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riadik2000 [5.3K]

2 years ago

11

Olivia and her children went into a grocery store where they sell peaches for $2 each and mangos for $1 each. Olivia has $15 to

spend and must buy no less than 8 peaches and mangos altogether. If x represents the number of peaches purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.

1 answer:

attashe74 [19]2 years ago

4 0

Answer:

if x represents the number of peaches purchased and y represents the number of mangos purchased

Step-by-step explanation:

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Amanda makes 3 biscuits in 2 minutes. How many biscuits can she make in 30 minutes?

Vinil7 [7]

45 because 30 divided by 2 is 15 the 15 times 3

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2 years ago

Read 2 more answers

The function y = x 2 - 10x + 31 has a ____

katrin [286]

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

$f(x) = x^2-10x+31$

Taking first derivative

$f'(x) = 2x-10$

Now the first derivative has to be put equal to zero to find the critical value

$2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5$

The function has only one critical value which is 5.

Taking 2nd derivative

$f''(x) =2$

$f''(5) = 2$

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

$f(5) = (5)^2-10(5)+31\\=25-50+31\\=6$

Hence,

<u>The function y = x 2 - 10x + 31 has a minimum value of 6</u>

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

8 0

2 years ago

Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?

dusya [7]

Answer: 11/23

Step-by-step explanation:

I used my calculator to convert those fractions into decimal form and found the biggest number. It was about 0.4789.

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2 years ago

Which of the following shows the best way to set up the product of (2x - 5) and<br> (4 - 3x + 4.)?

masha68 [24]

Answer:

C

Step-by-step explanation:

It usually works best to use the polynomial with fewer terms as the multiplier. A row of partial products is written for each term of the multiplier, so the fewer terms will result in fewer rows of partial products.

In order to keep like terms together, it is preferable to allocate a separate column of the multiplication tableau to each power of the operands or product. This means we want to make note of the fact that the cubic multiplicand has a coefficient of 0 for its x^2 term.

The best setup is the one shown in the attachment.

3 0

1 year ago

In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,

aivan3 [116]

Answer:

Case 1:

$AB = 30$

$BC = 50$

Case 2:

$AB = 15.9$

$BC = 36.7$

Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

$AB^2 = AN^2 + BN^2$

This gives:

$AB^2 = 24^2 + 18^2$

$AB^2 = 576 + 324$

$AB^2 = 900$

Take square roots of both sides

$AB = \sqrt{900$

$AB = 30$

To calculate BC, we consider ANC, where:

$AC^2 = AN^2 + NC^2$

$40^2 = 24^2 + NC^2$

$1600 = 576 + NC^2$

Collect like terms

$NC^2 = 1600 - 576$

$NC^2 = 1024$

Take square roots

$NC = \sqrt{1024$

$NC = 32$

So:

$BC = NC + BN$

$BC = 32 + 18$

$BC = 50$

Case 2:

Using Pythagoras theorem in ANB, we have:

$AN^2 = AB^2 + BN^2$

This gives:

$24^2 = AB^2 + 18^2$

$576 = AB^2 + 324$

Collect like terms

$AB^2 = 576 - 324$

$AB^2 = 252$

Take square roots of both sides

$AB = \sqrt{252$

$AB = 15.9$

To calculate BC, we consider ABC, where:

$AC^2 = AB^2 + BC^2$

$40^2 = 252 + BC^2$

$1600 = 252 + BC^2$

Collect like terms

$BC^2 = 1600 - 252$

$BC^2 = 1348$

Take square roots

$BC = \sqrt{1348$

$BC = 36.7$

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

3 0

2 years ago