At 5 p.m., Henry and Gordon have made 60 and 20 cranes respectively. Henry can make 30 cranes per
hour while Gordon can make 40 cranes per hour. When will they get the same number of cranes?​

Answer:

[tex]\boxed{ x = 0 \ \ OR \ \ x = 7}[/tex]

Step-by-step explanation:

[tex]8x^2 -56 = 0[/tex]

Greatest common factor = 8x

=> [tex]8x(x-7) = 0[/tex]

Setting results equal to 0

Either:

8x = 0                OR        x-7 = 0

x = 0                 OR           x = 7

Answer:

x= 0 or 7

Step-by-step explanation:

if you factor out the equation by 8, you get 8x(x-7)=0, which if you simplify that, gets you 0 or 7.

Answer:

Step-by-step explanation:

The commutative property lets you swap the order of operands. Here, the operands for addition, (8uv) and (9w), are interchanged. The Commutative Property of Addition lets you do that.

__

The associative property lets you group operands differently. Here, the operands in the product 8uv are changed from the grouping (8u)v to the grouping 8(uv). The Associative Property of Multiplication lets you do that.

Answers:

Step-by-step explanation:

Now let's see why these are the correct answers:

___________________________________________________________

Commutative Property of Addition states that changing the order of the addends will not affect the sum. For example 5 + 4 and 4 + 5 are both 9.

Here, this is a correct answer because 9w is moved from the end of the equation to the front.

___________________________________________________________

Commutative Property of Multiplication states that changing the order of multiplicands does not change the product. For example 5 x 2 and 2 x 5 both equal 10.

Here, this is not a correct answer because the multiplicands are associated differently in the parentheses.

___________________________________________________________

Associative Property of Addition states that the way in which addends are grouped within parentheses doesn't change the sum. For example (2 + 3) + 4 or 2 + (3 + 4) both equal 9.

Here, this is not a correct answer because the addends are not in parentheses, which is the only time this property applies.

___________________________________________________________

Associative Property of Multiplication states that the way in which multiplicands are grouped within parentheses does not affect the product. For example 2 x (2 x 2) and (2 x 2) x 2 both equal 8.

Here, this is a correct answer because the multiplicands are within parentheses and are regrouped in the second equation, the (8u)v having been regrouped as 8(uv).

___________________________________________________________

Answer:

plot 2

Step-by-step explanation:

put number in order from least to highest:

1 ,3,4,5,8,8,9,11,11,11,14,15,15,18,19,19,19,21,22,23,

from 1 to 5      4 terms

5 to 10             3 terms

from 10 to 15   4 terms (since you can put the 15 in either 10 to 15 or 15to 20)

from 15 to 20  6 terms

from 20 to 25   3

Answer:

Volume = 6467.492mm³

Surface area = 1332.035mm²

Step-by-step explanation:

volume of a cone is [tex]\pi[/tex]r²h. V=[tex]\pi[/tex]10²(24)=7539.822mm³

volume of a sphere is 4/3[tex]\pi[/tex]r³.  V=4/3[tex]\pi[/tex](8³)=2144.66mm³

Since it's a half of a sphere, it would be 1072mm.33³

7539.822-1072.33=6467.492mm³

Surface area of a cone is [tex]\pi[/tex]r(r+√h²+r²)=1130.97

area of a circle= [tex]\pi[/tex]r²=201.06

surface area of a sphere is 4[tex]\pi[/tex]r²=804.25

Since it's a half sphere, it would be 402.125

1130.97-201.06+402.125=1332.035mm²

Answer:

x = 14

Step-by-step explanation:

3x+1=43

Subtract 1 from each side

3x+1-1=43-1

3x = 42

Divide by 3

3x/3 = 42/3

x =14

Answer:

x =14

Step-by-step explanation:

Greetings,

I hope you and your family are staying safe and healthy!

So basically, we have 3 cats catching 3 mice in 3 minutes. That means 1 cat is catching 1 mouse, but it takes it 3 mn.

Now if we have 99 mice and we need to catch them in 99 minutes, we will need 99 cats.

99 cats will catch 99 mice in 99 minutes...meaning each cats will take 1 minute to catch their mice.

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

If you find my answer helpful, please kindly give 5 stars and press the heart. Thanks!

Answer:

No.

Step-by-step explanation:

100 000 000 = 10^8

So its square root = (10^8)^1/2

= 10^4

= 10,000.

  which is rational.

You can check out this answer on a calculator. It is correct.

Answer:

property of zero.

Step-by-step explanation:

It is given that, (4y + 1) × 0 = 0 . We need to tell out of four given options, which property is used in this case.

The property of zero states that if any number is multiplied by 0, then the answer is equal to 0.

Here, the number is (4y+1). It is multiplied by 0. It means that the result is 0.

Hence, it shows "property of zero".

Answer:

The area of the black square is equal to the sum of the areas of the gray squares.

Answer:

The area of the black square is equal to the sum of the areas of the gray squares.

Answer:

14,641.

Step-by-step explanation:

214,358,881 ÷ 14,641 = 14,641.

Answer:

x = -25

Step-by-step explanation:

Step 1: Write out equation

2/5x + 10 = 0

Step 2: Subtract 10 on both sides

2/5x + 10 - 10 = 0 - 10

2/5x = -10

Step 3: Multiply both sides by 5/2

5/2(2/5x) = -10(5/2)

x = -50/2

x = -25

Answer:

B.(x-3)(x+8)

Step-by-step explanation:

product of -3 and 8 is -24 and sum of -3+8 is +5

Answer:

(x+8) (x-3)

Step-by-step explanation:

x² + 5x – 24

What 2 numbers multiply to -24 and add to 5

8*-3 = -24

8+-3 = 5

(x+8) (x-3)

The total number of bacteria in the dish is 31457280

The expression is given as:

Total = (32)^4 * 30

Start by evaluating the exponent

Total = 1048576 * 30

Next, evaluate the product

Total = 31457280

Hence, the total number of bacteria in the dish is 31457280

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Answer:

A (3^8)

Step-by-step explanation:

I have this question on my test. I'm just assuming the person didn't put ^.

(3^2)^4 times 3^0

Answer:

Proof given by contradiction.

Step-by-step explanation:

Given that:

[tex]n \geq 2[/tex]

To prove:

[tex]n[/tex] is prime if and only if no positive integer > 1 and [tex]\leq[/tex] [tex]\sqrt n[/tex] divides [tex]n[/tex].

Solution:

First of all, let [tex]n[/tex] is a composite number i.e. not a prime number such that:

[tex]n =a\times b[/tex]

and [tex]a[/tex] and [tex]b[/tex] are prime and [tex]a[/tex] divides [tex]n[/tex] and [tex]b[/tex] also divides [tex]n[/tex].

Let [tex]\sqrt n = p[/tex]

or [tex]n = p\times p[/tex]

1. [tex]\underline{a < p}[/tex]:

[tex]a[/tex] is prime and is a divisor of [tex]n[/tex].

2. [tex]\underline{a>p}[/tex]:

[tex]n = a\times b = p\times p[/tex]

We have assumed that [tex]a > p \Rightarrow b <p[/tex]

[tex]b[/tex] is a prime number and is a divisor of [tex]n[/tex].

But we are given that no prime number [tex]\leq \sqrt n[/tex] divides [tex]n[/tex] but we have proved that [tex]b < \sqrt n[/tex] divides [tex]n[/tex].

So, it is a contradiction to our assumption.

Therefore, our assumption is wrong that  [tex]n[/tex] is a composite number.

Hence, proved that [tex]n[/tex] is a prime number.

Answer:

$121.82

Step-by-step explanation:

Okay, this is kind of complex, so let's go step by step.

First, we want to find the area of the rectangular lawn - we can do this by multiplying the length and width. The length is 100 and the width is 45 so [tex]45\cdot100=4500[/tex] m² is the area of the rectangle.

However, there are 3 ponds in which the grass seeds will not be going - so we need to find the area of all 3 of these circles and subtract it from 4500 (our rectangle area).

The area of a circle is represented by the formula [tex]\pi r^2[/tex]

The diameters are given here, which is double the radius, so to find the radius of each circle let's divide the diameters by 2.

First circle's radius: [tex]20\div2=10[/tex]

Second circle's radius: [tex]10\div2=5[/tex]

Third circle's radius: [tex]5\div2=2.5[/tex]

Now let's find the area of each circle.

First Circle: [tex]\pi \cdot10^2 = \pi\cdot100=3.14\cdot100=314[/tex]

Second Circle: [tex]\pi\cdot5^2 = \pi \cdot25 = 3.14\cdot25=78.5[/tex]

Third Circle: [tex]\pi \cdot 2.5^2 = \pi \cdot6.25 = 3.14\cdot6.25=19.625[/tex]

Adding all of these values gets us 412.125.

Now we can subtract from this from 4500 to get us 4087.875

If the grass seeds that cost £1.49 cover 50m² each, then we need [tex]4087.875\div50=81.7575[/tex] bags.

Each bag costs £1.49, so the total cost is [tex]81.7575\cdot1.49\approx121.82[/tex]

Hope this helped!!

Answer:

B. 25/4

Step-by-step explanation:

to calculate how many miles Jana ran everyday, divide the total distance by number of days

50/8

simplify, 25/4

the answer is B

Answer:

40

Step-by-step explanation:

4-3=1

9-1=8

32+8=40

52-40=12

12 is your final answer

Answer:

D

Step-by-step explanation:

Add real numbers and add imaginary numbers

(-7 + 3i)+(2 - 6i) = -7 + 2 + 3i - 6i

                        =  - 5 - 3i

[tex] &#128075 [/tex] Hello ! ☺️

Step-by-step explanation:

•What is the value of (-7+3i)+(2-6i)?

