Tom has 25 gallons of gas and needs to fill it equally in 3 1/2 gallon containers. How many containers can he fill?

Answer:

your answer is 7/2

Step-by-step explanation:

We will assume “a number” is “a”. When it is cubed it will be represented by

= “a³”.

When we multiply the number with 5 then the new cube will be

= (5a)³

Now distribute the exponent to the factors inside the parentheses.

= 125a³

What happens in the parentheses is 5*5*5 = 125

a*a*a = a³

So by multiplying your number with 5 it gets increased by 125 times.

Answer:

4n^2 + 5n.

Step-by-step explanation:

If the number is n, then:

4n^2 + 5n.

Answer:

Step-by-step explanation:

s = d/t = 100/2.5

Answer:

E) Line 5

Step-by-step explanation:

Line 5 contains the first incorrect mathematical process

Process

x−5(x+1)>3x+2

−4x−5>3x+2

−7x−5>2

−7x>7

x<−1

The correct answer is option D.

The polygon ABCD can be mapped on to WXYZ but first it must be enlarged and then it must be mirrored along BC.

The mirror image of ABCD along BC must be enlarged with a scale factor of 2 to map ABCD to WXYZ.

The scale factor is the ratio of the the object to be transformed to the object with which it is to be compared.

Here, the scale factor is 2 and we must enlarge the image of ABCD along BC to get the desired mapping.

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If a region’s average movie theater ticket price in 2007 was $6.51. For 2017, it was estimated to be $8.57, the percent of increase in average movie theater ticket price is 16%

A region's average movie ticket price in 2007 was $6. 51

A region's average movie ticket price in 2017 was $8. 57

Increase in price = 8.57 - 6. 51 = $1.06

Percentage of increase = (increase in price / original price)*100

= (1.06/6.51)*100

16%

If a region’s average movie theater ticket price in 2007 was $6.51. For 2017, it was estimated to be $8.57, the percent of increase in average movie theater ticket price is 16%

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Answer:

22.5

Step-by-step explanation:

∠EAB=2x (alternate interior angles)

∠AEB=180°-4x (linear pair)

.

3(x+5) + 2(x-3) = 6(3(1/6))

3x + 15 + 2x - 6 = 3 X 1

5x + 9 = 3

5x = - 7

x = - 7/5

The cost per item for maximum profit is $7.50 .

The maximum and minimum value of a function f(x) is calculated by finding the first and second derivative of f(x).

The cost to produce x pies is given by the cost function

[tex]C(x)=3x+36[/tex]

The price demand function for each pie is given by

[tex]p(x)=12-0.5x[/tex]

Revenue gained from selling x pies

[tex]R(x)=x\times p(x)\\or,R(x)=x\times(12-0.5x)\\or,R(x)=12x-0.5x^2[/tex]

Now profit function is given by

[tex]P(x)=R(x)-C(x)\\or,P(x)=-0.5x^2+12x-3x-36\\or,P(x)=-0.5x^2+9x-36[/tex]

Now we have to find the maximum profit. We know that for a function

[tex]P(x)=-0.5x^2+9x-36\\P'(x)=-x+9[/tex]

[tex]P''(x)=-1[/tex]

At P'(x)=0

or,-x+9=0

or, x=9

As P''(x)<0 therefore the profit function P(x) is maximum for x at P'(x)=0.

The profit is maximum at x=9

Price to charge per item=12-0.5x

Substituting the value of x we get:

[tex]p(x)=12-(0.5\times 9)\\or,p(x)=12-4.5\\or,p(x)=7.5[/tex]

Therefore the cost per item for maximum profit is $7.50 .

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the number x, you must deduct another number from it , conditions will the response be unfavorable,

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In an expression, a positive number is subtracted from two other integers. If the value of the negative number is higher than that of the positive number, then the expression's value will be considered negative. Additionally, according to the fundamental rule of integers, the number's sign-bearer must always have a higher value.

For instance,

1. 2 - 3 = -1

2. 10 + (- 8) + (- 11) = -9

3. -6 + 3 = -3

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Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

Answer:

Only one equation fits all the information on the table which is:

y = 1/6x

Answer:

y = 1/6x

Step-by-step explanation:

To find the equation, let's see if each option works by plugging in x into each equation.

y = –1/4x

Plug -6 into x

y = –1/4(-6)

y = 1.5

y = –1/4x doesn't work because we didn't get -1.

y = 6x

Plug -6 into x

y = 6(-6)

y = -36

y = 6x doesn't work because we didn't get -1.

y = 1/6x

Plug 1/6x into x

y = 1/6(-6)

y = -1

Let's see if the other x values work.

Plug 0 into x

y = 1/6(0)

y = 0

Plug 12 into x

y = 1/6(12)

y = 2

y = 1/6x works.

y = –2x

Plug -6 into x

y = –2(-6)

y = 12

y = -2x doesn't work because we didn't get -1.

y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.

Hope that helped and have a lovely rest of your day!

1. The number of edible portions (EP) is 64.

2. The food cost per portion = $0.75 per portion.

The number of edible portions can be determined by first converting the case weight in pounds into ounces.

There are 16 ounces in a pound. 20 pounds will equal 320 ounces by multiplication (16 x 20).

Then, divide 320oz by 5oz to determine the number of portions.

Yield:                      90%

Purchase Unit:       10 boxes = 1 case

Case Weight:        20 lbs

Case Cost:           $48.00

Portion Size:         5oz

1lb = 16oz

20lbs = 320oz (20 x 16)

Edible portions (EP) = 64 (320oz/5oz)

Food cost per portion = $0.75 per portion ($48/64).

Thus, the number of edible portions is 64 with the food cost per portion as $0.75.

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She will lease out 21 apartments in the month of October.

