Find the slope and y-intercept of each graph

A total of 676 different three-letter initials combinations end with the letter Z using the uppercase characters in English alphabets.

We have three letters which have to be filled in.

English alphabets consist of 26 letters (A-Z). Let's suppose A1, A2 & A3 are the three initials.

For A1, we have 26 alphabets to choose from i.e. A-Z

For A2, we again have 26 alphabets to choose from i.e. A-Z

For A3, we have only one option i.e. Z

Thus, total different three-letter initials combinations for "**Z" pairings are:

26 x 26 x 1 = 676

Please note that combinations allow repetition of values. If one wants to avoid repetition, permutation needs to be calculated.

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The number of small rooms reserved is 13 and the number of large rooms reserved is 12.

Given, Nolan is blocking off rooms for the guests. We will solve the problem using the linear equation. The number of small rooms is x and number of large rooms is y.

There are total of 25 rooms, which can be written as,

x+y=25 ------(1)

Small room can accommodate 3 people and large room 5 people, which can be written as follows,

3x+5y=99 --------(2)

Multiplying the equation 1 by 3, we get

3x+3y=75

Substracting equation 1 and 2, we get

3x+5y=99

3x+3y=75

-    -       -

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

0x+2y=24

2y=24

y=12

x+12=25

x=25-12

x=13

Therefore, the number of small rooms is 13 and large rooms is 12.

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The evaluation of the quadratic equations are as follows;

Question 5

Question 6

Question 7

Sometimes; Factoring

Always; Quadratic formula

Always; Completing the square

Sometimes; Square root method

Sometimes; Factoring by group

Question 8

The numerator are;

(a) 8

4

(b) The denominator value;

4

(c) The roots are;

2

1

A quadratic equation is an equation of the form; a·x² + b·x + c = 0

Question 5

The quadratic equation, x² + 6·x + 10 = 0

The discriminant is 6² - 4×1×10 = -4

The discriminant < 0, therefore, the equation does not have solution

Question 7

Factoring;

Method of solving equations work more when the coefficient of x and the constant can be expressed as a + b and a·b

Where;

a·b = The constant

a + b = The coefficient of x

Therefore, factoring works sometimes

Sometimes; Factoring

Quadratic formula

The quadratic formula is an equation that involves the use of the constant and the coefficients of x

The quadratic formula therefore works all the time

Always; Quadratic formula

Complete the square

The completing the square method works by rearranging the equation in the form;

a·x² + b·x + c ⇒ a·(x + m)² + n

Where;

m = b/(2·a),

n = c - (b²/(4·a))

The method therefore works all the time

Always; Completing the square

Square root method

The square root method involves placing the square term of the equation on one side of the equation and the constant term on the other side

The square root method  works for equations that can be expressed in the form x² = b

The method  works sometimes

Sometimes; Square root method

Factoring by group

The method involves finding the common factors and grouping based on the common factors

The method only works when there are common factors

Sometimes; Factoring by group

Question 8

The  equation is 2·x² - 5·x = x - 4,

Writing the equation so that we have;

2·x² - 5·x - x + 4 = 0

2·x² - 6·x  + 4  = 0

x = (6 ± √((6² - 4× 2 × 4))/(2×2) =

Therefore;

x = 8/(2×2)  or x =  4/(2×2)

The numerators are 8 and 4

8

4

(b) The denominator is (2 × 2) = 4

(c) The two roots of the quadratic equation are;

x = 8/4 = 2 and x = 4/4 = 1

2

1

Question 6

The equation, x² - 16·x + 64 = 4

The left side of the equation can be factored as follows;

x² - 16·x + 64 = 4

x² - 8·x - 8·x + 64 = 4

(x² - 8·x) + (64 - 8·x) = 4

x·(x - 8) - 8·(x - 8) = 4

(x - 8)·(x - 8) = (x - 8)² = 4

Yes; (x - 8)² = 4

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When the function g(x) = 4 - x and fog (x) = 11 - 2x then the function f(x) is

When a function is expressed in terms of another function it can be called a composite function

if g(x) = 4 - x and fog (x) = 11 - 2x

let f(x) = ax + b

fog = f(g(x))

11 - 2x = f((4 - x) + b)

11 - 2x = a(4 - x) + b

11 - 2x = 4a - ax + b

grouping by coefficients

11 - 2x = (4a + b) - ax

equating the coefficients

11 = 4a + b

-2x = -ax

a = 2

plugging a = 2 into 11 = 4a + b

11 = 4 * 2 + b

11 = 8 + b

b = 3

if a = 2  and b = 3 then f(x) = 2x + 3

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The half life of the substance is 828.37

The period of time it takes for one-half of a radioactive isotope to decay is known as the half-life. An individual radioactive isotope's half-life is unaffected by environmental factors and is independent of the isotope's starting concentration.

The amount of time needed for half of a radioactive sample's atomic nuclei to decay

Given:

As, The amount of a substance after t days is given by:

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

Original amount after 300 days.

p(300)= 0.778p(0).

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

0.778 = p(0)[tex]e^{-300k[/tex]

-300k= log (0.778)

-300k= -0.109020

k = 0.0003634

So, p(t)= [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

This is t for which P(t) = 0.5P(0). So

0.5p(0)=  [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

[tex]e^{-0.0003634t[/tex] = 0.5

log ( [tex]e^{-0.0003634t[/tex]) = log 0.5

-0.0003634 t = log 0.5

t= -0.30102999566/ -0.0003634

t= 828.37

Hence, the half life of the substance is 828.37

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Answer:

they all are odd numbers

Step-by-step explanation:

trick question they all are odd numbers, unless you can divide or subtract  the numbers

Answer:3716

Step-by-step explanation: any number landing in an even number is even

The solution to the compound inequality is 1 ≤ x < 21

Compound inequality are  type of inequality that has two or more parts.

In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them

(-4x [tex]\leq[/tex]x-5 -------------------------------Equation  1

(x-5< 16) --------------------------------Equation  2

Move all the term to the left side

(-4x +(-x+5) ≤ (x-5) +(-x+5) ---------Equation 3

(x-5) +(-16) < 16+(-16)------------------Equation  4

We need to get rid of expression interval. If there is a negative sign in front of it, each term within the expression changes sign

(-4x -x +5 ≤x-5-x+5)-------------------Equation 5

( X-5 -16 < 16 -16) ----------------------Equation 6

Rearrange and Simplify equation (5 & 6)

(-5x+5 ≤ ) ---------------------------------Equation 7

(x -21 < 0)----------------------------------Equation 8

We need to get rid of expression interval and subtract 5 from equation (7) and add 21 to equation (8)

(-5x ≤ -5) ---------------Equation (9)

(x  <  21)------------------Equation (10)

Divide equation (9) by 5 on both sides and flip the sign because of the negative

5x/ 5 ≥ 5/ 5  

( x  ≥  1 )  

(x  <  21 )

Therefore the solution to the compound inequality is 1 ≤ x < 21

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Tracking the food Timber eats and how many miles she runs each week is an example of Self-Supervision.

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The constant of proportionality that relates the cost in 72 dollars as y, to the number of gallons of unleaded gasoline in 22.5 gallons of unleaded gasoline as x is $3.20 per gallon of unleaded gasoline.

The constant of proportionality is the ratio of the so-called proportional relationship that relates two given values ​​to each other.

Other names for the constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.

The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.

y/x = k

k is the constant of proportionality.

Given that:

y = $72 and x = 22.5 gallons.

So, the value of the constant of proportionality (k) = 72/22.5

=> k = 720/225

Dividing both by the numerator and denominator by 45. We get,

=> k = 16/5

The value of the constant of proportionality (k) = $3.20 per gallon of unleaded gasoline.

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After using the Simplification method we will get the value (x - 3) / (x + 5)

What is Simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. We can —

By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.

By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.

Given,

(x^2-x-6) / (x^2+7x+10)

This equation can be separated into two parts, the top and the bottom, which we can simplify further.

Simplifying the top part

x² - x - 6

This can be factored into the following:

x² + 2x - 3x - 6

x(x + 2) - 3(x + 2)

(x + 2)(x - 3)

Now, Simplifying the bottom part

x²+7x+10

x² + 2x + 5x + 10

x(x + 2) + 5(x + 2)

(x + 2)(x + 5)

Now, we can write the new numerator and denominator

(x + 2)(x - 3) / (x + 2)(x + 5)

(x - 3) / (x + 5)

Hence, (x - 3) / (x + 5) is the answer when simplifying

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James bond should come ashore 3.464 miles from point A to reach B in least time.

Calculus  is defined as a branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).

Let's say the James bond travels x miles from point A.

We are aware that time = distance / speed

Total time taken by James bond to reach B is

t(x) = √(x^2+36)/6 + (10-x)/12

dt/dx = x/(6√(x^2+36)) - 1/12

for critical point dt/dx =0

= x/(6√(x^2+36)) - 1/12 = 0

√(x^2+36) = 2x

Squaring on both sides we get

X2 + 36 = 4x2

X2 = 12

X2 = 2√3

T(0) = √(0^2+36)/6 + (10-0)/12 = 41/6

= 6.833 hours

T(2√3) = √(12+36)/6 + (10-2√3)/12 = (5+3√3)/6

= 1.699 hours

T(0) = √(10^2+36)/6 + (10-10)/12 = √34/3

= 1.94 hours

Therefore James bond should come ashore 3.464 miles from point A to reach B in least time

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The percentage value of puppies weighing over 6 pounds is 25%

What is Percentage?

Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

Given that there are 12 puppies in total and 3 of them weighted above 6 pounds

To calculate the percentage we need to divide 3 by 12 and then multiply it by 100

= (3/12) * 100

= 25%

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0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

A division is a process of splitting a specific amount into equal parts.

Given,

5 inches of rain in 24 hours

We need to find the unit rate.

For this we need to use the division.

Divide five by twenty four

5/24

Zero point two zero eight

0.208

Zero point two one

0.21

Hence 0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

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Answer:

False

A saver has much more positives. It means you'll have more money in your future :)

The possible length of the rectangular garden is L ≥ 6225ft which has a perimeter of 540 feet,

The interior angles of a four-sided polygon are all 90 degrees. At each corner or vertex, the two sides meet at a right angle. The rectangle varies from the square in that its two opposite sides are of equal length.

Let L represent the garden's length.

Let W represent the garden's width.

The perimeter is 540 feet.

The rectangle's perimeter is equal to 2(L + W) = 540

L + W = 270      ....(i)

W = 270 - L      ....(ii)

The rectangle's area is equal to its length times its width, which is given  12000 square feet.

L × W ≤ 12000  ....(iiI)

Substitute the value of equation (ii) into (iii)

(270 - L)(L)   ≤   12000

270l  -  L²  ≤   12000

0   ≤  L²  -  270l +  12000

L²  -  270l  +  1200  ≥  0

Solving the quadratic inequality above, and we get

L ≥  6225

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Correctly complete the statement about the distance traveled by the water in 3 minutes and number of complete cycles the water makes in 3 minutes.

The water travels 450 feet and completes 15 cycles in 3 minutes.

Define distance.

A measurement of how far apart two objects or points are can be quantitative or occasionally qualitative is called distance. In mathematics, distance refers to the length that separates two points on a line or line segment. The fact that distance is a scalar quantity means that it is independent of an object's motion. Metre is the SI unit of distance.

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Answer:

[tex]y=\frac{\pi}{6}[/tex]

Step-by-step explanation:

Given that:

[tex]\sin(\frac{2\pi}{3})=\cos y[/tex]

Substitute the value [tex]\frac{2\pi}{3}=\frac{\pi}{2}+\frac{\pi}{6}[/tex].

[tex]\sin(\frac{\pi}{2}+\frac{\pi}{6})=\cos(y)[/tex]

(Using the formula: [tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/tex])

[tex]\sin\frac{\pi}{2}\cos\frac{\pi}{6}+\cos\frac{\pi}{2}\sin\frac{\pi}{6}=\cos y[/tex]

Using [tex]\sin\frac{\pi}{2}=1, \cos\frac{\pi}{2}=0[/tex], we obtain:

[tex]1\times\cos\frac{\pi}{6}+0\times \sin\frac{\pi}{6}=\cos y[/tex]

This is equivalent to:

[tex]\cos\frac{\pi}{6}=\cos y[/tex]

Applying cos inverse on both sides, we get:

[tex]y=\frac{\pi}{6}[/tex]

The measurement of m∠1 and m∠3 is 52° when a is parallel to b.

According to the question,

We have the following information:

The line a is parallel to b and they are being cut a line m.

m∠6 = 128°

We know that when two parallel lines are cut by another line then the sum of consecutive interior angles is 180°. And we also know that vertically opposite angles are equal.

m∠1 and m∠3 are vertically opposite angles.

m∠3 and m∠6 are consecutive interior angles.

∠3+∠6 = 180°

∠3 = 180-128

∠3 = 52°

So, we have:

∠1 = ∠3 = 52°

Hence, the measurement of m∠1 and m∠3 is 52° when a is parallel to b.

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The number in scientific notation is 2.1×10⁵.

Adjusting a number's digits so that it produces an approximation of a result is known as rounding.

The given number is 2.085×10⁵.

Round the number 2.085 to the nearest tenth:

2.085 ≈ 2.1

Therefore, the number in scientific notation is 2.1×10⁵.

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Using the difference, the difference between the number of heads and half the number of tosses is 1.

In the given question,

The proportion of heads is 0.49 in 100 tosses.

We have to find the difference between the number of heads and half the number of tosses.

The proportion of heads=0.49

Total tosses =100

So the total number of heads

=0.49*100

=49

Since we have to find the difference between the total number of head and half the number of tosses.

So the half on the number of tosses=Total number of tosses/2

The half on the number of tosses=100/2

The half on the number of tosses=50

So, The difference=The half on the number of tosses−Total number of heads

The difference=50−49

The difference=1

Hence, the difference between the number of heads and half the number of tosses is 1.

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The value of the sum of the arithmetic sequence from a₃ to a₆ is 38

An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.

The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3

The sum from n = 3 to n = 6 of aₙ is found as follows;

The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d

Where;

aₙ is the value of the nth term

a = The first term

d = The common difference

From the sequence, we have;

a = 20, d = -3, from which we have;

aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)

aₙ = 20 - 3·(n - 1)

From which we have;

a₃ = 20 - 3×(3 - 1) = 14

a₄ = 20 - 3×(4 - 1) = 11

a₅ = 20 - 3×(5 - 1) = 8

a₆ = 20 - 3×(6 - 1) = 5

a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38

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Answer: 55 rounded to the nearest tenth is 60.

Step-by-step explanation: Hope this helps!!!

Answer: 60

Step-by-step explanation

Answer:

it's I'd b yes so ya hope you do great

Step-by-step explanation:

As per the dividing system, If every box gets the same amount, then the mass of fruit in each box is 10 kilograms.

Division

Division refers a process of splitting a specific amount into equal parts.

Given,

Felipe has 8 boxes.

He puts a total of 80 kilograms of fruit into these boxes.

Here we need to find the mass of fruit in each box, if every box gets the same amount.

While we looking into the given question, we have identify the following this,

Number of boxes = 8

Total weight of fruits = 80 kilograms.

And we also know that, each box must has same amount of weight.

Therefore, it can be calculated as, by dividing the total weight by the number of boxes, then we get,

=> 80/8

=> 10

Therefore, each box has 10 kilograms of fruits.

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Kate bakes 20-inch by 18-inch pan of cornbread and divide it into 2 in x 2 in pieces. The number of pieces is 90.

The problem can be solved using associative property in multiplication and division. That is the factors can re-group and it will not change the product.

The given problem can be translated into an algebraic expression:

(20 x 18) : (2 x 2)

Let

length of cornbread pan = 20

wide of cornbread pan = 18

To cut the cornbread 2 inches by 2 inches means we divide the length by 2 inches and the wide by 2 inches. Hence, the algebraic expression can be re-group into:

(20 x 18) : (2 x 2) = (20 : 2) x (18 : 2)

                           = 10 x 9 = 90

Hence, the pan contains 90 pieces of cornbread.

Complete question:

Kate bakes 20-inch by 18-inch pan of cornbread. the cornbread is cut into pieces that measure 2 inches by 2 inches. how many pieces of cornbread does the pan contain?

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The equation for the function r (2) in general form is r(2) = 12.5.

Given:

f (x) = 4x

r (x) = f(x) + 4.5

substitute f(x) in r(x)

r(x) = f(x) + 4.5

r(x) = 4x + 4.5

r(2) means x = 2

r(2) = 4*2 + 4.5

r(2) = 8 + 4.5

r(2) = 12.5

Therefore The equation for the function r (2) in general form is r(2) = 12.5.

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The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.

acceleration = change in velocity / Time taken

a = 0 - 15.6 / 4.2

= -15.6 / 4.2

=  -3.71

The average acceleration is -3.71m/s²

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The sphere with the volume 1436.03 m³ has 7m long radius.

To find out the approximate length of its radius by using the formula to calculate volume of sphere is:

V= 4πr³/3

The value of π is 22/7 or 3.14.

So, V = 4 × 3.14 × r³ / 3

Volume of the sphere is given which is 1436.03 m³.

Thus, r³ = 1436.03×3 / 4×3.14

r = ³√ 4308.09/12.56 = ³√343 = 7 m.

Hence, the radius of the given sphere is 7 m.

The cube root of a number is the factor that we multiply by itself three times to get that number.

For example, the cube root of 27 is 3.

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