What is the slop of the line?

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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Answer:

A

Step-by-step explanation:

Answer:

a) x = 3

b) x = 10

c) x = 28

Explanation:

a)

[tex]\sf 6x + 3 = 21[/tex]

collect term

[tex]\sf 6x = 21-3[/tex]

simplify

[tex]\sf 6x = 18[/tex]

divide both both sides by 6

[tex]\sf x = 3[/tex]

b)

[tex]\sf 15(x - 5) = 75[/tex]

distribute

[tex]\sf 15x - 75 = 75[/tex]

collect terms

[tex]\sf 15x = 75 + 75[/tex]

combine

[tex]\sf 15x = 150[/tex]

divide both sides by 15

[tex]\sf x = 10[/tex]

c)

[tex]\sf \frac{3}{4} x +5 = 26[/tex]

collect like terms

[tex]\sf \frac{3}{4} x = 26-5[/tex]

combine

[tex]\sf \frac{3}{4} x = 21[/tex]

cross multiply

[tex]\sf x = \frac{ 21 (4)}{3}[/tex]

simplify

[tex]\sf x =28[/tex]

Answer: Look into step by step

Step-by-step explanation:

1. Multiply the second equation by 2; 6x - 2y = -2 then add to first equation

7x = -7 so x = -1, substitute x = -1 into the first equation -1 + 2y = -5 so y = -2

2. Multiply the first equation by 3; 3x + 6y = 6 then subtract it by second equation

y = 2, substitute y = 2 into first equation, x + 4 = 2, x = -2

3. Multiply the first equation by 2; 2x + 6y = 14 then subtract it by second equation

2y = 3 so y = 1.5, substitute y = 1.5 into the first equation x + 4.5 = 7, x = 2.5

I chose this method as it is easy

Answer:

27/31

Step-by-step explanation:

FIrst, construct a ratio. Isabelle needs 3/10 red to make 31/30 purple. So, we can divide red by purple to form a fraction to determine how much red paint for 1 fluid oz of purple. (3/10)/(31/30)=(9/30)/(31/30)=9/31. For every 1 oz of purple, we need 9/31 oz of red. Because we found how much red paint for 1 oz purple paint, we simply multiply by 3 to find how much red paint for 3 fluid oz of purple paint. (9/31)*3=27/31

Answer:

This is your answer!

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given the information from the question, we can deduce that:

3 - x = x - 3

Now our goal here is to find x.

3 - x = x -3

3 - x - 3  = x - 3 - 3

- x = x - 6

- x - x = x - 6 - x

- 2x = - 6

x = [tex]\frac{-6}{-2}[/tex] = 3

Answer: 3

Step-by-step explanation: The only value for x in which 3 - x is the same as x - 3 is where x does not affect the value of 3 whatsoever. We can also set this up algebraically to find this out algebraically.

x - 3 = 3 - x

Adding 3 to both sides, we have

x = 6 - x

Adding x to both sides we have

2x = 6

Dividing by 2 from both sides, we get

x = 3

The two stadiums are 2,871 meters

A blimp    = point A

stadium 1  = point B

stadium 2 = point C

height of the blimp ,  AD = 1600

depression angle of stadium 1 , ∠y = 71.7°

depression angle of stadium 2 , ∠x = 25.2°

distance between the two stadiums  = d

So, it forms 2 triangles  ABD and ACD,

Using the trigonometric ratios,

tan θ = Altitude / Base

DC = AD × tan (90° - x)

= 1600 × tan( 90° - 25.2° )

= 1600 × cot(25.2°)

= 1600 × 2.13

DB = AD × tan (90° - y)

= 1600 × tan( 90° - 71.7° )

= 1600 × cot(71.7°)

= 1600 × 0.33

∴ d = DC - DB

     = 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]

    = 2,871 meters

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Answer:

22480.000

Step-by-step explanation:

Cost of 1km²=6000

So,

Cost of 4.08km²=6000x4.08

=22480.000

I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.

The total cost nearest 100 is = $22500.

Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.

Cost of 1km2 = 6000

So,

Cost of 4.08km2 = 6000 * 4.08

                              =  22480.000

Rounding off to 100;

Cost = 22500.00

Hence,

Total cost of the land nearest 100 is = $22500.

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The area of the given parallelogram is 8 square units

A parallelogram is a 2 dimensional figure with 4 sides and angles. From the given diagram, the opposite sides are equal and the sum of the adjacent angles are supplementary

The formula for calculating the area of a parallelogram is expressed as:

A = base * height

From the given diagram

Base = (4, 0) = 4 units

Height. = (2, 0) = 2 units

Substitute the given values into the formula to have:

A = 4 units * 2 units

A = 8 square units

Hence the area of the given parallelogram is 8 square units

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x / 3 ≤ -6

---Multiply both sides by 3 to cancel out the denominator on the left side

x ≤ -18

Hope this helps!

Answer:

Answer:

(4, 1 )

Step-by-step explanation:

x = 3y + 1 → (1)

2x + 4y = 12 → (2)

substitute x = 3y + 1 into (2)

2(3y + 1) + 4y = 12

6y + 2 + 4y = 12

10y + 2 = 12 ( subtract 2 from both sides )

10y = 10 ( divide both sides by 10 )

y = 1

substitute y = 1 into (1)

x = 3(1) + 1 = 3 + 1 = 4

solution is (4, 1 )

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

Suppose an infinity sequence defined by:

[tex]\sum_{k = 0}^{\infty} f(k)[/tex]

Then we have to calculate the following limit:

[tex]\lim_{k \rightarrow \infty} f(k)[/tex]

If the limit goes to infinity, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

[tex]f(k) = \frac{k^3}{k^4 + 10}[/tex]

Hence the limit is:

[tex]\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0[/tex]

Hence, the infinite sequence converges, as the limit does not go to infinity.

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The series diverges by the comparison test.

We have for large enough [tex]k[/tex],

[tex]\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k[/tex]

so that

[tex]\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k[/tex]

and the latter sum is the divergent harmonic series.

Answer:  C

Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.

The standard form of the given quadratic equation in  factored form is

(x+2) (x-6) = x²-4x-12

(x-4) (x+3) = x²-x-12

(x-12) (X+1) = x²-11x-12

(x-3) (x+4) = x²+x-12

what are quadratic equations?

A quadratic function can be defined as a function having the highest degree 2. The standard form of a quadratic function is ax²+bx+c where a and b are not equal to zero

To convert a factored quadratic function into the standard form, we first need to open the brackets by multiplying the integers. Then carry out addition or subtraction operations to obtain the equation.

f(x) = (x+2) (x-6)

x²+2x-6x-12

x²-4x-12

similarly, the standard form of equations 2,3 and 4 are :

(x²-x-12)

(x²-11x-12)

(x²+x-12)

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Answer:

B, D, A, C

Step-by-step explanation:

f(x) = (x + 2)(x – 6)

✔ B

f(x) = (x – 4)(x + 3)

✔ D

f(x) = (x – 12)(x + 1)

✔ A

f(x) = (x – 3)(x + 4)

✔ C

There are 18c4 ways that RSM wants to send 4 of its 18 teachers into a conference. that means there are 3060 ways to send

there are 18 teachers and RSM wants to send 4 mem out of 18

so, we use combinatorics for this

Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.

It is used to find solutions easily for possible ways of a problem

For that we are using the formula for combinatorics

NCr = n!/ (r! (n – r)!)

similarly 18c4 = 18!/ (4! (18 – 4)!)

                       = 3060

Therefore , there are 3060 ways that RSM wants to send 4 of its 18 teachers into a conference.

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Answer:

Gustavo used a simulation where the data is quantitative’

Answer:

option c

Step-by-step explanation:

option c is a correct answer

The polynomial that should be subtracted from the dividend first is; x³ + 2x²

The long division we are given is;

        __________

x + 2 ) x³ + 3x² + x

Now, when we divide the polynomial by (x + 2), it means that the first quotient will be x².

Then by the multiplication of (x + 2) and x², we get a polynomial which will be subtracted from the dividend. Thus, we have;

(x + 2) * (x²) = x³ + 2x²

Thus, the polynomial to be subtracted is x³ + 2x²

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Answer: 42

Step-by-step explanation:

angle t is 42 degrees

Answer:

  ∠T = 42°

  PT = 14.4

  QT = 19.4

Step-by-step explanation:

An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

  Tan = Opposite/Adjacent   ⇒   Opposite = Adjacent×Tan

Then the missing side lengths are ...

  QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4

  PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.

  ∠T = 90° -48° = 42°

The solution to the triangle is ...

  ∠T = 42°

  PT = 14.4

  QT = 19.4

__

Additional comment

The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.

Answer:

403 (hope this helps)

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

100 - 56 is 44.  44% have still not done the project

.44 x 50 = 22

Answer:

22 coz 56% of 50 which is the total is 28. Then the remaining 44%is22

Step-by-step explanation:

The value of the x from the given equation is 1 and 6/7.

According to the statement

we have given that the quadratic equation and we have to find the solve for the value of the x.

So, For this purpose we know that the

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers.

So, The given equation is

7x^2 -x -6 =0

Find the factors of the equation

7x^2 -7x + 6x -6 =0

7x(x-1) -6(x-1) = 0

(x-1)(7x-6) =0

here the values of x becomes 1 and 6/7.

So, The value of the x from the given equation is 1 and 6/7.

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If the equation is 19-5=3z-11 then the value of z is 15/3.

Given an equation in terms of z is 19-5=3z-11.

We are required to find the value of variable z which exist in equation.

Equation is like a  relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.

The value of z can be find as under:

19-5=3z-11

4=3z-11

3z=4+11

3z=15

z=15/3

Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.

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Answer:

Isosceles

Step-by-step explanation:

An Isosceles triangle has an acute angle (less than 45°), and this photo shows a triangle with two matching sides with one side being longer.

A right triangle would have a 90° angle which this photo doesn't have

An Equilateral triangle has all 60° sides, since it doesn't have all matching sides, it cannot be the answer.

A Scalene triangle is similar to this photo except it has 30° 60° and 90° angles, which this photo doesn't have.

I hope this helps!

32 bottles are needed to poured 4 gallons of chocolate milk.

The correct option is D.

A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.

Pints to Gallons Ratio: 1:8

Permit x bottles to be present.

There are x bottles required for 4 gallons of chocolate milk.

Because of the direct proportion

4/x = 1/8

x = 4 x 8

x = 32

As a result, 32 bottles are required.

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The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively

Juan

Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

Mark

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

Barry

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

y = -0.001x^2 +0.4x +2.5

From the graphs, equations and tables, the distance travelled by the balls are:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

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The box-and-whisker plot for the given data is given below:

A box and whisker plot is defined as a graphical method of displaying variation in a set of data.

The results of a history test taken by 18 students: 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89.

Take note of how the scores are listed from lowest to highest.

The median for the given data is 73.

The Lower Quartile and the Upper Quartile would be found after that.

These represent the lower and higher halves' medians.

Lower quartile = 61.75

Upper quartile = 83.5

Make a number line. Mark your median, quartiles, and smallest and largest values.

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Using a system of equations, it is found that there were 4,000 children tickets sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

The attendance at the amusement park is 5,000 attendees, hence:

x + y = 5000 -> y = 5000 - x.

Considering the cost of parking and that the total money earned by the park is $100,000, we have that:

15x + 40y = 100000

Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:

15x + 40(5000 - x) = 100000

25x = 100000

x = 100000/25

x = 4000.

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Answer:

B

Step-by-step explanation:

Original form:

y=mx+b

m=slope

b=y interecept

By replacing those variables with the given we come up with the equation of:

y=3/2x-7

Answer:B

Step-by-step explanation: