

Do the substitution on the left side to get:

[tex] \sin^2 t = \sin ^2 t [/tex]

[tex] \cos \: t ( \sec \: t - \cos \: t) = \sin^{2}t \\ \\ 1. \: 1 - \frac{ \cos \: t }{ \sec \: t } = \sin^{2} t \\ 2. \: 1 - \cos \: t \cos \: t = \sin^{2} t \\ 3. \: 1 - \cos^{2} t = \sin^{2} t \\ 4. \: 1 - \cos^{2} t - \sin^{2} t = 0 \\ 5. \: 1 - 1 = 0 \\ 6. \: 0 = 0 \\ 7. \: infinitely \: many \: solutions[/tex]

Answer:

The expression would be 43x + 128

Step-by-step explanation:

43 dollars is multiplied by however many feet is used.  Then, the exception(the gate) is added to the charge that is 43x

chur answer is gonna be 63787 km

I think the answer is x > -8.

Answer:

x > - 8

Step-by-step explanation:

Given

- 2x + 7 < 23 ( subtract 7 from both sides )

- 2x < 16 ( divide both sides by - 2 )

Remembering to reverse the inequality symbol when dividing/ multipkying by a negative quantity, hence

x > - 8 ← reversed symbol

Answer:

a. 0.25

Step-by-step explanation:

The given expression is

[tex]\lim_{x \to 2} \frac{x-2}{x^2-4}[/tex]

Factor the denominator using difference of two squares.

[tex]\lim_{x \to 2} \frac{x-2}{(x-2)(x+2)}[/tex]

Cancel out common factors;

[tex]\lim_{x \to 2} \frac{1}{(x+2)}[/tex]

We plug in 2 to get

[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{2+2}[/tex]

[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{4}=0.25[/tex]

Answer:

The correct answer option is A. 0.25.

Step-by-step explanation:

We are given the following expression and we are to find its limit:

[tex] lim_\left \{ {{ x = 2 } [/tex] [tex] \frac { x - 2 } { x ^ 2 - 4 } [/tex].

First of all, we will simplify the expression by factorizing the term in the denominator:

[tex] \frac { x - 2 } { x ^ 2 - 4 } = \frac { x - 2 } { ( x - 2 ) ( x + 2 ) }[/tex]

Cancelling the common terms to get:

[tex]\frac{1}{x+2}[/tex]

Substituting the given value for x to get:

[tex]\frac{1}{2+2}[/tex] = 0.25

After 10 hours the temperature is shown on the graph as 30 degrees.

50 degrees - 30 degrees = 20 degrees.

The temperature dropped 20 degrees in 10 hours.

Divide the change by the time:

20 degrees / 10 hours = 2 degrees per hour.

Because the temperature dropped, the change would be negative.

The answer is D. -2 degrees per hour.

There are 67 total people and 28 people on the swim team.

The probability of picking someone on the swim team would be 28/67 which is equal to 41.8%

Answer:

The probability that a randomly selected person is on the swim team is 41.79%

Step-by-step explanation:

The favorable event will be 28

The total no of event will be 67

So The probability will be  =  [tex]\frac{no of favorable events}{Total no of event}[/tex]

                                           =  [tex]\frac{28}{67}[/tex]

                                           =  41.79%

Thus the probability that a randomly selected person is on the swim team is 41.79% .

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Answer:

a: z = -1.936

b: 0.0265

d: z < -1.645

Reject H0 if z < -1.645

Step-by-step explanation:

We are given:

H0:  µ = 20

HA:  µ < 20

n = 60, sample mean: 19.6, σ = 1.6

Since the alternate hypothesis has a < sign in it, it is a left tailed test.  The < or > sign in the alternate hypothesis points towards the rejection region.

For a:  We need to calculate the test statistic for our situation.  This is done with a z-score formula for samples.  

For b:  we need to use the z-score table to look up the p-value for the score we calculate in part a.  The p-value is 0.0265.  This means that there is only about a 2.65% chance that the sample values were a result of random chance.

