Which statement is true? Integers are always whole numbers or all whole numbers are rational or integers include all rational members or rational numbers do not include integers.

Answer:

x = [tex]\frac{y-1}{4}[/tex]

Step-by-step explanation:

Given

y = 4x + 1 ( subtract 1 from both sides )

y - 1 = 4x ( divide both sides by 4 )

[tex]\frac{y-1}{4}[/tex] = x

Answer:

total surface area = 936 in²

Step-by-step explanation:

total surface area  = surface area of the pyramid + surface area of the cube

1.  surface area of the pyramid = 4 * area of lateral triangle side

area of lateral triangle side = 12 * 9 /

area of lateral triangle side = 54 in²

2. surface area of the pyramid = 4 * 54

surface area of the pyramid = 216 in²

3. surface area of the cube = 5 * (12 x 12)

-surface area of the cube = 720 in²

therefore, the total surface area = 216 in² + 720 in²

total surface area = 936 in²

Answer:

C

Step-by-step explanation:

Please refer to the given picture (sorry, it's a rather bad drawing.)

Anyways, we know that the cube has side lengths of 12. Since the figure is a cube, all the side lengths are 12. Let's find the surface area of the cube first.

The cube has six faces. However, we only need to do five faces because one of the faces is the face that connects the cube to the pyramid. Because of this, we won't count it towards the surface area. Therefore, the total surface area of the cube would be:

[tex]5(bh)[/tex]

The bh represents the area of one face. The five multiplies that amount by five, giving us the surface area of the cube. Plug in 12 for the base and 12 for the height:

[tex]5(12)(12)=5(144)=720[/tex]

Therefore, the surface area of the cube (excluding one face) is 720 square inches.

Now, find the surface area of the square pyramid. The square pyramid is composed of four congruent triangles and one square base. Again, since the square base is connecting it to the cube, we won't count it. So, we only need to find the area of the four triangles and then add it to 720.

We are given that the height of the pyramid is 9. The base of all four triangles is 12 (since the side length of the cube is 12). However, to find the area, we first need to use the Pythagorean Theorem to determine x or the actual height of one of the triangles. We won't use 9 as the height because the 9 doesn't represent the height of the triangle, but rather of the pyramid. x is essentially the hypotenuse here. Thus:

Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Plug in 9 for a, 12 for b, and x for c:

[tex]9^2+12^2=x^2\\x^2=81+144=225\\x=\sqrt{225}=15[/tex]

Therefore, the height of the triangles is 15. Now, we can use the area formula for triangles:

[tex]A=\frac{1}{2} bh[/tex]

The base is 12 and the height is 15. Thus:

[tex]A=\frac{1}{2}(12)(15)=6(15)=90[/tex]

And there are four of them, so the total surface area is:

[tex]4(90)=360[/tex]

Therefore, the total surface area of the composite figure (excluding the one face) is:

[tex](720+360)=1080\text{ in}^2[/tex]

Answer:

(-2,1)

Step-by-step explanation:

Since this is an upwards opening parabola, the minimum point is at the vertex

We can find the x coordinate of the vertex by

y = 2x^2 +8x +9

where a=2  b =8 and c =9

x = -b/2a

x = -8/(2*2)

  = -8/4 = -2

The x coordinate is -2

Now substitute this in to find the y coordinate

y = 2(-2)^2 +8(-2)+9

  = 2*4 -16+9

  8-16+9

  =1

The vertex = (-2,1), which is the minimum point

Answer:

Step-by-step explanation:

y=2x²+8x+9

to find the minimum or maximum point x=-b/2a

x=-8/4=-2

y=2(-2)²+8(-2)+9

y=8-16+9

y=1

minimum point is (-2,-1)

Answer:

1) The equation in point and slope form is y - 56 = 3·(x - 17)

2) The above equation in slope and intercept form is y =  3·x + 5

3)  The height of the sidling when the botanist received it = 5 inches

4) The height of the tree on week 30 = 7 feet 11 inches

Step-by-step explanation:

The given parameters for the equation are;

The rate of growth of the young tree = 3 inches/week

The current height of the tree = 4 feet  8 inches = 56 inches

The current time since start of growth (time duration of growth) = 17 weeks

With the given information, we have;

The height of the tree, y = The dependent or y-variable

The time for the growth, x = The independent or x-variable

The slope = the rate of growth = 3 inches/week

At week, x = 17, y = 56 inches

1) The information presented in point and slope form is given as follows;

y - 56 = 3·(x - 17)

2) Simplifying the above equation to slope and intercept form, y = mx + c

Where;

m = The slope

c = The y-intercept

We have;

y = 3·x - 51 + 56 = 3·x + 5

y =  3·x + 5

Therefore the y-intercept = 5

3) The y-intercept = 5  which gives the value of the height of the tree at time x = 0 as follows;

At x = 0 when the tree was first received, the height of the tree, y = 3·x + 5 = 5 inches

4) On week 30, the height, y of the tree will be, y = 3 × 30 + 5 = 95 inches = 7 feet 11 inches.

Answer:

0.09

Step-by-step explanation:

When you divide a number by 100, you move the decimal to the left 2 steps because there are two zeros.

Answer: 12

Step-by-step explanation: In this problem,

we first determine the absolute value of -4.

The absolute value of -4 is 4 so we have 3(4) which is 12.

Answer: B. 33.1

Step-by-step explanation:

Use sin to solve (opposite/hypotenuse)

let x= length of CV

sin(37)=x/55

x=55sin(37)

x≈33.1

Answer:

49

Step-by-step explanation:

5^2 - 4(-3)(2)

5^2 - 4(-6)

25 - 4(-6)

25 - (-24)

49

Hope this helps!

49

25+24

you square 5 which is 25 than multiply -3 and 2 which is -6 than multiply by four

Answer:

b

Step-by-step explanation:

The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

hD = m

To solve for D make the subject as D

As we know the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Divide by h on both the sides:

hD/h = m/h

Here h ≠ 0

D = m/h

Thus, the expression in  terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

Answer:

$0.45

Step-by-step explanation:

$5.40/12 = $0.45

If A 12-pack of Cokes costs $5.40 then each Coke costs $0.45.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

Cost of 12- pack of Cokes = $5.40.

To find the cost of one Coke cost,

Use ratio property,

12 packs of cakes = $5.40
1 pack of cakes = 5.40/12

1 pack of cake = 0.45

The price of one pack of cake is $0.45

To learn more about Ratio on :

https://brainly.com/question/13419413

#SPJ2

Answer: B. 23.9 cm³

Step-by-step explanation:

V = AH

A (area of the triangle base): 6×3÷2=9cm²

H (height of the prism): 2.65 cm

------------------------

V =  AH

V =(9) (2.65)

V = (23.85)

V= 23.85cm²

 ≈23.9

Answer:

-18, -23, -28

Step-by-step explanation:

It looks like it is going down by -5

-18, -23, -28. Just subtract by 5 every time

Answer:

60 square feet

Step-by-step explanation:

area= length*width

a=5*12

a=60

Answer: 60 ft²

Step-by-step explanation: To find the area of the rectangular bedroom wall, we use the formula for the area of a rectangle, A = lw.

Since the length of the rectangle is 12 feet and the width of the rectangle

is 5 feet, we plug this information into the formula for length and width

and we have (12 ft)(5 ft) which simplifies to 60 ft².

So the area of the rectangular bedroom wall is 60 ft².

