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A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is: [tex]3x^2-15x+12[/tex]

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

For this case we have that the following function complies with the given conditions:

[tex]f(x)=3x^2-15x+12[/tex]

To prove it, let's find the roots of the polynomial:

[tex]3x^2-15x+12=0[/tex]

By doing common factor 3 we have:

[tex]3(x^2-5x+4)=0[/tex]

Factoring the second degree polynomial we have:

[tex]3(x-1)(x-4)=0[/tex]

Then, the solutions are:

Solution 1:

[tex]x-1=0 \ or \ x=1[/tex]

Solution 2:

[tex]x-4=0\ \ or \ x=4[/tex]

Hence A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:[tex]3x^2-15x+12[/tex]

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Answer:

f(x) = 3x² – 15x + 12

Step-by-step explanation:

I got it right on the unit test for edge

Answer:

im not really good at drawing but Can I ask a question can I help you with other questions?

Step-by-step explanation:

Step by step explanation :

Taking LCM in Left Hand Side

Now, By cross multiplying ,we get. ..

[tex]⇢5(x - 2) = 2(3 - x)[/tex]

[tex]⇢5x - 10 = 6 - 2x[/tex]

[tex]⇢5x + 2x = 6 + 10[/tex]

[tex]⇢7x = 16[/tex]

[tex]⇢ \boxed{ x = \frac{16}{7} }[/tex]

Answer:

x = 16/7

Step-by-step explanation:

Given

Solving

#1) Find the LCM.

#2) Multiply both sides by 10.

#3) Bring x terms to the left and numbers to the right.

Dan Hostetler purchases 2,000 shares of Ballon Synergy stock at $4.10 per share. Thus, The total cost of stock including the commission is $15917.

Stocks are types of security to shareholders that represent fractional ownership of equity in any organization.

Dan Hostetler purchases 2,000 shares of Ballon Synergy stock at $4.10 per share. He also purchased 500 shares of Matell Scientific at $26.76 per share.

We have a number of shares at $44.41 per share = 100

Number of shares at $19.08 per share = 600

Total number of shares = 700

Broker's charges per share = $0.04

Hence, The total cost of the stock including the commission

= Cost of stock + commission

= (100 × 44.41) + (600 × 19.08) + (700 × 0.04)

= 15,917

Thus, the total cost of stock including the commission is $15917.

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#SPJ1

Answer:

Figure D would be an 180 degree rotation of Figure A

Step-by-step explanation:

Figure B would have to be tilted to the right some more, and Figure C is all out of wack leaving Figure D

Answer:

Figure D

Step-by-step explanation:

From Figure A to B, it looks like a reflection (like a mirror) (over the y-axis)

From Figure A to C, it looks like a translation (5 units down) (x - 5, y)

From Figrue A to C, it looks like a rotation

Therefore, our final answer is Figure D

Hope this helps!

Answer:

87.375

Step-by-step explanation:

i think it that because you haft to do divison

Answer:

C ≈ 11.71 cm

Step-by-step explanation:

using the ratio arc  AC : circumference C = angle at centre of sector : 360°

[tex]\frac{AC}{C}[/tex] = [tex]\frac{123}{360}[/tex] , that is

[tex]\frac{4}{C}[/tex] = [tex]\frac{123}{360}[/tex] ( cross- multiply )

123 × C = 4 × 360 = 1440 ( divide both sides by 123 )

C = [tex]\frac{1440}{123}[/tex] ≈ 11.71 cm ( to the nearest hundredth )

Answer:

Step-by-step explanation:

A = l x w

l = length

w = width

Formula:

6 4/5 x 4 3/4

First, multiplying the integers:

6 x 4 = 24

Then you multiply the fractions(top x top and bottom times bottom):

4/5 x 3/4 = 12/20

Simplify:

12/20 = 3/5

Giving you 24 3/5

I hope this helps :)

Answer:

[tex]x = \frac{11}{2}[/tex]

Step-by-step explanation:

4+2 (x-1)=13

⇒ 2 (x - 1) = 13 - 4

⇒ 2 (x - 1) = 9

⇒ 2 x - 2 = 9

⇒ 2 x  = 9 + 2

⇒ 2 x  = 11

⇒  x  = 11/2

Answer:

see explanation

Step-by-step explanation:

(a)

the centre of the circle is at the midpoint of the endpoints.

using the midpoint formula

centre = ( [tex]\frac{-10+4}{2}[/tex] , [tex]\frac{-2+6}{2}[/tex] ) = ([tex]\frac{-6}{2}[/tex] , [tex]\frac{4}{2}[/tex] ) = (- 3, 2 )

(b)

the radius r is the distance from the centre to either of the endpoints

using the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = Q (4, 6 )

r = [tex]\sqrt{(4-(-3))^2+(6-2)^2}[/tex]

  = [tex]\sqrt{(4+3)^2+4^2}[/tex]

  = [tex]\sqrt{7^2+16}[/tex]

  = [tex]\sqrt{49+16}[/tex]

   = [tex]\sqrt{65}[/tex]

(c)

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius , then

(x - (- 3) )² + (y - 2)² = ([tex]\sqrt{65}[/tex] )² , that is

(x + 3)² + (y - 2)² = 65

Answer:

Step-by-step explanation:

a) Use midpoint formula to find the center.

[tex]\sf \boxed{Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]

P(-10 ,-2) ⇒x₁ = -10  & y₁ = -2

Q(4,6) ⇒ x₂=4   & y₂ = 6

[tex]\sf midpoint = \left(\dfrac{-10+4}{2},\dfrac{-2+6}{2}\right)[/tex]

            [tex]=\left(\dfrac{-6}{2},\dfrac{4}{2}\right)\\\\=\left(-3,2\right)[/tex]

b) To find the radius, use the distance formula

[tex]\boxed{distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Q(4,6)  & O(-3,2)

[tex]r=\sqrt{(-3-4)^2+(2-6)^{2}}\\\\=\sqrt{(-7)^{2}+(-4)^2}\\\\=\sqrt{49+16}\\\\= \sqrt{65}[/tex]

radius = √65

c) Equation of circle : (x - h)² +(y -k)² = r²

Where (h,k) is the coordinates of the center and r is the radius

(x -[-3])² + (y - 2)²= (√65)²

(x + 3)² + (y -2)² = 65

Step-by-step explanation:

find the egn of the line through (a.b)and perpendicular to the lime passing through (a.2b)and (b.2a)for a#b?

Answer:

what graph?

Step-by-step explanation:

The fact that Maria has decided to still put in more effort to get no grade lower than C shows that c. she is able to set and evaluate her goals.

Maria was able to set goals on the grades that she would like to earn throughtout her high school.

She was also able to evaluate her progress when she saw that she hadn't reached her overall goal. This then led to her taking even more lessons.

In conclusion, option C is correct.

Find out more on setting goals at https://brainly.com/question/24231566.

Answer: y≤−5

Step-by-step explanation:

Answer:

  533.3 mph

Step-by-step explanation:

You want the average round-trip speed if the speed to London was 480 mph and the return trip to Boston was 600 mph.

The average speed will be the total distance divided by the total time. The time is found by dividing the distance by the speed.

If the distance is d, the total time in hours is ...

  d/480 +d/600 = (3/800)d . . . . . hours

Then the average speed is ...

  2d/(3/800d) = 1600/3 ≈ 533.3 . . . . miles per hour

Alyssa's average speed on the round trip was 533.3 mph.

__

Additional comment

In the real world, eastbound speeds are usually faster than westbound speeds.

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Answer:

  (c)  6.00 M

Step-by-step explanation:

The given equation can be solved for the unknown concentration.

__

  [tex]m_iv_i=m_fv_f\\\\m_i(35.0\text{ ml})=(1.40\text{ M})(150.0\text{ ml})\\\\m_i=\dfrac{(1.40\text{ M})(150.0\text{ ml})}{35.0\text{ ml}}\\\\\boxed{m_i=6.00\text{ M}}[/tex]

The concentration of the stock solution is 6 M.

Answer: c- 6.00 m

Step-by-step explanation:

got it right on edge

Table of values

4 0

5 1

6 2

7 3

Answer:

5040 ways

Step-by-step explanation:

There will be 13 chairs altogether.

Since there are 7 girls who cannot sit together, the pattern will be alternate.

→ G, B, G, B, G, B, G, B, G, B, G, B, G

Total Ways

Answer:

$3

Step-by-step explanation:

If the soda was $4 and she spent a total of $28

then you do 28-4 to get the amount she spent on candy bars so 28-4 is 24 and divide 24 by 8 and you get 3

Answer:

12.25cm2

Step-by-step explanation:

Area of a square= S ×S

3 1/2 × 3 1/2 = 3.5×3.5 = 12.25

Step-by-step explanation:

a) 3×2×t=6t

b)500 years

For the local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of a population

N = number of observations of population

X = mean

μ = population mean

The 30-year average for July was 90°. The standard deviation for this average is 2.1°. Thus, the temperature lies in the range around of 90° in July.

Therefore, the range of the temperature is,

t = 90 - 2.1 = 87.9

t = 90 + 2.1 = 92.1

The last five summers recorded have an average of 93. 5° and the value of a is 5%. Thus, the reduction is,

t = 92 - (92 x 2.5/100)

t = 89.70

This value of temperature lies in the range of 87.9-92.1 degrees Celsius. Hence, the two averages are probably the same.

Hence, for the local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average. Option D is correct.

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Answer:

D, The average for the last five years fits with the 30-year average.

Step-by-step explanation:

edge

Answer:

30.51$

Step-by-step explanation:

15+12=27$

5% of 27$=1.35$

18% of 27=4.86

Do the math: 27+4.86-1.35=30.51

Answer:

20 Students chose bananas.

Step-by-step explanation:

You can see that the bananas take up 25% or 1/4 of the chart. To find 1/4 of a number find half of the number twice. Half of 80 is 40 and half of 40 is 20. So, 20 students chose bananas.

The weight of Jennifer's shelf if 1kg is equivalent to  2.20462 pounds  is 7.44kg

Fractions are written as the ratio of two integers

Given the following

Amount of pounds that Jennifer buuilt = 16.40 pounds

If 1 kg = 2.20462 pounds

Calcualate the measure of shelf in kg
Weight = 16.40/2.20462

Weight = 7.44kg

Hene the weight of Jennifer's shelf if 1kg is equivalent to  2.20462 pounds  is 7.44kg

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Answer:

the answer in the simplest form is 1/2 miles and if it's not in its simplest form is 6 /12 .hope it helps.

Step-by-step explanation:

Answer:

R.d. = 1/2 mile

Step-by-step explanation:

Facts of note

Solving

Answer:

70 if you walk directly across, 140 if you're running the bases

Step-by-step explanation:

So, if the distance between one is 70, than from home>first>second is 140 feet. Because it is a square, if you travel across the field from home directly to second, it is half that distance and only 70.

Answer:

1(-1/3)^8

Answer: 1/6561

hope this is better