Vesa has two different choices to buy popcorn at the movie
theater. She can buy them in cylinder-shaped boxes with a
length of diameter 20cm and length of height 40cm, or with
a length of diameter 30cm and length of height 20cm.
Which box should Vesa choose if she wants to buy more
popcorn?

From the given set of equation the one which has same solution as

x² + 4x + 13 = -10 is given by (x+2)² = -19.

As given in the question,

Given equation is equal to:

x² + 4x + 13 = -10

Simplify it we get,

x² + 4x + 13 +10 =0

⇒ x² + 4x + 23 =0  ___(1)

General quadratic equation is

ax² + bx + c =0

a = 1 , b =4 , c =23

Simplify the given options we have:

a. (x+2)² = -19

⇒ x² + 4x + 4 = -19

⇒ x² + 4x + 4 + 19 =0

⇒ x² + 4x + 23 =0

Has same solution as given one.

b.  (x-2)² = -27

⇒ x² -4x + 4 +27 =0

⇒x² -4x +31 =0

'b' and 'c' value are different

Not have same solution.

c. (x-2)² =-19

⇒ x² -4x + 4 +19 =0

⇒x² -4x +23 =0

'b' value is different.

Not have same solution.

d. (x+2)² = -27

⇒ x² +4x + 4 +27 =0

⇒x² +4x +31 =0

'c' value is different

Not have same solution.

Therefore, from the given set of equation the one which has same solution as x² + 4x + 13 = -10 is given by (x+2)² = -19.

The complete question is:

Which equation has the same solution as x² + 4x + 13 = -10?

a. (x+2)² = -19

b. (x-2)² = -27

c. (x-2)² =-19

d. (x+2)² = -27

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Answer:

positive 3

Step-by-step explanation:

Steps:

1. first you must get y by itself/isolate it to one side of the equation to get it in the format of y = mx + b

-3x + 2y = 6

+3x           +3x            add 3x to both sides to get 2y by itself
____________

2y = 3x + 6                -3x+3x cancels out and becomes 0

-------------------------
         2                        divides both sides by 2 to get y by itself

y = (3/2)x + 3

2. Looking at the equation, we know that 3 is the y-intercept because the "b" in the slope-intercept equation is always the y-intercept.

Answer:

300/100%=3%

Step-by-step explanation:

sorry, can't explain.Ihave class tomorrow

Answer:

5 bath towels

2 washcloths

Step-by-step explanation:

160 = 2⁵ × 5

64 = 2⁶

HCF= 2⁵ = 32

160 ÷ 32 = 5

64 ÷ 32 = 2

Answer:

9 m

Step-by-step explanation:

given,

area of floor of play pen = 5 m²

we know, area of a square = (side)² sq units

now according to the question,

5 = (side)²

⇒√(side)² = √5 [taking square root on both sides]

⇒ side = √5 m

now, we know,

perimeter of a square = 4 × side = 4 × √5 = 8.94 m (app.) ≈ 9 m

The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

Leticia contributes $200 at 5% interest. Assuming that y addresses how much cash after x time spans.

Then the exponential equation is written as,

y = 200(1 + 0.05)ˣ

y = 200 (1.05)ˣ

The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

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Answer:

x=2

Step-by-step explanation:

You can put the equation as 7=6x-5

Move equation

12=6x

Divide

x=2

If on the third day, she earns three times as much as the second day. The amount that she earn on the first day is $856.

Let  a = Amount earned on the first day

Let b = Amount earned on the second day

Let c = amount earned on the third day

Let a + b + c =2568,

Hence,

2b + b +3b =2568

6b =2568

b =2568/6

b =428 second day

So,

a = 2b

a =2(428)

a =856 first day

Thus

c = 3b where b = 428

c=3(428)

c=1284 third day

Check:

a +b + c = $2568

856 + 428 + 1284 = $2568

Therefore she earned $856 on the first day.

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Answer:

x > -2

Step-by-step explanation:

3x - 10 < 4x - 8

Collect like terms

3x - 4x < 10 - 8

-1x < 2

Divide both sides by -1

-1x/-1 < 2/-1

x > -2

Answer:

3

Step-by-step explanation:

first factor out both the numbers

12:2*2*3

39:3*13

find the common ones and multiply them together

they both share only 3, so 3

The y-intercept of the line will be equal to 7.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that a line that has a slope of 2 and ( - 2, 3 ). The y-intercept of the line will be calculated as,

y = mx + c

3 = (-2 x 2 ) +c

3 = -4 + c

c = 4 + 3

c = 7

Therefore, the y-intercept of the line will be equal to 7.

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Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function is given in the represented graph

According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.

Here the domain of the given function is  0 < x < 6

Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.

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A table of equivalent ratios for the miles and gallons of gas driven is as follows:

Miles        Gallons

39                 1

117                 3

312                8

The data points are plotted in the graph shown in the image attached below.

In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:

x = ky

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would calculate the constant of proportionality (k) as follows:

Constant of proportionality (k) = x/y

Constant of proportionality (k) = 312/8

Constant of proportionality (k) = 39.

When x = 39, the value of y is given by:

y = x/k

y = 39/39

y = 1 gallons.

When y = 3, the value of x is given by:

x = ky

x = 39 × 3

x = 117 miles.

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Step-by-step explanation:

so there sre 104 postcards .so what we do is 104 ÷ 4 post cards on each page , it will then = to 26 pages

Answer:

65c

Step-by-step explanation:

Answer:

33 degrees

Step-by-step explanation:

The square in the corner of these two vectors signifies that this is a right angle, which will always equal 90 degrees, so if you subtract angle 2's value of 57 degrees, you will be left with angle 1 as 33 degrees.

The Diameter of the cube would be 3 inches

What is Variation?

A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.

Solution:

We know that,

Horse Power is directly proportional to RPM * Diameter

So, we can write

Horse Power = k * RPM * Diameter

here, k is any constant

From the first case given, we can find the value of k

16 = k * 2 * 120

k = 1/15

Putting the value of k in second case,

30 = 1/15 * 150 * Diameter

Diameter = 3 inches

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Answer: 3.28 inches

Step-by-step explanation:

Fabric used for players and coaches is 776.32 inches.

Number of players is 29 and coaches is 3

So fabric used for each player and coach for the headbands is

776.32/29+3 = 24.26 inches

So, for the players 24.26 of fabric will be used for the headbands.

Total fabric used for the wristbands is 247.66 inches

Fabric used for the wristband is

247.66/29 = 8.54 inches

So, total amount of fabric used by Shelia for the wristband and headband is 24.26 + 8.54 = 32.8 inches.

Answer: Yes, Probably

When you have a square pyramid, the plane section that will produce a trapezoid is B. A cut parallel to the vertical axis, directly through the vertical axis

It is defined in geometry as a shape with a square base with equal side lengths and all of the square's joints at the top that are perpendicular to the center of the square.

Geometry, as we know, is the branch of mathematics concerned with the size, shape, and orientation of two-dimensional figures. A trapezoid, also known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.

It's parallel sides are known as the bases, and its non-parallel sides are known as the legs. A trapezoid can have parallel legs as well.

In this case, the cut parallel to the vertical axis, directly through the vertical axis will produce the trapezoid.

In conclusion, the correct option is B.

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Answer:

the slope is 1.75

Step-by-step explanation:

Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight.  For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb

The runner's speed If a runner traveled a distance of d(h)=/16h4 in time t(h) = 3h^4 - 3h^3 -5h^2 is  4 /3h^2 - 3h -5h.

The concept that will be used to calculate this is the concept of speed which is the ratio of the distance per time which can be expressed as

speed = distance/time

Then we were given distance as d(h)=/16h^4

time as  t(h) = 3h^4 - 3h^3 -5h^2

Speed = [tex]\sqrt{16h^4} /3h^4 - 3h^3 -5h^2[/tex]

Then we will have 4h^2 /3h^4 - 3h^3 -5h^2

then  take h^2 from both the numerator and denominator and then cancel them , then we will have

= 4 /3h^2 - 3h -5h.

Therefore, the first option is correct.

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The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.

let

x + y = 50

2.75x + y = 50 × 2

Solve the equation simultaneously

x + y = 50

2.75x + y = 100

2.75x - x = 100 - 50

1.75x = 50

x = 50/1.75

x = 28.57 pounds

Substitute into

x + y = 50

28.57 + y = 50

y = 50 + 28.57

y = 21.43 pounds

So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.

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Considering the given translation, the vertex that is not part of the image is:

H(3,0).

The translations to an image are represented as follows:

The vector notation of a translation is given as follows:

{x ± a, y ± a}

In this problem, this notation is:

{3, -3}.

Hence the rule applied to each vertex of the image is:

(x,y) -> (x + 3, y - 3).

The vertices of the original figure are as follows:

( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)

Applying the translation rule, the vertices of the image are given as follows:

(-4, 0), (-1, 3), (2, 0), (-1, -3).

The lone coordinate without a vertex of the image is H(3,0).

The problem is given by the image at the end of the answer.

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Both function in item I is decreasing, and the function in item II is increasing.

What is function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

What is domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

What is range?

The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.

1) As shown in the I that the function is in 3rd quadrant so thats why it decreases.

2)As show in II figure if ;

x1 = -1 ,y1 = -1

x2 = 0 , y2 =2

x3 = 1, y3 = 5

from the above observation it is clear that ;

x1<x2, y1<y2, x2<x3, y2<y3

So, the II item is increases (monotone increasing)

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Answer:

Step-by-step explanation:

The crate's density in pounds per cubic foot?

Since the crate of medicine with a density of 2050 kilograms per cubic meter will be shipped from England to the U.S, we require its density in pounds per cubic foot.

To do this, we convert the density in kilograms per cubic foot to pounds per cubic foot by using the ratios of conversion given

Since the density of the crate in kilograms per cubic meter is

2050 kg/m³, using the conversion ratios, we have

2050 kg/m³ = 2050 kg/m³ × 1 m³/35.3 ft³ × 2.2 lb/kg

= 4510 lb/m³ × 1 m³/35.3 ft³

= 127.76 lb/ft³

So, crate's density is 127.76 lb/ft³

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An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.

In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:

C' = C · (1 + r / 100)ⁿ

Where:

If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:

C = C' / (1 + r / 100)ⁿ

C = 300,000 / (1 + 4 / 100)³⁰

C = 92,495.60

The initial deposit must be $ 92,495.60.

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The missing values of the ordered pairs using the given equation are:

x = -1; y = 8

The computed table is:

x  | y  

-3   8

-1,   2

To complete a table of values, we can plug in the known value of each of the ordered pairs that are represented in a table into the given equation that models the relationship, then find the value of the missing variable.

The equation that represents the relationship between x and y is given as y = -3x - 1.

Find the value y in the ordered pair (-3, y) by substituting x = -3 into y = -3x - 1:

y = -3(-3) - 1 = 8

y = 8

Find the value x in the ordered pair (x, 2) by substituting y = 2 into y = -3x - 1:

2 = -3x - 1

Add 1 to both sides

3 = -3x

Divide both sides by -3

x = 3/-3

x = -1

The ordered pairs with the missing values are: (-3, 8) and (-1, 2).

The table would be computed as:

x  | y  

-3   8

-1,   2

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