For d:  Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645.  This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis

See attached photo for all the calculations!

The test statistic is approximately -4.84 with a p-value close to 0. The critical value is approximately -1.645. The rejection rule is to reject H0 if z < -1.645.

a. To compute the test statistic, we can use the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Given x = 19.6, μ = 20, σ = 1.6, and n = 60, we can calculate the test statistic as follows:

z = (19.6 - 20) / (1.6 / √60) = -1 / 0.2062 ≈ -4.84

b. The p-value can be determined by looking up the test statistic in the standard normal distribution table. However, in this case, the test statistic is already given as -4.84. The p-value associated with this test statistic is extremely small (close to 0), indicating strong evidence against the null hypothesis.

d. For a significance level α = 0.05, the critical value can be obtained by finding the z-score that corresponds to a cumulative probability of 1 - α = 0.95. Looking up this value in the standard normal distribution table, we find that the critical value is approximately -1.645.

The rejection rule using the critical value is: Reject H0 if z < -1.645.

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Answer:

-9 C

Step-by-step explanation:

Subtract 4 from -5 will equal -9

Answer:

True.

Step-by-step explanation:

Volume of a cylinder = π r^2 h   where h = height and π r^2 = the base area.

Volume / height =  π r^2 h  /  h  =   π r^2 = base area.

The base area of a cylinder is not the quotient of its volume and its height; it is determined by the area of its circular base. Understanding the relationship between base area and volume in a cylinder is essential in mathematics.

False. The base area of a cylinder is not the quotient of its volume and height. The base area of a cylinder is the same as the area of its circular base, which is equal to πr2 where r is the radius of the base.

The volume of a cylinder is calculated by multiplying the base area with the height of the cylinder. Thus, base area ≠ volume / height.

When the height of a cylinder is equal to its diameter, it minimizes the surface area, but it does not affect the calculation of the base area itself.

Answer:

9.48

Step-by-step explanation:

The perimeter of a rectangle is the distance around the the shape. It can be found by adding each side of the shape to find a total. In contrast, the area of a shape is the amount inside a shape. It is found using multiplication or A = l*w. Since the width is w and the length is twice its width or 2w, use these expressions in the area formula to find their amount. Then add them together to find the perimeter.

[tex]A = l*w5 = w(2w)\\5 = 2w^2\\2.5 = w^2\\1.58 = w[/tex]

The width of the rectangle is w = 1.58. The length is 2w = 2 (1.58) = 3.16.

Add these amounts by P = l + l + w + w to find the perimeter.

P = 3.16 + 3.16 + 1.58 + 1.58 = 9.48

Answer:

Option D. [tex]42.4\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cone (juice treats) is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=3\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(1.5)^{2}(3)=7.065\ in^{3}[/tex]

Multiply the volume of one juice treats by 6

[tex](6)7.065=42.39=42.4\ in^{3}[/tex]

Answer:

x = 1.723

Step-by-step explanation:

The  zeros of a function f(x) are the points where the function crosses the x-axis. At these points, the function will have a value of zero, that is;

f(x) = 0

We simply graph the function and determine the points where it crosses the x-axis. From the attachment, f(x) crosses the x-axis at;

x = 1.723

Answer:

Step-by-step explanation:

We have given the function:

f(x)=-3x³+6x+5.

We have to find the zeros of the function.

The zeros of the function are the points where the function cuts the x-axis.

And at that points function has value zero.

So to find these points put f(x)= 0 we get,

-3x³+6x+5=0

As from the graph the function cuts the x-axis at x = 1.723 so, this is the zero of the function.

To find a coterminal angle to 800 degrees within the 0 to 360-degree range, divide 800 by 360 and find the remainder, which is 80 degrees. Hence, 80 degrees is the angle that's coterminal with 800 degrees.

To find an angle that is coterminal with 800 degrees, which means an angle that shares the same terminal side as the 800-degree angle but is between 0 degrees and 360 degrees, we use the concept of coterminal angles. Since a complete circle has 360 degrees, we can subtract or add multiples of 360 degrees to any angle to find a coterminal angle.

