Find the sum of the numbers as a product of their GCF is 84 + 108

Answer:

1) Option D is correct.

The choice that represents the number of balloons in their bags is x² - 40x + 300 ≥ 0

2) Option A is correct

If Rob had more balloons than Loretta, the least number of balloons that Rob van have before using any = 30.

Step-by-step explanation:

Complete Question

To decorate for a party, Rob and Loretta were each given a bag of balloons. There were 40 balloons between both bags. Rob used 8 balloons from his bag, and Loretta used 8 balloons from hers. The product of the number of balloons left in each bag is no more than 44.

Let x represent the number of balloons that Rob had in his bag before he used any. Which choice represents the number of balloons left in their bags?

A. x² - 40x - 300 = 0

B. x² - 40x - 300 < 0

C. x² - 40x = 300

D. x² - 40x + 300 ≥ 0

If Rob originally had more balloons than Loretta, what is the least number of balloons that Rob could have had before using any?

A.30

B.20

C.10

Solution

If x is the number of balloons that Rob had at the start, the number of balloons that Loretta would have at the start = (40 - x)

Then, they both use 8 balloons each for their designs,

The number of balloons Rob has after the design = (x - 8)

The number of balloons Lorretta has after the design = (40 - x - 8) = (32 - x)

The product of the balloons left isn't more than 44

(x - 8) × (32 - x) ≤ 44

32x - x² - 256 + 8x ≤ 44

44 ≥ -x² + 32x + 8x - 256

44 ≥ -x² + 40x - 256

44 + x² - 40x + 256 ≥ 0

x² - 40x + 300 ≥ 0

To solve the second part of the question, we just solve the expression obtained in the first part.

x² - 40x + 300 ≥ 0

Simplifying the left hand side

(x - 30)(x - 10) ≥ 0

The solutions of the inequality is

x ≤ 10 or x ≥ 30

Hence, if Rob had more balloons than Loretta, the feasible solution for x would be x ≥ 30 and the least number of balloons that Rob van have before using any = 30.

Hope this Helps!!!

Answer:

D & A

Step-by-step explanation:

Answer:

1) Option D is the right answer.

x2 - 40x + 300 0 is the option that reflects the number of balloons in their bags.

2) Option A is the right answer.

If Rob had more balloons than Loretta, the minimum number of balloons Rob could have before using any would be 30.

Step-by-step instructions:

Question in its entirety, Rob and Loretta were each handed a bag of balloons to decorate for a party. Between the two bags, there were 40 balloons. Loretta used 8 balloons from her bag, while Rob used 8 from his.The total number of balloons left in each bag cannot exceed 44. Let x be the number of balloons in Rob's bag before he utilized any of them. Which option best depicts how many balloons they still have in their bags? x2 - 40x - 300 = 0 A. x2 - 40x - 300 0 x2 - 40x - 300 0 x2 - 40x - 300 0 x2 C. 40x - x2 = 300 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 - 40x + 300 0 x2 What is the smallest number of balloons that Rob has if he started with more than Loretta? What is the smallest number of balloons Rob could have had before using any if he had more than Loretta at the start? Solution A.30 B.20 C.10 If x is the number of balloons Rob had at the start, Loretta's number of balloons at the start would be = (40 - x) Then they each use eight balloons to create their creations. After the design, the number of balloons Rob possesses Equals (x - 8) Then there was (40 - x - 8) = the amount of balloons Lorretta possesses after the design (32 - x) The product of the remaining balloons is just 44. (x - 8) (32 - x) 44 x x x x x x x x x x x 32x - x2 - 256 + 8x 44 44 -x2 + 32x + 8x - 256 44 -x2 + 32x + 8x - 256 44 -x2 + 40x - 256 x2 - 40x + 256 0 x2 - 40x + 300 0 44 + x2 - 40x + 256 0 We just solve the equation acquired in the first half of the question to solve the second portion of the question. x2 - 40x + 300 ======================== Simplifying...

(x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - 10) 0 (x - 30)(x - The inequality's solutions are x 10 or x 30. As a result, if Rob has more balloons than Loretta, the viable solution for x is x 30, and the smallest number of balloons Rob may have before using any is 30. I hope this information is useful!!! ⭐️

Answer:

[tex] \boxed{Dimensions\: of \: the \: rectangle \: are \: 15 \: and \: 10 units} [/tex]

Step-by-step explanation:

Let the length of rectangle be 'x' units

So, width of rectangle will be = x - 5 units

Area of rectangle = 150 square units

[tex]=> Area \: of \: rectangle = length × breadth \\ \\ = > 150 = x \times (x - 5) \\ \\ = > 150 =( x \times x )- (x \times 5) \\ \\ = > 150 = {x}^{2} - 5x \\ \\ = > 0 = {x}^{2} - 5x - 150 \\ \\ = > {x}^{2} - 5x - 150 = 0 \\ \\ = > {x}^{2} - (15 - 10)x - 150 = 0 \\ \\ = > {x}^{2} - 15x + 10x - 150 = 0 \\ \\ = > x(x - 15) + 10(x - 15) = 0 \\ \\ = > (x - 15)(x + 10) = 0 \\ \\ = > x - 15 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x + 10 = 0 \\ \\ = > x = 15 \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x = - 10[/tex]

Dimension cannot be negative so the value of x is 15

Therefore,

Length of rectangle = 15 units

Width of rectangle = 15 - 5 = 10 units

Answer:

0.8 i think

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

[tex] {5.6}^{ - 5} \times {3.4}^{ - 7} \times {5.6}^{3} \times {3.4}^{ - 4} = {5.6}^{ - 2}. {3.4}^{ - 4} [/tex]

Hope this helps...

