A group of friends are sharing 2 & 1/2 lbs of berries. If 5 friends are sharing the berries how many lbs does each friend get ??????

Answer:

(1, -3)

Step-by-step explanation:

Solve the system of equations of the two lines:

10x-3y=19 ------> eq 1

5x+4y=-7 --------> eq 2

Solve by elimination:

eq 2 x 2

2( 5x+4y) = 2(-7 )

10x + 8y = - 14 ------> eq 3

eq3 - eq 1:

(10x + 8y) - (10x-3y) = - 14 - 19

10x + 8y - 10x + 3y = -33

8y + 3y = -33

11y = -33

y = -3  (substitute back into eq 1)

10x - 3y = 19

10x - 3(-3) = 19

10x + 9 = 19

10x  = 19 - 9

10x = 10

x = 1

Hence the intersection point is (1, -3)

Final answer:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

Explanation:

To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.

First, multiply (2x + 5) with (x² - 4x-9) using the distributive property.
(2x + 5)(x² - 4x-9) = 2x*(x² - 4x-9) + 5*(x² - 4x-9)
= 2x³ - 8x² - 18x + 5x² - 20x-45
= 2x³ - 3x² - 38x - 45

Answer:

2.16 inches so ya

The number of inches in 15 percent of 1.2 foot is obtained as 216.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The number of inches in 1 feet = 12.

Then, in 1.2 foot the inches are 1.2 × 12 = 14.4.

Now, the percent value 15% of 1.2 foot is given as below,

15% × 1.2 foot

⇒ 15/100 × 14.4 inch

⇒ 216 inch

Hence, the number of inches are given as 216.

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Answer:

∠Q = 75 °

Step-by-step explanation:

Since PR = PQ then Δ PQR is isosceles and the base angles are congruent, that is

∠R = ∠Q = 2x + 15

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

2x + 15 + 2x + 15 + x = 180, that is

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

Hence

∠Q = 2x + 15 = (2 × 30) + 15 = 60 + 15 = 75°

The slope of 0.5 represents the cost per additional topping, while the y-intercept of 5 represents the cost of the plain pizza. Option A provides the correct interpretations.

To interpret the slope and y-intercept of the equation C = 0.5m + 5, where  C  represents the cost of the pizza and m represents the number of additional toppings:

A. The correct interpretation is:

- Slope: The slope of 0.5 represents the cost per additional topping. This means that for each additional topping added to the pizza, the cost increases by $0.5.  

- Y-intercept: The y-intercept of 5 represents the cost of the plain pizza without any additional toppings. This is because when m = 0 (no additional toppings), the cost of the pizza is $5, which is the flat fee for the plain cheese pizza.

To confirm:

- When m = 0, the equation becomes C = 0.5(0) + 5 = 5 , which is the cost of the plain pizza without any additional toppings.

- When m = 1, the equation becomes C = 0.5(1) + 5 = 5.5, indicating that the cost increases by $0.5 when one additional topping is added.

Therefore, option A correctly interprets the slope and y-intercept of the equation.

Answer:

32 ounces

Step-by-step explanation:

128oz=1gal

4quarts=1gal

128÷4=32

32oz=1 quart

Answer:

1

Step-by-step explanation:

hope this helps some one

stay safe and pease still were a mask

Step-by-step explanation:

[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}\\\\\text{simplify 28 and 7 (divide both by 7)}\\\\=\dfrac{28\!\!\!\!\!\diagup^4\cdot4}{1\cdot7\!\!\!\!\diagup_1}=\dfrac{4\cdo4}{1\cdot1}=\dfrac{16}{1}=16[/tex]

[tex]\dfrac{28}{7}\cdot4=(28:7)\cdot4=4\cdot4=16[/tex]

[tex]\text{Both expressions give the same result.}[/tex]

[tex]28\cdot\dfrac{4}{7}=\dfrac{28}{7}\cdot4\\\\28\cdot\dfrac{4}{7}=\dfrac{28}{1}\cdot\dfrac{4}{7}=\dfrac{28\cdot4}{1\cdot7}=\dfrac{28\cdot4}{7\cdot1}=\dfrac{28}{7}\cdot\dfrac{4}{1}=\dfrac{28}{4}\cdot4[/tex]

Your question:

EXPLAIN HOW 28*4/7 IS CORRECT AND (28 / 7) x 4 IS NOT

It all depends on the content of the question for which these expressions are.

Qestion:

Mr. Chang’s class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class?

Correct is 28 * 4/7.

(You calculate a fraction of a number).

28/7 * 4 - gives the same result. But the expression does not match the content of the question.

Answer:

y = 5x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, thus

y = 5x + c ← is the partial equation

To find c substitute (2, 6) into the partial equation

6 = 10 + c ⇒ c = 6 - 10 = - 4

y = 5x - 4 ← equation of line

Answer:

[tex]x=30^o[/tex]

Step-by-step explanation:

step 1

Find the measure of angle KNL

we know that

[tex]m\angle KNL+m\angle LNM+m\angle ONM=180^o[/tex]----> by straight angle

we have

[tex]m\angle LNM=45^o[/tex] ---> given problem

[tex]m\angle ONM=105^o[/tex] ---> given problem

substitute the given values

[tex]m\angle KNL+45^o+105^o=180^o[/tex]

[tex]m\angle KNL+150^o=180^o[/tex]

[tex]m\angle KNL=180^o-150^o[/tex]

[tex]m\angle KNL=30^o[/tex]

step 2

Find the value of x

In the right triangle KNL

we know that

[tex]m\angle KNL+m\angle NKL=90^o[/tex] ----> by complementary angles

we have

[tex]m\angle KNL=30^o[/tex]

[tex]m\angle NKL=2x[/tex]

substitute

[tex]30^o+2x=90^o[/tex]

[tex]2x=90^o-30^o[/tex]

[tex]2x=60^o[/tex]

[tex]x=30^o[/tex]

Answer:

-1

Step-by-step explanation:

add the 3 numbers together and then you get 10 so then you divide -10 by 10 and you -1

Answer:

g=5/23

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Subtract 4 from 100

96

Divide by 3

32

The solution to the equation is x = 32, so Elijah baked 32 brownies last week.

To find out how many brownies Elijah baked last week, we need to solve the equation 100 = 4 + 3x, where x is the number of brownies he made last week. Here are the steps to solve the equation:

Therefore, Elijah baked 32 brownies last week.

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Answer:

C

Step-by-step explanation:

The slope is 4/1, written as 4

The y int is 4

Write the equation in y = mx + b form

y = 4x + 4

Answer:

y = 3

Step-by-step explanation:

Given:

x²+y²+3xy =-5  and x = -2

Substituting x=-2 into the equation:

(-2)² + y² + 3y(-2) = -5

4 + y² - 6y = -5

y² - 6y +4 + 5 = 0

y² - 6y +9  = 0   (solve by factorization)

(y-3) (y-3) = 0

y = 3

Answer:

What question? I mean all you said was 'this question' so I don't know ;-;

Step-by-step explanation:

Answer:

The correct option is

The origin is included in the shaded region and the shaded area is below the line.

Step-by-step explanation:

Y>3/2x + 2

Put x=0

Y= 2

(0,2)

Put y=0

X= -4/3

(-4/3,0)

See attached picture for the sketch

Answer:

The origin is included in the shaded region and the shaded area is below the line.

C. 2.3 miles

Step-by-step explanation:

The details of the image are as follows;

Ranger station to Nature Center = 90°

Nature center to petting zoo= 40°

Petting zoo to Tennis court =120°

Tennis court to Pool = 65°

Pool to Ranger station= 45°

The radius of the circular pattern = 1 mile

The formula to apply is;

Arc length = 2πr angle / 360° where r is radius and π=3.14

Finding arc length from Ranger Station to Nature Center will be;

Arc length = 2×3.14×1×90°/360°

Arc length=2×3.14×1×1/4 =1.57 miles

Finding distance from Nature Center to Petting Zoo

Arc length= 2×3.14×1×40°/360°

Arc length= 2×3.14×1×1/9 = 0.70 miles

Total =1.57+0.70 =2.27 miles

Answer to the nearest hundredth = 2.3 miles

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Step-by-step explanation:

Part A:

Let [tex]m[/tex] be the number of mittens and [tex]s[/tex] be the number of scarves. Then we have the inequalities:

[tex]s+m\leq 30.[/tex] This says Nivyana and Ana cannot make more than 30 scarves

[tex]50s+25m\geq 1000.[/tex] This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)

Answer:

20

Step-by-step explanation:

10 + 10 = 20

Hope this helps :)

Answer:

x=3/2, y=10. (3/2, 10).

Step-by-step explanation:

2x-y=-7

4x-y=-4

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

-2(2x-y)=-2(-7)

4x-y=-4

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

-4x+2y=14

4x-y=-4

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

y=10

2x-10=-7

2x=-7+10

2x=3

x=3/2

Answer:

No.

Step-by-step explanation:

If it is geometric  the quotient of the terms and the previous term will be a constant.

213 / 31 = 6.871

4459 / 213= 20.93

These are not equal so the sequence is not geometric.

Answer:

If X is the starting weight, total pounds lost in three months is

(0.132X + 2.37)lbs

Step-by-step explanation:

Let the starting weight be X(lb)

Let the target ending weight be Y(lb)

Since Rollie ended with 3(lbs) above goal weight, final weight is Y+3(lb)

Each month, Rollie lost 1/3 of the difference between current weight and goal weight, hence

In the first month, Rollie lost 1/3 of (X - Y)

but since Rollie ended up with 3lbs above target ending weight, the actual weight loss is 1/3(X - Y) + 3

Hence  by the end of the first month, Rollie's new weight is X - (1/3(X - Y)) + 3

which is equal to

X - 1/3X + 1/3Y - 3.

= 2/3X + 1/3Y - 3

By the second month, Rollie's starting weight is 2/3X + 1/3Y - 3(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the second month, Rollie lost 1/3(2/3X + 1/3Y - 3 - Y) + 3

= 2/9X + 1/9Y - 1 - 1/3Y + 3

=  2/9X - 2/9Y + 2

hence by the end of the second month, Rollie's new weight is

(2/3X + 1/3Y - 3) - (2/9X - 2/9Y + 2)

= 2/3X - 2/9X + 1/3Y + 2/9Y - 3 - 2

= 4/9X + 5/9Y - 5  

By the third month, Rollie's starting weight is 4/9X + 5/9Y - 5(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the third month, Rollie lost 1/3(4/9X + 5/9Y - 5 - Y) + 3

= 4/27X + 5/27Y - 5/3 - 1/3Y + 3

= 4/27X - 4/27Y + 4/3 ------------------------- eqn (*)

hence by the end of the third month, Rollie's new weight is

(4/9X + 5/9Y - 5) - (4/27X - 4/27Y + 4/3)

= 4/9X - 4/27X + 5/9Y + 4/27Y - 5 - 4/3

= 8/27X - 19/27Y - 19/3

Hence in three months, Rollie's new weight is 8/27X - 19/27Y - 19/3

To ascertain how much weight Rollie lost in three months, there is need to equate the estimated ending weight to the final weight (Y + 3)

Therefore:

8/27X - 19/27Y - 19/3 = Y + 3

this implies that

8/27X - 19/27Y - Y - 19/3 - 3 = 0

8/27X - 36/27Y -28/3 = 0

Since Y is the target ending weight

the ending weight is generated by solving the equation with respect to Y

36/27Y = 8/27X - 28/3

multiply through by 27/36

Y = 2/9X - 7

Hence weight lost in three months is generated by substituting for Y = 2/9X - 7  in eqn (*)

Since eqn * is 4/27X - 4/27Y + 4/3

the lbs lost in three months is

4/27X - 4/27(2/9X - 7 ) + 4/3

= 4/27X - 8/243X + 28/27 + 4/3

= (32/243)X + 64/27

which in decimal is

(0.132X + 2.37)lbs

The total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

The starting weight is illustrated by x. The target ending weight is illustrated by y.

In the first month, the weight list by Rollie will be 1/3 × (x - y) and her new weight will be:

= 2/3x + 1/3y - 3

In the second month, the starting weight will be 2/3x + 1/3y - 3. The weight lost by the end of the second month will be:

= 1/3 × (2/3x + 1/3y - 3) + 3

= 2/9x - 2/9y + 2

The new weight will be:

= (2/3x + 1/3y - 3) - (2/9x - 2/9y + 2)

= 4/9x + 5/9y - 5

In conclusion, the weight lost in three months will be:

= 4/27x - 4/27(2/9x - 7) + 4/3

= 4/27x - 8/243x + 28/27 + 4/3

= 32/343x + 64/27

= 0.132x + 2.37

In conclusion, the total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.

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Answer:

[tex]14 \frac{3}{8}[/tex]

Step-by-step explanation:

I assume you mean this:

[tex]8 \frac{7}{8} +(7 \frac{5}{6} -2\frac{1}{3} )[/tex]

Lets begin with the parentheses. When operating with fractions, we need them to have the same denominator. Looking at the expression in the parenthesis, we can see that the denominator of 5/6, that being 6, is twice that of 1/3, that being 3. Thus, if we multiply the numerator and denominator of 1/3 by 2, the result will be a fraction of same value, but with denominator 6, which we can work with.

[tex]\frac{1*2}{3*2}[/tex]

[tex]\frac{2}{6}[/tex]

Now we can replace this in the original parenthesis

[tex](7 \frac{5}{6} -2\frac{2}{6})[/tex]

We can now evaluate the parenthesis. 7-2=5, which leaves us with 5 5/6 - 2/6. Since the two fractions have the same denominator, we can subtract the numerator of 2/6 from 5/6. This gives us with 3/6, which we add to the 5 from before.

[tex]5\frac{3}{6}[/tex]

The numerator and denominator of 3/6 are both divisible by three, so we can simply the fraction.

[tex]5\frac{1}{2}[/tex]

Now that we have solved the parenthesis, we can plug our solution back into the original expression.

[tex]8 \frac{7}{8} +5\frac{1}{2}[/tex]

We now have a similar problem to the parenthesis, where our fractions have different denominators. However, you may notice that the denominator of 7/8 (8) is four times larger than the denominator of 1/2 (2). Thus, if we multiply the numerator and denominator of 1/2 by four, we will have a new fraction of equal value, but with denominator 8.

[tex]\frac{1*4}{2*4}[/tex]

[tex]\frac{4}{8}[/tex]

Now lets update our expression with this information.

[tex]8 \frac{7}{8} +5 \frac{4}{8}[/tex]

8+5=13[tex]13\frac{7}{8} +\frac{4}{8}[/tex], so we can further simplify the expression.

Since the denominators of the fractions are the same, we can combine the numerators. 7+4=11

[tex]13 \frac{11}{8}[/tex]

We can simplify the fraction by taking one whole out of it (8/8) and adding it as 1 instead. 11-8=3, thus the fraction that remains is 3/8.

[tex]14 \frac{3}{8}[/tex]

The operation 8 7/8+(7 5/6-2 1/3) evaluates to a final result of 14 3/8.

To evaluate this mixed number operation, we must first convert each mixed number into an improper fraction.

8 7/8 is the same as 71/8 and 7 5/6 as 47/6 and 2 1/3 as 7/3.

Now, conduct the operation inside the parenthesis, which is subtraction: 47/6 - 7/3.

To subtract fractions, they must have the same denominator. Here, the least common multiple of 3 and 6 is 6. So you have 47/6 - 14/6 equals 33/6 reduced to 5 1/2.

