Find an equation for the line below in y=mx+b

The number of ways to order the first, second and third place finishers is simply the number of permutations of 8 runners taken 3 at a time. This can be calculated using the formula for permutations

The formula for permutations, P(n,r), gives the number of ways to choose r items from a set of n items, where order matters. This formula is calculated as:

P(n,r) = n! / (n-r)!

where n! represents the factorial of n (i.e. n multiplied by n-1 multiplied by n-2, etc. down to 1).

In this problem, n = 8 and r = 3, so the number of permutations is:

P(8,3) = 8! / (8-3)! = 8! / 5! = 40320 / 120 = 336

So there are 336 different arrangements of first, second, and third place finishers in the 100-meter sprint.

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Let x be the no.of square feet for landscaping

Company A

Monthly consulting fee = $250

Cost of landscaping of 1 sq.feet = $10

Cost of landscaping of x sq.feet = $10x

So, Total charge by company A = 250+10x  ---1

Company B

Monthly consulting fee = $90

Cost of landscaping of 1 sq.feet = $12

Cost of landscaping of x sq.feet = $12x

So, Total charge by company B = 90+12x   ---2

Now we are supposed to find  how many square feet of landscaping will the two companies charge the same amount

So, Equate 1 and 2

\(250+10x=90+12x\\160=2x\\80=x\)

So, the two companies charge the same amount for 80 sq.feet

Total charge by company A for 80 sq.feet = 250+10(80)= $1050

Total charge by company B for 80 sq.feet = 90+12(90)=$1170

Answer:

(C)x=11.6, y=23.2

Step-by-step explanation:

Using Theorem of Intersecting Secant and Tangent

\(TQ$ X TP=TR^2\)

\(10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6\)

Next, we apply Theorem of Intersecting Chords

PV X VQ=SV X VR

4 X x= 2 X y

Recall: x=11.6

2y=4 X 11.6

2y=46.4

y=46.4/2=23.2

Therefore: x=11.6, y=23.2

The correct option is C

Note: Let us consider, we need to find the gradient of line L.

Given:

The given equation of a line is:

\(y=7-4x\)

The line L passes through the points with coordinates (- 3, 1) and (2, - 2).

To find:

The gradient of the given line and the gradient of line L.

Solution:

Slope intercept form of a line is:

\(y=mx+b\)                ...(i)

We have,

\(y=7-4x\)                   ...(ii)

On comparing (i) and (ii), we get

\(m=-4\)

Therefore, the gradient of the given line is -4.

The line L passes through the points with coordinates (- 3, 1) and (2, - 2). So, the gradient of line L is:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{-2-1}{2-(-3)}\)

\(m=\dfrac{-3}{2+3}\)

\(m=\dfrac{-3}{5}\)

Therefore, the gradient of the line L is \(\dfrac{-3}{5}\).

The probability of getting all heads when flipping a coin four times is 1/16.

(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.

There were 16 total outcomes.

Probability going out of control

HHHH P(A) = P(getting all heads) = 1/16

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∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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- BRAINLIEST answerer

Carli is correct and there is no error in her answer. Hence, it does not require any correction.

We have Carli made 9 greeting cards in 3/4 hour and she determined her unit rate to be 1/12 card per hour.

We have to find her error out and correct it.

The machine will make 1 pencil in -  \(\frac{x}{n}\) hours.

Therefore, the machine will make 'y' pencils in -   \(\frac{xy}{n}\)  hours

According to the question -

Carli made 9 greeting cards in 3/4 hour (45 minutes).

Therefore, she will make one greeting card in -    \(\frac{\frac{3}{4} }{9}\) = \(\frac{3}{4} \times\frac{1}{9}= \frac{1}{12}\)

This means that Carli is correct and there is no error in her answer. Hence, it does not require any correction.

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The missing step is XW/UT=VW/XV because corresponding side of similar triangle are proportional.

What is similar triangle?

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

When two triangles are similar, then their corresponding angles would be congruent while their opposite sides will be proportional to each other

In the proof, it is given, Both triangle are similar, by AA similarity theorem, hence, XW/UT=VW/XV because corresponding side of similar triangle are proportional.

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a university student is selecting courses for his next semester. he can choose from humanities courses and science courses. the number of ways in which he can  choose courses if or more must be humanities courses can be found using combinations

C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

To determine the number of ways a university student can choose courses for the next semester with a requirement of at least "r" humanities courses, we can use combinatorial techniques.

Let's assume there are "n" total courses available, "h" of which are humanities courses, and "s" of which are science courses.

