A(2h, h), B(p, t), and C(2p, 3t) are three points on a straight line. B divides AC internally in the ratio 2 : 3. Express p in terms of t.

method 1.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

simplify:

[tex](x - 9)(x + 2) = 0[/tex]

so the answer is (D) x =9 or x = -2

method 2.

if

[tex] {a}^{2}x+ bx + c = 0[/tex]

[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

so

[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]

[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]

[tex]x = 9 \: \: \: \: or - 2[/tex]

The given pairs of lines have been identified as parallel, perpendicular lines or neither as explained below.

Two lines are parallel if they have the same slope (m), while they are perpendicular to each other if their slopes are negative reciprocal of each other.

The slope in a given equation of a line that is in slope-intercept form, y = mx + b, is represented as "m" in the equation.

1. y = 3x - 7 and y = 3x + 1 both have the same slope (m) of 3. They are parallel lines.

2. y = -2/5x + 3 and y = 2/5x + 8 both have the different slope (m), which are not negative reciprocal to each other. They are neither parallel nor perpendicular lines.

3. The slope of y = -1/4x is -1/4. The slope of y = 4x - 5 is 4. -1/4 is the negative reciprocal of 4. Therefore, the lines are perpendicular.

4. 2x + 7y = 28 can be rewritten as y = -2/7x + 4, the slope (m) is -2/7.

7x - 2y = 4 can be rewritten as y = 7/2x - 2, the slope (m) is 7/2.

-2/7 and 7/2 are negative reciprocals.

They are perpendicular lines.

5. The slope of y = -5x + 1 is -5.

x - 5y = 30 can be rewritten as y = 1/5x - 6, the slope is 1/5.

The lines are perpendicular.

6.  3x + 2y = 8 can be rewritten as y = -3/2x + 4, the slope (m) is -3/2.

2x + 3y = -12 can be rewritten as y = -2/3x - 4, the slope (m) is -2/3.

The lines are neither.

7. The slope of y = -4x - 1 is -4.

8x + 2y = 14 can be rewritten as y = -4x + 7, the slope is -4.

They are therefore parallel lines.

8. x + y = 7 can be rewritten as y = -x + 7, the slope (m) is -1.

x - y = 9 can be rewritten as y = x - 9, the slope (m) is 1.

The lines are perpendicular.

9. They have the same slope of 1/3. They are parallel lines.

10. They have different slopes that are not negative reciprocals, therefore, they are neither.

11. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.

12. They have the same slope of 3/4. They are parallel lines.

13. They have the same slope of 1. They are parallel lines.

14. Their slopes are -5/4 and 4/5. Therefore, they are perpendicular lines.

15. Their slopes are not negative reciprocals and are not the same, therefore, they are neither.

16. Their slopes are 1/2 and -2. Therefore, they are perpendicular lines.

17. They are both vertical lines, therefore they are neither.

18. x = 1 is a vertical line while y = -8 is a horizontal line that meets perpendicularly. Therefore, the lines are perpendicular.

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The equation of line is found as y = 9x - 16.

For the given question;

The passing points of the line are (6, 2) and (-3, 1).

The slope of line is calculated as;

slope = m = (y₂ - y₁)/(x₂ - x₁)

Where,

(x₁, y₁) =  (6, 2)

(x₂, y₂) = (-3, 1)

Put the values;

m = (-3 - 6)/(1 - 2)

m = -9/-1

m = 9

Then, the equation of line using slope intercept form is-

y - y₁ = m (x - x₁)

Put the values;

y - 2 = 9(x - 2)

Simplifying;

y -2 = 9x - 18

y = 9x - 16

Thus, the equation of line is found as y = 9x - 16.

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The complete question is -

What is the equation of the line that passes through P( 6,2) and S (- 3,1)?

Answer: 1/6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's solve for x.

x+7y=−39

Step 1: Add -7y to both sides.

x+7y+−7y=−39+−7y

x=−7y−39

Let's solve for y.

x+7y=−39

Step 1: Add -x to both sides.

x+7y+−x=−39+−x

7y=−x−39

Step 2: Divide both sides by 7.

7y/7 = −x−39/7

y= −1/7x+−39/7

Answer: 11.78

Step-by-step explanation:

We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.

This will be discussed in further detail below.

Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.

Generally, the equation for the problem is mathematically given as

f(x)=x^3-x^2-17 x-15

Therefore,  If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this

[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]

In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).

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Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since slope is 5, equation is y = 5x + c.

Substitute (2,-4) into the equation to find c.

-4 = 5(2) + c

c = -14

Hence equation of line is y = 5x - 14

Answer:

A = 2x0 = 0

B= 2x2 = 4

Similarity: they both pass the origin

Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one

Step-by-step explanation:

A = 2x0 = 0

B= 2x2 = 4

Similarity: they both pass the origin

Difference: They have different gradients: y=2x has a gradient of 2 and y=x has a gradient of one

The missing numbers here are given by 9×(80+7)=(9×80)+(9×7)

What are missing numbers?

Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places.

Here, given 9×87=(9×some number)+(another number×7)

Let x and y be the missing numbers.

9×87=(9×x)+(y×7)

We can write 9×87=9×(80+7)

Using distributive property,

9×87=(9×80)+(9×7)

On comparing, we get x=80,y=9.

Hence, the missing numbers are 80, 9

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0.384  is the chance that joe has to pay the tab at least once by probability.

What is a math illustration of probability?

Every tuesday Joe has beer with 4 friends .

Each have unique token , and the person whose token is drawn pays the tab.

Since , there are Joe and 4 friends , so we have total of 5 persons.

Now, probability that Joe token will be drawn is =  1 / 5            { 1 (Favourable Outcome) \small / 5 (Total Outcome)  }

i.e there is 1/5  = 0.20 probability that Joe token will be drawn and he will pay the tab.

Over the next 3 weeks , we need to find the change that Joe pays the tab exactly one time.

Here we have n = 3 ( weeks ) , and probability of success is p = 0.20

i.e probability that Joe will pay tab (Success)  is p = 0.20  and probability that Joe will not pay tab ( failure ) is 1-p = 0.80.

So we can model it by binomial distribution , as we have only two outcome which are i) Joe pays the tab , ii) Joe do not pay tab.

X ~ B(n=3 , p =0.20)

We need to find P(X=1) , i.e exactly one time Joe pays the tab .

Since, we have approximate that X follows binomial distribution , so we have

f(x) = P(X=x) = \small \binom{n}{x}p^x(1-p)^{n-x}

Hence

  P(X=1) = ( n  1 ) p¹ ( 1 - p)ⁿ⁻¹

             = ( 3  1 ) 0.2¹ ( 1 - 0.2)³⁻¹

             =  3 * 0.2 * 0.8²

              = 0.384

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The $150 monthly payment on the $3,482.46 credit card loan at 1.55% monthly interest rate gives the number of fewer months it would take to repay the loan if the monthly payment is $200 as 10 months

A monthly interest rate is obtained from an annual interest rate by dividing it by 12.

The monthly payment formula is presented as follows;

[tex] \displaystyle{M = \frac{P \cdot r \cdot (1 + r)^{n} }{ (1 + r)^{n} - 1}} [/tex]

Where;

M = The monthly payments = $150

P = The loan amount = $3,482.46

r = The monthly interest rate = 1.55% = 0.0155

n = The number of periods (monthly payments) = 30

When the monthly payment, M = $150, it takes the career councilor approximately 30 months for the debt to be repaid.

