Which is a factor of 3x^2 − 33x + 84?

x+y=64 and x-y=16 can be used to solve the system.

Step-by-step explanation:

Let,

x,y be the two shirts.

According to given statement;

Bob spent $64 on both shirts;

x+y=64    Eqn 1

The difference between the costs of the shirts was $16 means subtraction;

x-y=16      Eqn 2

x+y=64 and x-y=16 can be used to solve the system.

Keywords: linear equation, addition

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Answer:

The cost of the shirts are $40 and $24

Step-by-step explanation:

Let

x ----> the cost of one shirt

y ----> the cost of the other shirt

we know that

[tex]x+y=64[/tex] ----> equation A

I assume that the cost x is greater than the cost y

so

[tex]x-y=16[/tex] ----> [tex]x=y+16[/tex] ---> equation B

solve the system by substitution

substitute equation B in equation A

[tex]y+16+y=64[/tex]

solve for y

[tex]2y=64-16[/tex]

[tex]2y=48[/tex]

[tex]y=\$24[/tex]

Find the value of x

[tex]x=y+16[/tex] ---->  [tex]x=24+16=\$40[/tex]

therefore

The cost of the shirts are $40 and $24

Answer:

A) 1/4 min

Step-by-step explanation:

Find the equation for the graph:

y = mx + b

Find the slope using two random points (0, 360) and (5, 0)

m = (y2 - y1) / (x2 - x1)

m = (0-360) / (5-0)

m = -360/5

m = -72

b is 360, the y-intercept.

Substitute m= -72 and b=360 into slope-intercept form.

y = -72x + 360

x represents time and y represents the total amount of water at the time.

We are looking for when only 18 liters were drained.

360 - 18 = 342  <= Total amount of water when 18 liters are drained

Substitute 342 for y in the equation and isolate x.

342 = -72x + 360

-18 = -72x

x = 18/72

x = 1/4

Therefore, it will take 1/4 of a minute to drain 18 liters.

Answer: 1/4

Step-by-step explanation:

I got it right on khan academy.

Hope this helps

Answer:

a) $13588.08

b) $688.08

Step-by-step explanation:

Melissa had to purchase $12,900 worth of machinery for her business.

She made a down payment of $2100 and after that made monthly payments of $478.67 for the business loan for the rest.

Given that after years of paying monthly payments of $478.67, she finally paid off the loan.

Assume that she took 2 years to repay the loan.

a) Therefore, the total amount Melissa ended up paying for the machinery was $[2100 + (478.67 × 24)] = $13588.08 (Answer)

b) Therefore, the amount of interest that Melissa pay on the loan is $(13588.08 - 12900) =$688.08. (Answer)

Steps to solve:

10.2x + 9.4y when x = 2 and y = 3 ​

= 10.2(2) + 9.4(3)

= 20.4 + 28.2

= 48.6

______

Best Regards,

Wolfyy :)

Answer:

48.6 is the answer

Step-by-step explanation:

Okay, first you plug in the variables  x and y .

So now the new equation is 10.2x2 this is ,because everytime a number get put next to another number you multiply.  So .....

(10.2x2) + (9.4x3)=

20.4+28.2=

48.6

Answer:

7 and up

Step-by-step explanation:

35 / 5 = 7

Dan buys at least 7 bags

Answer:

-7/48 in

Step-by-step explanation:

Assuming that the movement varies linearly with time,

3 years ------> -7/16 in

1 year -------> -7/16 ÷ 3 = -7/48 in

Answer:

false.

Step-by-step explanation:

$5 off is well $5 off so, we would be paying $45 for the item. If we took 25%, thats $12.50 therefore you would only pay $37.50. So the 25% saves you $7.50 so it si false. $5 is a worse deal.

Independent. Two events are dependent if knowing the result of the first one influences what you'd expect from the second.

Consider this example: if I have a sack with 3 black marble and 1 white marble, I have probability 75% of picking a blakc marble, and 25% of picking the white one.

If I pick the white one, and don't replace, the second pick will be dependent on the first one, because now I'm sure that I'll pick one of the black marbles, since they are the only ones left in the sack.

In your example, though, Wendy replaces the marble she picks first. This means that the second pick will take place in the exact same conditions of the first one, and knowing which marble she picked at first doesn't affect in any way the result of the second pick.

As another example, consider rolling two dice. Suppose that the first die lands showing 4. Does this affect in any way what you'd expect from the second die? Well, no: the numbers 1-6 are still equally probable to show up.

Answer:

City's Area = 507.44 sq. mi.

Step-by-step explanation:

We will use population density formula to solve this problem easily.

We have:

Population Density = Total Population/ Land Area

Given,

Population Density = 24,403

Total Population = 12,383,007

We want land area, so we simply plug in the numbers into the formula and solve for City's Area. Shown below:

[tex]Population  \ Density = \frac{Total \ Population}{Land \ Area}\\24,403=\frac{12,383,007}{Land \ Area}\\Land \ Area = \frac{12,383,007}{24,403}\\Land \ Area = 507.44[/tex]

THe units is Square Miles, so we can say:

City's Area = 507.44 sq. mi.

Answer:

c)1200

Step-by-step explanation:

Given: Students were packed shoulder to shoulder in a gym for a pep rally. The students were in a rectangular shaped area of [tex]7500[/tex] ft.

To Find: If each student on average took up a circular space with a diameter of [tex]2.5[/tex] ft what is the best estimate for the number of  students at the pep rally.

Solution:

Consider the figures attached

A student took up a circular space, if they were packed in rows each student acquired a circular space of [tex]2.5[/tex] ft and left some unused area as given in figures

Now,

Area acquired by a student is a square of side [tex]2.5[/tex] ft as given in figure

Area acquired by single student[tex]=(\text{length of square})^2[/tex]

                                                     [tex]=2.5\times2.5[/tex]

                                                     [tex]6.25\text{sq.ft}[/tex]

Total number of students            [tex]=\frac{\text{total area of rectangular gym}}{\text{area acquired by single student}}[/tex]

                                                     [tex]\frac{7500}{6.25}[/tex]

                                                     [tex]1200[/tex]

there are approximately [tex]1200[/tex] students in gym hence option b is correct.

Answer:

Step-by-step explanation:

[tex]8n=24[/tex]           divide both sides by 8

[tex]\dfrac{8n}{8}=\dfrac{24}{8}[/tex]

[tex]n=3[/tex]

Check:

[tex]8(3) = 24[/tex]

[tex]24=24[/tex]              CORRECT

Answer:

n=3

Step-by-step explanation:

8n=24

24 divided by 8

=3

the n is left behind so you r left with n =3

Answer:

12 and 8

Step-by-step explanation:

12 + 8= 20

12 x 8= 96

The two numbers are 12 and 8. They have a sum of 20 and a product of 96, satisfying the given conditions.

To find two numbers whose sum is 20 and whose product is 96, we can set up a system of equations. Let's call the two numbers x and y.

1. The first equation represents their sum:

  x + y = 20

2. The second equation represents their product:

  xy = 96

Now, we need to solve this system of equations. One way to do it is by substitution. From the first equation, we can express y in terms of x: y = 20 - x.

Now, we substitute this expression for y into the second equation:

x(20 - x) = 96

Expanding and simplifying this equation:

20x - x^2 = 96

Rearranging terms:

x^2 - 20x + 96 = 0

Now, we factor the quadratic equation:

(x - 12)(x - 8) = 0

This gives us two possible solutions for x: x = 12 and x = 8.

So, the two pairs of numbers that satisfy the conditions are (12, 8) and (8, 12). In both cases, the sum of the numbers is indeed 20, and their product is 96, as required.

In summary, the two numbers are 12 and 8, and they meet the criteria of having a sum of 20 and a product of 96. These solutions demonstrate how algebraic techniques can be used to solve real-world problems involving unknown values.

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Answer:

Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves.

Step-by-step explanation:

Let in each large bookshelves Henry uses x nails and in each small bookshelves, Henry uses y nails.

Now, he built 10 small bookshelves and 1 large bookshelf, using a total of 412 nails.

So, 10x + y = 412 ......... (1)  

Again, he built 10 small bookshelves and 8 large bookshelves, using a total of 776 nails.

So, 10x + 8y = 776 ........... (2)

Now, subtracting equation (1) from equation (2) we get, 7y = 364

⇒ y = 52

Again, from equation (1) we get, 10x = 412 - 52 = 360

⇒ x = 36

Therefore, Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves. (Answer)

Final answer:

Henry uses 36 nails for a small bookshelf and 52 nails for a large bookshelf, according to the system of equations derived from the information given.

Explanation:

Calculating the Number of Nails Used by Henry

To solve this problem, we will use a system of equations.
Let's define x as the number of nails used for a small bookshelf and y as the number of nails used for a large bookshelf. From the question, we have the following equations based on the information given:

10x + 1y = 412 nails (first scenario with 10 small and 1 large bookshelf)

10x + 8y = 776 nails (later scenario with 10 small and 8 large bookshelves)

We can use these two equations to find out the values of x and y. Let's subtract the first equation from the second to eliminate x from our calculations:

10x + 8y − (10x + 1y) = 776 − 412
7y = 364
y = 52

Now we know that Henry uses 52 nails for a large bookshelf. Next, we will find the number of nails for a small bookshelf by substituting the value of y into the first equation:

10x + 1(52) = 412
10x = 412 − 52
10x = 360
x = 36

Hence, Henry uses 36 nails for a small bookshelf.

Answer:

Step-by-step explanation:

B

Answer:

3

Step-by-step explanation:

According to the Triangle Inequality Theorem, the sum of any 2 sides of any triangle must be greater than the length of the third side. That is:

AB + BC > AC and AB + AC > BC and AC + BC > AB

So in this case:

if AC + AB > BC

x + 12 > 15

After substracting 12 from each side of the equation, we get that:

x > 3

Hence, the value of x must be greater than 3.

Answer:

Here we have to use the Triangle Inequality Theorem, because the problem it's asking about the restriction of one side, with two sides given. This theorem, in words, states that the sum of the minor sides is more than the length of the major sides of all three. So, if we translate this to equation, we have:

[tex]AB + BC > AC[/tex]

Where [tex]AB=12[/tex]; [tex]BC=x[/tex] and [tex]AC=15[/tex]

Assuming that [tex]AC[/tex] is the longest side we applied the theorem to this problem. Now, replacing all values we have:

[tex]12+x>15\\x>15-12\\x>3[/tex]

Therefore, the unknown side must be greater than 3 to not violate the Triangle Inequality Theorem, which is always true about every triangle.

Answer:

x=1+/-4i

Step-by-step explanation:

(x+1)/3-(2x-1)/x=-1

find the common denominator,

in this case, it's going to be 3x.

(x^2+x)/3x-(6x-3)/3x=-1

(x^2+x-6x+3)/3x=-1

x^2-5x+3=-3x

x^2-5x-(-3x)+3=0

x^2-5x+3x+3=0

x^2-2x+3=0

apply the quadratic formula in order to find the roots for x.

Since ax^2+bx+c=0, in this case,

a=1, b=-2, c=3

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

x=(-b+/-sqrt(b^2-4ac))/2a

x=(2+/-sqrt(4-12))/2

x=(2+/-8i)/2

x=1+/-4i

Answer:

6x - 3

Step-by-step explanation:

Distribute first.

4x + 6x - 3 - 4x = 10x - 4x - 3 = 6x - 3

The equivalent expression for 4x + 3(2x - 1) - 4x is 6x - 3, achieved by distributing the multiplier in the parenthese and then combining like terms.

The expression 4x + 3(2x - 1) - 4x can be simplified by first distributing the 3 in the term 3(2x - 1), then combining like terms.

1. Distribute the 3 to get : 4x + 6x - 3 - 4x

2. Combine like terms: 6x - 3

So, the equivalent expression of 4x + 3(2x - 1) - 4x is 6x - 3

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Answer:

Rhombi is the answer...

That is option C

Answer:

C

Step-by-step explanation:

Rhombi has quadrilateral with diagonal and are perpendicular.

Final answer:

The projectile takes 1.22 seconds to reach its maximum height.

Explanation:

To find the time it takes for the projectile to reach its maximum height, we can use the equation:

where t is the time, v_f is the final velocity, v_i is the initial velocity, and a is the acceleration.

In this case, the initial velocity is 12.0 m/s and the acceleration is -9.8 m/s² (negative because the projectile is moving upward). Since the final velocity at the maximum height is 0 m/s, we can substitute the values into the equation:

t = (0 - 12.0) / -9.8 = 1.22 seconds

Therefore, it takes 1.22 seconds for the projectile to reach its maximum height.

