graph shows the relationship between time and the number of soda bottles a machine can make. Use the points ​(4​,220​) and ​(7​,385​) to find the number of soda bottles the machine can make each minu

The right triangle Short leg: 14 feet and  Long leg: 85 feet.

Because you have a right triangle,  and you know the hypotenuse, you can use the Pythagorean Theorem:

x2 + y2 = 852

You are told the difference between the 2 sides:

x = y + 71

Now you have 2 equations.  Use the expression for x in the 2nd equation, and substitute into the first:

(y + 71)2  + y2  = 852

Originally known as a rectangle triangle , a right triangle or right-angled triangle  is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., It has two perpendicular sides.

The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The hypotenuse is the side that is opposite the right angle (side c in the figure). Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).

The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.

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The value of the short leg of the right angle triangle is 14 feet while the value of the long leg will be 85 feet.

You may apply the Pythagorean Theorem since you have a right triangle and know the hypotenuse:

x^2 + y^2 = 852

You are told the difference between the 2 sides:

x = y + 71

Now we have 2 equations.  

Now, we will use the expression for x in the 2nd equation, and substitute into the first:

Thus we will get it as:

(y + 71)^2+y^2=852

A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., it has two perpendicular sides.

The connection between the sides and angles of a right triangle is the basis of trigonometry.

The hypotenuse is the opposite side of the right angle.

Legs are the sides that are nearly at the right angle

The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.

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To go from the first town to the second town, you must drive 137.5 miles.

What is an proportion?

A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.

We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:

0.75 inch / 50 miles = x / distance

where x is the actual distance we want to find.

We can cross-multiply and solve for x:

0.75 inch * distance = 2.75 inches * 50 miles

x = (2.75 inches * 50 miles) / 0.75 inch

x = (137.5 miles)

To go from the first town to the second town, you must drive 137.5 miles.

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The equation of the slope is y = -5x + 72.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

Given that:

72 inches is the depth of the liquid level in water tank.

Water drains at a rate of 5 inches per minute.

Let y represent the tank's height, which is given as 72.

Let x be the total number of minutes, here x = 0.

Therefore, the slope's equation is the rate at which the water drains, that is:

m = -5

The equation of the line is given by the formula:

y = mx + c

Substitute the values:

72 = -5(0) + c

c = 72

And the equation is:

y = -5x + 72

Hence, the equation of the slope is y = -5x + 72.

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Answer: To find the number of students, you can multiply the number of teachers by the number of students per teacher.

3,461 teachers * 28 students/teacher = 96,668 students

So, there are 96,668 students in the school district.

Step-by-step explanation:

The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.

The inequality for this is therefore:

x ≥ 45

Assuming that the minutes she spends studying is x.

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Full question is:

Trina must spend at least 45 minutes studying for her math test. (find the inequality)

Answer: The explicit formula for a geometric sequence is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

Part A) In this sequence, the first term is 4, and the common ratio is 4/1 = 4.

So the explicit formula for this sequence is:

an = 4 * 4^(n-1)

To find the 8th term of this sequence, we can substitute n = 8 into the formula:

a8 = 4 * 4^(8-1)

a8 = 4 * 4^7

a8 = 4 * 16,384

a8 = 65,536

Therefore, the 8th term of this sequence is 65,536.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

(Hypotenuse)²=(Opposite)²+(Adjacent)²

(25)²=(15)²+(A)²

A²=625-225

A=✓400

A=20.00

Answer:

a = not viable

b = 265

c = 0

good?

Answer: a = not viable b= 265 c = 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright so let me try and explain this as best as I can:

So the graph isn't linear because the graph shows a parabola (a boomerang kind of shape that happens if you use an exponent somewhere in a y=mx+b formula if I remember correctly) and not a straight line. Linear graphs cannot curve, and this one does. Not sure why it it would be a function though. Assuming the answer chosen is correct, my best guess as to why it might be a function is because it continues to go in the same direction forever, there is a predictable amount of change between each point and you can follow a formula to find every point on the graph.

I really hope this helps a little!

Answer:

7/9 of the same money is 4900

Step-by-step explanation:

If 6/7 of a number is 5400, we can set up an equation to find the value of the number:

(6/7)x = 5400

To solve for x, we can multiply both sides by 7/6:

x = 5400 * (7/6)

x = 6000

Now that we know the number is 6000, we can find 7/9 of that value:

(7/9) * 6000 = 4900

So 7/9 of the same money is 4900.

Answer:

Step-by-step explanation:

Ahh hell nah

With compound interest of 3.8% compounded annually it will take 7 years  for the value of the account to reach $6,880.

What is Compound interest?

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

Formula to find compound interest:

A=P(1+r/n)^nt

Where,

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time (in years)

Alternatively, we can write the formula as given below:

CI = A – P

Where CI=Compound Interest

Now,

As given

A=$6880

P=$5300

r=3.8%

n=1

t=?

Therefore,

The time it would take to become $6880 will be

6880=5300(1+3.8/100)^t

From here t=7 years

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The digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.7 will be 548

The 8 in our number, 2,980.7, is in the tens place and hence represents an 80.

The value of the digit 8 is equal to 1/10 of 10 divided by 1, which is 10 times greater than the value of the digit 888.

We need a number that contains an 8 and has a value that is 1/10 of the previous number, hence we need:

1/10*80 = 8

So, the number we're seeking has an 8 in the position of the one.

Option C: 548 would be this.

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La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.

Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:

R = F · cos θ i + F · sin θ j

Donde:

La dirección del vector se determina mediante la siguiente función trigonométrica inversa:

θ = tan⁻¹ (Fy / Fx)

Donde:

Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:

θ ≈ 234.689°

R = F · cos 234.689° i + F · sin 234.689° j

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Answer:

10.9%

Step-by-step explanation:

You want to do the number of ways that can happen, which is [tex]_8C_2 = 28[/tex] divided by the total number of possibilities which is [tex]2^8[/tex] to get 10.9%

By using the combination theorem, it can be concluded that the value of m + n = 125

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

nCr = n! / (n - r)! r!

Let's denote the number of rectangles as r, and the number of squares as s:

r = ⁹C₂ x ⁹C₂

 = (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)

 = (9! / 7! 2!)   x   (9! / 7! 2!)

 = 36 x 36

 = 1296 rectangles

s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²

  = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64

  = 204 squares

Then we get the ratio of s : r as follows:

s / r = 204 / 1296

      = 17 / 108

Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.

Thus, it can be concluded that the value of m + n = 125

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We must sell 625 loaves of bread to break even.

If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.

Let N be the number of loaves you sell.

Your cost would be,

C = 500 + 0.2N

Your revenue would be,

R = 1. N

Now, find out when is C = R  

⇒500 + 0.2N = N

⇒500  = 0. 8 N

⇒N = 500/0. 8

⇒N = 625

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Answer:

9

Step-by-step explanation:

make them equal to each other

15x = 14x + 9

x = 9

The index form 4 ^–1  as a fraction or whole number without exponents is 1/4

The index form of a number described as the number that is written as an exponential expression

Index forms are also described as a single number that is raised to another number or variable.

The index or exponent of an exponential expression shows how many times to multiply the base by itself in the expression.

From the information given, we have the index form as;

4^-1

This is represented as a fraction;

1/4^1

Note that any number that is raised to 1 is equal to the number

1/4

Hence, the value is 1/4

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The triangle pairs that can be mapped to one another using both a translation and a reflection across the line containing AB will be A based on the provided information. Triangles A B C and X Y Z are similar. Triangle A is created by reflecting triangle X, Y, and Z across a line. The correct option is A.

The first triangle pair is a pair that can be mapped to one another using both translation and reflection across a line containing AB.

The first figure is made up of the coordinates XYZ and ABC, which are translations and reflections of one another across the line AB.

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Answer: it is A

Step-by-step explanation: just took the test

c) both statements together are sufficient, but neither statement alone is sufficient.

According to the question

The query asks if statements (1) and (2) by themselves are sufficient to determine whether x is an even number. The answer is that neither assertion by itself is adequate to ascertain what x is worth. However, when both claims are taken into account, they are adequate to decide whether or not x is an even number. This is due to the fact that if xyz is even and yz is odd, x must be even. If x were odd, both xy xz and y xz would be strange as well. Due to this, the proper response is "c) neither statement is adequate when read alone, but both assertions taken together are sufficient."

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Answer:

C. Mara wished she could visit the stars: she often dreamed of it.

Answer:

1. T, W, E, G

2. C, B, D, A

Step-by-step explanation:

For question 1:

G passes through (2, 3) and (0, -1). So, the slope is [tex]\frac{-1-3}{0-2}[/tex] = 2.

T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = [tex]\frac{1}{4}[/tex].

E has a slope of [tex]\frac{5}{3}[/tex] because the equation is y = mx+b where m is the slope.

W has a slope of  [tex]\frac{1}{3}[/tex]  since slope is increase in y divided by increase in x.

The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{3}[/tex], [tex]\frac{5}{3}[/tex], and 2.

Therefore, the answer is T, W, E, G.

For question 2:

A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = [tex]\frac{3}{2}[/tex].

B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = [tex]\frac{1}{2}[/tex].

C has a slope of [tex]\frac{1}{4}[/tex] since the equation is y=mx+b where m is the slope.

D has a slope of [tex]\frac{3}{4}[/tex] since the slope is increase in y divided by increase in x.

The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex], and [tex]\frac{3}{2}[/tex].

Therefore, the answer is C, B, D, A.

I hope this helps! :)

Didn't understand something? Some important formulas/things to remember that I used:

The equation of a linear function can be written as y=mx+b. m represents the slope.

The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.

The formula for the slope is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex], where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.

Answer: D

Step-by-step explanation: the amount per cashews (c) is $2.45. Therefore, its 2.45c

The amount per pounds of sugar is $0.61. Therefore, its 0.61s

And, since its "buying" (basically, adding), you gotta add them. So, the answer would be: 2.45c+0.61s

Answer:

what grid

Step-by-step explanation:

The rate of change of the linear function is the third option which is -3.

The linear function runs through the points (-3,14) and is specified in question (2,-1).

The function's rate of change must be determined.

Having said that,

The slope of a linear function determines how quickly it changes.

A line's slope

By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

In light of this, the slope of a line passing through the points (-3,14) and (2,-1) is

(-1-14)/(2-(-3)) = -15/5 = -3.

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36 pounds is equal to 16.344 kilograms.

Given that we need to convert 36 pounds to kilograms.

We have 1 pound = 0.454 kilogram,

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.454 kilogram.

Given that we have 36 pounds, we can multiply this value by the conversion factor to find the equivalent weight in kilograms:

36 pounds x 0.454 kilogram/pound = 16.344 kilograms

Therefore, 36 pounds is equal to 16.344 kilograms.

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Answer:

C

Step-by-step explanation:

(4+8x)/12 simplifies to (1+2x)/3x

Answer:

The number is 20

Step-by-step explanation:

First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.

Answer:

20

Step-by-step explanation: