Ask question

Ask question

All categories

1 year ago

10

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas

for a total of $5.25. Determine a system of equations that represents the given the situation. Let x be cost per pound of apples and let y be the cost per pound of bananas.

2 answers:

Anarel [89]1 year ago

8 0

5x + 3y= 8.50
3x + 2y= 5.25

Lydia is the first equation. She bought 5 pounds of apples which is x and bought 3 pounds of bananas which is y. Basically, remember each banana and apple weighs a price per pound. We don't know the price so we just put an x. This is the same for the second equation

GarryVolchara [31]1 year ago

4 0

B and c are the answer on edginuity

You might be interested in

Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist

Lera25 [3.4K]

Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

7 0

1 year ago

A rectangular exercise mat has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to

Karo-lina-s [1.5K]

<h2>Hello!</h2>

The answers are:

- Length

$length=2width=12feet$

- Width

$width=6feet$

- Area

$Area=72feet^{2}$

<h2>Why?</h2>

We are given the perimeter of a rectangular mat, and we are asked to find the area, and write an equation to determine the length, if feet, of the mat. To solve this problem we need to remember the equation of the perimeter of a rectangle, which is:

$Perimeter=2length+2width$

Using the given information we have,

$36feet=2length+2width$

Also, we know that the length is twice the width, so:

$length=2width$

Then, substituting the second equation into the first equation, we can find the width of the mat.

Substituting, we have:

$36feet=2(2width)+2width$

$36feet=4width+2width$

$36feet=6width$

$[tex]\frac{36feet}{6} =width$ \\width=\frac{36feet}{6} =6feet[/tex]

Then, substituting the width into the second equation, we can find the length of the mat,

Substituting, we have:

$length=2width$

$length=2(6feet)=12feet$

Then, finding the area, we have:

$A=length*width=12feet*6feet=72feet^{2}$

Have a nice day!

7 0

2 years ago

the graph of f(x) shown below has the same shape as the graph of g(x)=x^2 but is shifted down 5 units and to the left 4 units (t

schepotkina [342]

Answer:

Option C

Step-by-step explanation:

A function g(x) = x² has been given as the parent function.

This function then shifted 5 units down.

Translated function formed will be f(x) = x² - 5

Further this graph has been shifted 4 units to the left then the function will become

f(x) = [x - (-4)]² - 5

f(x) = (x + 4)² - 5

Therefore, option C is the answer.

6 0

1 year ago

Read 2 more answers

If 6j-5k =11 and 5j-6k =22, then what is the value of 2j+2k??

dsp73

Answer:

-22

Step-by-step explanation:

6j-5k=11

5j-6k=22

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

5(6j-5k)=5(11)

-6(5j-6k)=-6(22)

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

30j-25k=55

-30j+36k=-132

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

11k=-77

k=-77/11

k=-7

6j-5(-7)=11

6j+35=11

6j=11-35

6j=-24

j=-24/6

j=-4

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

2j+2k=2(-4)+2(-7)=-8-14=-22

8 0

1 year ago

Match with the sum of the monomial and binomial

Margarita [4]

Answer:

The answer to your question is below

Step-by-step explanation:

Just cancel the parentheses and simplify

Result Addition

5xy² + 2x²y ⇒ (5xy² - x²y) + 3x²y = 5xy² + 2x²y

-3x²y - 2xy² ⇒ x²y + (-2xy² - 4x²y) = -3x²y - 2xy²

3x²y - 2xy² ⇒ 2x²y + (x²y - 2xy²) = 3x²y - 2xy²

5x²y + xy² ⇒ 4x²y + (x²y + xy²) = 5x²y + xy²

5 0

1 year ago