Answer:

72

Step-by-step explanation:

13-5=8^2

16/2=8

(8*8)+8

64+8

=72

Answer: [tex]72[/tex]

Subtract

[tex](13-5)^2\\=8^2[/tex]

Multiply

[tex]8^2=64\\8*8=64[/tex]

Divide

[tex]16/2=8[/tex]

Add

[tex]64+8=72[/tex]

Answer:

200

Step-by-step explanation:

Janet = x + 75

Kathy = x

2x + 75 = 325

2x = 325 - 75

2x = 250

x/Kathy = 125

x + 75/Janet = 125 + 75

= 200

Answer:

Step-by-step explanation:

[tex]AB=\sqrt{(6-0)^2+(5-8)^2}=\sqrt{36+9}=\sqrt{45}=3\sqrt5\\\\BC=|-1-5|=|-6|=6\\\\CD=\sqrt{(-2-6)^2+(-4-(-1))^2}=\sqrt{64+9}=\sqrt{73}\\\\DE=\sqrt{(-5-(-2))^2+(3-(-4))^2}=\sqrt{9+49}=\sqrt{58}\\\\EA=\sqrt{(0-(-5))^2+(8-3)^2}=\sqrt{25+25}=\sqrt{25\cdot2}=5\sqrt2[/tex]

Answer:

$1,170

Step-by-step explanation:

Area around the pool = 20 x 30

Pool = 12 x 24

Carpet is sold $1.95 by square foot

Use formula A = bh

Plug it in: A = 20 x 30

So they need 600 sq ft of carpet.

Multiply 600 by 1.95 to get 1170

The total cost = $1,170

Answer:

$608.40

Step-by-step explanation:

Dimensions of pool: 12 ft by 24 ft

Dimensions of pool & cement walkways: 20 ft by 30 ft

The pool is a rectangle that sits inside the walkways. The area of the walkways (AW) is the area of the pool & walkways (the 20 ft by 30 ft rectangle) minus the area of the the pool (the 12 ft by 24 ft rectangle). Once we know the area of the just the walkways (AW), we multiply it by the price of the carpet too find the cost of the carpet.

area of walkways = area of pool & walkways - area of pool

AW = 20 ft * 30 ft - 12 ft * 24 ft

AW = 600 ft^2 - 288 ft^2

AW = 312 ft^2

The area of the walkways alone is 312 ft^2. Now we multiply it by the unit cost of carpet to find the cost of the carpet needed for the walkways.

cost = AW * unit rate

cost = 312 ft^2 * $1.95/ft^2

cost = $608.40

Answer:

7) a = 65; b = 50

8) c = 125; d = 55; e = 52

9) f = 105

Step-by-step explanation:

7)

a = 65

b + 130 = 180

b = 50

8)

c = 125

d + 125 = 180

d = 55

e = 52

9)

(180 - f) + 32 + (180 - 107) = 180

180 - f + 32 + 180 - 107 = 180

-f + 285 = 180

-f = -105

f = 105

Answer:

a = 65, b = 50, c = 125, d = 55, e = 52, f = 105, g = 128, h = 40, j = 21, k = 71

Step-by-step explanation:

7. a = 65 degrees - (corresponding angles theorem)   b = 50 degrees - (because of same sided interior angles theorem you have to do 180 - 130)

8. c = 125 (corresponding angles theorem)  d = 55 (c & d are a linear pair so you have to do 180-125)     e = 52 (alternate interior angles theorem)

9. f = 105 (Because of alternate interior angles theorem the angle that is 32 degrees and the angle next to it is 107. Next subtract 32 from it, which will make it a 75 degree angle. Lastly to find f use same sided interior angles theorem, this means subtract 180-75)

10. h = 40 (because of vertical angles theorem the other angle in the triangle is 52 degrees. Now find add 88 + 52 = 140, then subtract it from 180)     g = 128 (same sided interior angles theorem)

11. j = 21 (First find the missing angle in the triangle. To do that add up all of the angles and then subtract it from 180. This makes the missing angle 39. Now subtract that from 60)

12. k = 71 (Since this is an isosceles triangle the 2 base angles will be congruent. Because of same sided interior angles theorem subtract 148 from 180, making it 32. We are trying to find the top angle of the triangle so add 32 + 110 = 142. Then subtract it from 180, 38. Now subtract 38 from 180, 142. Lastly divide it by 2, 71.)

Answer:

4a^2-20a+24+6y-9y^2

Step-by-step explanation:

The expression 4a^2-20a+24+6y-9y^2 can't be simplified further since the terms in this expression are unlike terms

Hope this helps ;) ❤❤❤

Answer:

297 miles

Step-by-step explanation:

cost = 0.78 cents per mile + base fee

y = 0.78x + 15.88

247.65 = 0.78x + 15.88

subtract 15.88 from both sides

231.77 = 0.78x

divide by 0.78 on both sides

x = 297.14120256

297 miles

Answer:

297.1410256 = m

Step-by-step explanation:

charge = 15.88 + .78m where m is the miles driven

247.65 = 15.88 + .78m

Subtract 15.88 from each side

247.65-15.88 = .78m

231.77 = .78m

Divide each side by .78

231.77/.78 = m

297.1410256 = m

Answer:

x = 5

Step-by-step explanation:

Simplify. First, combine like terms:

3x - x + 2 = 12

(3x - x) + 2 = 12

(2x) + 2 = 12

2x + 2 = 12

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

& is your order of operation.

First, subtract 2 from both sides:

2x + 2 (-2) = 12 (-2)

2x = 12 - 2

2x = 10

Next, divide 2 from both sides:

(2x)/2 = (10)/2

x = 10/2

x = 5

5 is your answer for x.

Check: Plug in 5 for x in the equation. Solve:

3(5) - (5) + 2 = 12

15 - 5 + 2 = 12

10 + 2 = 12

12 = 12 (True)

~

Answer:

x = 5

Step-by-step explanation:

Combining like terms, we get 2x = 10.  Dividing both sides by 2 yields

x = 5

Answer:

The answer is 8 kilometers.

Step-by-step explanation:

Let X be the total cost of the taxi fare and Y be the distance traveled. If the taxi fare costs $5, $2.5 for each kilometer, we can write an inequality such as

X = 2.5 x Y.

If the total amount of money for the ride is $20, when we put it into the inequality, 20 = 2.5 x Y

                 Y = 20 / 2.5 = 8.

For $20 you can ride for a maximum distance of 8 kilometers.

I hope this answer helps.

Answer:

Equation: 5+2.5d≤20

Kilometers: 6

Step-By-Step Explanation

Answer for Khan Academy and also correct for sure promise ;)

Answer:

12%

Step-by-step explanation:

Cost Price of the MP3 player =$150

Sales Tax = 8 %

Total sales tax=  Tax * Cost Price

                   =   [tex]\frac{8}{100} * 150[/tex]

                   =12%                  

He payed a total of 12% sales tax

Answer:

2. aa

Step-by-step explanation:

youre given all the angles so its proven to be similar by angle angle

Answer:

aa

Step-by-step explanation:

The two triangles have angles that are equal so we need to use the angles to prove similarity

We have all three angles that are equal

We only need two angles to use the AA postulate of similarity, which is if two angles are the same then the triangles are similar

If you want fractions that are similar to the two fractions you have:

Because the fractions are already in their simplest form, you can continue to multiply the numerator (top number) and the denominator (bottom number) by two (one whole), which is represented by 2/2.

1/6 = 2/12 = 4/24...

1/9 = 2/18 = 4/36...

If you want to have the same value for each fraction but have the same denominator:

(1/6)(9/9) = 9/54

(1/9)(6/6) = 6/54

Answer:

x and x+1

Step-by-step explanation:

x+4

x+1-2=x-1

So the quotient of the numbers is x+4/x-1

Answer:

Markdown price is $60.

Step-by-step explanation:

The discount offered on the cloths by the clothing shop = 75%

Since we know that the markdown price is the amount by which the original price is decreased. So, the markdown price can be calculated by multiplying the original price with a discount rate. Here, below is the calculation.

Markdown price = $80 × 75% = $60

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

There are 24 hours in 1 day, thus 15 hours is

[tex]\frac{15}{24}[/tex] = [tex]\frac{5}{8}[/tex] of a day in simplest form

Answer: I think the answer is -x^2+x-6

Step-by-step explanation: I think it's like this as it is in the image below. I hope it's right and helps you!