Here’s how we find it for 800 degrees:

Therefore, 80 degrees is the angle between 0 degrees and 360 degrees that is coterminal with an angle measuring 800 degrees.

Answer:
Raise 3 to the number of days and then multiply this value by 2.

Step-by-step explanation:

TTM/Imagine Math.

The correct answer is:

C. Raise the number of days to the third power and then multiply this value by 2.

Sure, here's a step-by-step solution:

1. Initial Number of Infected People: Start with the initial number of infected people, which is 2 in this case.

2. Exponential Growth Model: Use the exponential growth model to represent the increase in the number of infected people each day. The model is given by the formula [tex]\(I = a \cdot 3^D\)[/tex], where:

  - [tex]\(I\)[/tex] is the number of infected people,

  - [tex]\(a\)[/tex] is the initial number of infected people (which is 2),

  - [tex]\(3\)[/tex] represents the tripling effect each day, and

  - [tex]\(D\)[/tex] is the number of days that have passed.

3. Raise 3 to the Power of Number of Days: Raise 3 to the power of the number of days that have passed. This accounts for the tripling effect each day.

4. Multiply by Initial Number of Infected People: Multiply the result from step 3 by the initial number of infected people (which is 2). This gives the total number of infected people after the given number of days.

So, to determine the number of infected people from the number of days that have passed, raise 3 to the power of the number of days and then multiply this value by 2. Therefore, option C is the correct answer.

The correct question is:

Two people become infected with a virus that spreads quickly. Each day that passes, the number of infected people triples. How can the number of infected people be determined from the number of days that have passed?

A. Raise 3 to the number of days and then multiply this value by 2 .

B. Add the number of days to 2 and then multiply this sum by 3.

C. Raise the number of days to the third power and then multiply this value by 2 .

D. Multiply the number of days by 3 and then add 2 to this product.

Answer:

D

Step-by-step explanation:

Exponential equation takes the form  [tex]y=ab^x[/tex]  where

a is the initial value ( a ≠ 0), and

b is the base ( b ≠ 1)

The equation given can be written as  [tex]y=3.1^x\\y=1*3.1^x[/tex]. Thus, it is an exponential equation.

So a = 1 and b = 3.1

Thus we can say that the initial value = 1 and the base is 3.3

Answer:

x = -1

Step-by-step explanation:

-2 to 2 is 4 units, so -3x + 1 = 4.

We subtract 1 from both sides to get -3x = 3.

Then we divide each side by -3 to get x = -1.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The greatest prime factor is 9951 is 107.

You divide 9951 by 3, and you get 3317.

You divide 3317 by 31 (which is a prime number), and you get 107, which is also a prime number.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

B

Step-by-step explanation:

We can see Part by Part to get this question.

-8*x + 9

Now we can finally write:

y > -8x + 9

Answer choice B is right.

Answer:

The total number of digits required in numbering the pages of a book that has 53 pages would be: 97.

Step-by-step explanation:

This answer would be 97 due to the first nine digits being singular.

The next 44 digits are double, so therefore, you multiply 44 by 2, and you end up with 88.

After that, you take 88 and add the 9, which, is 97 digits in total that you would need to number a 53 page book.

Answer:

The answers for your two questions are the following

a)11.606 m

b) As the number of swings approaches infinity

Step-by-step explanation:

We are dealing with an exponential equation  series, where the length of  each swing can be represented as

l = [ 15 *(0.95)^(n-1) ]

n is the corresponding number of the swing.

So, for the first swing, n = 1

[ 15 *(0.95)^(1-1) ] = 15 m

a) How far with the pendulum travel on its 6th swing?

We just need to evaluate the previous formula for n = 6

[ 15 *(0.95)^(6-1) ] =

[ 15 *(0.95)^(5) ] =

[ 15 *(0.7737) ] =

[ 15 *(0.7737) ] = 11.606 m

b) How far will the pendulum swing before it essentially stops? Hint: This is an infinite geometric series.