When the monthly payment, M = $200, we have;

[tex]\displaystyle{200 \approx \frac{3482.46 \times 0.0155 \times (1 + 0.0155)^{n} }{ (1 + 0.0155)^{n} - 1}} [/tex]

Which gives;

[tex] \displaystyle{200 \times ((1 + 0.0155)^{n} - 1)= 3482.76 \times 0.0155 \times (1 + 0.0155)^{n}} [/tex]

[tex] \displaystyle{200 \times (1.0155)^{n} - 200 = 53.98278 \times (1.0155)^{n}} [/tex]

[tex]\displaystyle{ 146.017 \times (1.0155)^{n} = 200 }[/tex]

n•ln(1.0155) ≈ ln(1.3697)

[tex] n = \frac{ln(1.3697)}{ln(1.0155)} \approx 20.45[/tex]

The number of months it will take to pay back the loan using a monthly payment of $200 is therefore approximately 20 months

The number of fewer months it takes to repay the loan is therefore;

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Answer:

4 seconds

Step-by-step explanation:

Given equation:

[tex]y=256-16x^2[/tex]

where:

The penny reaches the ground when the height is zero, so when y = 0.

Substitute y = 0 into the given equation and solve for x:

[tex]\begin{aligned}y&=256-16x^2\\y=0 \implies 0&=256-16x^2\\0+16x^2&=256-16x^2+16x^2\\16x^2&=256\\\dfrac{16x^2}{16}&=\dfrac{256}{16}\\x^2&=16\\\sqrt{x^2}&=\sqrt{16}\\x&=\pm4\end{aligned}[/tex]

As time is positive, x = 4 only.

Therefore, it takes 4 seconds for the penny to reach the ground.

From the given linear function, we have that:

A. The function is constant on the following interval: B.2 ≤ x ≤ 5.

B. The function is increasing on the following interval: A.0 ≤ x ≤ 2.

C. The function is decreasing the fastest on the following interval: D.5 ≤ x ≤ 6.

D. The justification for the previous item is: D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.

A function is constant when it's graph is an horizontal line, hence in this problem the function is constant for two intervals.

Hence, in item A, option B is correct.

A function is increasing on the intervals that y is increasing while x increases, that is, the function is moving right and up.

Hence, in item B, option A is correct.

A function is decreasing on the intervals that y is decreasing while x increases, that is, the function is moving right and down.

The decrease is faster when the division of the change in the output by the change in the input has the lower value(greater absolute negative).

Hence:

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The reflection of the coordinate (-3, 4) over the y-axis is (3, 4).

The Y-coordinates do not change when a point is reflected across the Y-axis. However, the X-coordinates are changed into their opposite signs.

Given the coordinates of the triangles RST as shown below;

R = (-3, 4)

S = (-1, -4)

T = (-4, -2)

If (x, y) for instance is reflected over the y-axis, the resulting coordinate will be (-x, y). Similarly, if the coordinate R (-3, 4) is reflected over the x-axis, the resulting coordinate point will be (3, 4)

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The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.

Hence, The function has a minimum if the x2 coefficient is positive. If it is negative, the function has reached its limit. If you have the function 2x2+3x-5, for example, the function has a minimum because the x2 coefficient, 2, is positive. Divide the x term coefficient by twice the x2 term coefficient.

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Zach's score, Z, and Nathan's score, N, are related by the formula

2Z-11=N.

This is further explained below.

Generally, Assume Nathan has a score of N and Zach has a score of Z.

Zach's score is 11 points higher than Nathan's.

It implies,

N equals twice of Z minus 11.

We may format it as follows:

2Z - 11 = N

There are now four possible outcomes for these two brothers' scores:

Zach's score will be determined using algebraic formulas if Nathan's score is 81.

2Z - 11 = 81

2Z = 92

Z = 46

Zach's score will be 61 if Nathan receives a score of 111.

Zach's score will be 121 if Nathan's score is 231 or higher.

Zach's score will be 456 if Nathan's score is 901.

The formula 2Z - 11 = Z is a rule that connects Nathan's and Zach's scores.

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The value of the variables 'x' in the equation is 0. 32

Algebraic expressions can be defined as expressions consisting of constants, factors, coefficients, variables as well as terms.