[tex] (- 7 + 3i) + (2 - 6i) = ( - 7 + 2 + 3i - 6i) = - 5 - 3i [/tex]

(-7+3i)+(2-6i) = [tex]\boxed{\color{gold}{ -5-3i}} [/tex]

[tex]<marquee direction="left" scrollamount="2" height="100" width="150">&#x1F498;Mynea04</marquee>[/tex]

Answer:

Cory bought 6.47 gallons

rate of change is $2.78 per gallon

Step-by-step explanation:

cost of gas per gallon = $2.78

it means that if one buy 1 gallon he will have to pay $2.78 and similary for each increase in 1 gallon of gallon gas he will have to pay $2.78.

Thus, rate of change is cost of gas per gallon as cost to buy gas changes with the change in quantity of gallon.

Let the quantity of gas bought be x gallon.

Total cost for x gallons = cost of gas per gallon*x = 2.78x

Given that total money paid by him is $18

2.78x = 18

x = 18/2.78 = 6.47

Thus, Cory bought 6.47 gallons

rate of change is $2.78 per gallon

Answer:

[tex]\Huge \boxed{y=3x+6}[/tex]

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

The slope can be found from two points.

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The two points from the graph are (1, 9) and (2, 12).

Plugging in the values and evaluating.

[tex]\displaystyle m=\frac{12-9}{2-1}[/tex]

[tex]\displaystyle m=\frac{3}{1}[/tex]

[tex]m=3[/tex]

The slope of the line is 3.

The y-intercept of the line is where the line cross the y-axis.

The line crosses the y-axis at (0, 6).

[tex]b=6[/tex]

The slope-intercept form of the line is:

[tex]y=3x+6[/tex]

Answer: x = 32

Step-by-step explanation:

x/8 - 5 = -1

Add 5 both sides : x/8 = 4

Multiply both sides by four: x=4 times 8

Answer: 36

Step-by-step explanation:

The 100% of the sweater is 45, we multiply 45 per 20 divided by 100, that will give you 9, you want to rest 45-20%

45-9=36

Answer: 36

Step-by-step explanation: The 100% of the sweater is 45, we multiply 45 per 20 divided by 100, that will give you 9, you want to rest 45-20%

45-9=36

18 shelves he needs to sell

Answer: C

Step-by-step explanation:

Answer:

[tex]\bold{a = \dfrac{24}{7}}[/tex]

Step-by-step explanation:

Kindly refer to the attached for the values labelled to the line XZ.

The point Y is in between XZ.

It can be clearly observed that XZ is made up of sum of two lines XY and YZ.

So, we can write:

XZ = XY + YZ ....... (1)

We are given the values of line segments:

XY = 4a

YZ = 9a and

XZ = 6a+24

To find: Value of variable 'a'.

Solution:

Putting all the values in equation (1):

[tex]6a+24 = 4a + 9a\\\Rightarrow 6a+24=13a\\\Rightarrow 7a=24\\\Rightarrow \bold{a = \dfrac{24}{7}}[/tex]

So, value of variable is

[tex]\bold{a = \dfrac{24}{7}}[/tex]

Answer:

see below the first three problems

Step-by-step explanation:

f(g(-2))

First, find g(-2) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(-2) = -2(-2) + 1

g(-2) = 5

f(x) = 5x

f(5) = 5(5)

f(5) = 25

f(g(-2)) = 25

g(h(3))

First, find h(3) using function h(x). Then use that value as input for function g(x).

h(x) = x^2 + 6x + 8

h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8

h(3) = 35

g(x) = -2x + 1

g(35) = -2(35) + 1 = -70 + 1

g(35) = -69

g(h(3)) = -69

f(g(3a))

First, find g(3a) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(3a) = -2(3a) + 1

g(3a) = -6a + 1

f(x) = 5x

f(-6a + 1) = 5(-6a + 1)

f(-6a + 1) = -30a + 5

f(g(3a)) = -30a + 5

Answer:

8x + 2 = 40 - 24x

Step-by-step explanation:

8x + 8-6 = 60 - 24x - 20

Next step is simplification and is:

The following steps:

Answer: 5x2+3x -dx x3 2x2

Step-by-step explanation:

Answer: 3 terms

Step-by-step explanation:

each term is separated by the plus or minus symbol

Answer:

3 terms

Step-by-step explanation:

5x + 3y - 6

We cannot combine any terms so there are 3 different terms

5x, 3y, -6

Answer:

i

Step-by-step explanation:

√-1 is always going to be imaginary i

That is a math rule needed to memorize.

Answer:

i

Step-by-step explanation: