The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square of the third. Find the integers. Please show work.

Answers

Answer 1

Answer:

6, 8 and 10  and  -2, 0, 2

There are two roots x = -2 and 6,    

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is  -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z    even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z²                                   substitiute x terms  in for y and z

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²           solve for x by graphing on DEMOS

                                                                 x = -2, 6  solved algebraically below

x = -2   y=0   z=2

x = 6    y=8   z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8                  when x = -2

   0   =  0

and

6(8)(10)  =  6³ + 8² +2(10)²      when x = 6

   480   =  216+64+200

             =  480

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²                           solved algebraically

(x²+2x)(x+4)   = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

      3x² - 12x - 36 = 0         factor out the 3

      3[x² - 4x - 12] = 0

       3(x+2)(x-6) = 0     x = -2 and -12


Related Questions

solve eqn by factorisation method
2x squre-50x=0​

Answers

Answer:

0 or 25

Step-by-step explanation:

To solve for x

we first factor

2x^2-50x=0

2x(x-25)=0

To make this equation 0 x has to be 0 or 25

HELP WILL GIVE BRAINLEASIT

Answers

Step-by-step explanation:

try to do 180 - 135 organise a 45-degree that is the first answer of a and b you're taking 180 - 144 you got the answer also 28 degrees

Find the value of k and x2
x^2+ 13x + k = 0, x1=-9

Answers

Given:

The quadratic equation is:

[tex]x^2+13x+k=0[/tex]

[tex]x_1=-9[/tex]

To find:

The value of k and [tex]x_1[/tex].

Solution:

We have,

[tex]x^2+13x+k=0[/tex]                ...(i)

Putting [tex]x=-9[/tex], we get

[tex](-9)^2+13(-9)+k=0[/tex]

[tex]81-117+k=0[/tex]

[tex]-36+k=0[/tex]

[tex]k=36[/tex]

Putting [tex]k=36[/tex] in (i), we get

[tex]x^2+13x+36=0[/tex]

Splitting the middle term, we get

[tex]x^2+9x+4x+36=0[/tex]

[tex]x(x+9)+4(x+9)=0[/tex]

[tex](x+9)(x+4)=0[/tex]

[tex]x=-9,-4[/tex]

Here, [tex]x_1=-9[/tex] and [tex]x_2=-4[/tex].

Therefore, the required values are [tex]k=36[/tex] and [tex]x_2=-4[/tex].

Which expression has a solution of 6, if r = 4?

1. r + 2
2. 4 - r
3. 10 + r
4. r - 10

Answers

Answer:

1.

Step-by-step explanation:

1. 4 + 2 = 6

2. 4 - 4 = 0

3. 10 + 4 = 14

4. 4 - 10 = -6

number 1 is the right answer

Answer:

1.

Step-by-step explanation:

Which of the following transformations shifts all points graphed in the standard (wy)
coordinate plane down 5 coordinate units?
A. (X, y-5)
B. (X, y+5)
C. (X-5y)
D. (K-5, y)
E. (X+5,y)

Answers

Answer:

B is your answer

Step-by-step explanation:

how many meters are their in centimeter​

Answers

Answer:

You mean how many centimerters are in a meter?

In that case 100.

Step-by-step explanation:

The larger of two numbers is 6 more than the smaller integer. Their sum is 52, What are the numbers?

Answers

Make x the variable to represent the smaller integer. Since the larger integer is 6 more, you are going to add 6 to the 2x. Solve.
x + x + 6 = 52
2x + 6 = 52
2x = 46
x = 23
The smaller integer = 23
The larger integer = 29
Check:
23 + 29 = 52

I need help with this please help me. ​

Answers

Answer:

a) $93, $117.80, $86.80, $68.20

b) $365.80

Step-by-step explanation:

a)

Add 12 hours to each p.m. time to make the subtraction of hours easier.

