Find the volume of the box

find two positive even consecutive integers such that a square of the smaller integer is 10 more than the larger integer

nalin [4]

Answer:

the two positive consecutive integers are 4 and 6.

Step-by-step explanation:

Let the smaller integer be s; then s^2 = (s + 2) + 10.

Simplifying, s^2 - s - 2 - 10 = 0, or

s^2 - s - 12 = 0.

Solve this by factoring: (s - 4)(s + 3) = 0.

Then s = 4 and s = -3.

If the first even integer is 4, the next is 6. We omit s = -3 because it's not even.

The smaller integer is 4. Does this satisfy the equation s^2 = (s + 2) + 10?

4^2 = (4 + 2) + 10 True or False?

16 = 6 + 10 = 16.

True.

So the two positive consecutive integers are 4 and 6.

6 0

3 years ago

I need help, an answer or how to- will be fine, thank you. (i’ll mark brainliest if i can)

siniylev [52]

by solving the first equation you'll get x= -24/13

if you solve the second option (B) then you'll the same result i.e x=-24/13

so option C is correct

7 0

2 years ago

How many times does the graph of 4x = 32 - x2 cross the x-axis?

garik1379 [7]

Answer:

The graph crosses the x-axis 2 times

The solutions are x = -8 & x = 4

Step-by-step explanation:

Qaudratics are in the form $ax^2 + bx+ c$

Where a, b, c are constants

Now, let's arrange this equation in this form:

$4x=32-x^2\\x^2+4x-32=0$

Where

a = 1

b = 4

c = -32

We need to know the discriminant to know nature of roots. The discriminant is:

$D=b^2-4ac$

If

D = 0 , we have 2 similar root and there is 2 solutions and that touches the x-axis
D > 0, we have 2 distinct roots/solutions and both cut the x-axis
D < 0, we have imaginary roots and it never cuts the x-axis

Let's find value of Discriminant:

$D=b^2-4ac\\D=(4)^2 -4(1)(-32)\\D=144$

Certainly D > 0, so there are 2 distinct roots and cuts the x-axis twice.

We get the roots/solutions by factoring:

$x^2+4x-32=0\\(x+8)(x-4)=0\\x=4,-8$

Thus,

The graph crosses the x-axis 2 times

The solutions are x = -8 & x = 4

6 0

3 years ago

Read 2 more answers

Solve for x. 3(x + 2) + 4(x - 5) = 10 x = 36/7 x = 24/7 x = 16/7 x = 9/7

IRISSAK [1]

3(x + 2) + 4(x - 5) = 10

Use the distributive property:

3x + 6 + 4x - 20 = 10

Combine like terms:

7x -14 = 10

Add 14 to both sides:

7x = 24

Divide both sides by 7:

x = 24/7

5 0

3 years ago

5(y+2)= -3 Whats the answer TvT

Iteru [2.4K]

Answer:

The answer is given below

Step-by-step explanation:

$(5y + 10) = - 3$

$5y = - 3 - 10$

$5y = - 13$

$y = - 13 \div 5$

This is the velue of y

<h2>PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE </h2>

8 0

1 year ago

Read 2 more answers