(15, 2); perpendicular to 5x - y = 2
(a) Write the equation of the line in slope-intercept form.
(b) Write the equation of the line in standard form.

a = 1st zero or root of the quadratic

b = 2nd zero or root of the quadratic

[tex]x^2-8x+k=0\implies (x-a)(x-b)=0\implies x= \begin{cases} a\\ b \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -ax-bx=-8x\implies -a-b=-8\implies -b=a-8\implies b=8-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{3a+4b=29}\qquad \implies \qquad \stackrel{\textit{substituting from above}}{3a+4(8-a)~~ = ~~29}\implies 3a+32-4a=29 \\\\\\ -a+32=29\implies 32=a+29\implies \boxed{3=a}\hspace{5em}\stackrel{ 8~~ - ~~3 }{\boxed{b=5}}[/tex]

[tex]~\dotfill\\\\ (x-3)(x-5)=0\implies x^2-8x+\stackrel{ \textit{\LARGE k} }{15}=0[/tex]

Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.

Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.

One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.

The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.

Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.

In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.

Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.

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Answer:

24 cars are green

Step-by-step explanation:

We know

Amir notices that 3 out of every 50 cars that pass by his window are green.

So, the ratio is 3:47

To get from 50 to 400, we time 8.

If he observes 400 cars, what is the best estimate of how many will be green?

We take

3 x 8 = 24 cars are green

So, there will be 24 cars that are green.

The initial investment cost using the equity method would be:

Investment account balance + Phillips' share of retained earnings = Initial investment cost = $54,000 + $10,400 = $64,400

Fair Value Method:

The cumulative increase in fair value over the three years would be:

$2,000 + $2,000 + $2,000 = $6,000

Therefore, the initial investment cost would be:  

$54,000 - $6,000 = $48,000

Equity Method:

By the equity method, Phillips would have recorded its share of Jones Bag's earnings each year, as well as its share of dividends received. Phillips' share of Jones Bag's earnings and dividends would be based on its 40% ownership interest.

Phillips' share of Jones Bag's earnings and dividends would be as following:

Year Earnings Dividends

20X1 $3,200 $6,000

20X2 $4,800 $4,000

20X3 $8,000 $4,000

$40,000 - $14,000 = $26,000

Phillips' share of retained earnings would be 40% of $26,000, or $10,400.

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Answer:

5x + y = 17

Step-by-step explanation:

y -2 = -5(x -3)

y-2 = -5x + 15  Add 5x to both sides

5x + y - 2 = 5x - 5x + 15

5x + y - 2 = 15   Add 2 to both sides

5x + y + 2 - 2 = 15 + 2

5x + y = 17

The maximum number of hours is 1.6 hours and the minimum  number of hours is 1.6 hours.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a plane is flying at a speed of 175 miles per hour.

The distance covered by the pilot, d = 250 ± 25 miles

We know that, speed = Distance/Time

The equation for the maximum number of hours is given as;

175 =(250+25)/t

t=275/175

t=1.6 hours

The equation for the minimum number of hours is given as;

175 =(250-25)/t

175=225/t

t=225/175

t=1.3 hours

Therefore, the maximum number of hours is 1.6 hours and the minimum  number of hours is 1.6 hours.

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The required measurement of the ingredient has been shown below for half a batch of cookies.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
When making 1/2 a batch of the cookie recipe, you will need to halve the amount of each ingredient.

Here is the list of ingredients for half a batch:

1 7/8 cups flour

5/8 cup brown sugar

1 egg

1/8 teaspoon salt

1/6 teaspoon baking soda

5/8 cup butter

3/4 cup white sugar

Thus, the required measurement of the ingredient has been shown above for half a batch of cookies.

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a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105

Total number of cards =52

No. of cards for each suit =13

Total types of four suit =4 (heart, spades, diamonds, clubs)

Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways

a) number of ways choosing four cards of the same suit

= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]

= [tex]4 \times ^{13}C_4\\[/tex]

= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]

=2860 ways

Probability that all four are the same suit is 2860/270,725 = 0.0106

b) Number of ways all four cards are red

=[tex]^{26}C_4[/tex]

= 4,950 ways

Probability that all four are red = 4950/270,725 =0.055

c)  Number of ways each card has a different suit

=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]

= 28,561 ways

Probability each has a different suit is 28561/270725 = 0.105

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The approximate cost of 5-hour trip if the price of fuel is R78 per liter by finding the average speed is R3000.68.

To find the the total distance travelled by the car in 5 hours at an average speed of 100 km/h is:

Distance = Speed x Time

Distance = 100 km/h x 5 h

Distance = 500 km

The total amount of fuel consumed during the trip is:

Fuel consumed = Distance / Fuel efficiency

Fuel consumed = 500 km / 13 km/l

Fuel consumed = 38.46 liters (rounded to two decimal places)

The cost of the fuel consumed during the trip is:

Cost of fuel = Fuel consumed x Price per liter

Cost of fuel = 38.46 liters x R78/liter

Cost of fuel = R3000.68 (rounded to two decimal places)

Therefore, the approximate cost of the 5-hour trip is R3000.68, assuming that the only cost incurred is for the fuel consumed during the trip.

