Writing  Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares.

The statement that is true about the quadratic functions is:

g(x) > h(x) for x = -1.

Here we have the two quadratic functions:

g(x) = x^2

h(x) = -x^2

Notice that h(x) = -g(x).

Also, g(x) is always positive or zero, while h(x) is always negative, but for x = 0 both have the same value.

g(0) = 0^2 = -0^2 = h(0)

Then the statement that is true is

g(x) > h(x) for x = -1.

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Answer: If a ball is chosen at random 80 times, with replacement, and there are an equal number of blue, green, pink, and red balls, then the probability of choosing a green ball each time is 1/4. Over many trials, the number of times a green ball is chosen would be roughly proportional to the probability of choosing a green ball, so we would expect the green ball to be chosen about 80 * (1/4) = 20 times.

However, since this is a random process, it is unlikely that the green ball will be chosen exactly 20 times. It is more likely that the actual number of green balls chosen will be slightly different, possibly higher or lower, than 20. So the answer is C: The color green would be chosen roughly 20 times, but probably not exactly 20 times.

Step-by-step explanation:

The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.

5/8 - 3/8 = x

5/8 = 5 ÷ 8

= 0.625

3/8 = 3 ÷ 8

= 0.375

0.625 - 0.375 = x

= 0.25

Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.

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The number of tons required when the central HVAC unit will be installed is 1. 73 tons

For the HVAC unit to be installed, the three separate incubation rooms will have to be installed.

This means that the tons required for the central HVAC unit would be the total sum of the three requirement for the other incubation rooms.

The sum would be :

= 1 / 5 + 5 / 6 + 25 / 36

= 0. 2 + 0. 8333 + 0. 69444

= 1. 72774

= 1. 73 tons

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The simplified ratios are shown below:

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have ratios

1. 30: 45

= 30/45

= 2 /3

2. 350 : 400

= 350/400

= 7/8

3. 600g : 4 Kg

= 600 / 4000

= 6/ 40

= 3/20

4. 65:91

= 5 / 7

5. 12 cm  : 1 m

= 12 / 100

= 3 /25

6. 3 Km: 50 m

= 3000 / 50

= 60

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The missing angles are

A. = 130 degrees

B. = 55 degrees

C. = 145 degrees

D. = 73 degrees

E. = 43 degrees

F. = 23 degrees

G. = 61 degrees

H. = 90 degrees

I. = 50 degrees

J. = 27 degrees

K. = 25 degrees

Assuming the missing angle in each case is x

A. Angle on a straight line = 180 degree

x + 50 = 180

x = 130 degrees

B. Angle at a point = 360 degrees

209 + 96 + x = 360

x = 360 - 96 - 209

= 55 degrees

C. Angle on a straight line = 180 degree

= 145 degrees

D. Vertical angles are equal, using vertical angle theorem

= 73 degrees

E.  vertical angle theorem

= 43 degrees

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Answer:

a = 6 ft.

------------------------------

Given is an isosceles right triangle.

As per property of a such triangle, its hypotenuse is √2 times its leg.

That is:

Answer:

a = 6 ft

Step-by-step explanation:

We have to find,

→ The value of a in the diagram.

Formula we use,

=> Using Pythagoras theorem.

→ (Hyp)² = (Opp)² + (Base)²

Forming the equation,

→ (6√2)² = (a)² + (a)²

Now the value of a will be,

→ (6√2)² = (a)² + (a)²

→ (a)² + (a)² = (6√2)²

→ 2a² = 36 × 2

→ 2a² = 72

→ a² = 72 ÷ 2

→ a² = 36

→ a = √(36)

→ [ a = 6 ft ]

Hence, the value of a is 6 ft.

Answer: The Number is 24.

Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.

3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.

The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².