Also, use decimal numbers to do the subtraction. Remember that 0:30 means 30 minutes which is 0.5 hour, so 7:30 is the same as 7.5 as a decimal.

Monday: 8:00 to 15:30

15:30 - 8:00 = 1.5 - 8 = 7.5 hours

7.5 hours * $12.40/h = $93

Wednesday: 7:30 to 17:00

17:00 - 7:30 = 17 - 7.5 = 9.5 hours

9.5 hours * $12.40/h = $117.80

Friday: 9:00 to 16:00

16:00 - 9:00 = 16 - 9 = 7 hours

7 hours * $12.40/h = $86.80

Saturday: 10:30 to 16:00

16:00 - 10:30 = 16 - 10.5 = 5.5 hours

5.5 hours * $12.40/h = $68.20

b) Add all the daily amounts above.

$93 + $117.80 + $86.80 + $68.20 = $365.80

Imagine drawing a figure with the following conditions:
VX
A quadrilateral with at least two right angles. Is the figure
described unique? Explain why or why not.

Answers

Answer:

with atleast two right angles in rectangle and it do not describe unique because it is simple

This equation shows how the size of Terrence's sticker collection is related to the number of sticker packs he buys.

s = 20p

The variable p represents the number of sticker packs he buys, and the variable s represents the total number of stickers he has. How many sticker packs does Terrence have to buy to have a total of 20 stickers?

Answers

Answer:

400

Step-by-step explanation:

Decide whether it is possible for a triangle to have the three angle measures or three side lengths given.
If it is possible, then decide whether all such triangles are congruent.

Answers

Answer:

Step-by-step explanation:

the first one cant be a triangle

im pretty sure the second one can

the third one can

im pretty sure the fourth one cant

pls help asap this is too hard helpme

Answers

Please mark me brainliest!!!

It’s a= -1/2

Hope this helps!

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon
1. ________________________

2.______________________

3. ______________________

4. ______________________

5. ______________________
sorry 32 points nalang meron ako​

Answers

Answer:

octagon  enneagon decagon hendeka

Step-by-step explanation:

The most efficient first step in the process to factor the trinomial 3x³-24x² + 36x is :
O A. factor out 3
O B. factor out 3x
O C. factor out (x - 2)
O D. factor out-1​

Answers

Answer:

B

Step-by-step explanation:

Find the surface area of the prism. Whoever solves this will guarantee get Brainliest Answer!!!

Answers

To find the total surface area of a prism, you need to calculate the area of two polygonal bases, i.e., the top face and bottom face. And then calculate the area of lateral faces connecting the bases. Add up the area of the two bases and the area of the lateral faces to get the total surface area of a prism.

Hope this helps!

628.319 rounded to the nearest tenth

Answers

Answer: 628.3

Step-by-step explanation: Tenth is always the first decimal point so 1 rounds down, making it 628.3.

Answer:

628.3

Step-by-step explanation:

A Tenth is the number after the dot. It rounds down 3, therefore, the answer is 628.3.

What is the midpoint of line segment RS with endpoints R(5, -10) and S(3, 6)?

Answers

Answer:

(4, -2)

Step-by-step explanation:

The midpoint of two points is found by averaging the X coordinates and averaging the Y coordinates to create a new pair.

X: (5+3)/2     = 4

Y: (-10+6)/2   = -2

Answer:

(4,-2)

Step-by-step explanation:

add the x and divide by two. do the same with the y. this is the same as finding the average

lily wants to put a bird food mix in her bird feeder.Her bird feeder can hold 8 cups of bird food.The bird food is a mix of 20% corn and the rest is sunflowers seeds how many cups of corn will lily need to fill the 8 cup bird feeder.If the rest of the mix is sunflower seed,what percent of the bird food is sunflower seed.

