Write an equation for line ℓ

a = 4, b = -21, c = -18

to keep from getting "mixed up", evaluate the discriminant first ...

b² - 4ac = (-21)² - 4(4)(-18) = 729

sqrt(729) = 27

x = (21 +/- 27)/8

x = -3/4, x = 6

since the discriminant is a perfect square, the original quadratic will factor ...

4x² - 21x - 18 = 0

(4x + 3)(x - 6) = 0

x = -3/4, x = 6

Answer:729

Step-by-step explanation: Use the values of a, b and c to find the discriminant. Which is 729

Answer:

x = 52.5

Step-by-step explanation:

The triangle on the left has 2 congruent sides, thus is isosceles

The base angles of an isosceles triangle are also congruent, thus

x = [tex]\frac{180-75}{2}[/tex] = [tex]\frac{105}{2}[/tex] = 52.5

Answer:

definitely  b.

Step-by-step explanation:

Answer:

I'm just going with the person above me that the answer is B. Yes, he used systematic random sampling.

Step-by-step explanation:

Tell me if I'm wrong.

Answer:

The area of shaded region is: [tex]13x^2+6x-15[/tex]

Step-by-step explanation:

We can see in the diagram that

[tex]Length\ of\ gray\ rectangle = l_g = 3x+5\\Width\ of\ gray\ rectangle = w_g = 4x-3[/tex]

The area of rectangle is given by:

Area = Length * width

Now for gray rectangle

[tex]A_g = l_g * w_g\\= (3x+5)(4x-3)\\= 3x(4x-3)+5(4x-3)\\= 12x^2-9x+20x-15\\=12x^2+11x-15[/tex]

For White Rectangle:

[tex]Length = l = 5-x\\Width = w = x\\A_w = l * w\\A_w = (5-x)(x)\\= 5x-x^2[/tex]

Now,

The area of shaded region will be calculated by subtracting the area of white triangle from the gray triangle.

[tex]A_s = A_g - A_w\\= (12x^2+11x-15) - (5x-x^2)\\=12x^2+11x-15-5x+x^2\\=12x^2+x^2+11x-5x-15\\=13x^2+6x-15[/tex]

Hence,

The area of shaded region is: [tex]13x^2+6x-15[/tex]

Given:

Height of statue or liberty from the ground = 305 feet

Model is [tex]\dfrac{1}{100}[/tex] the actual size of the statue of liberty.

To find:

The height of the model of statue.

Solution:

According to the question,

Model =  [tex]\dfrac{1}{100}[/tex] of the actual size

        [tex]=\dfrac{1}{100}\times 305[/tex]

        [tex]=3.05[/tex]

Therefore, the height of the model of statue is 3.05 feet.

Answer:

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Step-by-step explanation:

Answer:

Step-by-step explanation

Answer:

It would equal to a negative

Step-by-step explanation:

Have a good day!

Answer:

negative

Step-by-step explanation:

-63 and -88 are negative

-63-88 is -151

Answer: f = 12.5

Step-by-step explanation:

[tex]f = \frac{25}{2} \\decimal form = 12.5\\ mixed fraction form 12 \frac{1}{2}[/tex]

Answer:

hindi ko alam yan ha ano

Answer:

the difference between numbers of sequence is 0.5 or 1/2

here,

the formula to find n terms is 0.5n+1.5

this may help you(:

Answer:

812

Step-by-step explanation:

Answer:812

Step-by-step explanation: multiply 4 by 203

Answer:81%  or .81

Step-by-step explanation:

81%  or .81

Explanation:

243 ÷ 300 = .81

Answer:

the answer is 81%

Step-by-step explanation:

i used google and an answer key

Answer:

Everything except the finding the midpoint

Step-by-step explanation:

If the question states the points of a shape, you can find the perimeter and the area of the polygon because you would know the dimensions and the lengths of each side, but in the options, it says the area of a rectangle, and it doesn't have to be a rectangle

You can find the equation of the circle, by finding the diameter of the circle and the radius. With the diameter, you would be able to find the centre of the circle and then you need to divide the diameter by two to get the radius.

For the midpoint, you use the midpoint formula. You just need to sub in the points into the formula and you would get the midpoint

When you are given two points on a graph (or worded problem), and it says that for every x number of km it uses y amount of gas and the question asks to find how much gas is needed in between these two points, you can do this. Find the distance between the two points and then use algebra to work out the amount of gas required

Answer:

12 z abd and also 097

Step-by-step explanation:

Answer:

15 to10

Step-by-step explanation:

Answer:

1. AB ~= DF

2. Definition of Congruent

3. Reflexive Property of Congruency

4 BD=BD

6. AB+BD=AD; DF+BD=BF

7. Substitution Property of Equality

8. Definition of Congruent

Step-by-step explanation:

1. The given always goes first, and that's the first reason, so AB ~= DF must be the first statement (that should be the congruency symbol).

2. The definition of congruent is that if they are congruent then they are equal. Since that statement made two congruent lines equal, it must be the definition.

