Which of the following proves

Based on the quantity of the various items sold at the concession stand, the items that show a linear relationship include:

Items that show a linear relationship are those that are either increasing or decreasing by the same amount overtime.

Change in Hotdogs:

= 142 - 131                                 =  120 - 109

= 11                                             = 11

Hotdogs are changing by the same amount.

Change in Soft drinks:

= 161 - 154                                                       = 147 - 133

= 7                                                                   = 14

Change in Pretzels

= 96 - 64                                    = 120 - 112

= 32                                            = 8

Change in Nachos:

= 111 - 97                                         =  153 - 139

= 14                                                 = 14

Therefore, the only items that are linear are the Hotdogs and Nachos.

Find out more on linear relationships at https://brainly.com/question/837754.

The diamond rule creates a system of equation for variables m and n

The possible values of m and n are 8 and 4 or 4 and 8

The question is incomplete; so I will make use of the attached figure

When the diamond rule is applied to the figure, we have the following equations

[tex]mn = 32[/tex]

[tex]m + n = 12[/tex]

Make n the subject, in the second equation

[tex]n = 12 - m[/tex]

The first equation becomes

[tex](12 - m)m = 32[/tex]

Expand

[tex]12m - m^2 = 32[/tex]

Rewrite as:

[tex]-m^2 + 12m - 32 = 0[/tex]

Multiply through by -1

[tex]m^2 - 12m + 32 = 0[/tex]

Expand

[tex]m^2 - 4m - 8m + 32 = 0[/tex]

Factorize

[tex]m(m - 4) - 8(m - 4) = 0[/tex]

Factorize

[tex](m - 8)(m - 4) = 0[/tex]

Solve for m

m = 8 or m = 4

Recall that:

[tex]n = 12 - m[/tex]

So, we have:

n = 12 - 8 or n = 12 - 4

Solve

n = 4 or n = 8

Hence, the possible values of m and n are 8 and 4 or 4 and 8 (using the attached figure)

Read more about equations at:

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Explanation:

3 feet = 1 yard

14*(3 feet) = 14*(1 yard) .... multiply both sides by 14

42 feet = 14 yards

The carpet is 14 yards by 14 yards.

Its area is 14*14 = 196 square yards.

Since it costs $25 per square yard, this means the total cost is 25*196 = 4900 dollars

Answer:

2m + 3 I think.

Step-by-step explanation:

4m - 2m = 2m. So just put that in the equation now and poof. 2m + 3

Answer:

8

Multiply 0.25 by 8 ⇒ 2 [tex]in.[/tex]

I hope this helps!

Answer:

100

Step-by-step explanation:

Split it into 3 different rectangles, find the area of each, and add them together.

Rectangle 1: length=11   width=4    11×4=44

Rectangle 2: length=11-9=2   width=6    2×6=12

Rectangle 3: length=11   width=4    11×4=44

44+12+44=100

Answer:

2x + 3y = 12 …equation 1

x– y = 1 … equation 2

To solve it by elimination method, let us multiply the second equation by 3

3x — 3y = 3 …equation 3

Now add the first and third equation

5x = 15

x = 3

From equation 2, y = x-1

y = 2

Hence x = 3, y = 2.

(b) 3x + y = 10

Since we have one equation and 2 variables, it cannot be solved by the elimination method.

To solve this, we can go for trial and error

Say y = 1, x = 3 or x = 5, y = —5

(c) x – 3y=1 …eq 1

3x – 2y + 4 = 0 …eq 2

Multiply eq 1 by 3, 3x — 9y = 3 …eq 3

Eq 2 — eq 3,

7y = —7

y = —1, x = —2 Ans

Based on the line of best fit, the length of this catfish can be predicted to be 38 inches.

Given the following data:

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

From the graph of the data, we have the following linear equation:

[tex]y=\frac{1}{2} x+18[/tex]

Substituting the value of x, we have:

[tex]y=(\frac{1}{2} \times 40 )+18\\\\y=20+18[/tex]

y = 38 inches.

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Solution:

We know that:

This means that:

Step-1: Convert "40%" into a fraction.

Step-2: Find the discounted price.

Answer:

#1) A

#2) B

#3) C

#5) A

#7) D

#10) D

#11) D

#14) A

#15) D

#16) A

#19) D

Step-by-step explanation:

#1) If the data set is linear, the slope will be constant throughout the entire data set. For data set A, the slope between the first two points is:

m = (y₂-y₁)/(x₂-x₁) = (1--2)/(3-1) = 3/2

Between the second two points,

m=(4-1)/(5-3) = 3/2

Between the third pairs of points,

m=(7-4)/(7-5) = 3/2

The slope is constant throughout the entire set. The set is also increasing; as x increases, y increases as well.

#2) Substituting 4 for y and 1 for x,

y = (x+1)²

4 = (1+1)² = 2²

9 = (1+2)² = 3²

16 = (1+3)² = 4²

This works for each point, so this is the solution.

#3) Since he runs 10 laps per hour t, this is 10t. Adding the first lap to this, we get y=10t+1.

#5) If a sequence is arithmetic, each term is found by adding a constant (called the common difference) to the previous term. If the common difference is 2, this means that 2 was added each time. This only works for choice A.

#7) For x to vary directly as y, this means that y/x = k; in other words, the quotient of y and x is constant for every point.

#10) The formula for slope is:

m=(y₂-y₁)/(x₂-x₁)

Using the information we're given, we have

3=(d-5)/(4-2)

3=(d-5)/2

Multiply both sides by 2:

3*2 = ((d-5)/2)*2

6 = d-5

Add 5 to both sides:

6+5 = d-5+5

11 = d

#11) Using point slope form,

y-y₁ = m(x-x₁)

y-1 = 3(x--2)

y-1 = 3(x+2)

Using the distributive property,

y-1 = 3*x + 3*2

y-1 = 3x + 6

Add 1 to both sides:

y-1+1 = 3x+6+1

y=3x+7

#14) If two lines are parallel, they have the same slope. The slope of the given equation is 4; the only one with a slope of 4 is A.

#15) If two lines are perpendicular, they have slopes that are negative reciprocals (opposite signs and flipped). The slope of the given equation is 2; this means the slope of the perpendicular line would be -1/2. The only one with this slope is D.

#16) The two equations are not the same, so there are not infinitely many solutions. The variables do not both cancel, so there is at least one solution. This only leaves one solution as the answer.

#19) Using 1 for 7 and 4 for x, we check each equation. The only one that comes out correct is D.

i hope this work for you

and sory if im wrang

Answer:

16 ounces

Step-by-step explanation:

one pound is sixteen ounces

Step-by-step explanation:

Although it is right,

The rule is that we stop factoring, if we can't factor out a constant that isn't 1.

In your example, we can still factor out-1.

The factorization 2x(-7-6x) is not wrong because distributing the outer 2x to each term inside gets us

which leads back to -14x-12x^2

Therefore, 2x(-7-6x) = -14x - 12x^2 is true.

Convention usually has us pull out the negative so the terms inside are all positive. This is just a practice done. There technically isn't any right way vs wrong way to factor, when we compare the two different factorizations. I think it's more of a subjective style than anything.

Answer:

3/5

108

Step-by-step explanation:

Let there are 3x goldfish, then 2x belta fish

total 3x + 2x = 5x fish

so 3x/5x = 3/5 are goldfish.

total fish = 5x = 180, so x = 180/5 = 36

The store has 3x = 3*36 = 108 goldfish.

Given :

[tex]{\qquad \sf \dashrightarrow y= 4x + 1 \: –––– \sf \: (i)}[/tex]

[tex]{\qquad \sf \dashrightarrow 3x + 2y = 13 \: –––– \sf \: (ii)}[/tex]

Now, Substituing the value of y in equation (ii) :

[tex]{\qquad \sf \dashrightarrow \: 3x + 2y = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 3x + 2(4x + 1) = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 3x + 8x + 2 = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x + 2 = 13 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x = 13 - 2 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: 11x = 11 }[/tex]

[tex]{\qquad \sf \dashrightarrow \: x = \dfrac{11}{11} }[/tex]

[tex]{\qquad \sf \dashrightarrow \bf \: x = 1 }[/tex]

Now, substituting the value of x in equation (i) :

[tex]{\qquad \sf \dashrightarrow y= 4x + 1}[/tex]

[tex]{\qquad \sf \dashrightarrow y= 4(1) + 1}[/tex]

[tex]{\qquad \sf \dashrightarrow y= 4 + 1}[/tex]

[tex]{\qquad \bf \dashrightarrow y= 5}[/tex]

Answer:

D

Step-by-step explanation:

If n=minimum number of required words and the essay is 175 words long which is 5 times more words than the minimum number of required words, you multiply n with 5 and equate to 175. To get n, you divide 175 with 5(175/5) which is 35 words.

i) 15 students

ii) 15 students

Answer:

40°

Step-by-step explanation:

m∠DGE = mDE/2 = 80/2 = 40°

Answer:

2

Step-by-step explanation:

If ABC is equilateral, its angles are all equal to each other and each one measures 60°.

[tex]8x-44 =60\\8x = 16 \rightarrow x = 2[/tex]

Step-by-step explanation:

1 1/4

is also 5/4

5/4 * 3 * 1/2 * 40 =

answer in comments

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Answer:

  (d)  22

Step-by-step explanation:

For numbers of days above 19, the fine is constant. The answer choice that is above 19 is 22. For 22 days overdue, the fine will be the same as for 21 days overdue: $10.

 22 could be the number of days

Answer:

D. 22

Step-by-step explanation:

To identify the shape with one pair of parallel sides, we need to consider the given set of numbers: 3, 5, 8, 2, 6.

A shape with one pair of parallel sides is a trapezoid. In a trapezoid, two sides are parallel while the other two sides are non-parallel.

Looking at the given set of numbers, we can form the sides of a trapezoid by pairing the numbers in the following way: 3, 5, 8, 2, 6.

The sides of the trapezoid can be represented as follows:

Parallel sides: 3 and 5 (forming the top and bottom sides)

Non-parallel sides: 8, 2, 6 (forming the slanted sides)

Therefore, the given set of numbers forms a trapezoid with one pair of parallel sides.

For such more question on trapezoid

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Answer:

False

Step-by-step explanation:

[tex]the \: expression \: is \: 3x[/tex]

Answer:

false

Step-by-step explanation:

thrice a number means 3 times the number

if the number is m then thrice the number is

3 × m = 3m

Answer:

B) 236.25

Step-by-step explanation:

POQ is a diameter of circle with centre O having diameter 21 cm. Whereas radius is 21/2 cm (as radius is considered as half of the diameter).

Assume that the tip of the triangle that touches the circle is point 'N'. So,

NO = radius = 21/2 cm

At present time we have a triangle of radius or height 21/2 cm, base 21 cm is enclosed in circle of diameter 21 cm. And are asked to find the area of the remaining region or you can say asked to find area of the shaded region.

Shaded region = Area of Circle - Area of Triangle

= πr² - 1/2 × b × h

= 22/7 × 21/2 × 21/2 - 1/2 × 21 × 21/2

= 21/2 × 1/2 [ 22/7 × 21 - 21 ]

= 21/4 [ 22 × 3 - 21 ]

= 21/4 [ 66 - 21 ]

= 21/4 [ 45 ]

= 21 × 11.25

= 236.25

Hence, the area of the shaded region is 236.25 cm².

I don't know use a calculator

Answer:

She is 60 years old

Step-by-step explanation:

The first thing we can do is convert each fraction to have a common denominator. The LCM of 5, 3, and 4 is 60.

[tex]\frac{1}{4} =\frac{15}{60}[/tex]

[tex]\frac{1}{3} =\frac{20}{60}[/tex]

[tex]\frac{1}{5} =\frac{12}{60}[/tex]

Add the numerators:

[tex]15+12+20=47/60[/tex]

Meaning that the time she lived in Switzerland is the remaining 13/60, and since she lived there for 13 years that means she lived for a total of 60 years because the numerator and denominator both equal 60.

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Answer:

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

Let the age of Teresa be x.

Set up equation:

Multiply both sides by 3*4*5 = 60 to clear fraction:

Answer:[tex]2\sqrt{3}[/tex]

Step-by-step explanation:

Use pytha. theorem on leftmost triangle and get sqrt(13)

Use it again on the other triangle: 13+b^2=25

First, we find the hypotenuse of the first triangle

(Use the pythagorean theorem) : [tex]3^{2} + 2^{2} = 9 + 4 = 13[/tex]

So, the length of the side = [tex]\sqrt{13}[/tex]

Now, we find x :

x(squared) = [tex]5^{2} -\sqrt{13} ^{2}[/tex] = 25 - 13 = 12

-> x = [tex]\sqrt{12}[/tex] = 2[tex]\sqrt{3}[/tex]

Answer:

 13m²−35m+8−4m³

Step-by-step explanation:

Expand (1 − 4m)(m² − 3m + 8) by multiplying each term in the first expression by each term in the second expression.

1m² + 1 (−3m) + 1 ⋅ 8 − 4m ⋅ m² − 4m (−3m) − 4m ⋅ 8

Simplify terms.

13m²−35m+8−4m³