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PSYCHO15rus [73]
3 years ago
12

Using the Factor Theorem, which of the polynomial functions has the zeros 4,

Formula1" title="\sqrt7" alt="\sqrt7" align="absmiddle" class="latex-formula">, and -\sqrt{7\\}?
f (x) = x3 – 4x2 + 7x + 28
f (x) = x3 – 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x – 28
Mathematics
1 answer:
Serjik [45]3 years ago
8 0

Answer:

B

Step-by-step explanation:

According to the Factor Theorem, if (<em>x</em> - <em>a</em>) is a factor (where <em>a</em> is a zero) of the polynomial P(x), then P(a) must equal zero.

Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.

Testing each choice, we can see that only choice B is true. That is:

\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0  \end{aligned}

In conclusion, our answer is B.

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A line contains the points (4,2) and (0, -1).What is the equation of the line?
Lady bird [3.3K]

Find the slope:

y₂ - y₁ / x₂ - x₁

-1 - 2 / 0 - 4

-3 / -4

3/4

y = mx + b

y = 3/4x + b

Substitute any of the point's coordinate in the equation.

I'll pick (0,-1)

y = 3/4x + b

-1 = 3/4(0) + b

-1 = 0 + b

-1 = b

y-intercept = -1

y-intercept Equation:

y = 3/4x - 1

Point-slope form:

y - 2 = 3/4(x - 4)

Standard form:

-3/4x + y = -1

3 0
3 years ago
Read 2 more answers
Pls help I’m rlly confused. The question says “find the value of x using complementary angels” ty &lt;3
Arturiano [62]

Answer:

x=83. please look below for explanation. if anything isn't clear, please ask

Step-by-step explanation:

so complementary means adding up to 90 degrees in math. in this particular equation, you have to make sure that both (x-18) and 25 add up to 90.

if that other side is 25 degrees, the other side must be 65 because 90-25=65.

so now you have to set those equal to each other like this:

65 = (x-18)    now just solve for x

add the 18 to the other side. the -18 and +18 cancel.

x=83

so to test and to see if that is right, we can do

83-18 = 65

does 65+25 equal 90? yes

therefore, x=83

8 0
2 years ago
A cone has a slant height of a 26 cm and a radius of 10 cm what is the height of the cone
Vedmedyk [2.9K]

The height of the cone is 24 cm.

<h3>How is the slant height calculated?</h3>

The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.

Slant height(l)=26cm

Radius(r)=10cm

It is known that, l^{2}=r^{2}+h^{2}

Here, h is the height of the cone.

On substituting the values,

26^{2}= 10^{2}+h^{2}

\\676=100+h^{2}\\

h^{2}=676-100\\

h^{2}=576\\

h=\sqrt{576}\\

h=24

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7 0
2 years ago
1/8 of passengers of a train were children. if there were 40 children travelling in the train on a certain day, how many adults
lilavasa [31]

280 adults were there in the train.

What is linear equation definition and example?

  • The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
  • An example of linear equation is y=mx + b. noun. 20.
  • A polynomial equation of the first degree (such as x = 2y - 7)

Given,

      Total children are in the train = 40

     1/8  are children in train and no of children in train ,

      ∴ 1/8 × x = 40

     x = 40 × 8 ⇒ 320

The no of  passenger in train  = 320

in total passenger, 40 are children .

So, rest adults passengers are = 320 - 40 ⇒ 280

There fore, 280 adults were there in the train.

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7 0
2 years ago
2) The number of streetlights in a town is growing linearly. Four months ago (n = 0) there were 130 lights. Now (n = 4) there ar
IRINA_888 [86]

Answer:

Step-by-step explanation:

Since the number of streetlights in a town is growing linearly, the street lights are increasing in arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

For n = 0, T0 = 130, therefore,

130 = a + (0 - 1)d

130 = a - d - - - - - - - - - -1

For n = 4, T4 = 154, therefore,

154 = a + (4 - 1)

154 = a + 3d - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

- 24 = - 4d

d = - 24/- 4 = 6

Substituting d = 6 into equation 1, it becomes

130 = a - 6

a = 130 + 6 = 136

a) The explicit formula for the number of lights in n months is

Tn = 136 + 6(n - 1)

b) The number of months that it will take to reach 200 lights is

200 = 136 + 6(n - 1)

200 - 136 = 6(n - 1)

64 = 6(n - 1)

6n - 6 = 64

6n = 64 + 6 = 70

n = 70/6 = 11.66

Approximately 12 months

3 0
3 years ago
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