Suppose you bought supplies for a party. Three rolls of streamers and fifteen party hats cost $30. Later, you bought two rolls of streamers and four party hats for $11. Write and solve a system of equations to determine the cost of streamers and party hats, find their costs.

Answer:

Explanation:

8. Joe can chop vegetables in 5 minutes, and Rich can chop the same amount of vegetables in 4 minutes. Working together, how long will it take them to chop that batch of vegetables?

Name v the amount of vegetables

Working together, the combined speed is the sum of the two speeds: v/5 + v/4

Thus, the speed working together is:

            [tex]\frac{v}{5} +\frac{v}{4}=\frac{4v+5v}{20}=\frac{9v}{20}[/tex]

Hence, they can chop 9 times the given amount of vegetables (v) in 20 minutes.

And the time to chop the given amount of vegetables (v) is 20 divided by 9.

               [tex]time=amount/speed\\\\time=v/(9v/20)\\\\time=20v/(9v)=20/9=2.22[/tex]

That is 2.22 minutes to chop all the vegetables working together.

9. At Ricardo's Tacos, four tacos and two orders of chips cost the same as two tacos and four orders of chips. If Ricardo's charges $2.00 for a single order of chips, how much does Ricardo's charge for 1 taco?

Use T for the cost of tacos and C for the cost of orders of chips

Ricardo's charges the same for those orders:

Ricardo's charges $2.00 for a single order of chips:

Substitute C = 2 in 4T + 2C = 2T + 4C and solve:

   Substitution:

   Do the operations:

   Subtract 4 from both sides

   Subtract 2T from both sides

   Combine like terms

   Divide both sides by 2

Hence, Ricardo's charges $2.00 for one taco.

10. Broccoli is $1.69 per pound. Meg paid $8.45 for broccoli. How many pounds did she purchase?

You must divide the amount paid ($8.45) by the unit price ($1.69/lb)

        [tex]\$ 8.45/(\$ 1.69/lb)=5.00lb[/tex]

In the operation, $ appears both in the numerator and the denominator so they cancel out each other. The unit pounds (lb) appears dividing the denominator, thus it passes to the numerator.

Hence, Meg purchased 5.00 pounds

Final answer:

Solving these problems, Joe and Rich can chop vegetables in about 2.22 minutes together. Tacos at Ricardo's cost $2 each, and Meg purchased 5 pounds of broccoli.

Explanation:

Problem Solving in Mathematics

Joe and Rich Chopping Vegetables: Joe can chop vegetables in 5 minutes, while Rich can do the same in 4 minutes. When working together, the rate at which they can chop vegetables combines. This means Joe chops 1/5 of the vegetables per minute and Rich chops 1/4 per minute. Together, they can chop 1/5 + 1/4 = 9/20 of the vegetables per minute. Therefore, working together, they will take 20/9 minutes, or approximately 2.22 minutes, to chop the batch of vegetables.

Cost of Tacos at Ricardo's Tacos: Let's denote the cost of one taco as T. The equation based on the given information is 4T + 2(2) = 2T + 4(2). Simplifying this, we get 4T + 4 = 2T + 8, which reduces to 2T = 4, so one taco costs $2.00.

Meg's Broccoli Purchase: Meg paid $8.45 for broccoli that costs $1.69 per pound. To find out how many pounds she purchased, divide the total cost by the price per pound: $8.45 / $1.69. This calculation results in Meg purchasing 5 pounds of broccoli.

Answer:

386

Step-by-step explanation:

If you subtract the initial fee of 12 from 70 you get 68 you just divide that by .15 meaning you can plant no more that 386 trees.

Answer: 5 Trees

Step-by-step explanation:

12 x 5 = 60

.15 x 5 = . 75

If you go to six, you would get 72.9.

Replace x in the equation with 1 and solve.

F(x) = 2x

X = 1

F(1) = 2(1) = 2

The answer is 2

84 pounds of Type B coffee is used

Solution:

Let "x" be the pounds of type A coffee

Let "y" be the pounds of type B coffee

Cost per pound of type A = $ 5.50

Cost per pound of Type B = $ 4.20

This month, Chau made 143 pounds of the blend

x + y = 143

x = 143 - y -------- eqn 1

For a total cost of $677.30. Thus we frame a equation as:

pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30

[tex]x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2[/tex]

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

[tex]5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84[/tex]

Thus 84 pounds of Type B coffee is used

To determine how many pounds of type B coffee were used in Chau's coffee blend, we set up a system of equations based on the total weight and total cost of the blend. By substituting one equation into the other, we can solve for the quantity of type B coffee.

Calculating the Blend of Coffee:

To solve the problem, let's use a system of equations to determine how many pounds of type B coffee Chau used in his coffee blend. We have two unknowns here: the amount of type A coffee (let's call it A) and the amount of type B coffee (let's call it B). The total weight of the coffee blend is given as 143 pounds, and the total cost of the blend is $677.30.

The first equation comes from the total weight of the blend:

A + B = 143

The second equation comes from the total cost:

5.50A + 4.20B = 677.30

We can use either substitution or elimination to solve this system. If we solve the first equation for A (i.e., A = 143 - B) and substitute it into the second equation, we get:

5.50(143 - B) + 4.20B = 677.30

After simplifying, we can solve for B to find out how many pounds of type B coffee were used.

The area of the composite polygon is:

[tex]\boxed{A_{T}=376 \ m^2}[/tex]

Hello! remember you have to write complete questions in order to get good and exact answers. Here you haven't provided any figure, so I'll choose the figure below in order to illustrate this problem. A composite polygon is a polygon that can be divided into two or more basic shapes. So here we have a composite polygon formed by a triangle and a rectangle. So:

[tex]A_{total}=A_{T} \\ \\ A_{triangle}=A_{tr} \\ \\ A_{rectangulo}=A_{r} \\ \\ \\ A_{tr}=\frac{b\times h}{2} \\ \\ b:Base \ of \ the \ triangle \\ \\ h:height \ of \ the \ triangle \\ \\ \\ A_{r}=B\times H \\ \\ B:base \ of \ the \ rectangle \\ \\ H:height \ of \ the \ rectangle[/tex]

So the area of the composite figure is:

[tex]A_{T}=\frac{16\times 11}{2} + 16\times 18 \\ \\ A_{T}=88+288 \\ \\ \boxed{A_{T}=376 \ m^2}[/tex]

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Answer:

P - 4

Step-by-step explanation:

Sergio and the other painting collectors have decided to donate a total of 48 paintings all together.

We know that there are 12 collectors in total and they will each donate the same number of paintings.

48 paintings in total

12 collectors

48 / 12 = 4

We now know Sergio will donate 4 paintings from his collection of P paintings. Sergio will have P - 4 paintings left.

We do not know what "P" is equal to, so we cannot give an exact number for how many paintings he will have left. However, we know he will have 4 fewer paintings after donating.

Answer:

i think its Gas attacks allowed Germany to win major battles and defeat France before the United States

joined the war.

Step-by-step explanation:

Final answer:

Gas attacks during World War I contributed to the horrors and difficulties of trench warfare and had severe psychological impacts on soldiers, but they did not lead to major strategic victories or civilian efforts to end the war.

Explanation:

Gas attacks during World War I profoundly changed the nature of warfare, particularly during the era of trench warfare. These gas attacks made the act of fighting in trenches extremely challenging and induced significant psychological suffering among the troops. The use of poison gas was viewed as a horrific method of warfare by soldiers, burning the lungs, eyes, and skin, and leaving those who survived in a state of dread, with many considering the victims of gas attacks the unlucky ones. It did not lead to a significant shift in the outcome of battles, which remained largely stalemated with enormous casualties but minimal territorial gains.

Despite these devastating effects, gas attacks did not lead to military victories that decisively changed the war - at least not in favor of Germany before the United States entered the war, nor did these attacks result in the mass deaths of civilians or lead people to demand an immediate end to the war. The international tensions and problems that initiated the war were not resolved but were instead exacerbated by the new methods of modern combat. Gas attacks did terrify troops, but they did not lead them to demand a truce between the Allied Powers and the Central Powers.

In summary, the most apt answer to how gas attacks affected warfare during World War I would be that they made fighting in trenches difficult and had significant psychological effects upon troops, as discussed in option B.

Step-by-step explanation:

We have,

− 3( x + 1)

= − 3x - 3

A. - 3x + (-3)

= − 3x - 3, is equivalent to − 3( x + 1).

B. x - 3

= x - 3, is not equivalent to − 3( x + 1).

C. - 3x + 1

= - 3x + 1, is not equivalent to − 3( x + 1).

D. - 3x - 3

= - 3x - 3, is equivalent to − 3( x + 1).

Thus, A)  - 3x + (- 3) and D) - 3x - 3 are equivalent.

Answer:

it would be described as a collinear point as it is on the same line! hope this helps!

The term describing the relationship U has with R and N, assuming they lie on the same line, is called 'collinear'. In this scenario, points U, R, and N all lie on the same straight line.

If point U lies on the same line as points R and N in geometry, it means that these points are collinear. The term 'Collinear' refers to points that lie on the same straight line. For example, if we consider the line as a straight road, then points U, R, and N can be visualized as three different spots on this road, which are along the same path.

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Answer:

18 and 335

Step-by-step explanation:

y = 18x + 11

x * y = 6030

x * (18x + 11) = 6030

18x^2 + 11x = 6030

18x^2 + 11x - 6030 = 0

(18x + 335)(x - 18) = 0

18x + 335 = 0                 x - 18 = 0

18x = -335                      x = 18

x = -335/18

x is gonna have to be a positive number...so x = 18

y = 18x + 11

y = 18(18) + 11

y = 324 + 11

y = 335

so ur numbers are 18 and 335

The two positive integer numbers are 18 and 335

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the two numbers be a and b

Now ,

Positive integer is 11 more than 18 times another

a = 11 + 18b   be equation (1)

And , product of a and b is 6030

a x b = 6030   be equation (2)

Now , substituting the value of equation (1) in equation (2) , we get

( 11 + 18b ) x b = 6030

18b² + 11b = 6030

Subtracting 6030 on both sides , we get

18b² + 11b - 6030 = 0   be equation (3)

On simplifying , we get

18b² - 324b + 335b - 6030 = 0

18b ( b - 18 ) + 335 ( b - 18 ) = 0

So ,

( 18b + 335 ) ( b - 18 ) = 0

Now , we got two values for b ,

( 18b + 335 ) = 0

b = -335 / 18

And ,

( b - 18 ) = 0

b = 18

Since , b is a positive integer , the value of b is 18

Now , substituting the value of b in equation (2) , we get

a x 18 = 6030

Divide by 18 on both sides , we get

a = 335

Hence , the two positive integer numbers are 18 and 335

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Question:

Heather bought a large bag of bird seed and used 24% of the bag. How many pounds were originally in the bag if there are 15.2 pounds left?

Answer:

There were 20 pounds of seed in bag originally

Solution:

Given that,

Heather used 24 % of bag

There are 15.2 pounds left

To find: Pounds of seed in bag originally

Let "x" be the pounds of seed in bag originally

From given,

100 % - 24 % = 76 %

Thus 76 % of bag is unused

Also, given that there are 15.2 pounds left

Therefore, we can say,

76 % of x = 15.2

[tex]76 \% \times x = 15.2\\\\\frac{76}{100} \times x = 15.2\\\\0.76x = 15.2\\\\x = \frac{15.2}{0.76}\\\\x = 20[/tex]

Thus there were 20 pounds of seed in bag originally

Final answer:

The original weight of the seed bag is calculated by setting up a proportion comparing 76% to 15.2 pounds and 100% to the original weight, leading to the solution of 20 pounds.

Explanation:

To determine the original weight of the bag of seed, we need to calculate what 100% would represent if 15.2 pounds is what remains after using 24% of the bag. This means that 76% (100% - 24%) of the seed bag is equal to 15.2 pounds. We can set up a proportion where 76% is to 15.2 pounds, as 100% is to X pounds (where X represents the original weight).