We previously stated that the length of the arc of each swing can be represented as

l(n)  = [ 15 *(0.95)^(n-1) ]       ,      for n>=1

Since the function approaches zero if and only if n approaches infinity, we can say that the pendulum never stops.

Of course, this only happens mathematically, we can always fin a threshold for which the movement cannot be registered anymore.

Please see attached graph for a representation of the function

Answer:

a) It will travel approx 79.47 meters,

b) It will travel 300 meters.

Step-by-step explanation:

Given,

The initial distance travel on first swing = 15 meters,

Also, Each subsequent swing is 95% of the previous swing.

Thus, there is a G.P. that shows this situation,

Having first term, a = 15,

And, the common difference, r = 95 % = 0.95,

a) Also, for the 6th swing,

Number of terms, n = 6,

Hence, the distance covered by the pendulum on its 6th swing,

[tex]S_{n}=\frac{a(1-r^n)}{1-r}[/tex]

[tex]S_{6}=\frac{15(1-0.95^6)}{1-0.95}[/tex]

[tex]=79.4724328125\approx 79.47\text{ meters}[/tex]

b) When [tex]n=\infty[/tex]

The distance will the pendulum swing before it essentially stops is,

[tex]S_{\infty}=\frac{a}{1-r}[/tex]

[tex]=\frac{15}{1-0.95}[/tex]

[tex]=300\text{ meters}[/tex]

Answer:

Option d

Step-by-step explanation:

We know that 52,000 fans can fit into the stadium.

Then the amount of tickets that can be sold must equal 52,000.

If we call H the number of tickets for the home team and call V the number of tickets for the visiting team, then:

[tex]H + V = 52,000[/tex]

Then, we know that the local team has 5 times more fans than the visiting team. So we can write that:

[tex]H = 5V\\H-5V = 0[/tex]

Finally, the system of equations sought is:

[tex]H - 5V = 0\\H + V = 52 000[/tex]

Answer:

the answer is a

Step-by-step explanation:

5x7= 35, 5x8= 40    40-35=5  

Ans: It's C

'Cause (2/3 * 3/4x)+(2/3 * (-3/2)) = 1/2x - 1.

The expression which isequivalent to (1/2)x - 1 will be 2/3(3/4x - 3/2). Then the correct option is C.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Let's check all the options, then we have

a) 1/3(3/2x - 1), simplify the expression, then we have

⇒ 1/3(3/2x - 1)

⇒ (1/2)x - 1/3

b) (3/2x + 1) - (x - 2), simplify the expression, then we have

⇒ (3/2x + 1) - (x - 2)

⇒ (1/2)x + 3

c) 2/3(3/4x - 3/2), simplify the expression, then we have

⇒ 2/3(3/4x - 3/2)

⇒ (1/2)x - 1

d) (3/4x - 2) + (1/4x + 1), simplify the expression, then we have

⇒ (3/4x - 2) + (1/4x + 1)

⇒ x - 1

The expression which isequivalent to (1/2)x - 1 will be 2/3(3/4x - 3/2). Then the correct option is C.

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Answer:

Academy A, Arithmetic, and difference makes most sense to me.

Academy A's professional tennis player numbers can be described by an arithmetic sequence due to a constant increase of 10 every year. In contrast, Academy B's numbers can be represented by a geometric sequence because the increase each year is proportionate to the current number of students, at a rate of a 10% increase per year.

The number of players who went on to play professionally at Academy A can be represented by an arithmetic sequence because the numbers of players who went on to play professionally in successive years have a common difference of 10. For Academy A, each year the number increased by a consistent amount, 10 more players, hence the use of an arithmetic sequence.

On the other hand, the number of players who went on to play professionally at Academy B can be represented by a geometric sequence because the numbers of players who went on to play professionally in successive years have a common ratio of 10%. For Academy B, the rate of increase is proportional to the current number of students, which makes it a geometric sequence.

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