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Variable y in equilateral 60°, Thus correct option is C) 60°.

An equilateral triangle is one with equal-sized sides on all three sides and angles that can all reach a maximum of 60 degrees. An equilateral triangle is a triangle with three equal sides, also referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a special case of an isosceles triangle. Three equal angles of 60 degrees also make up an equilateral triangle.

The sum of all the angles in a triangle is 180.

It is given that the triangle ABC is an equilateral triangle.

So ∠A+∠B+∠C =180°

∠A=B=∠C

3∠A=180°

∠A=60°

Therefore y in ΔABC is C) 60°

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The equation -13x+12-(-13x+12)-13x+12 = -13x+12   is equivalent to the given expression that is -13x+12.

10x^2 - 23x + 12 = (5x - 3)(2x - 4) = 0

So the solutions to the equation are x = 3/5 or x = 2.

Therefore, this expression is not equivalent to -23x + 12 for all values of x.

10x^2 - 7x - 12 = 0 can be factored as (2x - 3)(5x + 4) = 0.

So the solutions to the equation are x = 3/2 or x = -4/5.

Therefore, this expression is not equivalent to -7x - 12 for all values of x.

-13x+12-(-13x+12)-13x+12  = -13x+12

-13x+12  = -13x+12

This expression is equivalent to -13x+12 .

7x^2 - 23x - 77 = (7x + 11)(x - 7) = 0

So the solutions to the equation are x = -11/7 or x = 7.

Therefore, this expression is not equivalent to -23x - 7 for all value x.

The given expressions of each case are not equivalent to the given equations for all values of x, except −13x+12-(-13x+12)-13x+12  = -13x+12 which is equivalent to -13x+12 .

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______The given question is incorrect, the correct question is given below:

An expression is given on equation

Which expression is equivalent to the given expression of each case

?

A

10x2−23x+1210x^2-23x+1210x = −23x+12

B

10x2−7x−1210x^2-7x-1210x = −7x−12

C

−13x+12-(-13x+12)-13x+12 = -13x+12

D

7x2−23x−77x^2-23x-77x = −23x−7

Answer:

110°

Step-by-step explanation:

]%}}%¶¢{^[€{¢¶¢¶€¶

Answer: 110˚

Step-by-step explanation:

Complementary angles have a sum of 90˚

With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚

Supplementary angles have a sum of 180˚

With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚

∴ Measure of angle C = 110˚

Angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let the triangle be ABC.

The angle A is 27 degrees.

The angle B is 75 degrees,

We need to find the angle of C

From Angle sum property the sum of three angles is 180 degrees.

∠A+∠B+∠C=180

27+75+∠C=180

102+∠C=180

∠C=78 degrees.

Hence, angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.

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Complete Question below:

In Triangle ABC, angle A is 27 degrees, angle B is 75 degrees then the angle C?.

Answer:

X=0

Y=4

Step-by-step explanation:

4X+2y-8=0

2y=4x+8

y=2x+4

Substituting y in the equation

4x+2(2x+4)-8=0

4x+4x+8-8=0

8x=0

X=0

Substituting in equation y=2x+4

y=2(0)+4

Y=4

The table to explain the equation will be:

x (minutes) y (altitude, in feet) Worked-out equation

0                          300                 -10x + 300 = 300

5                              250                   -10x + 300 = 250

8                         220                         -10x + 300 = 220

10                         200                   -10x + 300 = 200    

30                     0                         -10x + 300 = -0

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario

I used the equation y = -10x + 300 to find the altitude of the airplane for each x value.

The altitude after 5 minutes is 250 feet and 0 after 30 minutes.

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The value of x in the triangle is 8 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, the sides x of the triangle can be found using proportion as follows:

x / x + 8 = x + 8 / 32

cross multiply

32x = (x + 8)(x + 8)

32x = x² + 8x + 8x + 64

x² + 16x - 32x + 64 = 0

x² - 16x + 64 = 0

Therefore,

x² - 16x + 64 = 0

x² - 8x - 8x + 64 = 0

x(x - 8) - 8(x - 8) = 0

(x - 8)(x - 8) = 0

Therefore,

x = 8

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There is no real solution to the given equation s = 4 + sqrt(s+2) with value of s = 2, s = 7, s = 2 or s = 7.

To solve the equation:

s = 4 + sqrt(s+2)

We can start by isolating the square root term on one side:

s - 4 = sqrt(s+2)

Then, we can square both sides to eliminate the square root:

(s - 4)^2 = s + 2

Expanding the left side:

s^2 - 8s + 16 = s + 2

Bringing all terms to one side:

s^2 - 9s + 14 = 0

We can solve for s using the quadratic formula:

s = (9 ± sqrt(9^2 - 4(1)(14))) / 2(1)

s = (9 ± sqrt(49)) / 2

s = (9 ± 7) / 2

So the two possible solutions are:

s = 8/2 = 4

s = 2/2 = 1

However, we need to check if these solutions satisfy the original equation.