What is a prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

The formula for area of rectangle is -

Area = length × breadth

The area of rectangle ABFG is -

Area = AB × BF

The value for line segment AB = 15 m

The value for line segment BF is -

BF = BC + CE + EF

BF = 14 + 7 + 15.65

BF = 36.65 m

So, the area of rectangle ABFG is -

Area = 15 × 36.65

Area = 549.75 m²

Now, the triangular prism has triangle part left.

The formula for area of triangle is -

Area = 1/2 × base × height

So, the area of triangle IJH is -

Area = 1/2 × IJ × JH

The value for line segment IJ = 14 m

The value for line segment JH = 7 m

So, the area of triangle IJH is -

Area = 1/2 × 14 × 7

Area = 49 m²

Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -

Total area = Area of ABFG + 2(Area of Δ IJH)

Total area = 549.75 + 2(49)

Total area = 647.75 m²

Therefore, the area of triangular prism box is 647.75 m².

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The value of sin a + cos a is √7/2.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows

Here we have

sin a × cos a = 3/8  

Multiply with 2 on both sides

=> 2(sin a × cos a) = 2(3/8)

=> 2 sin a cos a = 3/4  

Add sin²a + cos²a on both sides

=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a    

As we know (a + b)² = a²+ b² + 2ab  

=> (sin a + cos a)² = 3/4 + 1

=> (sin a + cos a)² = 7/4

=> sin a + cos a = √7/2

Therefore,

The value of sin a + cos a is √7/2.

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Answer: 44, -14, 4

Step-by-step explanation:

plug the f(x) into the x and solve itself.

(5)^2 + 3(5) + 4 = 44

(-3)^2 + 3(-3) + 4 = -14

(0)^2 + 3(0) + 4 = 4

Answer:6

Step-by-step explanation:

day one-2 bread

day two-4 bread

10-4=6

6 at the end of the day

The number of loaves of bread remaining at the end of second day = 6 loaves of bread

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let number of loaves of bread remaining at the end of second day be A

The total number of loaves of bread = 10 loaves

The number of loaves of bread sold each day = 2 loaves

Substituting the values in the equation , we get

So , the number of loaves of bread remaining at end of first day = 10 - 2 = 8

Now , the number of loaves of bread remaining at end of second day = 8 -2

The number of loaves of bread remaining at the end of second day = 6

Therefore , the value of A is 6 loaves of bread

Hence , the equation is A = 6 loaves

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Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

In a case whereby Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs the system of equation involving the number of sodas, s, and the bags are:  (3s + 4p )= $26  and s+p = 7 .Then Shana bought 5 sodas and 2popcorn.

We know that :

Sodas cost =$3 each

popcorn costs= $4 per

total =$26

The system of equation can be written as :

(3s + 4p )= $26

We were also told that he bought things equal to the 7 things which can be expressed as:

s+p = 7

Then we can solve the equations as:

3s + 4p = 26 .............................................(1)

s+p = 7................................................................(2)

multiply equation by -3

-3s - 3p =-21  ..................................................................(3)

Then add (1) and 3

4p-3p = 26-21

p=5

Then substitute the value of p into equation 2 we have

s+5 = 7

s= 7-5

=2

s=2

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complete question:

Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought

For the given table -

The equation for line of best fit is Y = -1.000 · X + 11.25.

The correlation coefficient is -0.443533.

x and y have negative and strong correlation.

What is correlation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The table of data is given.

The formula for equation of the line of best fit is -

Y = b·X + a

On adding the values in a graphing calculator the equation is -

Y = -1.000 · X + 11.25

Here, the slope is -1 and y-intercept is 11.25.

The formula for correlation coefficient is -

r = [n(∑xy) - (∑x)(∑y)] / [n∑x² - (∑x²)][n∑y² - (∑y²)]

n = Number of values or elements

∑x = Sum of 1st values list

∑y = Sum of 2nd values list

∑xy = Sum of the product of 1st and 2nd values

∑x² = Sum of squares of 1st values

∑y² = Sum of squares of 2nd values

For the given table the values are -

n = 8, ∑x = 68, ∑y = 22, ∑xy = 145, ∑x² = 620, ∑y² = 274

Plug in all the values in the equation -

r = [8(145) - (68)(22)] / [8(620) - (620)][8(274) - (274)]

r = -0.443533

When the values of two variables grow while one variable's values fall. The correlation coefficient would be negative in that situation.

The weak and adverse association is indicated by the coefficient's negative value. And if "r" keeps moving in the direction of -1, the relationship is moving in the negative direction.

Therefore, the equation is Y = -1.000 · X + 11.25 and r value is -0.443533.

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=4t + 8

=4×3 + 8

= 12 +8

= 20

[tex]...[/tex]

The value of x is given as follows:

x = 155º.

For the triangle at the left, considering that the sum of the measures of the internal angles of a triangle is of 180º, the angle measures are given as follows:

For the triangle at the right, considering the ray formed at the top, the measures are given as follows:

An angle is supplementary with it's external angle, meaning that the sum of their measures is of 180º, hence the value of x is obtained as follows:

x = 180 - 25

x = 155º.

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The value of the areas are;

1. 24 cm²

2. 304cm²

3. 28. 36cm²

4. 5cm²

5. 189cm²

The formula for calculating the area of a triangle is expressed as;

Area = 1/2bh

Substitute the values

Area = 1/2 × 4 × 12

Multiply

Area = 24 cm²

For the area of a parallelogram

Area = ab, length of its sides

Substitute the values

Area = 304cm²

For the area of a rectangle

Area = lw, length and width

Area = 28. 36cm²

For the area of a pentagon

Area = 1/2 base × height

Area = 1/2 × 2.5 × 4

Area = 5cm²

For the area of a trapezium

Area = 1/2 (a + b)h

Area = 1/2 (18+24)9

Area = 189cm²

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The total value of the investment of $1000.00 at 5% simple interest for 5 years equals $1,250.

Total principal 'P' amount invested by Ivy is equal to $1,000.

Time period of investment 't' = 5 years

Rate of simple interest 'r' = 5%

Simple interest = ( Principal × rate of interest × time ) / 100

⇒ Simple interest = ( 1000 × 5 × 5 ) / 100

⇒ Simple interest = $250

Total value of the invested principal amount is equal to

= Principal amount + simple interest

= $1,000 + $250

= $1,250

Therefore, the total investment value of the principal amount at simple interest rate for 5 years is equal to $1,250.

The above question is incomplete, the complete question is:

Ivy invested $1000. 00 at 5% simple interest per annum for 5 years. How much was her investment worth after her investment ?

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There are quadratic equations as many as lead coefficients are. The functions that represent each parabola are:

Case A: y = (1 / 3) · (x + 4) · (x - 2)

Case B: y = (x + 4) · (x - 2)

Case C: y = 2 · (x + 4) · (x - 2)

Case D: y = - (1 / 3) · (x + 4) · (x - 2)

Case E: y = - 2 · (x + 4) · (x - 2)

In this problem we find five case of quadratic equations whose roots are x = - 4 and x = 2, but whose vertices are different. Quadratic equations can be described as a factor product of the form:

y = a · (x + 4) · (x - 2)

Where a is the lead coefficient.

The following parameters are for each parabola:

Case A: (x, y) = (- 1, - 3)

Case B: (x, y) = (- 1, - 9)

Case C: (x, y) = (- 1, - 18)

Case D: (x, y) = (- 1, 3)

Case E: (x, y) = (- 1, 18)

Now we determine the lead coefficient for each case:

Case A

- 3 = a · (- 1 + 4) · (- 1 - 2)

- 3 = - 9 · a

a = 1 / 3

Case B

- 9 = a · (- 1 + 4) · (- 1 - 2)

- 9 = - 9 · a

a = 1

Case C

- 18 = a · (- 1 + 4) · (- 1 - 2)

- 18 = - 9 · a

a = 2

Case D

3 = a · (- 1 + 4) · (- 1 - 2)

3 = - 9 · a

a = - 1 / 3

Case E

18 = a · (- 1 + 4) · (- 1 - 2)

18 = - 9 · a

a = - 2

All differences between all quadratic equations are due to different lead coefficients.

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The price per can of a 12 pack of soda is 8.25.  the price per can of a 12 pack of soda is 0.6875.

To calculate this, we can use the following formula: Price per Can = Total Price of 12 Pack / 12 Price per Can = 8.25 / 12 Price per Can = 0.6875 Therefore, the price per can of a 12 pack of soda is 0.6875. To better understand the price per can of a 12 pack of soda, it is important to understand the concept of unit pricing. Unit pricing is the cost of a single item compared to a larger quantity. When shopping, it is beneficial to look at the unit pricing of items to ensure that you are getting the best deal. For example, if a 12 pack of soda is 8.25 and a 6 pack of soda is 4.00, then the unit price of the 12 pack is lower, which means it is a better deal. By understanding unit pricing, you can make the most cost-efficient decisions when shopping.

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The coordinates of point H are (-1,-3). This is obtained by using the midpoint formula and solving for the coordinates of point H, given the midpoint of GH and the coordinates of point G.

To find the coordinates of point H, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.

If the midpoint of GH is (1,-4) and the coordinates of point G are (3,-5), we can write: (1,-4) = [(3 + x)/2, (-5 + y)/2]

where x and y are the coordinates of point H. We can solve for x and y as follows:

2(1,-4) = (3 + x, -5 + y)

(2, -8) = (3 + x, -5 + y)

2 = 3 + x --> x = -1

-8 = -5 + y --> y = -3

Therefore, the coordinates of point H are (-1, -3).

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Answer:

[tex]49[/tex]

Step-by-step explanation:

[tex]\frac{US}{UD}=\frac{UT}{UC} \implies US=\frac{(56)(14)}{16}=49[/tex]

(a) The rate at which the amount of water is changing is -1/2.

(b) It will take 20 more minutes to drain the water completely.

(c) The tank was completely full 3 minutes before Kiran arrive.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

(a) Given that,

When Kiran first sees the tank, it contains 12 gallons of water. Four minutes later, the tank contains 10 gallons of water.

Rate at which the amount of water is changing = (10 - 12) / 4 = -2/4 = -1/2 gallons per minute.

(b) Time taken to drain 1/2 gallon = 1 minute

There are 10 gallons of water remaining in the tank.

Time taken to drain 10 gallons of water = (1 ÷ 1/2) × 10 = 20 minutes

It will take 20 more minutes to drain the water completely.

(c) When Kiran arrived, water tank has 12 gallons of water.

Total amount of water in the tank is 15 gallons.

Tank has lost 3 gallons of water before Kiran arrived.

Time taken to drain 3 gallons = (1 ÷ 1/2) × 3 = 6 minutes

So the tank was completely full 3 minutes before Kiran arrive.

Hence the rate is -1/2 gallons per minute.

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To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.

When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.

A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.

To convert a percentage to a decimal, divide the percentage by 100.

So, 60.9% as a decimal would be:

60.9 / 100 = 0.609

Therefore, The correct answer is B. 0.609.

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The value of length of z is 5.06 cm.

The value of length of z is calculated by determining the radius of the sector as shown below;

The formula for the perimeter of a sector is given as;

P = 2r  +  (θ/360) × 2πr

where;

20 cm = 2r  + (40/360) x 2πr

20 = 2r  +  0.7r

20 = 2.7r

r = 20/2.7

r = 7.4 cm

A perpendicular bisector of 40⁰ will cut line z into two equal parts, the length of half of z is calculated as;

sin (20) = (z/2) / r

r x sin (20) = (z/2)

2r x sin (20) = z

2 x 7.4 cm x sin(20) = z

5.06 cm = z

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