Answer:

-6r + 5

Step-by-step explanation:

-4r - 2r + 5

= (-4 -2)r + 5

= -6r + 5

Answer:

Infinitely many solutions.

Step-by-step explanation:

10+x=5(1/5x+2)

10+x=x+10

infinitely many solutions

The equation 10+x=5(1/5x+2) has an infinite number of solutions.

To solve the equation 10+x=5(1/5x+2), we need to simplify both sides and then isolate the variable x. Let's start by distributing the 5 to the terms inside the parentheses.

10+x = 5(1/5x+2) becomes:

10+x = 1x+10

Next, we can combine like terms on each side of the equation. Subtracting x from both sides:

10 = x+10-x

The x terms cancel out, leaving us with:

10 = 10

This equation is always true, which means that there are an infinite number of solutions.

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The complete Question is given below

10+x=5(1/5x+2)

Determine whether it has one solution, an infinite number of solution, or no solutions

Answer:

1/6

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

1/2 of 12 is 6 so she has 6 yellow stickers

1/3 of 12 is 4 so she has 4 green stickers

that means she only has 2 stickers left because 6+4=10

2/12 of her stickers are blue but you can simplify it to 1/6 by dividing the numerator and denominator by 2

Answer:

10(x+9)

Step-by-step explanation:

Answer: 14

Step-by-step explanation:

Answer:

41.2876137159

Step-by-step explanation:

100 divided by 7 is 14.2857142857 km per litres. Then 590 divded by 14.2857142857 is 41.2876137159 or 41.29 rounded

Answer:

Simple interest = PRT/100

1380 = P x 12 x 2/100

138000 = 24P

Therefore P = 5750 Rs.

Hope this helps!

To find the principal amount given the simple interest, rate, and time, use the formula P = SI / (R × T). Substituting the values, the principal amount is 5750 rupees.

To find the sum of money (principal) using the given simple interest, we can use the simple interest formula:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Here, we know that:

Rearranging the formula to solve for the principal (P):

[tex]P = \frac{SI }{(R * T)}[/tex]

Substitute the known values:

P = 1380 / (0.12 × 2)

Solving the equation:

P = 1380 / 0.24

P = 5750 rupees

Therefore, the sum of money is 5750 rupees.

Answer:

The rate of change for each reader is :

For J K Rowling :  17 and a half pages per hour

For R L Stone :  15   pages  per hour

Step-by-step explanation:

Here the reading rate of each reader is given as:

J.K. Reads 35 pages every 2 hours.

So, the number of pages read by J K  in 2 hours  = 35 pages

⇒ The number of pages read per hour  =  35 / 2  = 17 . 5 pages

So, the pages read by J K Rowling in 1 hour is 17 and a half pages.

R L Stone reads 45 pages every 3 hours.

So, the number of pages read by R L  in 3 hours  = 45 pages

⇒ The number of pages read per hour  =  45 / 3  = 15 pages

So, the pages read by R L Stone in 1 hour is 15 pages.

Hence, the rate of change for each reader is :

For J K Rowling :  17 and a half pages  per hour

For R L Stone :  15   pages  per hour

Answer:

Step-by-step explanation:

sin67° = 12/13

Answer:

The correct answer is that AC = 4x - 2 or 2(2x - 1)

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

AD = 6x + 10

CD = 2x + 12

2. Let's find the length of AC

AC = AD - CD

Replacing with the real values:

AC = (6x + 10) - (2x + 12)

AC = 6x + 10 - 2x - 12

AC = 6x - 2x + 10 - 12

AC = 4x -2 or 2(2x - 1)

Answer:

50 Apples

Step-by-step explanation:

10x2=20 tomatoes

10x5=50 apples

Answer:

50 apples

Step-by-step explanation:

well the ratio of tomatoes to apples is 2:5

so if you have 20 tomatoes times 5 apples by ten to get the answer

2 x 10 = 5 x 10

Answer:

The slope of the table is [tex]m=\frac{5}{2}[/tex]   or  [tex]m=2.5[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have the following ordered pairs

(2,6),(0,1),(-2,-4) and (-4,-9)

take two points

(2,6) and (-4,-9)

substitute in the formula

[tex]m=\frac{-9-6}{-4-2}[/tex]

[tex]m=\frac{-15}{-6}[/tex]

simplify

[tex]m=\frac{5}{2}[/tex]