1. 4x + 3y = 15
2. 3.x - 4y = 8
3. y +1 = (x – 6)
4. y = – 5
Which pair of lines are parallel?
a. 3 and 4
b. 1 and 2
c. 1 and 3
d. 2 and 4​

Answer:

Step-by-step explanation:

Use distributive property. Then use exponent law.

Exponent law used here = \(a^{m}*a^{n}=a^{m+n}\)

\(-p^{2}(p^{2} - p - 1) = -p^{2}*p^{2} - p *(-p^{2}) - 1*(-p^{2}) \\\\= -p^{4} + p^{3}+p^{2}\)

The equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5

We need to find the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3

The point slope form of a equation of a line is

y - y₁ = m(x - x₁)

y - (-2) = 3 (x - 1)

y + 2 = 3x - 3

y = 3x - 3 - 2

y = 3x - 5

Therefore the equation in point slope form of the line that passes through the point (1, −2)and has a slope of 3 is y = 3x - 5.

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Answer: Linear

Step-by-step explanation: This is because you can find the slope.

Answer:

Linear because it is in the form Ax+By=C

Step-by-step explanation:

We know that the 'x' coordinate represents the perpendicular distance from y-axis, and the 'y' coordinate represents the perpendicular distance from x-axis.

It can also be visualized that (x,y) is a point obtained by moving x units horizontally, and then y units vertically, with respect to the origin.

In the given graph, it is observed that on the x-axis 1 and -1 are marked at 10 grid lines, so the length that each grid step represents is calculated as,

So we found that each step represents 0.1 units.

33.

Consider the given coordinate (0.5,-0.5).

In order to reach this point, move 5 steps right and then 5 steps down. We see that this is the location of Red Rock Canyon.

Thus, Red Rock Canyon is located at (0.5,-0.5).

34.

Consider the given coordinate (-1/2 , 2/5) i.e. (-0.5 , 0.4)

In order to reach this point, move 5 steps left and then 4 steps up. We see that this is the location of Mystery Mountain.

Thus, Mystery Mountain is located at (-0.5 , 0.4).

35.

Consider the location of Brown Bat Cave.

It is situated at distance 8 steps on the right, and 7 steps down.

So it's location can be represented by the coordinate (0.8,-0.7) .

36.

Given that the origin is the location of the treasure.

The Pirate's cove is 7 steps left and 6 steps down. The shortest distance from this point to the treasure will be equal to the hypotenuse of the right triangle with base 0.7 units and height 0.6 units.

Solve for the hypotenuse (H) using Pythagoras Theorem as follows,

Thus, the treasure is approximately 0.922 units from the Pirate's Cove.

37.

Consider that the reflection about origin is characterized as,

The location of Parrot's lake is (-5,5) while the Red Rock Canyon is located at (5,-5).

Both these points satisfy the condition of reflection.

So they will be the image of each other, while considering the reflection about the origin.

Thus, the required locations are Parrot's lake and Red Rock Canyon .

a. The graph of the curve is given in the below attachment.

b. The slope of the tangent line to the parametric curve at the point (2,1) is 6.

c. The area underneath the curve from t=0 to t=1 is 1/2

a. To sketch the curve, we can create a table of t, x, and y values using the given values for t.

Let's calculate the values for t, x, and y using the given parametric equations:

When t = -2:

x = 2t = 2(-2) = -4

y = t³ = (-2)³ = -8

When t = -1:

x = 2t = 2(-1) = -2

y = t³ = (-1)³ = -1

When t = 0:

x = 2t = 2(0) = 0

y = t³ = 0³= 0

When t = 1:

x = 2t = 2(1) = 2

y = t³ = 1³ = 1

When t = 2:

x = 2t = 2(2) = 4

y = t³ = 2³ = 8

Now we can plot the points (-4, -8), (-2, -1), (0, 0), (2, 1), and (4, 8) on a graph to sketch the curve.

b. Given: x = 2t and y = t³

Differentiating both equations with respect to t:

dx/dt = 2

dy/dt = 3t²

Substituting t = 2 into the derivatives:

dx/dt | t=2 = 2

dy/dt | t=2 = 3(2)²= 12

The slope of the tangent line at the point (2, 1) is given by dy/dx:

dy/dx = (dy/dt)/(dx/dt) = (12)/(2) = 6

c. To find the area underneath the curve from t = 0 to t = 1, we can use the formula for the area under a parametric curve:

A = ∫[a, b] y(t) × dx/dt dt

In this case, a = 0 and b = 1. We need to calculate the integral:

A = ∫[0, 1] t³× 2 dt

Integrating the function, we get:

A = [2/4 × t⁴] evaluated from 0 to 1

Plugging in the values and simplifying, we have:

A = 2/4 × (1⁴ - 0⁴) = 2/4 × 1 = 1/2

Therefore, the area underneath the curve from t = 0 to t = 1 is 1/2 units squared.

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The number of days would be 10 and the maximum percent of the population infected would be 25.752%.

What are exponential functions?

The exponential function, denoted by \(e^x\), is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

\(p(t) = 7te^{-\frac{t}{10}}\)

percentage of infected people a maximum when p '(t) = 0

                    \(p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10\)

Hence percentage of infected people reaches a maximum after 10 days

maximum percent of the population infected = p(10)

    \(p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%\)

Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.

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The annual rate of decay is r = 0.87

We know that if a quantity has a half-life of T, then the rate of decay must be such that:

r^T = 0.5

This means that when a time T passes, the original quantity becomes half of what it originally was.

