Slope of Linear Equations
Which description best compares the graph given by the following equations:
5x-3y = -5
2x-y = 8

parallel

perpendicular

intersecting but not perpendicular

Answer:

Some lists which you can choose:

3:1

6:2

12:4

24:8

Step-by-step explanation:

Answer: The two ratios would be 9:3 and 3:1 because

27:9 divided by 3 on both sides, equals

9:3

27:9 divided by 9 on both sides,

3:1

Therefore, the two ratios would be 9:3 & 3:1.

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Answer:

a geometric figure labeled CD would be a segment

Step-by-step explanation: you need to attached the pictures with the question

Answer:

We can compute this in 2 ways:

305 downwind - 260 still air = 45 mph wind velocity

260 still air - 215 downwind = 45 mph wind velocity

Step-by-step explanation:

By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².

In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:

(a · cos A + b · sin A)² + (a · sin A - b · cos A)²

Second, expand the expression by algebra properties:

a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A

(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A

(a² + b²) · (cos² A + sin² A)

Third, use the fundamental trigonometric formula:

a² + b²

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Answer:

54<48

Step-by-step explanation:

If you add 45+3, you get 45.

Hope this helped.

The quadratic function is y = 2x^2+3x-4.

Given:

The quadratic function y = ax² + bx + c whose graph passes through the given points.(-1,-5), (1,1),(-2,-2)

(-1,-5) passes.

y = ax^2+bx+c

-5 = a(-1)^2+b*-1+c

-5 = a-b+c

(1,1) passes.

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

1 = a+b+c

(-2,-2) passes.

-2 = a(-2)^2+b*-2+c

-2 = 4a-2b+c

on solving three equations

a = 2 , b = 3 and c = -4

The quadratic equation is y = 2x^2+3x-4.

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Answer:

Rectangular prism          

Step-by-step explanation:

Answer:

(0,7)

Step-by-step explanation:

use desmose it will show you (0,7)

The displacement of the particle at t = 1 second is -3 .meters

The displacement of a particle in a straight line can be calculated using the following formula:  Displacement (d) = 2sin(πt) + 3cos(πt). This formula takes into consideration the sine and cosine of the angle, pi (π), multiplied by the time (t). The sine of the angle represents the vertical displacement, while the cosine represents the horizontal displacement.

For example, let's say we want to calculate the displacement of a particle at t = 1 second. First, we'll plug in the values into the formula:

d = 2sin(πt) + 3cos(πt)

d = 2sin(π*1) + 3cos(π*1)

d = 2sin(π) + 3cos(π)

d = 0 + (-3)

d = -3

Therefore, the displacement of the particle at t = 1 second is -3 meters.

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Answer:

6/20

Step-by-step explanation:

multiply 3 x 2 then 10 x 2 and you will have an equivalent ratio. Theres alot more of them but heres a simple one.

Answer:

6/20

12/40

24/80

Step-by-step explanation:

Answer:

2 2/5

Step-by-step explanation:

Keep, Change, Flip!!!

3/4 x 16/5

Use The Butterfly Method!!!

3/1 x 4/5

Multiply!!!

12/5

Simplify!!!

Answer:

54.5

Step-by-step explanation:

To find the median, first we have to put the numbers in ascending/increasing order.

43, 60, 50, 36, 58, 50, 73, 59, 69, 51 is your set

36, 43, 50, 50, 51, 58, 59, 60, 69, 73 is your set in order.

The median is the middle number of the data set. Your set has an even number of entries, so we have to average the 2 middle numbers, which are 51 and 58.

36, 43, 50, 50,     51, 58,         59, 60, 69, 73

51 + 58 = 109

109/2 = 54.5

Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

The meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.

The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.

Also, if the parameters are given then the class c is not defined.

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Answer:

More infomation.

