Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.

(PLEASE HELP!!!)

A student is not correct when he stated that a triangle can be formed with side lengths 3 in, 5 in, and 9 in because 3 + 5 < 9.

A triangle is a polygon with three sides and three vertices.

To know if a set of numbers is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 3, b = 5, and c = 9

a + b > c : 3 + 5 > 9     8 > 9     False

a + c > b : 3 + 9 > 5     12 > 5     True

b + c > a : 5 + 9 > 3     14 > 3     True

If at least one of these statements does not hold true, the measurements can't be the sides of a triangle.

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Using relations in a right triangle, we have that:

1 - a) x = 54.28º.

1 - b) y = 57.794º.

1 - c) z = 31.056º.

2) The angle is of 62.8º.

3) The angle is of x = 53.017º.

4) The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

5) The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

The relations in a right triangle are given as follows:

For item 1a, we have that the sides, hence:

tan x = 8.9/6.4

x = arctan(8.9/6.4)

x = 54.28º.

For item 1b, we have the adjacent side and the hypotenuse, hence:

cos y = 9.7/18.2

y = cos^-1 (9.7/18.2)

y = 57.794º.

For item 1c, we have the opposite side and the hypotenuse, hence:

sin z = 6.5/12.6

z = sin^-1(6.5/12.6)

z = 31.056º.

For item 2, we have the sides, given at the graph at the end of the answer, hence:

tan x = 7.2/3.7

x = tan^-1(7.2/3.7)

x = 62.8º.

The angle is of 62.8º.

For item 3, first we find the hypotenuse of the bottom triangle, by the Pythagorean Theorem, as follows:

h² = 7.9² + 18.6²

h = sqrt(7.9² + 18.6²)

h = 20.21.

Then:

sin x = 20.21/25.3

x = sin^-1(20.21/25.3)

x = 53.017º.

For item 4, we have the adjacent side and the hypotenuse, hence:

cos(x) = 3/3.2

x = cos^-1 (3/3.2)

x = 20.364º.

The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

For item 5, we have the opposite side and the hypotenuse, hence:

sin y = 1.8/2.9

y = sin^-1 (1.8/2.9)

y = 38.37º.

The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

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The required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

Given that,
f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2
(f / g)(x) =  To be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here.
f(x) = 2x² - 5x - 3
f(x) = (2x + 1) (x - 3 )
g(x) = 2x² + 5x + 2
g(x) = (2x + 1)(x + 2)

(f / g)(x) = (2x + 1) (x - 3 ) /  (2x + 1)(x + 2)
(f/g)(x) = (x - 3) / (x + 2)

Thus, the required simplified value of the function is (f/g)(x) = (x - 3) / (x + 2). Option C is correct.

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Answer:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

Explanation:

Equation:

[tex]V = \dfrac{4}{3} \pi r^3[/tex]

Task: make pie the subject.

cross multiply

[tex]\sf \dfrac{3V}{4} = \pi r^3[/tex]

divide both sides by r³

[tex]\sf \dfrac{3V}{4} \div r^3= \pi r^3 \div r^3[/tex]

simplify following

[tex]\sf \dfrac{3V}{4r^3} = \pi[/tex]

Hence:

[tex]\sf \pi = \dfrac{3V}{4r^3}[/tex]

The dimensions of the container is r = 6.828 cm and h = 13.656 cm.

Volume of the Cone:

Volume of the cone is define the space or the capacity of the cone.

The formula for the volume of the cone is,

V = πr²h

Where

r represents the radius of the cone

h represents the height of the cone

Given,

Cylindrical container must hold 2l or 2,000 cm³ of liquid.

Here we need to find the dimensions of the container which will minimize the amount of material needed.

Let height = h and radius of the base = r.

We know that the volume of the container,

V = 2000

We know the formula of volume of the cone is,

V = πr²h

2000 = πr²h

Here we need the value of h,

So,

h = 2000/πr²

and surface area of the can

S = 2πr² + 2πrh

Apply the value of h,

S = 2πr² + 2πr (2000/πr²)

S = 2πr²+ (4000/r)

S = 2πr²+ 4000 x r⁻¹

S′=(−1)(4000r⁻²)+4πr

S′=4πr−(4000/r²)

Consider,

4πr−(4000/r²) = 0

4πr³−4000 = 0

πr³−1000 = 0

πr³ = 1000

r³ = 1000 / π

r = √1000 / π

r =  6.828 cm

Apply the value of r on the equation to find the value of h,

h = 2000/(π∗(6.828)²)

h = 2000/146.46

h = 13.656

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Answer:

= 65

Step-by-step explanation:

= 2×(-5)² - 5×(-5) - 10

= 2×25 + 25 - 10

= 50 + 15

= 65

Answer:

65

Step-by-step explanation:

Answer: 1024 inches

Step-by-step explanation:

New Murals,

Length= 245+33 =278 inches

Width = 234 inches

Perimeter= 2*(278+234) = 1024 inches

The Segment Addition Postulate states if three points J, K, and L are collinear and J is between K and L, then KJ + JL = KL.

The segment addition postulate states that if a line segment has two endpoints, say, A and C, then a third point B will lie somewhere on the line segment AC if and only if the following equation is satisfied-

AB + BC = AC

The segment addition postulate is applicable only to a line segment, and does not apply to a ray or a line. A line segment differs from a ray or a line as it is bounded by two defined endpoints.

Here, if three points J, K, and L are collinear and J is between K and L, then as per Segment Addition Postulate-

KJ + JL = KL

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Answer:

27 units

Step-by-step explanation:

First lets add the 2 segments on the top.

8x-11 + 14x-15

Then we can add the like terms together to get

22x-26

The equation above is equal to the equation below the number line, since we added the two on top together, so:

22x-26=19x-17

Now we can start solving

Add 26 to both sides and subtract 19 from both sides

3x=9

Now we can divide by 3

x=3

TU is 14x-15, so we can substitute in 3 for x

14*3-15

42-15

27

Answer:

27 units

Step-by-step explanation:

Set up an equation:

8x -11 + 14x -15 = 19x - 17

Combine like terms:

22x - 26 = 19x -17

Subtract 19x on both sides:

(22x - 26) - 19x = (19x - 17) - 19x

3x - 26 = -17

Add 26 on both sides to isolate the x term:

(3x - 26) + 26 = (-17) + 26

3x = 9

Then, divide by 3 on both sides to fully isolate x:

3x / 3 = 9 / 3

x = 3

Plug 3 for x into the formula for TU:

14(3) - 15 = x

42 - 15 = x

x = 27

TU = 27 units

Hope this helps!

Answer:

.7456

Step-by-step explanation:

The question is asking for the area under the curve from 1 to 2 ....see diagram.....this is approx .75

Answer:

Julia is 15

Step-by-step explanation:

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers

therefore Julia is 15

Julia's age out of the three is equal to 15 years.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42.

Julia's age will be calculated as,

13 + 14 + 15 = 42

Julia is the oldest and 15 is the greatest of the 3 numbers.

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Distance between two cars travelling in opposite directions with the equation 6x - 8 = 4x where x is the distance in miles is equal to 4 miles.

As given in the question,

Two cars travelling in opposite directions

x represents the distance in miles

Equation :

6x - 8 = 4x

⇒ 6x - 4x = 8

⇒ 2x = 8

⇒ x  = 4miles

Therefore, the distance between two cars travelling in opposite directions with the equation 6x - 8 = 4x where x is the distance in miles is equal to

4miles.

The complete question is:

The equation 6x - 8 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. what is the distance, in miles, between the cars?

A.  x = 0.8miles    B. x = 4miles      C. x = 8miles      D. x = 16miles

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1.5 doller = 100* $ 1.5  = 150 peniess

After 50 minutes = 20 gallons of water

Solution :

Pennies :

The dollar is the United States' 100-cent coin. It takes 100 pennies to equal a dollar

1. Girl deposit 5 pennies for each day

which means after 10 days = 50 pennies

Her sister gave her 3 pennies = 53 pennies total she has

To make the $1.50  into her piggy beg

She needs how many pinnies to do so.

1 doller = 100 pennies

1.5 doller = 100* $ 1.5  = 150 peniess

2.

Gallons :

A gallon of water by definition is 128 fluid ounces in the United States. Water bottles can vary in size, but the total number of bottles making up 128 ounces can fit in a gallon. For example, if the water bottle is 16 ounces in size, then 8 of these make up a gallon.

pool capacity = 1500 gallons of water

then

every 5 minutes = 2 gallons of water

then,

after 50 minutes = 2*10 gallons of water

= 20 gallons of water

After 50 minutes = 20 gallons of water

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The average speed was 60[tex]\frac{k+300}{96+t}[/tex]

We are given that a plane travelled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 =8/5 hours

We are also given that the Plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average Speed = total distance/ total time

Average Speed = (k +300)/(8/5 + t/60)

Average speed = (k + 300) / ((96 + t)/60)

Hence, Average Speed = 60(k + 300)/ (96 + t)

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Answer: 6

Step-by-step explanation: Each person can get first or second place prize.

First chance :3 people x 1st chance =3 chances

Second chance: 3 people x 2nd chance =3 chances

3+3=6 chances

The pedestrian route that runs diagonally across the​ park will be [tex]6\sqrt{10}[/tex] miles long.

Here, we are given that a rectangular park is 18 miles long and 6 miles wide.

As we know that the angles formed by any two adjacent sides of a rectangle are all 90°, the diagonal divides the rectangle into 2 right angled triangles.

One side of the right angled triangle will be 18 miles and another side will be 6 miles.

According to the Pythagoras theorem,

[tex]hypotenuse^{2} = base^{2} + height^{2}[/tex]

Here, the diagonal will be the hypotenuse as it is the side opposite the right angle.

Hence we get the following equation-

[tex]hypotenuse^{2} = 18^{2} + 6^{2}[/tex]

[tex]hypotenuse^{2}[/tex] = 324 + 36

[tex]hypotenuse^{2}[/tex] = 360

Hypotenuse = [tex]\sqrt{360}[/tex]

Hypotenuse = [tex]6\sqrt{10}[/tex]

Thus, the pedestrian route that runs diagonally across the​ park will be [tex]6\sqrt{10}[/tex] miles long.

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Answer: 30, 60, 90 triangle ==> Option 3

Step-by-step explanation:

Lets say Angle A is the angle opposing the line of a triangle that has the length of 6. Lets say Angle B is the angle opposing the line of the same triangle that has the length of [tex]6\sqrt{3}[/tex].

sin A=6/12=1/2

sin A=30 degrees.

sin B=[tex]\frac{6\sqrt{3}}{12}[/tex]=[tex]\frac{\sqrt{3}}{2}[/tex]

sin B=60 degrees.

Hence, triangle is 30, 60, 90 triangle ==> Option 3

Step-by-step explanation:

2.1

2.2

2.3

2.4

2.5

2.6

2.7

i don't know if thats what you were asking for but yea

The cost of the one canoe is $25.

According to the statement

We have to find that the cost of the one canoe.

So, For this purpose, we know that the

The cost function will be accustomed find the common cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The girls group rented 2 canoes and three inner tubes for a complete cost of $80. The boys group rented 1 canoe and seven inner tubes for a complete cost of $95.

Then

Let c is that the cost of renting a canoe and t is that the cost of renting inner tubes.

For the ladies,

2c + 3t = 80

For the boys,

c + 7t = 95

Solving the system of equations, multiply the second equation by 2 and subtract them.

2c + 3t  = 80

2c + 14t = 190

11t = 110  

t = 10

Now,

Substitute t to either equations,

c = 95 - 7t

c = 95 - 7(10)

c = 25

So, The cost of the one canoe is $25.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

The girls group rented 2 canoes and 3 inner tubes for a total cost of $80. The boys group rented 1 canoe and 7 inner tubes for a total cost of $95. What is the cost to rent 1 canoe?

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Answer:

Hi the proof steps shown in the picture are correct.

Answer:

or, 147-4x=180

or, 4x=180-147

or, 4x=33

or, x=33÷4

×=8.25

Answer:

Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.

Step-by-step explanation:

Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.

Hope this helps!

Answer:

The formula for scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape

To simplify the ratio just reduce it to the simplist form.

