Please fill the blanks

Given:

A cube has square sides with area [tex]x^2+24x+144[/tex].

To find:

The expression that represents the surface area of the cube.

Solution:

We have

The area of each side of cube = [tex]x^2+24x+144[/tex]

Number of sides of a cube = 6

We know that, the total surface area of the cube is the product of number of sides of the cube and the area of each side. So, the total surface area of the cube is

[tex]SA=6(x^2+24x+144)[/tex]

[tex]SA=6(x^2)+6(24x)+6(144)[/tex]

[tex]SA=6x^2+144x+864[/tex]

Hence, the expression that represents the surface area of the cube is [tex]6x^2+144x+864[/tex].

Answer:

QR = 65.4 m

Step-by-step explanation:

a. Apply Law of Cosines to find QR:

p² = q² + r² - 2qr × Cos P

p = QR = ?

q = PR = 150 m

r = PQ = 120 m

P = 25°

Plug in the values

p² = 150² + 120² - (2)(150)(120) × Cos(25°)

p² = 22,500 + 14,400 - 36,000 × 0.9063

p² = 36,900 - 32,626.8

p² = 4,273.2

p = √4,273.2

p ≈ 65.4 m (nearest tenth)

QR = 65.4 m

Answer:

a = 45 millimeters

Step-by-step explanation:

In order to solve this, we need to know that for right-angled triangles the following is true:

[tex]c^{2} = a^{2} + b^{2}[/tex] (where c is the hypotenuse and "a" and "b" are the legs)

From the formula above we can conlude that...

[tex]a = \sqrt{c^{2} - b^{2} }[/tex]

Now we just substitute the variable that we know and get that...

[tex]a = \sqrt{c^{2} - b^{2} }\\a = \sqrt{75^{2} - 60^{2} } \\a = \sqrt{5,625 - 3600} \\a = \sqrt{2025} \\a = 45[/tex]

Therefore a = 45millimeters.

Answer:

C

Step-by-step explanation:

The option that has the same range than f(x) is:

[tex]g(x) = -\sqrt{x + 3} + 8[/tex]

Here we first have the function:

[tex]f(x) = -2*\sqrt{x - 3} + 8[/tex]

Remember that the square root only can be evaluated arguments equal or larger than zero.

So the minimum value of x that we can use is x = 3.

[tex]f(3) = -2*\sqrt{3 - 3} + 8 = 8[/tex]

And as x increases, the outcome will decrease (because the square root is being mulitiplyed by a negative number). So we can conclude that the range is y ≤ 8.

So, we need another function that has a maximum value in the range equal to positive 8, so we need to have a constant equal to 8, and a square root being multiplyed by a negative number.

The option that meets these two conditions is the third one:

[tex]g(x) = -\sqrt{x + 3} + 8[/tex]

If you want to learn more about domains and ranges, you can read:

https://brainly.com/question/10197594

Answer:

Step-by-step explanation:

Answer:

p(10) = 306

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

p(x) = 3(x² - 2) + 12

p(10) is x = 10 for function p(x)

Step 2: Evaluate

Answer:

166.8 feet

Step-by-step explanation:

tan = opp/adj

opp = height of tree

adj = distance

tan27 = 85/distance

distance = 85/tan27

use calculator

distance = 166.821892967937799

166.8 feet

Answer:

a(n) = -20 + 3(n - 1)

Step-by-step explanation:

a(n) = -20 + 3(n - 1)

Answer:

$1865

The gold calculator is a gold melt value calculator which can be used to determine the value of gold metal inside an item with a known weight and gold purity. These items may include gold jewelry (such as, bangles, bracelets, chains, earrings, necklaces, pendants, and rings), gold bullion and gold coins.

The gold calculator is designed to calculate the gold metal value for one item at a time. If you would like to calculate the gold metal value for multiple items simultaneously consider using the scrap gold calculator for scrap gold, the gold bullion calculator for gold bullion bars and coins, and the gold coin calculator for gold coins.

Answer: -7y = 21

explanation:

x+y=2;3x−4y=27

Step: Solve x+y=2 for x:

x+y+−y=2+−y (Add -y to both sides)

x=−y+2

Step: Substitute −y+2 for x in 3x−4y=27:

3x−4y=27

3(−y+2)−4y=27

−7y+6=27 (Simplify both sides of the equation)

−7y+6+−6=27+−6 (Add -6 to both sides)

−7y=21 (answer)

first option

manipulate line 1 to

x = 2 - y

then substitute x in line to for the righthand side above

then solve towards y.

Answer:

x = -2

When we multiply a negative number with a positive number the answer is always negative.

Hope it helps:)

Answer:

Option D: (0,-5)

Step-by-step explanation:

Comparing the given points to the graph.

So, the point that will lie at the shaded area represent  solution to the linear inequality.

So, point (0,-5) is a solution to the linear inequality.

The answer is option D. (0,-5)

Note: the line y = 6x-4 is graphed using the table on the graph.

Answer:

81

Step-by-step explanation:

It depends on how many different grades you have and the values of each one of them.

I don't have those things, so Ill just use average.

