If a, b, and c are solutions to the
equation 3x3 – 25x2 - 50x = 0 and
a < b < c, evaluate 10c – 6a.

Answers

Answer 1

Answer:

[tex]\displaystyle 10c - 6a = 110[/tex]

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle 3x^3 - 25x^2 -50x = 0[/tex]

Where a, b, and c are solutions to the equation and where a < b < c, we want to determine the value of 10c - 6a.

To find the solutions of the equation, we can factor:

[tex]\displaystyle \begin{aligned} 3x^3 - 25x^2 -50x & = 0 \\ \\ x(3x^2 - 25x -50) & = 0 \\ \\ x(3x+5)(x-10) & = 0 \end{aligned}[/tex]

From the Zero Product Property:

[tex]\displaystyle x = 0 \text{ or } 3x + 5 = 0 \text{ or } x - 10 = 0[/tex]

Solve for each case:

[tex]\displaystyle x = 0 \text{ or } x = -\frac{5}{3} \text{ or } x = 10[/tex]

We can see that -5/3 < 0 < 10. Thus, a = -5/3, b = 0, and c = 10.

Therefore:

[tex]\displaystyle \begin{aligned} 10c - 6a & = 10(10) - 6\left(-\frac{5}{3}\right) \\ \\ &= 100 + 10 \\ \\ & = 110 \end{aligned}[/tex]


Related Questions

como buscar a una perzona a qui en brainly

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Answer:

can l

Step-by-step explanation:

can l? can l? can l~

escribe el enunciado de las siguientes expresiones algebraicas

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Answer:

la familia es cristiana por algebraicas

If a rectangle has a length of 12 and width of 8 then its area is 96. This rectangle has an area of 96. Therefore it has a length of 12 and a width of 8. Valid or invalid

Answers

Answer: Valid

8 * 12 = 96

Answer:

The answer is invalid

Step-by-step explanation:

Choose Invalid .

You welcome

HELP ITSTHE LAST QUESTION AND ONLY GOT 2 AND A HALF MINUTES LEFT TILL TEST IS OVER PLEASE

Answers

Answer:

-1

Step-by-step explanation:

Here you go, has to be 100 characters and did it quick

-6 + 8 = 2
2/-2 = -1

Answer = B

[tex]\sf 14+4x=38[/tex]

Answers

Answer:

your answer will be 6

Step-by-step explanation:

14+4x=38

4x=38-14

4x=24

x=24/4

x=6

hope ur help

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Value of x is equal to :

[tex]6[/tex]

[tex] \large \boxed{ \mathfrak{Explanation}}[/tex]

Let's solve for x :

[tex]14 + 4x = 38[/tex]

[tex]4x = 38 - 14[/tex]

[tex]4x = 24[/tex]

[tex]x = 24 \div 4[/tex]

[tex]x = 6[/tex]

[tex]\mathrm{✌TeeNForeveR✌}[/tex]

Factor this using guess and check thank you :)

Answers

Answer:

(x-2) (x+5)

Step-by-step explanation:

2 * 5 = 10

(-2) + 5 = 3

3x + x² - 10 = (x-2) (x+5)


Name the property of the real numbers illustrated by the equation.
2. (18.7) = (2-78-7
OA Commutative Property of Multiplication
OB Associative Property of Addition
C Associative Property of Multiplication
OD Distributive Property

Answers

B. Associative property of addition

If ∆ABC is an isosceles triangle and angle B = 65° . What is X?
a) 70°
b) 60°
c) 50°


Ps: If you can send the working Please thank you

Answers

Answer:

60° option b) is the answer

Estimate 17.154+5.46 by rounding each number to the nearest tenth

Answers

Answer:

Step-by-step explanation:

If you like to round 17.154 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post.

The weight of the of an object to is equal to 3/4 of its own weight plus 3/4 of a pound.
How much does the object weigh? Explain.

Answers

Answer:

[tex]x=\frac{3}{7} lbs[/tex]

Step-by-step explanation:

[tex]x=\frac{3}{4}(x)+\frac{3}{4}[/tex]

[tex]x+\frac{3}{4}(x)=\frac{3}{4}[/tex]

[tex]\frac{7}{4}(x)=\frac{3}{4}[/tex]

[tex]x=\frac{12}{28} =\frac{3}{7}lbs[/tex]

Does 10^25 equal 4^42

Answers

Answer:

They are almost equal but not exactly equal so no. 10 to the power of 25 is 1e+25 and 4 to the power of 42 is 1.9342813e+25.

Step-by-step explanation:

Please mark brainliest

Answer:

No examples of equivalents to 10/25 are:

2/5, 4/10, 6/15, 8/20, 10/25, 12/30, 14/35, 16/40, 18/45, 20/50, 22/55, 24/60, 26/65, 28/70, 30/75, 32/80, 34/85, 36/90, 38/95, 40/100

its very close but not quite

Step-by-step explanation:

Hope this helps :)

pls make brainliest :p

And have an amazing day <3

simultaneous linear equation 2x+y=4 3x-y=2

Answers

Answer:

[tex]2x + y = 4 \\ 3x - y = 2 \\ y = 4 - 2x \\ 3x - (4 - 2x) = 2 \\ 3x - 4 + 2x = 2 \\ 3x + 2x = 2 + 4 \\ 5x = 6 \\ x = \frac{6}{5} \\ x = 1.2 \\ y = 4 - 2x \\ y = 4 - 2(1.2) \\ y = 4 - 2.4 \\ y = 1.6 \\ [/tex]

Step-by-step explanation:

Hope that this is helpful.

Have a great day.

Which situation best represents causation?

The more you study, the more A’s you will make in class.

The more you study, the more classes you will fail.

The older you are, the less battery life you will have on your cell

The taller you are, the more pencils you will buy for school.

Answers

Answer:

the first one

Step-by-step explanation:

Solve: 2x-5/3 + 3/5 = 0​

Answers

Answer:

The value of x is 8/5.

Step-by-step explanation:

Solution :-

[tex]\sf \leadsto \dfrac{2x - 5}{3} + \dfrac{3}{5} = 0[/tex]

[tex]\sf \leadsto \dfrac{10x - 25 + 9}{15} = 0[/tex]

[tex]\sf \leadsto \dfrac{10x - 16}{15} = 0[/tex]

[tex]\sf \leadsto 10x - 16 = 0[/tex]

[tex]\sf \leadsto 10x = 0 + 16[/tex]

[tex]\sf \leadsto 10x = 16[/tex]

[tex]\sf \leadsto x = \dfrac{16}{10}[/tex]

[tex]\sf \leadsto x = \dfrac{8}{5}[/tex]

Answer:

x = 1 3/5 or 8/5

Step-by-step explanation:

[tex]\frac{2x-5}{3}+\frac{3}{5} =0[/tex] [tex]\frac{2}{3}x - \frac{5}{3} + \frac{3}{5} = 0[/tex] [tex]\frac{2}{3}x-\frac{16}{5} =0[/tex] [tex]\frac{2}{3}x-\frac{16}{15} +\frac{16}{15}= 0 + \frac{16}{15}[/tex] [tex]\frac{2}{3}x=\frac{16}{15}[/tex] [tex]\frac{2}{3}x * \frac{3}{2} = \frac{16}{15} * \frac{3}{2}[/tex] [tex]x= \frac{8}{5}[/tex] [tex]x = 1\frac{3}{5}[/tex]

WILL MARK BRAINLIEST!!! +15 POINTS!!! REAL ANSWERS ONLY PLEASE!!!

Answers

Answer:

2

Step-by-step explanation:

all real number x smaller than or equal to -2


Write 750 g as a fraction of 5 kg. Give your answer in its
simplest form.

Answers

Answer:

3/20 is the answer.......

Which pair of angles are congruent?
A. 4 and 5
B. 1 and 7
D. 6 and 8
C. 2 and 5

Answers

4 and 5 because they are alternate interior angles

help please!! I will give brainliest! :)

Answers

Y=10x+2 if that’s what your asking

Answer: Y=10x+2

Step-by-step explanation:

4
= 5
Find the x-intercept and y-intercept of the line.
4x + 5y = -20
-intercent:
10

Answers

Answer:

y-intercept is (0, -4)

x-intercept is (-5, 0)

Step-by-step explanation:

Remember the x-intercept and the y-intercept are the points on the graph where the line crosses the x-axis and the y-axis respectively.

We can find the x intercept and the y intercept a couple of ways. One way is to graph the line, which I will do later. The other way is to do a little math.

The equation of a line in y-intercept form is

[tex]y = mx + b[/tex]

where b = the y-intercept

In our equation above and solving for y we get the y-intercept is -4

[tex]4x + 5y = - 20 \\ 5y = - 4x - 20 \\ y = - \frac{4}{5} x - 4[/tex]

Doing more algebra and solving for x we get the x intercept is negative 5.

[tex]y = - \frac{4}{5} - 4 \\ y + 4 = - \frac{4}{5} x \\ x = - \frac{5}{4} y - \frac{20}{4 } \\ x = - \frac{5}{4} y - 5[/tex]

45 + 15 = (3 + ) What the best answer for this question

Answers

Answer:

45+15=60 (3+?)

Step-by-step explanation:

?=57

For a cube whose side length the lexpression

Answers

Can you give more information?

Evaluate the given expression. P(9, 3)

Answers

Step-by-step explanation:

p=9

p=3

p-9=0

p-3=0

(p-9)(p-3)=0

p*2-3p-9p+27=0

p*2-12p+27=0

find the measure of the indicated angle

Answers

Answer:

∠ E = 57°

Step-by-step explanation:

Since DF = EF then the triangle is isosceles with 2 base angles congruent , so

∠ E = ∠ D = 4x + 1

The sum of the 3 angles in the triangle = 180°

Sum the 3 angles and equate to 180

4x + 1 + 4x + 1 + 5x - 4 = 180 , collect like terms

13x - 2 = 180 ( add 2 to both sides )

13x = 182 ( divide both sides by 13 )

x = 14

Then

∠ E = 4x + 1 = 4(14) + 1 = 56 + 1 = 57°

Write the equation of the line in fully simplified slope intercept form

Answers

Answer:

y = 6x - 5

Step-by-step explanation:

In order to determine the slope-intercept form, y = mx + b, of the given line:

You need to find the slope (m) and determine the y-intercept (b).  

Given the points (1, 1) and (0, -5):

Let (x1, y1) = (1, 1)

(x2, y2) = (0, -5)

Use the following formula for slope:

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

m = (-5 - 1)/(0 - 1)

m = -6/-1

m = 6

The slope of the line is 6.

Next, the y-coordinate (b) of the point, (0, b ) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Looking at the graph, you'll see that the line crosses at point (0, -5). We used this point earlier to solve for the slope. Hence, the y-coordinate, b =  -5, is the y-intercept.

Given the slope, m = 6, and the y-intercept, b = -5:

The linear equation in slope-intercept form is: y = 6x - 5.

Please mark my answers as the Brainliest if you find this helpful :)

A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 340^\circ340

340, degrees.
What is the length of the arc?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answers

Answer:

length of arc ≈ 17.8 (to the nearest tenth)

Step-by-step explanation:

To find the length of the arc we use the formula for finding length of an arc.

length of arc = ∅/360 × 2πr

where

∅ = central angle

r  = radius

∅ = 340°

r = 3

length of arc = ∅/360 × 2πr

length of arc = 340/360 × 2 × π × 3

length of arc = 340/360 × 6π

length of arc = 2040π/360

length of arc = 204π/36

length of arc = (204 × 3.14)/36

length of arc = 640.56/36

length of arc = 17.7933333

length of arc ≈ 17.8 (to the nearest tenth)

Answer: [tex]6\pi[/tex]

Step-by-step explanation: Khan academy

CAN SOMEONE HELP ME WITH THIS QUESTION!!!

Answers

Answer:

E

Step-by-step explanation:

let a, b, c represent the number of students in 6th, 7th, 8th grade

ratio of students : teachers = 28 : 1

There are 82 teachers , so 28 × 82 = 2296 students

Then

a + b + c = 2296 , that is

828 + b + c = 2296 ( subtract 828 from both sides )

b + c = 1468 → E

Pa help po, thank u ☺​

Answers

Answer:

[tex]a) \: \: e = 11 \: \: and \: \: f = 7 \\ \\ \frac{e + 5}{4f - 4} \\ \\ \frac{11 + 5}{4(7) - 4} \\ \\ \frac{16}{28 - 4} \\ \\ \frac{16}{24} \\ \\ \frac{2}{3} \\ 0.666 \: \: \: ans \: \\ \\ \\ b) \: \: e = - 1 \: \: and \: \: f = - 4 \\ \\ \frac{e + 5}{4f - 4} \\ \\ \frac{ - 1 + 5}{4( - 4) - 4} \\ \\ \frac{ - 1 + 5}{ - 16 - 4} \\ \\ \frac{4}{ - 20} \\ \\ - \frac{1}{5} \\ - 0.2 \: \: ans \: \: [/tex]

Step-by-step explanation:

Solution:

a. when e = 11 and f = 7

[tex] \\ \: \: \frac{e + 5}{4f - 4} [/tex]

[tex] \\ = \frac{11 + 5}{4 \times 7 - 4} [/tex]

[tex] \\ = \frac{11 + 5}{28 - 4} [/tex]

[tex] \\ = \frac{16}{24} [/tex]

[tex] \\ = { \cancel \frac{16}{{24}}}[/tex]

[tex] \\ = \frac{2}{3} [/tex]

b. when e = -1 and f = -4

[tex] \\ \: \frac{e + 5}{4f - 4} [/tex]

[tex] \\ = \frac{{ - 1 + 5} }{4( - 4) - 4} [/tex]

[tex] \\ = \frac{ - 1 + 5}{ - 16 - 4} [/tex]

[tex] \\ = \frac{4}{ - 20} [/tex]

[tex] \\ = { \cancel\frac{4}{ - 20}} [/tex]

[tex] \\ = \frac{ - 1}{5} [/tex]

answer all plss I need it !

Answers

4. whole number
1. integer
2.rational
3.rational
5.whole number

brainliest?

What is root 3 x root 7?

Answers

Answer:

[tex] \sqrt{3} \times \sqrt{7} = \sqrt{21} [/tex]

I hope I helped you^_^

Dilation 5 Q (1,5) R (3,-1) S (0,0) T (-2,3) find the coordinates of Q’
A. (5,25)
B. (25,5)
C. (-5,-25)
D. (.20,1)

Answers

Answer:

A

Step-by-step explanation:

because if you multiply 1 times 5 it's 5 and if you multiply 5 times 5 it would be 25 which would be A

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