If we plug s=4 into the equation, we get:

4 = 4 + sqrt(4+2)

4 = 4 + sqrt(6)

This is not true, since the right-hand side is greater than the left-hand side.

If we plug s=1 into the equation, we get:

1 = 4 + sqrt(1+2)

1 = 4 + sqrt(3)

This is also not true.

Therefore, there is no real solution to the equation s = 4 + sqrt(s+2).

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Answer:

B

Step-by-step explanation:

Answer:

3y(y + 4)

Explanation:

[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]

The mentioned  scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.

The distance covered by the object is equal to the  product of the speed of object and the time required for it.

Distance = Time x speed

Firework A :

D = 360xt - - - (1)

Firework B:

D = 280x(0.25) + 280xt

D= 70 + 280xt - - - (2)

Equate equation (1) and (2) :

360t = 280t + 70

Collect like terms

360t - 280t = 70

80t = 70

t = 70/80

t = 0.875 seconds

0.875 + 0.25 = 1.125 seconds

Hence, the fireworks will explode after 1.125 seconds of launching Firework B.

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The cost of one plum in pence is 9p. The cost of 1 lime in pence is 12p.

Comparing the cost plum is cheaper.

The cost of 1 plum can be found by dividing the total cost of 7 plums by 7:

63 p / 7 = 9 p

Therefore, the cost of 1 plum is 9 p.

The cost of 1 lime can be found by dividing the total cost of 5 limes by 5:

60 p / 5 = 12 p

Therefore, the cost of 1 lime is 12 p.

Comparing the costs of 1 plum and 1 lime, we see that 1 plum costs 9 p and 1 lime costs 12 p. Therefore, the plum is cheaper per item.

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____The given question is incomplete, the complete question is given below:

A grocery shop sells plums and limes. 7 plums cost 63 p. 5  limes cost 60p a) Work out the cost of  1 plum, in pence (p).

b) Work out the cost of 1 lime, in pence (p).

c) Which type of fruit is cheaper per item?

The area of a four-sided regular pyramid, given the base edge and the side edge is 340 cm ² .

The area of a four-sided regular pyramid can be found by the formula :

= Area of base + 1 / 2 x perimeter of base x side edge

Area of base :

= 10 x 10

= 100 cm ²

Perimeter of base ;

= 10 + 10 + 10 + 10

= 40 cm

The area of the four-sided regular pyramid is;

= 100 + ( 1 / 2 x 40 x 12 )

= 340 cm ²

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A polygon with a sum of interior angles of 3960 has 22 sides.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180

where n is the number of sides of the polygon. This formula is derived from the fact that the total degree measure of a polygon is equal to the sum of the degree measures of its interior angles. In a polygon with n sides, there are n angles, each measuring 180 degrees. So the total degree measure of a polygon with n sides is n * 180.

Now, if we subtract the degree measures of two angles, we are left with the sum of the degree measures of the remaining n-2 angles. This is why the formula for the sum of the interior angles of a polygon is given as (n-2) * 180.

To find the number of sides of a polygon given its sum of interior angles, we can rearrange the formula as follows:

n = (Sum of interior angles / 180) + 2

So, if the sum of the interior angles is given as 3960, we can plug that into the formula:

n = (3960 / 180) + 2

n = 22

Therefore, a polygon with a sum of interior angles of 3960 has 22 sides.

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How many sides does a polygon have if the sum of the interior angles is 3960?

The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.

The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.

Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,

there are 2^3 or 8 possible combinations of heads and tails.

Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).

So, the probability of obtaining the same number of heads is 3/8 or 0.375.

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Answer:

Below

Step-by-step explanation:

1 + 19/10 + 8/100   = 1   +  1.9    + .08   =  2.98

Answer:

11 glasses

Step-by-step explanation:

There are 200 ml glasses and we have 2.21 liter of bottels. So first of all covert liter into ml so we get 2210 ml of coca cola.now divide 2210 by 200 so we get 11 glasses

Answer:

51 stamps

Step-by-step explanation:

since salman's amount is going from 5 to 45 its being multiplied by nine. to keep the ratio true, you need to multiply the other two numbers by 9 too. Nathan then has 12 stamps and Gordon has 63. 63-12=51

Answer:

75%

Step-by-step explanation:

If you have a calculator, you can divide 39/52. If not,

39/52 = x/100

52x = 3900

x = 75

75/100 = 75%

Answer:

89

Step-by-step explanation:

903 - 814 =

= (900 + 3) - (800 + 14) =

= 900 + 3 - 800 - 14 = 100 - 11 =

= 89

Answer:

Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X

Step-by-step explanation:

Self-explanatory

Every value of y in Table A is 2.5 times  x value

and

every value of y in table B is 3 times x value

Answer:

a) y - 4 =3(x - 1)

b)  y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Step-by-step explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line