Then add this quantity to 8 7/8 which equals to 14 3/8 when converted to a mixed number.

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Option C

Total amount paid by Alberto is $ 1745.7

Given that Alberto paid for seven large tables to be delivered to the restaurant

Alberto paid a delivery fee of  $95.45

Cost of 1 table = $ 235.75

To find: total amount Alberto paid

cost of seven tables = cost of 1 table x 7

[tex]\text {cost of seven tables }=235.75 \times 7=1650.25[/tex]

Total amount paid = 1650.25 + 95.45

Total amount paid = 1745.7

Thus total amount paid by Alberto is $ 1745.7 Therefore option C is correct

The markup percentage is 45.14%

Step-by-step explanation:

The given is:

We need to find the markup percentage

The markup percentage = [tex]\frac{New-Old}{old}[/tex] × 100%

∵ The selling price of a box of crackers is $1.75

∴ Old = 1.75

∵ You mark the crackers up to $2.54

∴ New = 2.54

- Substitute these values in the rule above

∵ The markup percentage = [tex]\frac{2.54-1.75}{1.75}[/tex] × 100%

∴ The markup percentage = [tex]\frac{0.79}{1.75}[/tex] × 100%

∴ The markup percentage = 0.4514 × 100%

∴ The markup percentage = 45.14%

The markup percentage is 45.14%

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Answer:

The markup percentage is 45%.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 60 + 60 = 120

Exterior angle equals the sum of opposite interior angles.

Answer:

Step-by-step explanation:

It is given that, each child bike requires 4 hours to build and each adult bike requires 6 hours to build.

Hence, c child bikes and a adult bikes require [tex](4c + 6a)[/tex] hours to build.

It is also given that, each child bike requires 4 hours to test and each adult bike requires 4 hours to test.

Total time to test, c child bikes and a adult bikes is [tex](4c + 4a)[/tex]

The company will be able to make c child bikes and a adult bikes if [tex](4c + 6a) \leq 120\\(4c + 4a)\leq 100[/tex]

If c = 20 and a = 6, then (4c + 6a) = 116 < 120.

and (4c + 4a) = 104 > 100.

Answer:

The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle.

Step-by-step explanation:

To determine the students selected to go to the board, start with the fourth student and then select every ninth student thereafter. Thus, the students chosen are the 4th, 13th, 22nd, and 31st students who enter the classroom.

The question involves determining which students a professor will select to go to the board based on a specific selection process. The professor decides to randomly select the fourth student who enters the classroom and every ninth student after that. To find out who these students are, we begin by identifying the fourth student initially. After the fourth student, every ninth student subsequently means we add 9 to the initial student's number to find the next student.

The fourth student who enters

The fourth student + 9 = the 13th student

The 13th student + 9 = the 22nd student

The 22nd student + 9 = the 31st student

Therefore, the students selected to go to the board are the 4th, 13th, 22nd, and 31st students who enter the classroom.

The students who will be going to the board are students 4, 9, 18, and 27.

Let’s determine the students who will be going to the board based on the professor’s selection criteria:

1. The fourth student who enters the classroom.

2. Every ninth student after that.

Let’s find the student numbers:

1. The fourth student corresponds to the 4th position.

2. The ninth student corresponds to the 9th position.

3. The 18th student corresponds to the ninth student after that (since 9 + 9 = 18).

4. The 27th student corresponds to the ninth student after the 18th student (since 18 + 9 = 27).

Therefore, the students who will be going to the board are students 4, 9, 18, and 27.

Answer: 3,000

Step-by-step explanation:

Divide 48,000 by 16

48,000 ÷ 16 = 3,000

Answer:

3000

Step-by-step explanation:

If they produce 48,000 in 16 hours, that means in one hour they produce 48,000 divided by 16.

48000 ÷ 16 = 3000

Answer:

2.5 or 2 1/2 in

Step-by-step explanation:

Area = width x length

width = area / length = 11.25 / 4.5 = 2.5