The equation is 76/100 = 15.2/X. To solve for X, we multiply both sides by X and divide both sides by 76 to isolate X on one side of the equation, which gives us X = (15.2 * 100) / 76. After calculating, we find that the original weight (X) of the bag is 20 pounds.

Answer:

•{(-2,6), (-1,3), (0,0), (1, -3), (2,-6)}

Step-by-step explanation:

Answer:

100 ÷ 50 = 2.

Answer:

a) C= 275+1.5n b)151 tickets

Step-by-step explanation:

b) 500= 275 +1.5n

500-275=1.5n

225=1.5n

150=n

if n equals 151 Band A would be cheaper because

C=275+1.5n

C= 501.5

500<501.5

Final answer:

The question seems to be asking for two decimals that equal 5.5 when added together, which can have many solutions such as 2.75 and 2.75. In the context of significant figures and rounding, rules differ based on whether the significant figure is odd or even when followed by a 5.

Explanation:

The question seems to be asking for two decimals that add up to 5.5. There are an infinite number of decimal pairs that can do this, for example, 2.75 and 2.75, or 3.00 and 2.50. However, without additional constraints, it's not possible to determine a unique pair of decimals.

Significant figures and rounding

When dealing with significant figures and rounding, the specific rules you mentioned come into play. According to the rules provided, we round differently based on whether the last significant digit is odd or even when the next digit is 5. For example, if we have 2.525 and we need to round to three significant figures, we round to 2.52 because the last significant figure, 2, is even. On the other hand, if we have 2.535, we would round to 2.54 because the last significant figure, 3, is odd and the next digit is 5.

Rounding in Complex Calculations

It's important to round off numbers at the end of calculations to ensure accuracy. For instance, 2.6525272 rounded to three decimal places, considering rounding rules, would be 2.653.

Answer:

a = -2.3

Step-by-step explanation:

a + 0.3 = -2

Subtract 0.3 from both sides

We have,

a + 0.3 -0.3 = -2 - 0.3

a = -2.3

Answer:

2007

Step-by-step explanation:

we have

[tex]p(x)=0.65x^{2} -0.047x+2[/tex]

This is a vertical parabola open upward

The vertex represent a minimum

p(x) is the population in thousands for a species of fish

x is the number of years since 1997

Remember that p(x) is in thousands

so

If the population reach 66,530 fish

then

the value of p(x) is equal to

p(x)=66.53

substitute in the quadratic equation

[tex]66.53=0.65x^{2} -0.047x+2[/tex]

[tex]0.65x^{2} -0.047x+2-66.53=0[/tex]

[tex]0.65x^{2} -0.047x-64.53=0[/tex]

Solve the quadratic equation by graphing

The solution is x=10 years

see the attached figure

therefore

Find the year

Adds 10 years to 1997

1997+10=2007

Answer:

1. p=1.3333

2. k=1

3. n=4

4. x=6.6666

5. m=17.5

6. r=8.75

Answer:

y = - 5x

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 10 when x = 2, thus

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5

y = - 5x ← equation of variation

Final answer:

You could partially fill one 10-liter gas can with the 7 liters of gas, as 7 divided by 10 is 0.7, and you cannot have a fraction of a physical can.

Explanation:

To find out how many cans we could fill with 7 liters of gas, when a gas can holds 10 liters, we need to perform a simple division.

The calculation is as follows:
Number of cans = Total liters of gas / Liters each can holds = 7 liters / 10 liters = 0.7.

Since you cannot have a fraction of a physical gas can, you would not be able to completely fill a single can with 7 liters of gas.

Therefore, we could partially fill one 10-liter gas can with the 7 liters of gas we have.

Answer:

Solving by method of factorization ,

(y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1)

Step-by-step explanation:

A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a^2-ab+b^2)

here a = y and b = 1

hence , expanding y^3+1 in cubic formula ,

(y^3+1) = (y+1)(y^2-(y)(1)-1^2)

(y^3+1)=(y+1)(y^2-y+1)

putting this value of (y^3+1) in the given expression ,

= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).

Trinomial cannot be factored , hence the final answer is ,

= (y^4-y^3+2y^2+y-1)/(y+1)(y^2-y+1).

We have been given that Carla plans to invest $9,000 for 10 years. Better Bank offers a 10 year CD at an annual rate of 4% using simple interest. We are asked to find the amount after 10 years.

We will use simple interest formula to solve our given problem.    

[tex]A=P(1+rt)[/tex], where

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

[tex]4\%=\frac{4}{100}=0.04[/tex]

[tex]A=\$9000(1+0.04\times 10)[/tex]

[tex]A=\$9000(1+0.4)[/tex]

[tex]A=\$9000(1.4)[/tex]

[tex]A=\$12600[/tex]

Therefore, the investment will be worth $12600 in 10 years. and option C is the correct choice.

Answer:

10x + 3 = 6x + 5

Based on this, we have the lines y=10x+3 and y=6x+5. Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.

Solution:

x = 1/2

y = 8

(1/2 , 8)

Step-by-step explanation:

Start by expanding with the distributive property, then simplify by collecting like terms.

5(2x + 1) - 2 = 6x + 5     Multiply "5" with each term in the brackets.

10x + 5 - 2 = 6x + 5       Collect left side's like terms (5 - 2 = 3)

10x + 3 = 6x + 5

Based on this, we have the lines y=10x+3 and y=6x+5. A solution is the same as the POI (point of intersection). Both of the equations are linear, so they are straight lines when graphed. A system of straight lines can only have one solution maximum.

Some linear systems might have no solutions (when the lines are parallel) or infinite solutions (when the lines are equivalent, the same).

To find the solution, continue with the equation and isolate "x". This will give you the x-coordinate of the point of intersection.

To isolate 'x', move everything to the other side of 'x'. To move something, you do its reverse operation to both sides in reverse BEDMAS order.

10x + 3 = 6x + 5

10x - 6x + 3 = 6x - 6x + 5     Subtract 6x from both sides

4x + 3 = 5     "6x" cancelled out on the right. Simplified left (10x-6x=4x)

4x + 3 - 3 = 5 - 3      Subtract 3 on both sides. "3" on the left will cancel out

4x = 2      The right side was simplified (5 - 3 = 2).

4x/4 = 2/4      Divide both sides by 4 to isolate 'x'. Simplify right side.

x = 1/2          Solution's x-coordinate

Substitute what you found for 'x' into any equation that has 'y' (either y=10x+3 or y=6x+5). I will choose the first equation.

y = 10x + 3      

y = 10(1/2) + 3        Multiply 1/2 and 10

y = 5 + 3       Add

y = 8          Solution's y-coordinate

Therefore the solution is when x=1/2 and y=8, or as an ordered pair, (1/2 , 8).

The volume of cylinder is 1205.76 cubic inches

Solution:

We have to find the volume of cylinder

The volume of cylinder is given by formula:

[tex]V = \pi r^2h[/tex]

Where "r" is the radius and "h" is the height of cylinder

Given dimensions are:

Radius = 8 inches

Height = 0.5 feet

Convert feet to inches

1 feet = 12 inches

Therefore,

0.5 feet = 12 x 0.5 = 6 inches

Thus, we have got,

height = 6 inches

Substitute r = 8 inches and h = 6 inches in formula:

[tex]V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76[/tex]

Thus volume of cylinder is 1205.76 cubic inches

Answer:

A. 45 in

Step-by-step explanation:

To find area you multiply length and width so you would multiply 9 and 10 but since it is a triangle you would divide by two

Hope this helps!

Answer:

yes

Step-by-step explanation:

1 1/2 is greater than 1 4/10. Wich is 1/10 less then 1 1/2

Answer:

Yes

Step-by-step explanation:

1 1/2 > 1 4/10

Step 1:  Covert to Improper Fraction

1 1/2 = 2/2 + 1/2 = 3/2

1 4/10 = 10/10 + 4/10 = 14/10

Step 2:  Find Common Denominator

The least common denominator is 10

3/2 * 5/5 = 15/10

14/10 is already good

Step 3:  Evaluate

Is 15/10 more than 14/10?

Yes!!!!

So, 1 1/2 is more than 1 4/10