They are also composed of certain mathematical operations such as;

Given the expression;

2.54 - x + 12 = 21 - 42.5x + 7

To determine the value of x, we have to follow the following steps;

collect like terms

-x + 42. 5x = 21 + 7 - 12 - 2. 54

Add or subtract like terms

41. 5x = 13. 46

Make 'x' the subject of formula by dividing both sides by the coefficient of x

x = 13. 46/41. 5

Divide the values

x = 0. 32

Hence, the value of x is 0. 32

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Using algebraic expression and equation, he invested $2000 in fund b.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Let x = amount he invested in fund b

If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

Solving for x,

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

$60 + 0.07x = $120 + 0.04x

0.07x - 0.04x = $120 - $60

0.03x = $60

x = $2000

amount he invested in fund b = $2000

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Answer:

0.003, 0.03, 0.303, 0.383, 3.03, 33.03

Step-by-step explanation:

Value of x [tex]\frac{36}{5}[/tex]

value of m∠3 = [tex]\frac{462}{5}[/tex]

When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.

Given Data

m∠3 = 17x - 30

m∠6 = 12x +6

Angle pair - exterior alternate angle

For the value of x,

17x - 30 = 12x + 6

17x - 12x = 6 + 30

5x = 36

x = [tex]\frac{36}{5}[/tex]

For m∠3,

17x - 30

Equating value of x,

17([tex]\frac{36}{5}[/tex]) - 30

[tex]\frac{612-150}{5}[/tex]

[tex]\frac{462}{5}[/tex]

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Answer:

 (7 x 10) + (1 x 1) + (0/10) + (4/100)

70 + 1 + 0.04

70 + 1 + 4/100

Step-by-step explanation:

Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!

Answer:

Step-by-step explanation:

855555555555fhhhhhhhhhhhhhhhhg6

Answer:

g(3) = 9

Step-by-step explanation:

replace 3 in x

g(3) = 2(3) +3 = 6 + 3 = 9

Hope this helps

Answer:

3.3⁷

Step-by-step explanation:

To make a scientific notation the whole number must be more than 1 and less that 9.9 repeating. To do this, move the decimal however many times it takes to make the whole number (the number before the decimal) more than one and less that 9.9 repeating. For the number 33,900,000, the decimal must be moved 7 times, which is why I added the 7 exponent. Also when making a number into a scientific notation, be sure to add the number after the whole number, placing it after the decimal.

We can check this using Pythagoras' theorem.

Explain Pythagoras' theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It asserts that the area of the square with the hypotenuse (the side opposite the right angle) equals the sum of the areas of the squares with the other two sides. This theorem may be expressed as an equation linking the lengths of the legs a, b, and the hypotenuse c, which is known as the Pythagorean equation: a² + b² = c²

According to Pythagoras' theorem, as we see a² + b² = c²

6² + 8² = 10², so the photo frame is still a rectangle.

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The new workshop can produce as many as 180 toys each year compared to the old workshop

The approximation of numbers is the estimates of the said number.

This means that the approximation of a number is close to the said number, but it has a slight different value

The given parameters are:

Old capacity = 22,912,546,992 toys per year

New capacity = 4,134,232,638,937 toys per year

The approximate number of times is calculated as

Number of times = New capacity/Old capacity

Substitute the known values in the above equation

So, we have

Number of times = 4,134,232,638,937 toys per year/22,912,546,992 toys per year

Remove the units

So, we have

Number of times = 4,134,232,638,937/22,912,546,992

Evaluate the quotient

So, we have

Number of times = 180.435315217

Approximate

Number of times = 180

Hence. the approximate number of times is 180

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It will take 11 days to place all of the 100 tiles needed to finish the floor.

The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.

Given Data

She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.

Points are:

(1,5) (4,35)

Slope = [tex]\frac{30}{3}[/tex]

Slope = 10

y - y₁ = m(x -x₁)

y - 5 = m(x- 1)

For 100, it will need,

100 - 35 = 10(x-4)

65 = 10x - 40

105 = 10x

x = 10.5

It will take 11 days to place all of the 100 tiles needed to finish the floor.

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