We are given that a leading agent leases 15 apartments in the month of September.

Number of apartments in the month of September = 15.

Now, it is also given that she leases 40 % more apartment in the next month that is October.

Number of apartments in the month of October. = 15 + 40 % of 15

Number of apartments = 15 + 40 / 100 × 15

Number of apartments = 15 + 6

Number of apartments = 21 apartments.

Therefore, she will lease out 21 apartments in the month of October.

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Equation giving the length of this rod at temperature is g = 0.000085t + 84.991075 cm.

What is temperature ?

Given that,

Temperature denoted by T

G - L = aL(t - T)

G = aLt +  L(1 - aT)

Slope = aL

Intercept = L(1 - aT)

g = 0.000085t + 84.991075 cm

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the domain of the following graph= [-5,10)

Domain :

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

For example, when we use the function notation f: R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real numbers R (and its set of possible outputs or codomain is also the set of real numbers R).

To,  identify the domain and range of functions by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the

x-axis. The range is the set of possible output values, which are shown on the

y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

We can observe that the horizontal extent of the graph is -5 to 10, so the domain of f is [-5,10)

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Answer:

Step-by-step explanation:

Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100.

The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending

the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

Answer:

Step-by-step explanation:

This article is about the basic inequality {\displaystyle z\leq x+y}{\displaystyle z\leq x+y}. For other inequalities associated with triangles, see List of triangle inequalities.

Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows a case where z is much less than the sum x + y of the other two sides, and the bottom example shows a case where the side z is only slightly less than x + y.

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that

{\displaystyle z\leq x+y,}z\leq x+y,

with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):

{\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}\|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,

Answer:

bca

Step-by-step explanation:

5x5=25 5 to the power of 2 is 25 plus the power of x on all of them

[tex]1/3 \longrightarrow 0.33 \\ \\ 1/2 \longrightarrow 0.50 \\ \\ 1/4 \longrightarrow 0.25 \\ \\ 3/4 \longrightarrow 0.75 \\ \\ 2/3 \longrightarrow 0.66[/tex]

Answer: One Solution

Step-by-step explanation:

Only the number 0 can solve this equation so it may be correct.

First approaching this problem, I would try to get x on one side of the equation by subtracting 2.5x from both sides.

This leaves us with 7.5x = 0

Therefore, this equation has only one solution, 0.

Shirley will take 8 hours to complete mowing the field alone.

We are given that Shirley and Pam, working together, can mow the lawn in 6 hours.

So, work done if 1 hour together = 1 / 6

Also, we are given that Pam takes three times as long as Shirley when she works alone.

Time taken by Pam = 3 times Time taken by Shirley.

Let the time taken by Shirley be y.

Job done in 1 hour = 1 / y

Time taken by Pam = 3 y

Job done in 1 hour = 1 / 3y

ATQ:

1 / y + 1 / 3 y = 1 / 6

4 / 3 y =1 / 6

24 = 3 y

y = 24 / 3

y = 8 hours.

Therefore, Shirley will take 8 hours to complete mowing the field alone.

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Answer is ADEF

Given that, two right tringle = R + ΔHEL , R +ΔPME

Hypotenuse equal , A set of corresponding right angles are equal.{HL};

LL=LE

So ∠E(M tringle HEL)∠LM (M tringle PME)

∠H=∠P 90°

∠L=∠E                        ⇒AAS

HE PM or LE =EM

∠E = ∠M

EL = ME                      ⇒ASA

∠L = ∠E

HF = PM

∠E = ∠M                       ⇒SAS

EL = ME

Hence choose A.D.E.F

{Determination of congruence of right tringle }

explanation of  Determination of congruence of right tringle

A plane figure bounded by three finite line segments to form a closed figure is known as a triangle. A right-angled triangle is a special case of the triangle. In a right-angled triangle, one of the interior angles measures 90°. Two right triangles are said to be congruent if they are of the same shape and size. In other words, two right triangles are said to be conger

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{a\times b}}[/tex]

[tex]\mathsf{= 24\times8}[/tex]

[tex]\mathsf{= 192}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{192}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

Given the quadratic equation y = 2x² +7x -9, you want the coordinates of the x- and y-intercepts.

The values of x where y=0 can be found by factoring the equation.

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

The constants 9 and -2 in the binomial terms are factors of the product of leading and trailing coefficients (2)(-9) = -18. Those factors are chosen because their sum is 7, the middle coefficient.

The x-intercepts are the values of x that make these factors zero:

  2x +9 = 0   ⇒   x = -9/2

  x -1 = 0   ⇒   x = 1

Points A and B are ...

The y-value at point C is where x=0. It is the constant in the quadratic equation.

  y = 2(0²) +7(0) -9 = -9

Point C is ...

The batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins

The given parameters can be represented on the following table

                 Bread (x)                    Muffins (y)

Prepare         4                                 1                         16

Bake             0.5                            0.5                        10

Profit            35                               10

The parameters from the above table are

Max P = 35x + 10y

Subject to

4x + y <= 16

0.5x + 0.5y <=10

x, y > 0

Solving the above constraints using a graphing calculator, we have the following points

(x, y) = (4, 0) and (0, 16)

Substitute these values in Max P = 35x + 10y

So, we have

P = 35 x 4 + 10 x 0 = 140

P = 35 x 0 + 10 x 16 = 160

160 is greater than 140

Hence, the batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins

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We use parenthesis if an interval is infinite on both boundries in order to exclude end-points .

Square brackets mean the set of all points from a to b .

If we use square brackets , it would mean we are including - infinity and + infinity , which is practically impossible .

When we , use parenthesis only the nos . lying between the two points are taken into consideration , the two points are not included .

So , we use parenthesis to exclude - infinity and + infinity .

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