Divide each number in the ratio by the same amount to get the answer.

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

First we Need to write the Equation as It is

K + 12 = 8

Then we keep the Variable which is K in the right of the equal to and move the rest to the left.

K = 8 - 12 ( Note that when moving a number to the other side, the sign will

                  change)

Then Do 8 - 12 or -12 + 8

The answer will come

K = -4

Hope you Are clear

Answer:

1. 2.4*10^-11

2. 5.6*10^12

3. 1.5*10^-13

4. 2.1*10^-1

Step-by-step explanation:

1) (6 x 10^-8) x (4 x 10^-4)=

6*4*10^-8 *10^-4=

24*10^(-8-4)=

24*10^-12=

2.4*10^1 *10^-12=2.4*10^-11

2) (7 x 10^6) x (8 x 10^5)=

7*8*10^6 *10^5=

56*10^11=

5.6*10^1 *10^11=5.6*10^12

3) 0.000 000 000 05 x 0.003=

5*10^-11 *3*10^-3=

5*3*10^-11 *10^-3=

15*10^-14=1.5*10^-13

4) (3 x 10^-8) x (7 x 10^6)=

3*7*10^-8 *10^6=

21*10^(-8+6)=

21*10^-2=2.1*10^-1

The transformation that will move vertex B (-2,3) to (-2,5) is transforming the point B up 2 units into y axis.

Translation in geometry means moving a figure on x-y coordinate without changing it's size and shape.We can translate a triangle with given vertices by adding or subtracting values for points(x,y)

The triangle ABC has vertices  A(-1,1), B(-2,3) and C(-1,-4).

Now to transform vertex B to(-2,5) from (-2,3) we have to make a transformation of 0 units on x axis and 2 units up on y axis which is translation.

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The correct question is Triangle ABC has vertices A(-1,1), B(-2,3) and

C(-1,-4). Which composition of transformations will move vertex B to the Point(-2,5)?

0.528176817681768176 is a rational number as it is non terminating but repeating decimal number.

A rational number is a number that can be expressed in the form of p / q where q is not equal to 0.

It can be terminating or non terminating but repeating number.

We are given a decimal number:

0.528176817681768176

We can see that, after .52, the digits 8176 keeps on repeating itself.

So, the number can also be written as:

0.528176 ( bar on 8176)

This means that the decimal number that is given is a non terminating but repeating rational number.

Therefore, 0.528176817681768176 is a rational number as it is non terminating but repeating decimal number.

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Answer:

[tex]\sf 2^{8}[/tex]

Step-by-step explanation:

             [tex]\sf \boxed{(a^m)^n=a^{m*n}}[/tex]

To convert to single power, multiply the powers.

[tex]\sf (2^2)^4= 2^{2*4}[/tex]

        [tex]\sf =2^8[/tex]

[tex] \bf\implies \: {2}^{8} [/tex]

The exponent (^) rule to solve this problem that is :

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \bf \longrightarrow \: {(a^{m})}^{n} = {(a)}^{m \times n} [/tex]

According to the question :-

[tex] \bf \longrightarrow \: {(2^{2}) }^{4} [/tex]

[tex] \bf \longrightarrow \: (2)^{2 \times 4} [/tex]

[tex] \bf\longrightarrow \: {2}^{8} \: \boxed { \bf \: \red{ ans.}}[/tex]

The option a. 13,000,090,416 is correct standard form.

Firstly, separating the numbers and finding the number of zeroes each unit will have. As per the known fact, the number in billion contains nine zeroes. The number ninety thousand will contain four zeroes. The number four hundred will contain two zeroes.

In the given options, every 13 is succeed by nine zeroes. So, checking the number of values after digit nine. Option a has four digits, option b has seven digits, option c has 5 digits and option d has three digits. So, option a will be correct. The number 416 will be at end, and it correct in each option.

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From the graph, the average rate of change of the function is negative, which means that the number of farmland is decaying.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

This problem is incomplete, and the options were not found on a search engine, but from the graph, what we can see is that the graph is decaying, that is, for any interval [a,b], f(a) > f(b), hence the average rate of change of the function is negative.

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