You'll have an 81

Answer:

(x+6)^2 + y^2 = 1 then isolate y^2  by subtracting (x +6)^2 from both sides, we get

                y^2 = 1 - (x + 6)^2

expanding the right side, we now have

                y^2 = 1-(x^2 + 12x +36)

          y^2 = 1-x^2-12x -36

          y^2 = -x^2 -12x - 35  therefore the solution is  choice A

Step-by-step explanation:

Answer:

14 5/24

Step-by-step explanation:

Ariana's rode the bus 5 3/8 miles to the mall

She rode 2 3/4 miles to her friends place

Then she rode anrhe 6 1/12 miles back home

Therefore the total distance can be calculated as follows

= 43/8 +11/4 + 73/12

= 5456/384

= 341/24

= 14 5/24

Hence the total distance is 14 5/24 miles

Answer:

13 + 3i

Step-by-step explanation:

I just used a app for this problem.

Answer:

[tex]13 + 3i[/tex] is the sum of the numbers

Step-by-step explanation:

[tex]13 + 3i[/tex]

[tex]15 - 6i - 2 + 9i[/tex]  → Sum

collect like terms

[tex](15 - 2) + ( - 6i + 9i) =13 + 3i[/tex]

Answer:

10+3pi

Step-by-step explanation:

The perimeter of of the shaded region is

AC+CT+marcSBT+SA

*Finding AC

The diagonals of a rectangle are equal is measurement. Since RB is a radius of the circle, then RB is 6. Since AC and RB are both diagonals of the rectangle, then AC is also 6.

*Finding CT

CT=RT-RC where RC is the width of the rectangle

Also RT is a radius so we have that

CT=6-RC

*Finding marcSBT

The circumference of a whole circle is 2pi*r.

We have a quarter of this with r=6.

1/4*2pi(6)

1/4*12pi

3pi

*Finding SA

SA=RS-AR

RS is a radius of the circle and AR is the length of the rectangle.

So we have that this can be rewritten as

SA=6-AR

Let's put these parts together:

6+6-RC+3pi+6-AR

Simplifying:

18-RC-AR+3pi

18-(RC+AR)+3pi

18-8+3pi (Remember length plus width equal 8)

10+3pi

Answer:

She earns $0.65 per paper

Step-by-step explanation:

1. She earns $3.90 per 6 papers

2. take $3.90 and divide by 6.

3. you will get the cost per paper.

4. to check the work if you'd like then take 7.80 and divide it by 12 and again you will get $0.65 per paper.

(you don't need to find a special calculator you can use one on your phone since each dollar has 100 cents so you just need to go out to the hundredths place in a decimal or the second decimal place)

Answer:

x = 5±sqrt(26)

Step-by-step explanation:

x^2-10x=1

Take the coefficient of x

-10

Divide by 2

-10/2 = -5

Square it

(-5)^2 = 25

Add this to both side

x^2-10x+25=1+25

(x-5)^2 = 26

Take the square root of each side

sqrt((x-5)^2) = ±sqrt(26)

x-5 = ±sqrt(26)

Add 5 to each side

x = 5±sqrt(26)

Answer:

-0.0990195 and 10.09902

Step-by-step explanation:

To complete the square, the same value needs to be added to both sides

x^2-10x+?=1+?

To complete the square x^2-10x+25=(x-5)^2 add 25 to the expression.

x^2-10x+25=1+?

Since 25 was added to the left-side, you need to add it to the right-side as well.

x^2-10x+25=1+25

use a^2-2ab+b^2=(a-b)^2 to factor this expression.

(x-5)^2=1+25

Then add the numbers together.

(x-5)^2=26

Solve for x.

x1=-squareroot26+5

x2=squareroot26+5

therefore you have 2 solutions

x1=-squareroot26+5

=-0.0990195

and

x2=squareroot26+5

=10.09902

Answer:

2,023

Step-by-step explanation:

P(8) = 25(8)²-24(8)+615

= 1600- 192 +615

= 2,023

Answer:

3rd choice

Step-by-step explanation:

Similar triangles have congruent angles and proportional sides

They look similar but size may vary

Find the distance of each trip:

68 km / 34 trips = 2 km per trip

Divide total distance by distance per trip:

348 km / 2 km per trip = 174 trips

Answer: 174 trips

Answer:

can u plz rewrite the question

Answer:

….

Step-by-step explanation:

You will need an image for that!

Answer:

1) V

2) V

3) V

4) V

5) V

Step-by-step explanation:

Answer: [tex]180\ cm^2[/tex]

Step-by-step explanation:

Given

Height of a cuboid [tex]h=45\ mm[/tex]

Volume of the cuboid is [tex]V=162\ cm^3[/tex]

End faces are square. So, assume its length to be x

[tex]\therefore x^2\times h=162\\\Rightarrow x^2\times 4.5=162\\\Rightarrow x^2=36\\\Rightarrow x=6\ cm[/tex]

Surface area of cuboid

[tex]\Rightarrow 2(lb+bh+hl)=2(6\times 6+6\times 4.5+4.5\times 6)\\\Rightarrow 2(36+27+27)\\\Rightarrow 180\ cm^2[/tex]