Step-by-step explanation:

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Answer:

Step-by-step explanation:

x + x + (2x + 50) = 180

4x = 130

x = 32.5°

Answer:

x = 16

Step-by-step explanation:

0=x^2-14x+46 is to be solved for x by completing the square.  The first two terms, x^2 and -14x, are the incomplete square.  We must find a term to add to, and then subtract from x^2 - 14x, so that we have a perfects square on the left and a negative number on the right:

x^2 - 14x = x^2 - 14x + (half of -14)^2 - (half of -14)^2 results in transformation of the original 0=x^2-14x+46 to

x^2 - 14x + 49 - 49 + 46 = 0, which simplifies to:

(x - 7)^2 - 3 = 0.  We want to solve this for x.

To do that, rewrite (x - 7)^2 - 3 = 0 as (x - 7)^2 = 3, and then square both sides.  We get:

x - 7 = 9, or x = 16

Answer:

x1=7-(square)3 x2=7+(square)3

Step-by-step explanation:

Swipe the sides of equation

Solve the quadratic equation ax^2+bx+c=0

Then using: x=((-)b+-(square)b^2-4ac):2a

Separate the solutions

Simplify

Answer:

I think it is 18(A)

Step-by-step explanation:

I multiplied 8x3 then I did 6x3 and got 18

We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

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Answer:

7 schools have fewer than 50 classrooms.

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.

A mathematical word used to define a line's direction and steepness is its slope or gradient.

If a line is rising from left to right, it is growing. The slope is positive, or m>0

If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0

A line has zero slopes if it is horizontal. This function is constant.

The slope of a line is y - y₁ = m(x - x₁)

Slope m = (y₂ - y₁)/(x₂ - x₁)

m = (- 2 - 2)/(2 + 4)

m = - 4/6

m = - 2/3

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Based on the system of equations, the cost of using 19 HCF of water is $35.43

An equation is a mathematical statement that two or more values are equivalent.

Equations are stated to show that two mathematical expressions are equal using the equation sign (=).

Cost of using 17 HCF of water = $32.13

Cost of using 35 HCF of water = $61.83

Total cost of 17 HCF water = 17x + a

17x + a = 32.13 ... equation 1

Total cost of 35 HCF water = 35x + a

35x + a = 61.83 ... equation 2

35x + a = 61.83

-17x + a = 32.13

18x = 29.70

18x = 29.7

x = 29.7/18

x = 1.65

17x + a = 32.13 ... equation 1

17(1.65) + a = 32.13

28.05 + a = 32.13

a = 4.08 (32.13 - 28.05)

= 19(1.65) + 4.08

= $35.43

Thus, using the equations above, we can conclude that 19 HCF of water costs $35.43.

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Step-by-step explanation:

For this problem, we need to focus on the exponent rule for multiplying.

Rule:

\(x^{a} \times {x}^{b} = {x}^{a + b} \)

In words:

When multiplying with exponents, the exponents add.

For this problem, we'll be adding the exponents of 7 and 4.

Solve:

\({x}^{7} \times {x}^{4} = {x}^{7 + 4} = {x}^{11} \)

Your product is x^11 (x to the 11th power)

All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The differential equation representing the model of the number of words memorized by the students is equal to option C. dL/dt = k(100 - L).

Let us consider function 'L' represents the number of words memorized at time 't'

Total number of words students asked to memorized = 100 words

Rate of change of number of words with time 't' is equal to ( dL/dt )

Number of words left to memorized by the students = 100 - L

Differential equation representing the situation is

= Rate of change of number of words memorized ∝ number of words left to memorized

= dL/dt ∝ ( 100 - L )

⇒ dL/dt = k( 100 - L )

Where 'k' is the constant of proportionality .

k is a positive number.

Therefore, the differential equation representing the situation of memorizing word is given by option c. dL/dt = k( 100 - L ).

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The above question is incomplete, the complete question is:

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized.

1. Which of the following differential equations could be used to model this situation, where k is a positive constant?

A. dL/dt = kL

B. dL/dt = 100 - kL

C. dL/dt = k(100 - L)

D. dL/dt = kL - 100

Answer: Slope: 2/3

Step-by-step explanation: