Name a value for x that will make the statement true.

x<-4

Step-by-step explanation:

the original side length is x.

the volume of a block is length × width × height.

so, for a cube with all sides being equal, the volume in our case is x³ (x × x × x).

now, with the same formula but with every side shortened by 1 cm we get

(x-1)(x-1)(x-1) = x³ - 91 (the original volume minus 91)

now, we have to do the multiplications.

(x-1)(x-1) = x² - 2x + 1

(x²-2x+1)(x-1) = x³ - x² - 2x² + 2x + x - 1 = x³ -3x² + 3x -1

x³ - 3x² + 3x - 1 = x³ - 91

-3x² + 3x = -90

-x² + x = -30

x² - x = 30

x² - x - 30 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -1

c = -30

x = (1 ± sqrt((-1)² - 4×1×-30))/(2×1) =

= (1 ± sqrt(1 + 120))/2 = (1 ± sqrt(121))/2 =

= (1 ± 11)/2

x1 = (1 + 11)/2 = 12/2 = 6

x2 = (1 - 11)/2 = -10/2 = -5

a negative number does not make any sense for a side length, so our solution is x = 6 cm.

the original side length of the cube is 6 cm.

to check :

6³ = 216

(6-1)³ = 5³ = 125

216 - 125 = 91

perfect.

[tex]a = 6(4) - 3 = 24 - 3 = 21[/tex]

Answer:

695

Step-by-step explanation:

So for thus, you need to follow PEMDAS

First, Parentheses

(-14 + 2.5) = -11.5

Skip E, there are no Exponents

Now for Multiplication

30 * (-11.5) = -345

Lastly, Subtraction

350 - -345

Becomes 350 + 345 = 695

Answer:

The answer is 695.

350-30(-14+2.5)=695.

Answer:

=2,133 3/7cm^2

Step-by-step explanation:

sides

15x16=240

240x2

=480cm^2

24×16=384

384×2= 768cm^2

768+480

a=1248cm^2

24x15=360cm^2

22/7x4x4

=50 2/7cm^2

360- 50 2/7

=354 5/7cm^2

(354 5/7)2

b=709 3/7cm^2

22/7x8x7

=22x8

c=176cm^2

a+b+c

1248+709 3/7+ 176

=2,133 3/7cm^2

Answer:

118.25

Step-by-step explanation:

Answer:

Im confused w ur question or i dont know maybe im just dum.b

Step-by-step explanation:

The approximate difference of the volume of the two spherical fruits is: C. 19 in.³.

Volume of sphere = 4/3πr³

The orange and the grapefruit are spherical in shape. Therefore:

Volume of orange = 4/3πr³ = 4/3π(1.5)³ = 14.14 in.³

Volume of grapefruit = 4/3πr³ = 4/3π(2)³ = 33.51 in.³

Difference in volume = 33.51 - 14.14 = 19.37

Therefore, the approximate difference of the volume of the two spherical fruits is: C. 19 in.³.

Learn more about the volume of sphere on:

https://brainly.com/question/22807400

The volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone

The volume of a cone is calculated as:

For the small cone, we have the following parameters:

Diameter = 3 inches

Height = 3.5 inches

Diameter = 4.5 inches

Height = 5.1 inches

So, the volume of the large cone is:

Calculate the difference of both volumes

Hence, the volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone

Read more about volumes at:

brainly.com/question/8994737

Answer:

3x - 2

Step-by-step explanation:

Collect like timers. -x + 4x = 3x and -3 + 1 = -2, 3x - 2

Hey there!

-x + 1 + 4x - 3

= -1x + 1 + 4x - 3

COMBINE the LIKE TERMS

= (-1x + 4x) + (1 - 3)

= -1x + 4x + 1 - 3

= 3x - 2

Therefore, your answer is: 3x - 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

A conversion calculator gave me 8800

The number of lateral faces for a hexagonal prism or pyramid is 6.

A prism is a three dimensional figure consisting of pair of opposite bases and lateral faces which are parallelogram.

Given that the base off the prism has two sides of length 3 inches and four sides of length 2 inches. Hence the base is hexagonal. The lateral faces would be 6.

