A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum is 4.

7x + 6y is a binomial that is a factor of given equation

Solution:

A binomial is a mathematical expression which has only two terms

Given expression is:

[tex]49x^2 + 84xy + 36y^2[/tex]

We have to find the binomial that is a factor to given expression

Let us find the factors of given equation

[tex]49x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}49x^2+84xy+36y^2\mathrm{\:as\:}\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\mathrm{Rewrite\:}49\mathrm{\:as\:}7^2\\\\7^2x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}36\mathrm{\:as\:}6^2\\\\7^2x^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\7^2x^2=\left(7x\right)^2\\\\Therefore,\\\\\left(7x\right)^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\6^2y^2=\left(6y\right)^2\\\\[/tex]

[tex]Therefore\\\\\left(7x\right)^2+84xy+\left(6y\right)^2\\\\\mathrm{Rewrite\:}84xy\mathrm{\:as\:}2\cdot \:7x\cdot \:6y\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\[/tex]

[tex]\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=7x,\:b=6y\\\\Therefore,\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2 = \left(7x+6y\right)^2[/tex]

Thus we get,

[tex]49x^2 + 84xy + 36y^2 = (7x+6y)^2\\\\49x^2 + 84xy + 36y^2 = (7x+6y)(7x+6y)[/tex]

Thus the binomial which is a factor is 7x + 6y

Answer:

←

Step-by-step explanation:

less than as 4.567 is less than 4.576

The correct symbol to use between 4.567 and 4.576 is '<', since 4.567 is less than 4.576.

The question is asking to choose the correct mathematical symbol that makes the given number sentence true. The two numbers are 4.567 and 4.576. In this case,  since 4.576 is greater than 4.567, the correct symbol would be less than ('<'). Thus, the correct number sentence is 4.567 < 4.576.

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a relationship or expression involving one or more variables

Answer:

1 ≤ x ≤ 6 (Answer D)

Step-by-step explanation:

Look for the stretch of graph that is horizontal.  The function is constant on that time interval:  from 1 to 6, or 1 ≤ x ≤ 6 (Answer D)

Answer:

Step-by-step explanation:

Plant B is taller than Plant C.  We need to determine by how much.  To do this, we divide 6 2/3 inches by 4 4/15 inches.  The LCD is 15, and so we have:

6 10/15       100/15

----------- or ------------- = 100/64 = 20/16 = 5/4

4 4/15           64/15

Plant B is 1 and 1/4 times taller than Plant C.  This can be restated as Plant C is four fifths as tall as Plant B.

Plant C is shorter than Plant B, as we saw earlier.  The difference is found through subtraction:  100/15 - 64/15 = 36/15 inches = 12/5 inches shorter, or 2 2/5 inches shorter

Plant C is approximately 12 4/5 times as tall as Plant B. Plant C is approximately 2 2/5 inches shorter than Plant B.

To find out how many times larger Plant C is compared to Plant B, we need to divide the height of Plant C by the height of Plant B. In this case, Plant C is 4 4/15 inches tall and Plant B is 6 2/3 inches tall.

So, the calculation would look like this:

4 4/15 ÷ 6 2/3

To divide fractions, we need to convert the mixed numbers into improper fractions. So, Plant C is 64/15 inches tall and Plant B is 20/3 inches tall.

Now we can divide the fractions:

64/15 ÷ 20/3 = (64/15) x (3/20)

Cancel out common factors:

64/5 ÷ 1/1 = 64/5 = 12 4/5

Plant C is approximately 12 4/5 times as tall as Plant B.

To find out whether Plant C is taller or shorter than Plant B, we need to subtract their heights. Plant C is 4 4/15 inches tall and Plant B is 6 2/3 inches tall.

So, the calculation would look like this:

4 4/15 - 6 2/3

Again, we need to convert the mixed numbers into improper fractions:

Plant C is 64/15 inches tall and Plant B is 20/3 inches tall.

Now we can subtract the fractions:

64/15 - 20/3 = (64/15) - (20/3

To subtract fractions, we need to have the same denominator. So, we need to find a common denominator for 15 and 3, which is 15.

64/15 - 100/15 = -36/15 = -2 6/15 = -2 2/5

Plant C is approximately 2 2/5 inches shorter than Plant B.

Answer:

Step-by-step explanation:

4005.09

The amount that she earned in 10 years is $4,005.09.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \$3,000 \times (1+ 2.9\% \div 4)^{10\times 4}[/tex]

= $4,005.09

Here the rate of interest should be divided by 4 and time period should be multiplied by 4.

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Answer:

3168 feet / minute

Step-by-step explanation:

Answer: (2.2 × 10)(1 × 10) = 2210.

Step-by-step explanation:Step 2: Multiply both top and bottom by 10 for every number after the decimal point: As we have 1 numbers after the decimal point, we multiply both numerator and denominator by 10. So, 2.21 = (2.2 × 10)(1 × 10) = 2210.

Answer

1/5+ 2

Step-by-step explanation:

.2 equals a fith so when you add that to the whole number the answer will be 2  1/5

1/5 +2 = 2 1/5

2 1/5= 2.2

Answer:

[tex]They\ stayed\ for\ 2\ hours\\\\And\ each\ one\ payed=\$12[/tex]

Step-by-step explanation:

[tex]Let\ both\ spend\ x\ hours[/tex]

Payment by Ronald:

[tex]Ronald\ paid\ \$ 12.[/tex]

Payment by Tyler:

[tex]Tyler\ paid\ $4\ up\ front\ and\ $4\ per\ hour\\\\Total\ amount\ paid\ by\ Tyler=4+4\times number\ of\ hours\\\\Total\ amount\ paid\ by\ Tyler=4+4\times x\\\\Total\ amount\ paid\ by\ Tyler==4+4x[/tex]

[tex]Amount\ paid\ by\ both\ of\ them\ are\ equal\\\\4x+4=12\\\\4x=12-4\\\\4x=8\\\\x=2[/tex]

[tex]They\ stayed\ for\ 2\ hours\\\\And\ each\ one\ payed=\$12[/tex]

Step-by-step explanation:

[tex] \sqrt{ - 144} = \sqrt{144 \times ( - 1)} \\ = \sqrt{144} \times \sqrt{ - 1} \\ = 12 \times i.. (\because i^2 =-1)\\ = 12i \\ \\ \therefore \: \sqrt{ - 144} = 12i[/tex]

Answer:

[tex]=12*i[/tex]

Step-by-step explanation:

Given: [tex]\sqrt{-144}[/tex]

The square root of some negative value can be find by splitting it in the way given below:

             [tex]\sqrt{-144}= \sqrt{144*(-1)}[/tex]

                   [tex]=\sqrt{144} *\sqrt{-1}[/tex]                                                                   as,    

                                                                                                         [tex]\sqrt{144}=12 \\\sqrt{-1}=i[/tex]

               [tex]\sqrt{-144}[/tex]      [tex]=12*i[/tex]

look at the number next to the thousands place. it's less than 5 so you round it down to the nearest thousand which is 6000.

Answer:

A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

Step-by-step explanation:

Just took the test y'all Trust me the answer is A.

The statement *(A) "A rewards' customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same" is correct,

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

We have a graph represents the customer pays for 106 ounces and 12 ounces of much a rewards' customer pays based on the number of yogurt.

Based on the graph, we can say a rewards' customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.

Thus, the statement *(A) "A rewards' customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same" is correct,

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Equation: L= -0.5D+34.

The water level be 26 feet in 16 days.

Step-by-step explanation:

Let us consider the initial level (x=0) of the water is 34 feet. Then its coordinate point can be written as (0,34).

The water is receding at the rate 0.5 feet per day, which given us the information that 0.5 is the slope since it is the rate of change and it is decreasing so it is a negative slope.

⇒m= -0.5.

The line equation is  y = mx+c. Let us rewrite as L= mD+c.

Where L is the level of water(y-axis) and D is the days(x-axis) and c is y-intercept.

⇒L= (-0.5)D+c.

To find y-intercept, substitute (0,34) (the known point from the graph) in the equation. Also, the point in y axis when x=0 is y-intercept.

34=  (-0.5)(0)+c.

c=34.

∴L= (-0.5)D+34.

To find the days when the water achieves level as 26 feet:

26 = (-0.5)D+34.

26-34= (-0.5)D.

-8 =  (-0.5)D.

D= [tex]\frac{-8}{-0.5}[/tex].

D= 16.

Answer: Associative Property of Multiplication

It states that a(b*c) is the same as (a*b)*c

Hope this helped!

Answer:

3.16227766017

Step-by-step explanation:

I think so

Answer:

Plot a point at 5 on the y axis then move up 2 spaces and right 3 spaces and plot a point there

Answer:

Equal

Since OK and JK are radii of the same circle, they are equal. This means that OK = 12.

Step-by-step explanation:

Edge 2021

Answer:

2.19

Step-by-step equation:

Yes, because AB and CD are parallel and GH is perpendicular to CD, AB is perpendicular to GH. So you are right.

Answer:

1 - 1/3 - 1/4 - 1/5

Step-by-step explanation:

Let's take it one step at a time.

Day 1 he completes 1/3 of the garage, so you subtract 1/3 from 1 which means he left 2/3

Day 2 he completed 1/4 more, so you again subtract, this time though 2/3 - 1/4, or in other words 1 - 1/3 - 1/4

So you do this one more time.  1 - 1/3 - 1/4 - 1/5

Can you handle this or do you need help with fraction subtraction.  

The simplified form of the given expression is 6x+3.

The given expression is x+3+5x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be simplified as follows

Now, x+3+5x

Add like terms

(x+5x)+3

= 6x+3

Therefore, the simplified form of the given expression is 6x+3.

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Answer:

Step-by-step explanation:

Cost of stock (without the broker's fee) : 3000 * 6.30 = 18,900

Cost of broker's fee: 3000 * 0.02 = $ 60

For a total cost of (18,900 + 60) = $18,960

Answer:

1. Cost of stock = $ 18,900

2. Total paid = $ 18,960

Step-by-step explanation:

1. Let's review the information provided to us to answer the questions correctly:

Number of GTI petroleum shares purchased by Enice = 3,000

Cost per share = $ 6.30

Broker's commission was $19.95 for fewer than 1,000 shares or $0.02 per share for 1,000 or more

2.  What was the cost of the stock? What was the total paid?

Let's calculate the cost of the stock, this way:

Cost of stock = 3,000 * 6.30

Cost of stock = $ 18,900

Cost of brokers' commission = 3,000 * 0.02

Cost of brokers' commission = $ 60

Total paid = Cost of stock + Cost of broker's commission

Total paid = 18,900 + 60

Total paid = $ 18,960

Answer:

Steps. (6x - 3) - (2x -2)= 6x - 3 - 2x + 2. = (6x - 2x) + (-3 + 2) = 4x + (-1 ) 4x - 1 ---> Answer.

Use the red dots as two points in the line.

Slope = change in y over the change in x.

point 1: (-5,4)

Point 2: (5,-2)

Slope = (-2 - 4) / ( 5 - -5)

Slope = -2/10

Slope = -1/5

Answer:

3/-5

Step-by-step explanation:

The formula for the slope of a line is rise over run, rise/run

So from any given two points, you can calculate this.

rise is 3

run is 5, but it would be negative 5 because the slope of the line is negative.

Please find the attachment on the Frequency table with 2 categories. It is 2X2 2 rows and 2 colums.

Step-by-step explanation:

Answer:

C) 188.5 in2

Step-by-step explanation:

The solution is 188.5 in2. To determine the surface area, plug 3 and 7 into the formula.

S = 2π32 + 2π(3)(7) ≈ 188.5 in

Answer:

131.4

Step-by-step explanation:

Answer:

The price of an item has dropped to $63 today. Thus, The percentage decreased will be 45%.

Answer: [tex]5y - x = -25[/tex]

Step-by-step explanation:

The formula for calculating equation of line when a point and a slope is gives is :

[tex]y - y_{1} = m ( x - x_{1})[/tex]

[tex]x_{1} = 10[/tex]

[tex]y_{1} = -3[/tex]

[tex]m = \frac{1}{5}[/tex]

substituting into the formula , we have

[tex]y - (-3) = \frac{1}{5}(x - 10 )[/tex]

[tex]y + 3 = \frac{1}{5}(x - 10 )[/tex]

multiply through by 5 ,

[tex]5 (y+ 3 ) = x - 10[/tex]

[tex]5y + 15 = x - 10[/tex]

in standard from , we have

[tex]5y - x = -10 - 15[/tex]

[tex]5y - x = -25[/tex]

Answer:

A) The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute.

Step-by-step explanation:

The function for cell duplication where the cells duplicate every minute, is given by [tex]f(x)=75(2)^x[/tex]

The initial number of cells occurs when x=0:

[tex]f(0)=75(2)^0[/tex]

Note that every non-zero number to the exponent of zero is 1.

[tex]\implies f(0)=75(1)=75[/tex]Therefore the initial number of cells  is 75

The two is the multiplicative rate of change, therefore the 2 indicates that the number of cells doubles every minute.