The student needs to select "r" or more humanities courses. We can calculate the number of ways to choose "r" or more humanities courses by summing the combinations for "r" to "h" humanities courses.

The formula to calculate the number of ways to choose "k" items from a set of "n" items is given by the combination formula: C(n, k) = n! / (k! * (n - k)!)

Using this formula, the calculation for the number of ways to choose "r" or more humanities courses can be expressed as:

Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

Now, let's substitute the values and calculate the number of ways:

Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

In conclusion, the number of ways the university student can choose courses, with a requirement of at least "r" humanities courses, is obtained by summing the combinations for "r" to "h" humanities courses using the combination formula.

the number of ways in which he can  choose courses if or more must be humanities courses can be found using combinations

C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

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Answer:

987

Step-by-step explanation:

yeah my teacer =

Answer: He walked 2.76 more miles.

Step-by-step explanation: In this problem, we would subtract James' miles from Richard's miles to get the answer.

15.74 miles - 12.98 miles = 2.76 miles.

Therefore, Richard walked 2.76 more miles than James.

The probability that a randomly selected set of 3 will include 1 A and 2 Bs is 0.3 or 30%.

To find the probability that a randomly selected set of 3 will include 1 a and 2 bs, we first need to determine the total number of possible sets of 3 that can be selected from the sample space.

Since the sample space contains 6 as and 4 bs, the total number of possible sets of 3 that can be selected is:

10C3 = (10!)/(3!*(10-3)!) = 120

This means there are 120 different ways to select a set of 3 from the sample space.

Next, we need to determine the number of sets of 3 that include 1 a and 2 bs. To do this, we can use the combination formula:

6C1 * 4C2 = (6!)/(1!*(6-1)!) * (4!)/(2!*(4-2)!) = 6*6 = 36

This means there are 36 different sets of 3 that include 1 a and 2 bs.

Finally, we can calculate the probability of selecting a set of 3 that includes 1 a and 2 bs by dividing the number of sets that meet this condition by the total number of possible sets:

36/120 = 3/10

Therefore, the probability that a randomly selected set of 3 will include 1 a and 2 bs is 3/10.

Given that the sample space contains 6 As and 4 Bs, let's find the probability that a randomly selected set of 3 will include 1 A and 2 Bs.

1. First, calculate the total number of ways to choose 3 elements from a set of 10 (6 As and 4 Bs). We use the combination formula:

C(n, r) = n! / (r!(n-r)!)
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = 120

2. Next, find the number of ways to choose 1 A from the 6 As and 2 Bs from the 4 Bs:

C(6, 1) = 6! / (1!(6-1)!) = 6! / (1!5!) = 6
C(4, 2) = 4! / (2!(4-2)!) = 4! / (2!2!) = 6

3. Multiply the number of ways to choose 1 A and 2 Bs:

Number of favorable outcomes = C(6, 1) × C(4, 2) = 6 × 6 = 36

4. Finally, calculate the probability:

Probability = Number of favorable outcomes / Total number of outcomes = 36 / 120 = 3/10 or 0.3

So, the probability that a randomly selected set of 3 will include 1 A and 2 Bs is 0.3 or 30%.

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If a customer is 48.282 years old, we would expect them to make approximately 19.52 claims in a given year.

According to the regression relationship provided by the insurance company, the number of claims per year is determined by the customer's age. The equation given is: (claims per year) = 0.217 * (age) + 9.04.

To find the expected number of claims for a customer who is 48.282 years old, we substitute the age value into the equation:

Claims per year = 0.217 * 48.282 + 9.04

Claims per year ≈ 10.48

Therefore, if a customer is 48.282 years old, we would expect them to make approximately 10.48 claims in a given year. The correct answer is option B.

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Answer:

Step-by-step explanation:

Q1

AT = 8.5 ft

AT is radius, the diameter is:

Q2

AH = 6 yd, AH is radius

Q3

Q4

∠MAT = 115°

Arc MT is:

Q5

C = 6π, A = ?

A = πr² = π*3² = 9π

Rationalizing the denominator of 15/(-5 + 4) by mutiplying the numerator and denominator by 1. Now, we can write:15/(-5 + 4) × (-1/-1)15/(-5 + 4) × (1/1) × (-1/-1)=-15/1-15

Given, the rationalizing denominator of 15/(-5 + 4) is to be found.To rationalize the denominator of the given fraction,

we first need to find the Least Common Denominator (LCD) of the given fraction.

Let us write the given expression as: 15/(-5 + 4) = 15/-1

Since the denominator is only a single number i.e., "-1,"

we do not have to worry about radicals or complex numbers in this case.

So, we do not have to multiply or divide by the conjugate of a complex number.

The denominator "-1" cannot be zero, so the fraction is well-defined.

Rationalizing the denominator of 15/(-5 + 4) by mutiplying the numerator and denominator by 1:

L.C.D. of the given fraction is -1.

Now, we can write:15/(-5 + 4) × (-1/-1)15/(-5 + 4) × (1/1) × (-1/-1)=-15/1-15

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Answer:

The statement is false. Vertical angles are the left and right angles of the four angles formed by two intersecting lines.

Answer:

Option 4 shows the point (-4, 5)

Step-by-step explanation:

In the coordinates (-4, 5), x value is -4 so we got left 4 units from 0, and then y-value is 5, so we go up 5 units form -4 from earlier

Hope this helps!

Answer:

option 4 or D

Step-by-step explanation:

It is not option 1 because when going across and down you end up at 5,-4 instead of -4,5. Option 2 is incorrect because the graph is showing -5, 4. Option three is wrong because it shows 4,-5. Finally option four is correct. This is because when graphing you start with the x-intercept going to left to right or across when plotting on the x-axis, when doing that the points is at -4. When doing the same with the y-intercept you get 5.

Answer:

B

Step-by-step explanation:

Convert from mixed numbers to improper fractions:

\(\sf area=90 \frac{3}{10}=\dfrac{90 \cdot 10+3}{10}=\dfrac{903}{10}\)

\(\sf length=10\frac12=\dfrac{10 \cdot 2+1}{2}=\dfrac{21}{2}\)

Area of a rectangle = length x width

⇒ width = area ÷ length

\(\sf \implies width=\dfrac{903}{10} \div \dfrac{21}{2}\)

\(\sf \implies width=\dfrac{903}{10} \times \dfrac{2}{21}\)

\(\sf \implies width=\dfrac{1806}{210}\)

\(\sf \implies width=\dfrac{1806 \div 42}{210 \div 42}\)

\(\sf \implies width=\dfrac{43}{5}\)

\(\sf \implies width=8\frac35\)

\( \pink{ \text{Given:}}\)

\( \\ \)

\( \star \sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \star \sf{}Length =10 \dfrac{1}{2} \)

\( \\ \\ \)

\( \purple{ \text{To~Find:}}\)

\( \\ \\ \)

\( \star \sf Width \: of \: rectangle\)

\( \\ \\ \)

\( \orange{ \text{Solution:}}\)

\( \\ \\ \)

So first convert length and area from fraction form to decible.

\( \leadsto\sf{}Area =90 \dfrac{3}{10} \)

\( \\ \)

\( \leadsto\sf{}Area = \dfrac{903}{10} \)

\( \\ \)

\( \leadsto\sf{}Area =90.3\)

\( \\ \)

Now convert value length into decibel .

\( \\ \)

\( \leadsto\sf{}Length =10 \dfrac{1}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = \dfrac{21}{2} \)

\( \\ \)

\( \leadsto\sf{}Length = 10.5\)

\( \\ \)

We know :-

\(\bigstar\boxed{\rm Area~of~rectangle= length \times width}\)

\( \\ \\ \)

So:-

\( \\ \)

\(: \implies\sf Area~of~rectangle= length \times width \\ \\ \\ : \implies\sf 90.3= 10.5 \times width \\ \\ \\: \implies\sf 90.3 \div 10.5=width \\ \\ \\: \implies\sf \dfrac{ 90.3}{10.5}=width \\ \\ \\: \implies\sf \dfrac{ 90 \cancel.3}{10 \cancel.5}=width \\ \\ \\: \implies\sf \dfrac{ 903}{105}=width \\ \\ \\: \implies\sf width = \dfrac{ 903}{105} \\ \\ \\: \implies \underline{\boxed{\sf width = 8.6}} \pink\bigstar\)

\(\\\\\\\)

\(\begin{lgathered}\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}\end{lgathered}\)

Answer:

10

Step-by-step explanation:

My guy just plug in the number for x it's not that hard

The value of t is -9. The equation of the curve is y = x² + 8x -9.

What is a curve?

An abstract term used in mathematics to describe the path of a continuously moving point (see continuity). An equation is typically used to generate such a path. The term can also refer to a straight line or a series of linked line segments.

The given curve cuts y-axis at -9 and  x-axis at 1 and ‘t’ where t < 0.

The equation of a quadratic curve is y = (x-a)(x-b) where a, b are x-intercepts.

Putting a = 1 and b = t in y = (x-a)(x-b):

y = (x-1)(x-t)

Since the y-intercept of the curve is -9. The curve passes through the point (0,-9).

Putting x = 0, y=-9:

-9 = (0-1)(0-t)

-9 = t

Now putting t = -9, in y = (x-1)(x-t):

y = (x-1)(x-(-9))

y = (x-1)(x+9)

y = x² - x+ 9x - 9

y = x² + 8x -9

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Answer:

6.25

Step-by-step explanation:

c

Answer:

$6

Step-by-step explanation:

48÷8=6

keep the questions coming

The final equation would be: ∫[0,2] π(y²/4) dyπ/4 ∫[0,2] y² dyπ/4 × [y³/3] [0,2]π/4 × (8/3)π/6π/2

The volume of the solid generated in the given situation is π/2 cubic units.

The situation states that the region r bounded by the graphs of x=0, y=2x, and y=2 is revolved around the line.

We need to determine the volume of the solid generated.

We can find the volume by using the disk method.

The equation of the line is x=0. We will have to integrate concerning y. It can be observed that the region r is bound between the lines y = 0 and

y = 2.

We will integrate the area of the disks along the line of revolution (x = 0). The area of each disk is given by A=πr² where "r" is the radius of the disk. For the given situation,

the radius is x = y/2.

Substituting the value of the radius, the equation becomes (y/2)²A=π(y²/4)

The limits of integration are y = 0 and

y = 2.

We will substitute these limits in the above equation and integrate them. The final equation would be:

∫[0,2] π(y²/4) dyπ/4 ∫[0,2] y² dyπ/4 × [y³/3] [0,2]π/4 × (8/3)π/6π/2

The volume of the solid generated in the given situation is π/2 cubic units.

Given that, the region r bounded by the graphs of x=0,

y=2x, and

y=2 revolved around the line.

The given region r is shown below: graph{y=2x [-5, 5, -2.5, 2.5]}graph{y=2 [-5, 5, -2.5, 2.5]}graph{x=0 [-5, 5, -2.5, 2.5]}

The axis of revolution is x=0. For the given situation, we use the disk method to determine the volume of the solid generated. The equation of the line is x=0. We will have to integrate concerning y. It can be observed that the region r is bound between the lines y = 0 and

y = 2.

We will integrate the area of the disks along the line of revolution (x = 0).

The area of each disk is given by A=πr² where "r" is the radius of the disk.

For the given situation, the radius is x = y/2.

The limits of integration are y = 0 and

y = 2.

We will substitute these limits in the above equation and integrate them.

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the required equation is 5x - 6y + 5z = 7

Given that;

points : (1, 4,4) and (-4, 1,2).

mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]

⇒ midpoint : ( -3/2, 3/2, 3 )  

                       x₀    y₀    z₀

Direction vector n = [-4-(1)], [  1-4], [ 2-4]

⇒ Direction vector n = < -5, -3, -2 >

General equation plane : n(x-x₀, y-y₀, z-z₀) = 0

so we substitute

⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0

⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0

⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0

⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0

⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2

⇒ 5x - 6y + 5z = 7

Therefore, the required equation is 5x - 6y + 5z = 7

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Subtract the dessert from the total:

52.95 - 2.50 = 50.45

Now divide that by the number of people:

50.45/5 = 10.09

Each person would pay $10.09

She would pay 10.09 + 2.50 = 12.59

The sum of integers is: S = n(a + l)/2

Integer numbers are those without fractional or decimal parts. When there are fewer numbers to add, it is possible to determine the sum of integers using basic mathematics. However, we employ the sum of integers formula if we need to add multiple consecutive integers at once. Our computations are made easier, and the amount of time we spend adding is reduced.

The sum of an arithmetic sequence's n terms is what is meant by the sum of integers formula. The formula for the sum of integers is:

S = n(a + l)/2

where,

S = sum of the consecutive integers

n= number of integers

a= first term

l = last term

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The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

The recursive equations for the given two interacting population of hares and foxes are

h(t+1)=4h(t)-2f(t)

f(h+1)=h(t)+f(t)

for the given initial population in parts from a to c we need to create a close formula for h(t) and f(t)

h(t) = 100(2t+1)

f(t) = 100(2t-1)

h(t) = 200(2t+1)

f(t) = 100(2t-1)

h(t) = 300 + 200(2t+\((-1)^{t}\))

f(t) = 200 - 100\((-1)^{t}\)

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

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Answer:

A: 21 minutes

Step by step explanation:

If he loses 3 minutes everyday then it would be A because 7 days times 3 minutes he loses everyday equals 21 minutes.

Answer:

19

Step-by-step explanation: