Students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached

to the top of the flagpole, and the other end will be attached to the ground.

String

of lights

-Flagpole

String

of lights

15 ft

- 8 ft + 8 ft

Which measurement is closest to the length of one string of lights in feet?

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:

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:

Answer:

what grid

Step-by-step explanation:

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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The school need to hire additional teacher to get 1:18 ratio is 20.

The teacher and student ratio in a school is 1:30,

let the number of teachers in a school=x,

then the number of students in school=30x,

total number of students in school=900

So, the number of teachers in school x=900÷30

                                                                x=30.

We want to take ratio of students and teachers =1:18

So, according to this ratio number of students=18x

and the number of required teachers x= 900 ÷ 18

                                                                x=50,

the school required 50 teachers,

Hence, the school need to hired teachers = 50-30=20

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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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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 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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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 predicted demand of a bobblehead that has price of $6.00 is given as follows:

49.093 units.

The function in the context of this problem is defined as follows:

y = -0.227x + 50.445.

In which:

For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:

y = -0.227(6) + 50.445

y = 49.093 units.

Meaning that the second option is the correct option.

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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:

a = not viable

b = 265

c = 0

good?

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

Step-by-step explanation:

The straight line distance between the northbound and eastbound cars is 5.7 kilometres.

The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.

Distance between the two cars = ✓4² + 4²

Taking square of the numbers

Distance between the two cars = ✓16 + 16

Performing addition

Distance between the two cars = ✓32

Taking square root

Distance between the two cars = 5.66

Round to nearest tenth = 5.7

Thus, the distance is 5.7 kilometres.

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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: 108 mph

Step-by-step explanation: 378 divided by 3.5= 108mph

Answer: 108mph

Step-by-step explanation: 378 divided by 3.5= 108mph

15 + 6t >= 63

t >= (63 - 15) / 6

t >= 4.5

t >= 5 (since t must be a whole number of minutes)

So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.

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.

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

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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0.3 pounds of oranges are left and this can be calculated by following steps :

Convert the 8 2/5 oranges to pounds.

8 2/5 oranges = 8.4 oranges

1 orange = 0.5 pounds

8.4 oranges x 0.5 pounds = 4.2 pounds

Subtract the amount of oranges eaten (4 5/8 pounds) from the total amount of oranges (4.2 pounds).

4.2 pounds - 4 5/8 pounds = 0.3 pounds

Answer: 0.3 pounds of oranges are left.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction.

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The last temperature will be 73.2 degrees Fahrenheit.

The parameter f(m) 15.2m+58 in the straight capability addresses the rate at which the water temperature increments over the long haul. In particular, it addresses the number of degrees Fahrenheit that the water temperature increments for each 1 moment of warming. So assuming the water has been warming for 2 minutes, its temperature will have expanded by 2 * 15.2 = 30.4 degrees Fahrenheit.

Parameter 58 in the linear function addresses the underlying temperature of the water when it begins warming. It is estimated in degrees Fahrenheit. So on the off chance that the water begins at a temperature of 58 degrees Fahrenheit and is warmed for 1 moment, its last temperature will be 15.2 + 58 = 73.2 degrees Fahrenheit.

Subsequently, The last temperature will be 73.2 degrees Fahrenheit.

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Answer:

Step-by-step explanation:

Ahh hell nah

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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The answer is the fourth one: Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

Answer:

Your answer is 9x^6*y^2π

Step-by-step explanation:

The formula for a circle is πr^2, with r as the radius.

Since 3x^3*y is the radius, you put that value in to get the equation:

(3x^3*y)^2*π

Once simplified, you get 9x^6*y^2π.

You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.

I hope this was helpful.

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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Answer:2216 feet

Step-by-step explanation:

Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).

Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.

Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.

Hope this helps you!

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:

9

Step-by-step explanation:

make them equal to each other

15x = 14x + 9

x = 9