Pythagorean Theorem & Irrational Numbers:Question 2
What is the length, in units, of the line segment with
endpoints at (1, 4) and (3, 7)?
Select one: answer is to the power of
13
15
137
5

Of the part, the whole, and the percent, a. the exact number of students that are athletes is unknown to Ms. Morgan, which is 36, and b. the total strength of the students is unknown to Mr. Gregory which is 180.

Here we need to know 3 things- the total no. of students each teacher has, the percentage of athletes, and no. of students that are athletes.

a)

As we can see in the case of Ms. Morgan, we know the total strength of the students and the percentage of the students that are Athletes. Hence what we don't know here is the exact number of students that are athletes.

Hence we need to find 30% of 120

= 30/100 X 120

= 36 students.

b)

Here, in Mr. Gregory's case, we know the percentage and the actual number of students that are athletes. Hence, here we don't know the total strength of the students Mr. Gregory has.

Total strength = no. of athletes X 100/percent of athletes

= 27 X 100/15

= 180 students.

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Complete Question

Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his students, are athletes. a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value. b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.

Answer:

20 gallons

Step-by-step explanation:

set up proportion

15/x=75/100

cross multiply

75x=1500

x=20 gallons

Answer:

[tex] \frac{m}{12} - 8 = 4 \\ \frac{m}{12} = 4 + 8 \\ m = 12×12 \\ m = 144[/tex]

Hope it will help u...

The solution of the expression will be Cos(3x+x).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The solution will be calculated by using the formula:-

Cos(A+B)   = (CosA CosB  -  SinA SInB)

Cos(3x+x). = Cos 3x os x - Sin 3x Sin x

Therefore the solution of the expression will be Cos(3x+x).

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The missing angle of a triangle where only the measure of all sides are given can be calculated by using the Cosine Law .

What is Law Of Cosine ?

The law of cosine is also known as Cosine Rule. This law is useful in finding  the missing information of  any triangle.

For example, if you know the lengths of three sides of a triangle , this rule helps to find the angle between the two sides of the triangle.

Let a , b and c be the sides of the triangle and let A , B and C be the angle corresponding to the respective sides .

Then by the Cosine Law the angles are represented as : [tex]CosA = \frac{b^{2} +c^{2} -a^{2} }{2bc}[/tex] ;

[tex]CosB = \frac{c^{2} +a^{2} -b^{2} }{2ac}[/tex] ; [tex]CosC = \frac{a^{2} +b^{2} -c^{2} }{2ab}[/tex] .

Therefore , The Law Of Cosines is used to find the missing angle .

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Answer: Ok to solve this question you would have to do $7.50 divided by  

3 and your answer should come out to be $2.5 or $2.50 per each pound.

Step-by-step explanation:

$7.50 divided by 3 = 2.5

and with money if you get a $2.5 it would be $2.50 because you have to add the zero to the end of it.

Answer:

15

Step-by-step explanation:

Answer:

31.4 m

Step-by-step explanation:

(i) Find the circumference correct to 1 decimal place.

The formula is given as:

C = 2πr

Radius = 5m

Hence,

C = 2 × π × 5m

C = 31.415926536 m

Therefore, the circumference of a circle to 1 decimal place = 31.4 m

Answer:

[tex] \huge\green{ \mid{ \underline{ \overline{ \tt ♡ ANSWER ♡ }} \mid}}[/tex]

[tex]6k + 50.5 = 0 \\ 6k = - 50.5 \\ k = \frac{ - 50.5}{6} \\ k = - 8.4166..[/tex]

[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]

Answer:

Step-by-step explanation: 2(q+p)=1+5q

2q+2p=1+5q

2q-5q=1-2p

-3q=1-2p/:(-3)

q=-1/3+2/3 p

A linear graph is one whose equation is in the form y = mx + b, where m and b are constants. A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants.

To determine if a given graph is linear, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = mx + b.

For example, if the two points on the graph are (2, 3) and (5, 7), then plugging these values into the equation gives us:

y = mx + b

3 = m*2 + b

7 = m*5 + b

Solving this system of equations gives m = 2 and b = -1, so the equation of the line is y = 2x - 1.

A quadratic graph is one whose equation is in the form y = ax^2 + bx + c, where a, b, and c are constants. To determine if a given graph is quadratic, calculate the equation of the parabola by finding three points on the graph and plugging them into the equation y = ax^2 + bx + c.

For example, if the points on the graph are (1, 6), (2, 13), and (3, 24), then plugging these values into the equation gives us:

y = ax^2 + bx + c

6 = a*1^2 + b*1 + c

13 = a*2^2 + b*2 + c

24 = a*3^2 + b*3 + c

Solving this system of equations gives a = 4, b = -5, and c = 6, so the equation of the parabola is y = 4x^2 - 5x + 6.

An exponential graph is one whose equation is in the form y = a*b^x, where a and b are constants. To determine if a given graph is exponential, calculate the equation of the line by finding two points on the graph and plugging them into the equation y = a*b^x.

For example, if the two points on the graph are (2, 16) and (3, 24), then plugging these values into the equation gives us:

y = a*b^x

16 = a*b^2

24 = a*b^3

Solving this system of equations gives a = 2 and b = 2, so the equation of the line is y = 2*2^x.

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Answer:

72

Step-by-step explanation:

The area of a kite is half the product (multiplication) of the diagonals.

Each diagonal has length 12, so A = (1/2)(12)(12) = (1/2)(144) = 72.

Note:  You can also find the area by finding the areas of the 4 right triangles.  By the way, the diagonals are perpendicular, so all 4 triangles are right triangles.

Area of a small triangle:  Area = (1/2)(base)(height)  A = (1/2)(2)(6) = 6.

Area of a larger triangle:  A = (1/2)(10)(6) = 30

Total area: 2 small triangles plus 2 larger triangles A = 2(6) + 2(30) = 72

Answer:

13.8 square feet

Step-by-step explanation:

To find the area of a triangle you use the formula a = 1/2 bh

a = 1/2 (6.9) (4) = 13.8

(simplier to understand) a = 1/2 (6.9) (4) = 27.6 divided by 1/2 = 13.8

Jolene will have 4096 virus cells in her body after 12 divisions

Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.

The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.

2^12 = 4096.

So, Jolene will have 4096 virus cells in her body after 12 divisions.

Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.

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∠DAC = 28°

∠BAC = 56°

PL = 20

BD =​ 31

Bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

An angle bisector divides an angle into equal angles. If the angle is p°, the two angles made will be (p/2)°. This angle bisector passes through the vertex of an angle.

Example: Consider an Angle ∠ABC = 90°. An angle bisector will cut it into two equal angles of 45° each.

Given, AD bisects ∠BAC

MP = 20

DC = 31

∠BAD = 28°

AD bisects ∠BAC

⇒ ∠BAD = ∠DAC

⇒ ∠DAC = 28°

∠BAC = ∠BAD + ∠DAC

∠BAC = 28° + 28°

∠BAC = 56°

Since, In a figure, sides opposite to the equal angles are also equal

∠BAD = ∠DAC

⇒ BD = DC

⇒ BD = 31

⇒ BD = 31

By the figure,

∠MAP = ∠BAD and ∠PAL = ∠DAC

⇒ ∠MAP = ∠PAL

⇒ MP = PL

⇒ PL = 20

Hence, by the above calculation the measure of ∠DAC = 28°,

∠BAC = 56°, PL = 20, BD = 31.

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Answer:

y=4x+2

Step-by-step explanation:

The slope of the line is 4 and the y-intercept (b) is 2.

Hope this helped :)

here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.

To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.

so we have,

John had paid $8.00 an hour and waits tables

Therefore,

In 29 hours, he earns -

[tex]= 40 X 8\\= 320 $[/tex]

Via tups, he earned 210.50$

So, in total he earns

[tex]= 320 + 210.50\\= 530.50 $[/tex]

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Answer:

C Ethan I just took the test

person's sampling distribution is most likely to closely approximate the population distribution is Ethan.

Probability is a mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring.

The most likely to closely approximate the population distribution is the sampling done by Ethan as he had maximum data, which helps to get to approx of the population distribution.

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The dimensions of the building are (x² - 2)(5x + 4). The result is obtained by using the expression for the dimensions.

Grouping is a specific technique used to factor polynomial equations. You can use it with quadratic equations and polynomials that have four terms. The method is slightly different.

Here is how to factor by grouping:

The area of the new high school building in a rectangular shape is 5x³ + 4x² - 10x - 8. Factor by grouping to find the dimensions!

Follow the steps on how to factor by grouping.

5x³ + 4x² - 10x - 8

= (5x³ + 4x²) - (10x - 8)

= x²(5x + 4) - 2(5x - 4)

= (x² - 2)(5x + 4)

Hence, the dimensions of the building are (x² - 2)(5x + 4).

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Answer:

15.33mg

Step-by-step explanation:

Given the number of plants in a terrarium is given by the function

P(c) = -1.2c^2 + 4c + 12

At the hihest number of plants produced, dP(c)/dc = 0

dP(c)/dc = --2.4c + 4

0 = -2.4c + 4

2.4c = 4

c = 4/2.4

c = 1.67

To get the highest number of plant produced, we will substitute c = 1.67 into the original function

P(c) = -1.2c^2 + 4c + 12

P(1.67) = -1.2(1.67)^2 + 4(1.67) + 12

P(1.67) =  -3.34668 + 18.68

P(1.67) = 15.33332

Hence the amount of plant food that produces the highest number of plants is 15.33mg (round to the nearest hundredth).

According to the compound interest formula, the population is 5 years is 422,385.

The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Here we have given that the population of 210,000 people is increasing by 15% each year.

And then while looking into the given question, we have identified that the value of

interest rate = 15%

principal count = 210,000

time period = 5

Here we have to convert R as a percent to r as a decimal, then we get

=> r = R/100

=> r = 15/100

=> r = 0.15 rate per year,

Now, we have to solve the equation for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Apply the values on it , then we get,

[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]

When we simplify this one then we get

[tex]A = 210,000.00(1 + 0.15)^5[/tex]

Therefore, the value of A is 422,385.

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Answer:

8x + 6

Step-by-step explanation:

(4x + 3)2

Distributive Property:

(4x)2 + (3)2 =

8x + 6

If my answer is incorrect, pls correct me!

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Answer:

i do not know the answer sorry

Answer: 10

Step-by-step explanation:

4 to 20 which is times by 5 so 2 times by 5 is 10

Answer:

129

Step-by-step explanation:

600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.

Given that a recipe for 3 people uses 150 g of flour.

We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.

So if the number of people will increase so the quantity of flour will be needed more.

The flour needed to make the recipe for 1 people is = 150/3 = 50 g.

The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.

Hence 600 g flour is needed to make the same recipe for 6 people.

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Answer: [tex]\$18,629[/tex]

Step-by-step explanation:

Given

The unit cost is given by

[tex]C(x)=0.6x^2-168x+30,389[/tex]

find the derivative of the unit cost and equate it to zero to obtain the minimum value

[tex]C'(x)=0.6\times 2x-168\\\Rightarrow 0.6\times 2x-168=0\\\Rightarrow 1.2x=168\\\\\Rightarrow x=\dfrac{168}{1.2}\\\\\Rightarrow x=140[/tex]

Substitute 140 for [tex]x[/tex] in the cost function, we get

[tex]C(140)=0.6[140]^2-168(140)+30,389\\C(140)=11,760-23,520+30,389\\C(140)=\$18,629[/tex]

Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

As we know that,

(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.

(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.

Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

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