The number of lateral faces for a hexagonal prism or pyramid is 6.

Find out more on prism at: https://brainly.com/question/23963432

The probability of having tails is 9/11

Data;

This is the possibility of an event occurring. In a sample space of 11 coin flips, tails came up 9 times and head came up 3 times

Number of time head came up = [tex]11-9 = 3[/tex]

The probability of having tails is calculated as

[tex]p = \frac{9}{11}[/tex]

The probability of having head is calculated as

[tex]p = \frac{3}{11}[/tex]

The probability of having tails is 9/11

Learn more on probability here;

https://brainly.com/question/24756209

Answer:

C, D, and E are the answers.

Answer:

  a. 314.2 in²

  b. 36 m²

  c. 60 m²

Step-by-step explanation:

The areas of these plane figures can be found by substituting the given dimensions into the area formula.

The area of a circle can be found from its diameter to be ...

  A = (π/4)d²

  A = (π/4)(20 in)² = 100π in² ≈ 314.2 in²

__

The area of a parallelogram can be found as ...

  A = bh

  A = (9 m)(4 m) = 36 m²

__

The area of a triangle can be found from ...

  A = 1/2bh

  A = 1/2(15 m)(8 m) = 60 m²

_____

Additional comment

A triangle with sides 17 and 15 and height 8 cannot be obtuse. It is a right triangle. (Those side lengths are a Pythagorean triple.)

Answer:

2x + y = 5

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - 2x + 5 ( add 2x to both sides )

2x + y = 5 ← in standard form

Answer:

 y=-2x+5 as standard form is 2x+y=5

Answer:

b. translation, rotation

Step-by-step explanation:

When a shape is translated, that just means nothing about it has changed except it's location on the coordinate plane. This is that happened with shape 1 - it was translated, and that created shape 2.

When a shape is rotated, that just means it is turned (or rotated) at a specific point. This is what happened to shape 2 that changed it to shape 3.

The other two transformations that aren't shown in this specific example are dilation, which means that the shape either shrinks or grows, and reflection, which means that the shape is reflected across the y-axis or the x-axis.

I included a picture with all four transformation examples in it. I hope this helps! Have a lovely day!! :)

Answer:

Answer: 3 + 97

Step-by-step explanation:

Just off the top of my head, I'm pretty sure that the answer you want is 3 and 97.

The single digit primes are 2 3 5 7

2 + 98 is what you are forced to use. 98 is not prime

3 + 97 is the answer I gave.

5 and 95 Ninety five is not prime (5 divides into it).

7 and 93 but 93 is not prime. 3 will divide into it.

Answer: 7

Step-by-step explanation:

This means we substitute x=3 into f(x).

f(3) = 3^2 - 2 = 7.

Answer: 6 units squared.

Step-by-step explanation: The equation for area of a triangle is 1/2 * length of base * the length of the height.

The length of the base is D to E, which is 3 units.

The length of the height is from F to the base of the triangle, which is 4 units.

Therefore, the area of the triangle would be 1/2 * 3 * 4 = 6 units squared.

Answer:

all real numbers

Step-by-step explanation:

the domain for normal linear and quadratic equations is always all real numbers

Answer:

11. b

10.d

9.c

7.b

1.d

the rest I can't see clearly

please give brainiest

Step-by-step explanation:

11.

3/x-4=7/x

*cross multiply

3x=7 (x-4)

3x=7x-28

28=7x-3x

28=4x

x=7

10.

SOHCAHTOA

Cos☆=11/14

cos^-1 (11/14)

☆=38.21 degrees

9.

MLN CONGRUENT TO WBN

ML/WB=LN/BN=MN/WN

LN/BN=10/6

ML/WB

24/x=10/6

24x6=10x

144÷10

=14.4

6^2+14.4^2

=243.36

squareroot

=15.6

Answer:

a) 5/2

b) 1/3

Step-by-step explanation:

a) 3y-2x=5 to find the value of y let we replace x by 0

then solve it

Answer:

(a) y = 2/3x + 5/3

(b) y = 1/3

Step-by-step explanation:

(a) Make y the subject of 3y - 2x = 5

3y - 2x = 5

    + 2x + 2x ==> isolate the variable y, by adding 2x to both sides

3y = 2x + 5 ==> divide both sides by three

/3       /3

y = 2/3x + 5/3 ==> y now becomes the subject, or our final answer

(b) Using 3y - 2x = 5 or y = 2/3x + 5/3,  find the value of y when x= -2

y = 2/3x + 5/3

y = 2/3(-2) + 5/3 ==> substitute -2 for x

y = -4/3 + 5/3 ==> add the fractions

y = 1/3 ==> the value of y, our final answer

OR

3y - 2x = 5

3y - 2(-2) = 5 ==> substitute -2 for x

3y - (-4) = 5

3y + 4 = 5 ==> --4 makes a +4, the subtract 4 (-4) from both sides

     - 4  - 4

3y = 1 ==> divide both sides by 3

/3    /3

y = 1/3 ==> your final answer

Hope this helps!

Answer:

The answer is D

Step-by-step explanation:

This is because 5π is equal to 15.7

Answer:

105/330 = 21/66 = 7/22

7/22 is the answer I think

Step-by-step explanation:

n(U) = 330

n(A) = 85

n(B) = 200

n(A n B) = 60

Now,

n(A U B) = n(A) + n(B) - n(A n B)

or, n(A U B) = 85 + 200 - 60

or, n(A U B) = 285 - 60 = 225

Now,

n(A U B) compliment = n(U) - n(A U B)

n(A U B) compliment = 330 - 225

so, n(A U B) compliment = 105

Now,

probability = 105/330

Answer:

14/23

Step-by-step explanation:

There are 253 tokens in all. Since 77 are blue and 77 are green, the probability of selecting either a blue token or a green token is 154/253, which reduces to 14/23.

Answer: C

Step-by-step explanation:

Statement C is true

The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

Interquartile range =  [tex]\underline{Q_{3} - Q_{1}}[/tex]

For bus drivers  = 30 - 5 = 25 miles

For teachers = 25 - 5 = 30 miles

Distance of bus drivers = distance of teachers - 5 miles

Answer:

Step-by-step explanation:

Initial value ( y - value) for  Function A is 12.

For B its 3(-1) + 2 = -1   so the answer is Function A.

Answer:

Find 'Function A's linear equation by using point-slope formula;

Where y1 = your first y-coordinate in any pair, and x1 = your first x-coordinate in the following pair used for the y-coordinate, and lastly m = slope.

But, we do not have the slope so we use the formula to find the slope(rise/run) of any two random points;

y2(second y-coordinate) - y1(first y-coordinate)

______________________________________

x2(second x-coordinate) - x1(first x-coordinate)

We plug in these values using any two ordered pairs, so I'll just use (-1,12) and (0,8).

12 - 8           4

_____ = ______ = -4/1 or -4 is the slope, so now we utilize this slope into

-1 - 0           -1

our point slope formula:-

y - y1 = m(x - x1)

For this, we just use one arbitrary pair, I'll use (-1,12).

So,

y - 12 = -4(x - (-1))

simplify

y - 12 = -4x - 4

isolate y by adding 12 to both sides (inverse operation of subtraction is addition)

+12         +12

y = -4x + 8, is the function for A.

Now let's compare the y-intercepts of both of these functions because we want to see which one has the greatest initial value.

Function A: y = -4x + 8, 8 is the y-intercept in this case.

Function B: y = 3x + 2, 2 is the y-intercept in this case.

Compare;

8 > 2, therefore Function A has a greater initial value.

Answer:

the decimal is 1.75 and  The percentage is 175%

Step-by-step explanation:

Answer:

year boy built an igloo =3/4

year3 girl built same igloo=3/7

To find out all together how much have built =3/4+3/7

if we take alceam

4×7=28

in fraction down we need to make 28

so 3/4 we multiply by 7 and 3/7we multiply by 4

3×7/4×7+3×4/7×4=21/28+12/28=21+12/28

33/28

to find out we divide fraction we will know what left .

1,5/28

5is left.