Answers

Answer:

80%

Step-by-step explanation:

100% is full so you do 100%-20%=80% so thats the answer

-7 = 2x - 7
A. 0
B. 4
C. Infinite Solutions
D. No solutions

Answers

Answer:

A

Step-by-step explanation:

the variable is how many times the two will be multiplied, so 2 times 0 equals 0, there by making the problem. -7= - 7

Answer:

that will be A. 0

Step-by-step explanation:

first, i flip the equation

2x - 7= -7

next, i add both side by 7

2x−7+7=−7+7

2x=0

and finally, you divided by 2

2x/2 = 0/2

you get x = 0

Find the surface area of the prism.

Answers

Answer:

30 i think

Step-by-step explanation:

On Tuesday afternoon at camp, Eve did archery and sailing before dinner. Archery started at 12:30p.m. Eve spent 1 hours and 25 minutes at archery and 45 minutes sailing. What time did sailing end?

Answers

Answer:

2:40

Step-by-step explanation:

Add 85 minutes to 45 minutes and then add that to 12:30

Need help as soon as possible pls help

Answers

1. The value of x is:

180° - 40° - 30° = 110°

2. The value of x is:

90°- 38° = 52°

Answer:

Step-by-step explanation:

180 = 40 + x + 30

110 = x

90 = 38 + x

52 = x

A bakery sells glazed donuts for $1.09 each. Cinnamon bagels and onion bagels are $1.59 each. Max buys x donuts, y cinnamon bagels, and z onion bagels. Which expression represents the total amount Max spent at the bakery?
A.
1.09x + 1.59yz
B.
1.09x + 1.59y + 1.59z
C.
1.09x + 3.18(y + z)
D.
(1.09 + 1.59)(x + y + z)

Answers

Answer:

The answer is B.

Step-by-step explanation:

Answer:

B.

1.09x + 1.59y + 1.59z

I hope this helps

Which is the correct stem-and-leaf plot for the data set?
16, 15, 47, 41, 40, 39, 16, 37

Answers

Answer:

the first plotting was correct.

Step-by-step explanation:

the values will be arranged in an ascending order from their roots which are the first digit

Which of the following graphs best represents a function that has a minimum value and x-intercepts of 3 and -1?

Answers

Answer:

a

Step-by-step explanation:

Help me pls I give points

Answers

Answer:

c=14.87

Step-by-step explanation:

use pythagorean theroem

10^2 + 11^2 =c^2

solve

100+121=c^2

c^2=221

c=14.87(rounded to nearest hundredths )

Expert Answer Please Find The Area Of A Circle With R=13.8 Explain Answer!

Answers

Answer:

if r= to 13.8 so the answer is 598.28

Question 7: The red line has an equation of y = -1/2 x + 2. The blue line is perpendicular to the red line. Write the equation for the blue line. EXPLAIN PLS

Answers

Answer:y=2+2x

Step-by-step explanation:

Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2

How do I solve this arithmetic sequence?

Answers

Answer:

The 16ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 9

Common Difference = (d) = 2

Now, For 16ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₁₆ = 7 + (16 - 1) × 2

a₁₆ = 7 + 15 × 5

a₁₆ = 7 + 75

a₁₆ = 82

Thus, The 16ᵗʰ term of this sequence is 82

-TheUnknownScientist

The function h defined by h(t)=(-4.9t + 29.4)(t+2) models the height in meters, of an object t seconds after it is launched. When will the object hit the ground?

Answers

Answer:

The time the object will hit the ground is 2 s.

Step-by-step explanation:

Given;

h(t) = (-4.9t + 29.4)(t + 2)

Open the bracket;

h(t) = -4.9t² + 29.4t  -9.8t + 58.8

h(t) = -4.9t²  + 19.6t + 58.8

When the  object hit the ground, the final velocity will be zero;

[tex]v = \frac{dh}{dt} = 0 \\\\\frac{dh}{dt} = -9.8t + 19.6 = 0\\\\9.8t = 19.6\\\\t = \frac{19.6}{9.8} \\\\t = 2 \ s[/tex]

Therefore, the time the object will hit the ground is 2 s.

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