Gus is buying juice drinks, x, and snack packs, y, for a school picnic. The system of inequalities models how many of each item Gus needs to buy and how much he can spend. Which of the following points represents a viable solution to the system?
I will give Brainliest to whoever answers



x + y ≥ 150

1.5x + 3.5y ≤ 600

A. (−10, 170)

B. (80, 90)

C. (250, −50)

D. All real whole numbers, with x ≥ 0 and y ≥ 0

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

replace y with 1/4

x=2(1/4)

x=2/4

x=1/2

Hopes this helps please mark brainliest

Answer:

YT= 23

We know that:

line RU is 32 and US is 16

line RY is 46

In other words, RU = 32, US = 16, and RY = 46

so we use the triangle proportionality theorem to state that:

[tex]\frac{RU}{US}=\frac{RY}{YT}[/tex]

Input your values

[tex]\frac{32}{16} =\frac{46}{YT}[/tex]

Use cross products :

[tex]32YT=(16)(46)[/tex]

Simplify:

[tex]32YT=736[/tex]

[tex]\frac{32YT}{32} =\frac{736}{32}[/tex]

[tex]YT=23[/tex]

I hope this answers you question :)

Answer:

-1/2

Step-by-step explanation:

Ignore the (2,2) just use (-2,1) and (-4,2)

Answer:

Step-by-step explanation:

Since the two angles of both triangles are congruent, it makes the remaining angles congruent too:

Then we have:

So both C and F are 30°.

x = 14.8 (OR) x = 74/5.

Step-by-step explanation:

If you add 5 times a number to 6 you will get 80.

We don't know what number is multiplied with five and that number should added with 6. So,

Let, the unknown number be named as x.

The eqⁿ will be

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} → Eqⁿ(1) [/tex]

Shift 6 to the right side.

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{80 - 6}}}[/tex]

[tex]{ \red{ \sf{5}}}{ \green{ \sf{x}}} = { \red{ \sf{74}}}[/tex]

Divide both the sides by 5. then,

[tex]{ \red{ \sf { \cancel{\frac{5}{5}}}}} { \green{ \sf{x}}} = {{ \frac{ \cancel{74} {}^{ \green{ \sf{{ 14.8}}}} }{ \cancel5}}} [/tex]

[tex]{ \red{ \boxed{ \purple{ \sf{x = 14.8}}}}} \: { \tt{(or)}} \: { \red{ \boxed{ \purple{ \sf{x = \frac{74}{5}}}}}} [/tex]

___________________________________

[tex]{ \red{ \sf{ \underline{verification}}}} [/tex]

Let us substitute the value of x in Eqⁿ(1) then,

[tex]{ \red{ \sf{5}}}{ \green{ \sf{(14.8)}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]

[tex]{ \red{ \sf{74}}} \: + \: { \red{ \sf{6}}} = { \red{ \sf{80}}} [/tex]

[tex]{ \red{ \sf{80}}} = { \red{ \sf{80}}} [/tex]

Hence, our answer is correct

Answer:40

Step-by-step explanation:

so 14 less means that 14 was subtracted. So we need to add that to our main number, 66. When we do that we get 80. Then since 80 is twice the number we are looking for, we divide by 2 (twice is 2 times), and we get 40. Hope this helps

Answer:

f(-8) = 31

Step-by-step explanation:

f(-8) = -3(-8) + 7

      = 24 + 7

      = 31

Answer:

A = Research question

B = Hypothesis

C = Analysis of data

D = Reflecting on the results

Step-by-step explanation:

Im 85% sure

Answer:

Step-by-step explanation:

365 day a year

24 hour per day

60 second in a minute

1440 minutes in a day

86400 second in a day!

Answer:

Step-by-step explanation:

This seems complicated, huh.  

So think about the question.  They want to know the distance from a line, to a point.  first decide if the point could possibly be on the line and there is zero distance.   The given point is at  (-1, 7)    our coordinates of the point are at  -1 in the X direction and at 7 in the Y direction.  If we were to plug in those two number into the given line equation,   y = 3x  would it be a true statement?  no.    7 = 3(-1)  is not true.   so our given point is not on the line.  Next,  find the right angle to the line and point.  make your own line equation that does have our given point in it.  and is at a right angle to the given line.    recall that using a reciprocal can give you a right angle to your line.  y = (- 1/3)X .  Now we just need the given point to plug into our made up line equation and be true.    7 = (-1/3)(-1) + b    .  we need to make this equation true by moving a number into "b" that makes it true.

b = 6[tex]\frac{2}{3}[/tex]  or [tex]\frac{20}{3}[/tex]

7 = (-1/3)(-1) + [tex]\frac{20}{3}[/tex]

now, when does our made up line, y =(-1/3)x + [tex]\frac{20}{3}[/tex], intersect with the given line, y=3x,  that is,  set the two equal

3x = (-1/3)x + [tex]\frac{20}{3}[/tex]

3[tex]\frac{1}{3}[/tex] X = [tex]\frac{20}{3}[/tex]

[tex]\frac{10}{3}[/tex]X = [tex]\frac{20}{3}[/tex]

X=[tex]\frac{20}{3}[/tex] * [tex]\frac{3}{10}[/tex]

X = [tex]\frac{20}{10}[/tex]

X=2

our two equations intersect at 2,  how handy  :)

now we have our two points that are at a right angle from each other and we just need the distance from them

(given) A(-1,7)   and (found) B(2,6)

Distance = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

then our given points are A(x1,y1)  and B(x2,y2)

Distance = [tex]\sqrt{(2-(-1))^{2}+(6-7)^{2} }[/tex]

Distance =[tex]\sqrt{3^{2}+(-1)^{2} }[/tex]

Distance = [tex]\sqrt{9+1}[/tex]

Distance = [tex]\sqrt{10}[/tex]

Distance = 3.1622

Distance =3.2 (rounded to nearest 10th)

Yes, that was kinda a lot  :/

Answer:

vertex = (- 1, - 4 )

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x + 1)² - 4 ← is in vertex form

with vertex = (- 1, - 4 )

Answer:

(−1,−4)

Step-by-step explanation:

f(x)=3(x+1)2−4

Answer:13234

Step-by-step explanation:

13234 is

By finding the slopes of the two segments we can see that the segments are not parallel nor perpendicular.

The slope for a segment whose endpoints are:

(x₁, y₁) and (x₂, y₂) is:

slope = (y₂ - y₁)/(x₂ - x₁)

Two segments are:

Segment AB has endpoints (-1, -1) and (1, 5), so the slope is:

s = (5 + 1)/(1 + 1) = 3

For segment CD the endpoints are (1, 2) and (5, 4), so the slope is:

s' = (4 - 2)/(5 - 1) = 2/4 = 1/2

So the slopes are different and their product is obviously not -1, then the lines are neither parallel nor perpendicular.

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The choice that best represents David monthly interest rate is 0.625%. The correct option is C.

From the information, David opens a savings account with a 7.5% annual interest rate.

It should be noted that there are 12 months in a year.

Therefore, the monthly interest rate will be:

= Annual interest rate / Number if months in a year

= 7.5% / 12

= 0.625%

The interest is 0.625%.

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Complete question

David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?

A. 7.5%

B. 12%

C. 0.625%

D. 5%

The statement that best describes the rate of change of the linear function is given as follows:

For each increase of 1ºF in temperature, the average weight of the strawberries decays by 7/3 grams.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

The coefficients are listed as follows:

The input and the output variables for this problem are given as follows:

The function is defined as follows:

y = -7x/3 + 72.75.

Hence the slope is:

m = -7/3.

And the interpretation, considering the input and output variables, is that for each increase of 1ºF in temperature, which is the input variable, the average weight of the strawberries, which is the output variable, decays by 7/3 grams.

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Answer: The answer is 28.

Step-by-step explanation: 8a-y is our problem and we are given two variables, a and y. It is revealed that a=3 and y= -4. So our problem would now look like this: 8*3-(-4). Now see the two minuses (-) next to each other? We have to convert that into a plus (+) sign because two negatives make a positive. So our equation now looks like this: 8*3+4. Now, 8 times 3 (8*3) is equal to 24. Now our equation looks like this: 24+4. Add them together and the sum is 28.
Hope this helps!

Answer: The correct answer is B.

Step-by-step explanation:

In a line with a slope of 0 the x can change but the y cannot in a (x, y).

The total attendance for Lincoln school for month of March is 7308.

What is average attendance?

Divided by the total number of days in the ordinary school year, is the total number of days that students were present. One ADA(Avg. Daily attendance) would be the number of students who attend every day. The number of kids enrolled in each school and district, known as enrollment, is not the same as ADA.

Main Body:

So according to formula ,

Average daily attendance = Total attendance / total days of school

348 = total attendance/ 21

total attendance = 348* 21

                            = 7308

Hence total attendance is 7308.

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The variable y vary directly with respect to x , and the equation to denote this direct variation is y = 1.375 x .

From the table we can see that the values of x are 8 for the y value of 11

Any direct variation is represented by the equation :

y = k x , where k is a constant

now we put the values of x and y in the equation to calculate k

11 = k × 8

or, k = 11 / 8 = 1.375

again , at x = 16 , y is 22

∴ k = 22/16 = 1.375

Hence the equation for direct variation will  be given by

y = kx

or, y = 1.375 x

When one quantity changes directly in reaction to a change in another quantity, this is a type of proportionality known as "direct variation." This implies that if one quantity rises, the other will rise correspondingly as well.

Like in the previous illustration, if one quantity decreases, the other quantity also decreases. Direct variation will have a linear relationship with the graph, resulting in a straight line.

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From the given table

Part a

The equation of the function is y = ( - 0.7/277)x + 16

Part b

The slope of the line =  - 0.7/277 and the y intercept of the line = 16

From the table

Choose two points

(242, 14.8) and (519, 14.1)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (14.1 - 14.8) / (519 - 242)

= -0.7 / 277

The slope of the line = - 0.7/277

From the table at x = 0, the value of y = 16

Therefore the y intercept is 16

The slope intercept form is

y = mx + b

Substitute the values in the equation

y = ( - 0.7/277)x + 16

Part b

The slope of the line =  - 0.7/277

The y intercept of the line = 16

Hence, from the given table

Part a

The equation of the function is y = ( - 0.7/277)x + 16

Part b

The slope of the line = - 0.7/277 and the y intercept of the line = 16

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the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.

what is expression  ?

An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It does not have an equal sign, so it cannot be solved.

In the given question,

The correct answer is C.

To simplify the given polynomial expression using the distributive property, we need to distribute the first term (2a³) to each term in the second parentheses, and then add it to the third term.

So, we have:

(2a³) (2a²+ 66²) + (6a²b + 12ab² - 76³)

= 4a⁵ + 132a³ + 6a²b + 12ab² - 76³

Now, we can simplify further by combining like terms:

= 4a³ (a²+ 33) + 6ab (a + 2b) - 76³

Therefore, the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.

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The standard deviation of the number of residents in the sample who were born in Colorado is 7.82

Standard deviation:

The measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists is know as standard deviation.

Given,

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. if a sample of 250 Colorado residents is selected at random.

Here we need to find the standard deviation of the number of residents in the sample who were born in Colorado.

Here we know that following details,

Number of sample = 250

Estimated proportion for residents born in Colorado = 42.7% which is equal to = 0.427.

Let us consider X be the random variable of interest (number of residents in the sample), on this case we now that:  

X ~ (n = 250, p = 0.427)

Now, according to the probability mass function for the Binomial distribution is given as:  

E(X) = n x p = 250 x 0.427 = 106. 75.

Now, the standard deviation for the random variable is given by:

SD = √106.75 (1 - 0.427)

SD = √106.75(0.563)

SD = 7.82

Therefore, the standard deviation is 7.82.

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The burj khalifa is 7.56 football fields tall .

We have the height of the  Burj Khalifa as = 2722 feet

And the given height of  one football field is = 360 feet

Now using the Unitary method we can calculate the number football fields that would be equal to the height of the burj khalifa .

So ,

360 feet is equal to football fields = 1

1 feet is equal to football fields = 1/360 fields

therefore

2722 feet will be equal to fields = (1/360) x 2722

                                                     =  7.56 fields

So the Burj Khalifa is equal to  7.56 football fields.

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For any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.

And when "a" is a number greater than one then graph of a function get horizontal compress.

As given in the question,

For any graph of a function,

When "a" is a number between zero and one than the graph of the function get horizontal stretch.

f(x) = ax²

let a = 1/2 , 0 < 1/2 < 1 so satisfied the condition of "a" between zero and one.

f(x) = x²/2

In this case , graph of the given function get horizontal stretch compare to original graph.

When a = 2 , 2 > 1 satisfied the condition of "a" greater than one.

f(x) = 2x²

In this case , graph of the given function get horizontal compress compare to original graph.

Therefore, for any given graph when "a" is a number between zero and one then graph of the function get horizontal stretch.

And when "a" is a number greater than one then graph of a function get horizontal compress.

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The correct statement is,

''The smallest number that both denominator numbers will include into.''

What is Least common multiple?

The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.

Given that;

The statement is,

The smallest number that both denominator numbers will __ into.

Now,

We know that;

The LCM of two or more numbers is divided by the numbers or its include all the numbers.

Thus, The correct statement is,

''The smallest number that both denominator numbers will include into.''

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Using the normal distribution, it is found that:

a) The 10th percentile for incubation times is of: 18.72 days.

b) The incubation times that make up the middle 95​% are of: Between 18.04 and 21.96 days.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the incubation times are presented as follows:

[tex]\mu = 20, \sigma = 1[/tex]

The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:

-1.28 = (X - 20)/1

X - 20 = -1.28

X = -1.28 + 20

Z = 18.72 days.

Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:

Hence the lower bound is:

-1.96 = (X - 20)/1

X - 20 = -1.96

X = -1.96 + 20

Z = 18.04 days.

The upper bound is:

1.96 = (X - 20)/1

X - 20 = 1.96

X = 1.96 + 20

Z = 21.96 days.

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The equations 2.3p - 101 = 6.49p -4 and 23p - 101 = 65p - 40 - p are the equation that has the same solution:

The given equation is:

2.3p - 10.1 = 6.5p - 4 - 0.1p

The first option is:

2.3p - 10.1 = 6.4p - 4

which is equal to the given equation.

The second option:

230p - 1010 = 650p - 400 - p

which is not equal to the given equation

The third option:

23p - 101 = 65p - 40 - p

which is equal to the given option.

The last option:

2.3p - 14.1 = 6.4p -4

which is not equal to the given option.

Therefore equations 2.3p - 10.1 = 6.4p - 4 and 23p - 101 = 65p - 40 -p are the correct option.

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Using distributive law and the greatest common factor , the expression (32 + 16) can be factored as 16(2 + 1)

The GCF(greatest common factor) is defined as the largest number that is a factor of two or more numbers.

In a simpler term, the greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF.

Using distributive law and the greatest common factor we can factor an expression.

Therefore, let's factor the expression (32 + 16).

The greatest common factor of 32 and 16 is 16.

Therefore, the expression can be express as follows:

(32 + 16) = 16(2 + 1)

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