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3 years ago

What are the x-intercepts of the graph of the equation above?

Mathematics

2 answers:

julsineya [31]3 years ago

6 0

Answer: Option B.

Step-by-step explanation:

The graph of the quadratic equation is a parabola.

The parabola intercepts the x-axis when $y=0$ .

Then, you need to substitute $y=0$ into the equation:

$y=x^2+9x+18\\0=x^2+9x+18$

Factor the quadratic equation: find two number that when you add them you get 9 and when you multiply them you get 18. In this case these numbers are 6 and 3. Then:

$0=(x+6)(x+3)\\\\x_1=-6\\x_2=-3$

Therefore, the x-intercepts are:

(-3,0) and (-6,0)

VLD [36.1K]3 years ago

3 0

Answer:

B. (-3, 0) and (-6,0)

Step-by-step explanation:

x intercept when y = 0

so x^2 + 9x + 18 = 0

Factor

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

x+6 = 0; x = -6

x+3 = 0; x = -3

Answer

B. (-3, 0) and (-6,0)

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Guys, determine the equation of each line, given the information below:

KIM [24]

Answer:

The equation is;

4y = 7x + 2

Step-by-step explanation:

The general equation of a straight line is;

y = mx + b

where m is the slope and b is the y-intercept

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

(x1,y1) = (2,3)

(x2,y2) = (-2,-4)

m = (-4-3)/(-2-2) = -7/-4 = 7/4

So we have the equation as;

y = 7x/4 + b

get the value of b, we will substitute any of the points (let us use 2,3)

We simply substitute 2 for x and 3 for y

We have this as:

3= 7(2)/4 + b

3 = 7/2 + b

b = 3-7/2 = -1/2

So we have the equation as;

y = 7x/4 + 1/2

multiply through by 4

4y = 7x + 2

3 0

3 years ago

A pyramid with a square base is cut by a plane that is parallel to its base and is 2 units from the base. The surface area of th

icang [17]

Answer:

6.83 units

Step-by-step explanation:

Let the height of the original pyramid be represented by h. Then the cut off top has a height of (h -2). The scale factor for the area is the square of the scale factor for height, so we have ...

(height ratio)^2 = 1/2

((h -2)/h)^2 = 1/2

(h -2)√2 = h . . . . . . square root; multiply by h√2

h(√2 -1) = 2√2 . . . . add 2√2 -h

h = (2√2)/(√2 -1) ≈ 6.8284 . . . units

The altitude of the original pyramid is about 6.83 units.

7 0

2 years ago

Nine minus the quotient of two and a number x

Dennis_Churaev [7]

9-2/x is the equation

7 0

3 years ago

Four plumbers estimated the length of the radius of a cylindrical pipe. The estimates made by

o-na [289]

Answer:

B. $\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}$

Step-by-step explanation:

The question is not properly presented. See attachment for proper presentation of question

From the attachment, we have that:

$W = \frac{3}{25}$

$X = \frac{\sqrt{3}}{11}$

$Y = \frac{9}{100}$

$Z = \frac{\pi}{24}$

Required

Order from greatest to least

First, we need to simplify each of the given expression (in decimals)

$W = \frac{3}{25}$

$W = 0.12$

$X = \frac{\sqrt{3}}{11}$

Take square root of 3

$X = \frac{1.73205080757}{11}$

$X = 0.15745916432$

$X = 0.16$ --- approximated

$Y = \frac{9}{100}$

$Y = 0.09$

$Z = \frac{\pi}{24}$

Take π as 3.14

$Z = \frac{3.14}{24}$

$Z = 0.13083333333$

$Z = 0.13$ --- approximated

List out the results, we have:

$W = 0.12$ $X = 0.16$ $Y = 0.09$ $Z = 0.13$

Order from greatest to least, we have:

$X = 0.16$ $Z = 0.13$ $W = 0.12$ $Y = 0.09$

Hence, the order of arrangement is:

$X = \frac{\sqrt{3}}{11}$ $Z = \frac{\pi}{24}$ $W = \frac{3}{25}$ $Y = \frac{9}{100}$

i.e.

$\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}$

6 0

3 years ago

Jay wants to make a box, with no lid (or top), out of a 10" x 6" rectangular piece of cardboard. If Jay cuts squares with dimens

LiRa [457]

Answer:

a. $V(x)=x(10-2x)(6-2x)$

b. $S(x)=4(15-x^2)$

Step-by-step explanation:

Dimensions of rectangular piece of cardboard= $10\times 6$

According to question

Length of box,l=10-2x

Breadth of box,b=6-2x

Height of box,h=x

Volume of box= $l\times b\times h$

Substitute the values in the formula

Volume of box= $x(10-2x)(6-2x)$

$V(x)=x(10-2x)(6-2x)$

b.Surface area of box= $2(b+l)h+lb$

Because the box has no lid

Substitute the values in the formula

Surface area of box= $2(10-2x+6-2x)x+(10-2x)(6-2x)$

Surface area of box= $2(16-4x)x+60-20x-12x+4x^2$

Surface area of box= $32x-8x^2+60-32x+4x^2$

Surface area of box= $60-4x^2=4(15-x^2)$

Surface area of box, S(x)= $4(15-x^2)$

4 0

3 years ago