Answer:

y= mx+b

Step-by-step explanation:

Slope intercept formula:

y=mx+b

m= slope

b= y intercept

Answer:

The equation of a horizontal line is y = b where b is the y-intercept. Since the slope of a horizontal line is 0, the general formula for the standard form equation , y = mx + b becomes y = 0x +b y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-intercept.

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

The reference angle of 240° is 60°

y = mx + b

You need to isolate m.

1. Bring b to the other side by subtracting it from both sides

y - b = mx

2. Divide out x to isolate m on the right

(y - b)/x = m

You answer is B. m = y - b / x

Answer:

Opposites are basically the negative and positive of a number.  I cannot think of something for a real world situation though.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ur not dumb I’m the dumb one XD

Answer: 324 cards.

Step-by-step explanation:

Hi, to answer this question we have to multiply the number of pages in the album (72) by the number of cards that each page holds (9):

Mathematically speaking:

72(9) = 648 cards in the album

Since half of the pages are full, we have to divide the previous result by 2.

648/2 = 324 cards

Feel free to ask for more if needed or if you did not understand something.

Answer:

205.2 units

Step-by-step explanation:

If you are solving for the S.A. of a rectangular prism, then simply multiply the numbers together as each stands for length (l), height (h), and width (w).

l*w*h

4.7 * 5.9 * 7.4 = ‭205.202‬

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!    

Answer:

The price of 1 adult ticket is $ 11 and price of 1 child ticket is $13

Step-by-step explanation:

Let x be the cost of 1 adult ticket

Let y be the cost of 1 child ticket

Cost of 8 adult tickets = 8x

Cost of 9 child tickets = 9y

We are given that A local kids play sold 8 adult tickets and 9 child tickets for a total of $205

So, 8x+9y=205 ----- 1

Cost of 4 adult tickets = 4x

Cost of 3 child tickets = 3y

We are given that 4 adult tickets and 3 child tickets for a total of $83.

4x+3y=83 ----2

Plot 1 and 2 on graph

8x+9y=205  -- Red line

4x+3y=83  -- Blue line

Intersection point provides the solution

So, Intersection point =(11,13)

So, The price of 1 adult ticket is $ 11 and price of 1 child ticket is $13

Answer:

x = -2

Step-by-step explanation:

7(2 - x) = 28

Distribute

14 -7x = 28

Subtract 14 from each side

14-7x-14 = 28-14

-7x = 14

Divide each side by -7

-7x/-7 = 14/-7

x = -2

Answer:

Step-by-step explanation:

7a - 3 = 3 + 6a

7a = 6 + 6a

a = 6

Answer:

a = 6, Nice work!

Step-by-step explanation:

7a - 3 = 3 + 6a

First step is to subtract 6a from the right, also subtracting it from the left. This will leave you with:

a -3 = 3

Now you need to isolate the variable, so to get rid of -3, you have to add 3 to both sides.

a -3 = 3

 +3   +3

a = 6

Answer:

it would be like 90 feet

Step-by-step explanation:

hope this helps give me brainiest please

Answer:

D . 2x = 5

Step-by-step explanation:

cause it seems like the hanging thing is in balance -> both sides need to be equal in value. the left side contains 2 x-es, and the right side contains 5 ones.

Answer:

dy/dx = d/dx sin(x-3/x+2)

dy/dx = cos(x-3/x+2) . d/dx (x-3/x+2)

dy/dx = cos(x-3/x+2) . (x + 2 - x + 3)/(x+2)²

dy/dx = [5cos(x-3/x+2)]/(x + 2)²

Answer:

No.

Step-by-step explanation:

If you find the volume of the box which is 300, then divide by 2, you get 150. That's a whole number.

Answer:

10 so A

Step-by-step explanation:

Answer:

5133 1/3

Step-by-step explanation:

[tex]3.5 \cdot 880 = 0.6x\\3080=0.6x\\x=5133 1/3[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

(-3,6)

Answer:

-3, 4, -4

Hope this helps :)

Answer:

-3

Step-by-step explanation:

they all go to the negative side of them every other number. Hope that this helps you and have a great day :)

Answer:

49 and 46

Step-by-step explanation:

because they are greater than 45 but less than 50.

Answer:

Length of rectangle = 10in.

Breadth " " =x

Perimeter= 2( l+b)=30in.

Perimeter=2(10+b)=30in.

=(10+b)=30/2=15

=b=15-10

Breadth=5in.

Answer: 50 in²

Explanation: Remember that the formula for the area of a rectangle is length · width so we need to find the width of the rectangle.

To find the width of the rectangle, let's use our formula

for the perimeter of a rectangle which is 2l + 2w.

Since we know that the perimeter of the rectangle is 30 inches and the length of the rectangle is 10 inches, we have 30 = 2(10) + 2w.

Simplifying on the right side gives us 30 = 20 + 2w.

Now subtract 20 from both sides to get 10 = 2w.

Finally, dividing both sides by 2, we find that 5 = w.

So the width of the rectangle is 5 inches and remember

that the length of the rectangle is 10 inches.

So the area of the rectangle, l · w, is 10 · 5 or 50 in².

Answer: 58.016

Step-by-step explanation:

Answer:

58.016

Step-by-step explanation:

9.8×5.92=58.016

Answer:

if the two bottles are 1 liter each then those two bottles would hold more juice because in total they would hold two liters of juice

Step-by-step explanation:

the 12 cans of 150 ml would hold a total of 1.8 liters which is less than 2 liters

Answer:

a

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Mean is more affected by the highest salary because 890 is an outlier and using mean makes middle salary inaccurate. Outliers do not affect the median because you are just counting.