3. The reflexive property means something is congruent to itself, and BDis BD, therefore it is the reflexive property.

4. Remember if something is congruent then it is equal.

6. The segment addition postulate states that if we are given two points on a line segment, then AB+AC=AC.

7. In this statement AD was substituted for DF+BD. This can be done because of AB=DF and BD=BD as aforementioned.

8. If two things are congruent then they are equal by definition of congruency.

Answer:

1. V = D/t => D=Vt. as V = 16mph

D = 16t

2. Prya has been riding for t+½ hours

3. Prya has gone 12(t+½) miles

4. When Prya and Han meet

16t = 12t +6

4t = 6

t = 3/2 hours

Answer:

c

Step-by-step explanation:

–2.24, 2, 2.24

The solution to the equation of the polynomial function [tex]x^3 - 5x + 5 = 2x^2 - 5[/tex] is (c) –2.24, 2, 2.24

The function is given as:

[tex]x^3 - 5x + 5 = 2x^2 - 5[/tex]

Split the function.

So, we have:

[tex]y = x^3 - 5x + 5[/tex]

[tex]y = 2x^2 - 5[/tex]

Using a graphing calculator, we have the x coordinate at the point o intersection of both equations to be

x = –2.24, 2, 2.24

Hence, the solution to the equation is (c) –2.24, 2, 2.24

Read more about system of equations at:

https://brainly.com/question/14323743

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[tex]5 {x}^{2} - 5x + 1 = 0[/tex]

[tex](x - \frac{5 + \sqrt{5} }{10} )(x - \frac{5 - \sqrt{5} }{10} ) = 0 \\ [/tex]

Thus :

[tex]x = \frac{5 + \sqrt{5} }{10} \\ [/tex]

[tex]x = \frac{5 - \sqrt{5} }{10} \\ [/tex]

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Answer:

-211

Step-by-step

Answer:

2+2+2+2=8-3=5

Step-by-step explanation:

so what about This

Answer:

it is 4x + -3 < 16

Answer:I think 57Step-by-step explanation:

Cuz its adding 2 every time then I just did 28 x 2 and added the extra. Does that make sense?

4 x 8 = 28

28 x 2 = 56

56 + 1 = 57

Answer:

Cameron found 23 quarters and 57 dimes.

Step-by-step explanation:

Let the number of quarters Cameron found = Q

And the number of dimes = D

Since, total number of coins were 80,

Q + D = 80 -----(1)

Total amount of the coins was $11.45,

0.1D + 0.25Q = 11.45

10D + 25Q = 1145

2D + 5Q = 229 -----(2)

Equation (1) multiplied by 2 then subtracted by equation (2),

(2D + 5Q) - 2(Q + D) = 229 - 2(80)

(2D - 2D) + (5Q - 2Q) = 229 - 160

3Q = 69

Q = 23

From equation (1),

23 + D = 80

D = 57

Cameron found 23 quarters and 57 dimes.

Answer:

(x - 1)(x^2 + x + 1)

Step-by-step explanation:

they said it was the answer.

Answer:

The answer is 25.

Step-by-step explanation:

hope this helps

Answer:

y + 1 = 6(x - 4)

Answer: y + 1 = 6(x - 4)

Answer: 12

Step-by-step explanation:

This is a direct proportion and we use the formula:

y = kx

If y = −4 when x=2, we need to find the constant of proportionality. This will be:

y = kx

-4 = 2k

k = -4/2

k = -2

To find y when x=−6 guess this:

y = kx

y = -2 × -6

y = 12

Hence, The value of y = 12 when x = -6.

Given that , Y varies directly with x .

If y=−4 when x=2,

Find y when x=−6.

According to the question,

This is a direct variation , y = kx

If,

y = −4  when x=2,

y = kx

-4 = 2k

[tex]k = \frac{-4}{2}[/tex]

k = -2

To find ;

y when x = −6

y = kx

y = (-2) (-6)

y = 12

Hence, The value of y = 12 when x = -6.

For more information about Direct variation click the link given below.

https://brainly.com/question/13977805

Answer:

"The relationship is proportional."

"The relationship is proportional."

"The equation of the line is y = -3x"

Step-by-step explanation:

First, a proportional relationship can be written as:

y = k*x

where k is called the constant of proportionality. (or the slope)

You can see that if we take x = 0, we have

y = k*0 = 0

Then this type of line always passes through the point (0, 0).

And in the graph you can see that this line does that, then:

"The relationship is proportional." is true.

We also can see that as x increases, the value of y decreases, this must imply that k is a negative number, then:

"The slope is negative." is true.

To find the value of the slope, we can take two points that belong to the line.

I will choose:

(0, 0) and (2, -6)

For the slope, we just take the quotient between:

Δy = -6 - 0 = -6  (the difference in the y-components)

Δx = 2 - 0 =  2   (the difference in the x-components)

the slope is:

k = Δy/Δx = -6/2 = -3

Then the slope is -3, and we can write the equation as:

y = -3*x

Then:

"The equation of the line is y = -3x" is true.