find the zeros or x-intercepts (values of r and s) of a quadratic relation y=x^2-5x+6 by factoring using the sum and product method

Answers

B, D and E are proportional

A, C, and F are not proportional

y = 3+x .... not proportional

y = 1.6x .... proportional

y = 3/(4x) .... not proportional

y = x .... proportional

y = 12x .... proportional

y = 2x+1 ... not proportional

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Explanations:

Anything in the form y = k*x is a direct proportional equation. As x goes up, so does y. The same happens if x decreases, and we'll have y also decrease. They go up together or down together. This is where the "direct" comes from. Specifically they change the same amount each time (hence the term "proportional").

For something like y = 1.6x, we have k = 1.6

In the equation y = x, we have y = 1x in reality so k = 1 here.

Lastly, y = 12x has k = 12.

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The other equations are not in the form y = kx. Whenever we have y = mx+b, with b nonzero, then y = mx+b is not proportional. The value of b must be 0 for it to fit y = kx form. This rules out y = 2x+1 and y = 3+x or y = x+3.

The equation y = 3/(4x) is an inversely proportional equation in the form y = k/x. It cannot be written as y = kx. Note how x is in the denominator for y = 3/(4x) while the same can't be said for y = kx. Inversely proportional equations have x increase and y decrease, or vice versa. They go in opposite directions.

Answer:

           [tex]\bold{P(A) =\dfrac{11}{20}}[/tex]

Step-by-step explanation:

A - an occurrence that Steve encounters the green light

number of all counted ligths:    |Ω| = 20

number of counted green ligths:  |A| = 11

Probability that Steve encounters a green light on any given day:

[tex]P(A) = \dfrac{|A|}{|\Omega|}=\dfrac{11}{20}[/tex]

Answer:

4.625 gallons

Step-by-step explanation:

1. 11 pints plus 13 quarts is 18.5 quarts

2. 18.5 quarts is equal to 4.625 gallons

The number of gallons of ice cream he sold was equal to 4.625 gallons.

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Therefore suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

We need to find the number of gallons of ice cream he sold.

A dealer sold 13 quarts containers and 11 pint containers of ice cream in one day.

1. 11 pints plus 13 quarts is 18.5 quarts.

2. 18.5 quarts is equal to 4.625 gallons.

Hence, The number of gallons of ice cream he sold was equal to 4.625 gallons.

Learn more about unit price here:

https://brainly.com/question/945712

#SPJ2

Answer:

A

Step-by-step explanation:

We know that (15, 11) (which means x = 15, y = 11) is a solution to Line Q so therefore:

11 = 4/3 * 15 + (k + 1)

11 = 21 + k

k = -10

Answer:

-10 = k

Step-by-step explanation:

y = 4/3x + ( k+1)

We know a point on the line is ( 15,11)

Substitute this point into the equation

11 = 4/3(15) + (k+1)

11 = 20 + k+1

Combine terms

11 = 21+k

Subtract 21 from each side

11-21 = k

-10 = k

Answer:

243 m³

Step-by-step explanation:

The volume of a rectangular pyramid is given by:

[tex]V = \frac13lwh[/tex]

Where

l = length = 9m

w = width = 9m

h = height = 9m

so the volume is 1/3*9*9*9 = 243 m³

Answer:

243

Step-by-step explanation:

The formula for the volume of a square-based pyramid is

[tex]V=\frac{lwh}{3}[/tex]

[tex]l[/tex] = length

[tex]w[/tex] = width

[tex]h[/tex] = height

[tex]V=\frac{9 \times 9 \times 9}{3}[/tex]

[tex]V=\frac{729}{3}[/tex]

[tex]V=243[/tex]

The area is 243 cubic meters.

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The perpendicular line bisect the base of isosceles triangle.

Then,

9^2=y^2-x^2

81=324-243

81=81

So the correct answer is D

I Hope this will be helpful for you

Answer:

$96.00

Step-by-step explanation:

Perimeter formula, 2w+2l

2(23)+2(25)=96 feet

1$ per foot

96 feet,

so $96

Answer:

I think it 96.00

Step-by-step explanation:

Answer:

To find ? we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 50

The opposite is 25

So we have

sin ? = 25 / 50

sin ? = 1/2

? = sin-¹ 1/2

To find ? we use tan

tan ∅ = opposite / adjacent

From the question

the opposite is 8

the adjacent is 33

So we have

tan ? = 8/33

? = tan-¹ 8/33

? = 13.62

Hope this helps you

Answer:

255 pounds.

Step-by-step explanation:

We can set up a proportion.

1 pound / 1.18 euros = x pounds / 300.9 euros

1.18 * x = 1 * 300.9

1.18x = 300.9

x = 255

255 pounds.

Hope this helps!

Answer:

300.90 € = £ 255

Step-by-step explanation:

£ 1 = 1.18 €

So,

1 € = £ 1/1.18

=> 1 € = £ 0.847

Multiplying both sides by 300.90 for getting the exchange rate of 300.90 euros

=> 300.90 € = £ 0.847 * 300.90

=> 300.90 € = £ 255

Answer:

A and C

Step-by-step explanation:

The line is at 3, and no number is within reach except 3. So the answer is A and C.

Answer:

Step-by-step explanation:

25p = (25)(p)

50q = (25)(2q)

therefore

25p + 50q = (25)(p) + (25)(2q) = (25)(p + 2q)

Answer:

p + 2q = 1

Step-by-step explanation:

25(p + 2q) = 25

p + 2q = 1

Answer:  7.8 days

Step-by-step explanation:

Painter can get the job done in 15 days so gets [tex]\dfrac{1}{15}[/tex] of the job done in 1 day.

Coworker can get the job done in 10 days so gets [tex]\dfrac{1}{10}[/tex] of the job done in 1 day.

Together, they get [tex]\dfrac{1}{15}+\dfrac{1}{10}[/tex] of the job done in 1 day.

Painter worked for 3 days so completed [tex]\dfrac{1}{15}(3)=\dfrac{1}{5}[/tex] of the job.

That leaves a remaining of [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job to be completed.

Let x represent the number of days it will take them to work together.

Painter + Coworker = Together

[tex]\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}[/tex]

Multiply by 30 to eliminate the denominator:

[tex]\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)[/tex]

Simplify and solve for x:

    2x + 3x = 24

            5x = 24

              [tex]x=\dfrac{24}{5}[/tex]

              x = 4.8

Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.

So the total time to paint the building is 3 + 4.8 = 7.8

Answer:

1.ED5 LOL

Step-by-step explanation:

It's (8,-2), (5,-1), (2,0), (-1,1), (-4,2).  Just took it and suffered the fate of the wrong answer.

Answer:

C

Step-by-step explanation:

Answer:

$43.24

Step-by-step explanation:

First, find the amount of $ she deposited and spent separately.

She deposited 22 in her first week and then 38.5 on the next week. This is a total of $60.50.

The first week, she spent 7.27, then next week, 9.99. This means she spent a total of $17.26.

Second, subtract the total $ she spent from the amount she deposited.

$60.50 - $17.26 = $43.24

Answer:

she has $43.24 left in her bank account .

Answer:

x^4-5x^2y^2+ 4y^4 = (x^2-4y^2)(x^2-y^2)

Step-by-step explanation:

Here in this question, we are to resolve the given expression into factors

x^4-5x^2y^2+ 4y^4

That can be rewritten as;

x^4-x^2y^2-4x^2y^2+4y^4

= x^2(x^2-y^2)-4y^2(x^2-y^2)

= (x^2-4y^2)(x^2-y^2)

Answer:

If I'm correct she bought 5 pounds of coffee.

Step-by-step explanation:

$70 (gift card)

-$26.80 (remainder on g.c.)

= $43.20 ($ spent on money)

$43.20/ $8.64 = 5

(remainder)/ cost per lb. = lbs of coffee bought

Answer: She bought 5 pounds of coffee

Step-by-step explanation:

This situation can be represent by the equation

70 - 8.64 x = 26.80  where x is the number of coffee she bought.   solve for x

-70                   -70

-8.64x = -43.20

x = 5

Answer:

No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

We are given the measure of two angles in ∆XYZ, as 90 and 30 respectively. The 3rd angle can be known without being given. Since sum of angles in a triangle is 180°, the 3rd angle would be 180 - (90+30) = 60°.

Same applies to ∆TUV.

We only know the 3 angles of each triangle, but we are not given any of the side lengths. Therefore, we cannot make any congruency statement since the side lengths are unknown.

Answer:

15√3

Step-by-step explanation:

This is a 30-60-90 triangle, so in order to solve for v, we can multiply the short leg by √3, which we will get 15√3.

Answer:

v = 25.98

Step-by-step explanation:

You could do this a number of ways. Some are much longer than others. The shortest way is to use the tangent.

Formula

Tan(theta) = opposite / adjacent

Givens

Theta = 30o

Opposite = 15 km

Adjacent = x

Solution

tan(30) = 15 / v                       Multiply both sides by v

v*tan(30) = 15                         Divide by tan(30)

v = 15/tan(30)

tan(30) = 0.5774

v = 15 / 0.5774

v = 25.98

Answer:

3

Step-by-step explanation:

In Set A, the minimum is 4 and the maximum is 7 without X which would make the range 7 - 4 = 3 but we want the range to be 4, therefore X has to be 4 + 4 = 8. Unfortunately, this would then make the range of Set B 8 - 1 = 7 so X has to be the smallest number in Set A which would be 7 - 4 = 3.

Answer:

Ok, i cant drag the endpoints of the segment, but i can tell you how to do it.

First, we know that h(x) joins the points (1, -5) and (9, 1), then h(x) is a line:

h(x) = s*x + b

First, for a line that goes through the points (x1, y1) and (x2, y2), the slope will be:

s = (y2 -y1)/(x2 - x1)

Then in this case, the slope is:

s = (1 - (-5))/(9 - 1) = 0.75

Then we have

h(x) = 0.75*x + b

now, the value of b can be found as:

h(1) = -5 = 0.75*1 - b

b = - 5 - 0.75 = -5.75.

Then our equation is:

h(x) = 0.75*x - 5.75

Now, i gues you want to find the graph of:

y = h(-x)

Then our new function is:

g(x) = h(-x) =  -0.75*x - 5.75.

Now to find the points, we evaluate this function in the same values of x as before.

g(1) = -0.75*1 - 5,75 = -6,5

the point is (1, -6.5)

the second point is when x = 9.

g(9) = -0.75*9 - 5.75 = -12.5

The second point is (9, -12.5)

Answer:

(−6,7) (-1,-2)

Step-by-step explanation:

Khan

Answer: 0.28157

Step-by-step explanation:

Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75

Number of citizens are chosen: n= 10

Let x be the binomial variable that represents the number of citizens favor the building of the police substation.

Then, the probability that exactly 8 of them favor the building of the police substation will be :

[tex]P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2[/tex]

 [Using binomial probability function [tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]]

[tex]=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157[/tex]

Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157

Answer:

65

Step-by-step explanation:

The sum of the first 16 terms of an arithmetic progression (A.P) is 240

The sum of the next 4 terms is 220

The sum of n terms in an A.P is given by;

[tex]s_{n}[/tex] = n/2(2a + (n - 1)d)

240 = 8(2a + 15d) ... (i)

460 = 10(2a + 19d) .... (ii)

Simplifying this gives;

2a + 15d = 30 ... (i)

2a + 19d = 46 ... (ii)

Subtracting (i) from (ii) we get;

4d = 16

d (common difference) = 4

and a (first term) = (30 - 60)/ 2 = -15

The sequence upto 21 terms is here:

-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65

So the next term (21^st term) is 65.

Answer:  a₂₁ = 65

Step-by-step explanation:

The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.

[tex]a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\[/tex]

Let's find the 16th term (n = 16)

[tex]a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d[/tex]

Now let's find the sum of the first 16 terms. This will be Equation 1:

[tex]S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}[/tex]

************************************************************************************

Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:

[tex]a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d[/tex]

[tex]S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}[/tex]

*********************************************************************************************

Now we have a system of equations. Solve using the Elimination Method:

2a₁ + 15d = 30   → -1(2a₁ + 15d = 30)     →    -2a₁ - 15d = -30    

2a₁ + 35d = 110  →  1(2a₁ + 35d = 110)    →     2a₁ + 35d = 110  

                                                                             20d = 80

                                                                                  d = 4

Input d = 4 into one the equations to solve for a₁:

Equation 1: 2a₁ + 15d = 30

                  2a₁ + 15(4) = 30

                    2a₁ + 60 = 30

                             2a₁ = -30

                               a₁ = -15

Given a₁ = -15 and d = 4, we can find the next term (n = 21)

[tex]a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65[/tex]

Answer:

-95

Step-by-step explanation:

Answer: The Answer is C

Step-by-step explanation: I just took the quiz on ed and this is the correct answer.

Answer: C: the estimated amount of feed per day for the start of the farm

Step-by-step explanation: 100% on quiz

Answer:

625.

Step-by-step explanation:

(5+5×5÷5-5)⁵/5

=[ ( 5 + 25 / 5 - 5)^5] /  5

= [(5 + 5 - 5)^5] /  5

= [ (10 - 5)^5] /  5

= 5^5 / 5

= 5^4

= 625.

Answer:

625

Step-by-step explanation:

The rule is to do Parentheses/Brackets, then Exponents/Orders, followed by doing Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. The answer is 625

Answer:

y =2x

Step-by-step explanation:

Slope intercept form is

y= mx+b where m is the slope and b is the y intercept

y = 2x+0

y = 2x

Answer:

Step-by-step explanation:

e

Answer:

The answer is C.

Step-by-step explanation:

In order to find the solution of the linear equation, you have to find the coordinates where they intersect.

So according to the graph, both lines intersect at the coordinates of ( 0 , 1 ).

(Correct me if I am wrong)