In this case we know that the half-life is T = 5 years, then we have:

r^5 = 0.5

r = 0.5^(1/5) = 0.87

Then the annual rate of decay is r = 0.87, and if the initial quantity is 18 grams, we can write the exponential decay as:

f(t) = 18g*(0.87)^t

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Answer:

13%

Step-by-step explanation:

I took the test on edge and got it right

Answer: x=25

Step-by-step explanation:

x²+5=30

30-5=25

x²=25

\(\sqrt{x^2}=\sqrt{25}\)

x=25

Answer:

x = -5 or 5

Step-by-step explanation:

1. subtract 5 from both sides

x^2 = 25

2. take the square root of both sides and remember to use positive and negative roots

x = ± 5

3. separate both solutions

x = -5 or x = 5

Answer:  If the original equation is y = 3x -4,  the slope is 3.

Any equation of a line parallel to the line y = 3x -4 will have a slope of 3.

Step-by-step explanation:

In slope-intercept form, y =mx + b the coefficient of x, m is the slope.

Here 3 is that value.

It is very unusual to have two equal signs in a question about slope.

I am not sure what to do with the =8y + 1

Is this supposed to be another equation in the system, missing a term?

The three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .

In the question ,

it is given that

Ari walked a distance of 22 miles with speed of 2 miles per hour .

Beth walked a distance of 1 mile with the speed of 1 mile per hour.

Cindy walked for the time 1 hour and 21 minutes .

converting 21 minutes to hours , we get

= 1 hr 21 min

= 1+21/60

= 27/20

= 1.35 hours     ....(i)

time required for Ari to walk 22 miles with speed of 2 miles per hour is

time = distance/speed

time = 22/2 = 11 hours         ...(ii)

time required for Beth to walk 1 miles with speed of 1 miles per hour is

time = 1/1 = 1 hours        ....(iii)

From equation (i) , (ii) and (iii) ,

the order of the time they spent walking from least to greatest time is

1 hours < 1.35 hours < 11 hours

Therefore , the three people in order of the times they spent walking from least time to greatest time is Beth < Cindy < Ari .

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Each of the expressions has been simplified by using properties of exponents as shown below.

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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a^2 + b^2 = c^2

18^2 + 18^2 = 36^2;

324 + 324 = 1296

not equal, no

Number line that number of workers in San diego is  260, 290, 320, 350, 380, 410, 440, 470, 500. The correct answer is 260

To find the number of workers in San Diego, we need to subtract the number of workers in New York (90) and Denver (130) from the total number of workers (480). Subtracting 90 and 130 from 480, we get 260. This means that 260 workers are in San Diego.

The number line represents the possible number of workers in San Diego. Since there are only three cities, the number of workers in San Diego must be positive (as there are workers in that city). Therefore, we can eliminate numbers less than 0. Additionally, the number of workers in San Diego cannot exceed the total number of workers (480). Thus, we can eliminate numbers greater than 480.

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The vertices of the image of quadrilateral LMNP after a rotation of 180° clockwise about P are (-2, 2), (-3, 4), (-1, 4), and (-2, 2). To rotate a figure 180° clockwise about a point, we need to reflect it across a line passing through that point. In this case, we need to reflect quadrilateral LMNP across the line passing through point P.

To do that, we first need to find the coordinates of the midpoint of line segment LM and line segment NP. The midpoint of LM is [(Lx + Mx)/2, (Ly + My)/2] = [(-4 - 3)/2, (2 + 4)/2] = [-3.5, 3]. The midpoint of NP is [(Nx + Px)/2, (Ny + Py)/2] = [(-1 - 2)/2, (4 + 2)/2] = [-1.5, 3].

Next, we need to find the slope of line segment LP. The slope of a line passing through two points (x1, y1) and (x2, y2) is (y2 - y1)/(x2 - x1). The slope of LP is (2 - 4)/(-2 - (-4)) = 1.

The equation of the line passing through point P with slope 1 is y - Py = 1(x - Px), or y - 2 = x + 2. We can rewrite this equation as y = x + 4.

Now, we can find the coordinates of the image of point L by finding the intersection of line LP and the line y = x + 4. Substituting y = x + 4 into the equation of LP, we get x + 4 - 2 = 1(-x - 2), or 2x = -4, or x = -2. Substituting x = -2 into y = x + 4, we get y = 2. Therefore, the image of point L is (-2, 2).

We can repeat this process for points M and N to find their images. The image of point M is the intersection of line MP and the line y = x + 4. The slope of MP is (2 - 4)/(-2 - (-3)) = 2, so the equation of line MP is y - 2 = 2(x + 2), or y = 2x + 6. Substituting y = x + 4 into this equation, we get x + 4 = 2x + 6, or x = -2. Substituting x = -2 into y = x + 4, we get y = 2. Therefore, the image of point M is (-2, 2).

Similarly, the image of point N is the intersection of line NP and the line y = x + 4. The slope of NP is (4 - 4)/(-1 - (-2)) = 0, so NP is a horizontal line passing through (-1, 4). Therefore, the image of point N is (-3, 4).

Finally, the image of point P is just itself. Therefore, the vertices of the image of quadrilateral LMNP after a rotation of 180° clockwise about P are (-2, 2), (-3, 4), (-1, 4), and (-2, 2).

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it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

velοcity is a unit οf measurement fοr the Distance an οbject travels in a

the predetermined periοd οf time. Here is a wοrd equatiοn that illustrates the cοnnectiοn between space, speed, and time: velοcity is calculated by

dividing the tοtal Distance traveled by the jοurney time.

Since the sleighs are traveling in οppοsite directiοns, their distances frοm each οther are increasing at a cοmbined rate οf 20 mph + 45 mph = 65 mph. We can use the fοrmula:

distance = rate x time

Let's call the time it takes fοr the sleighs tο be 390 miles apart "t". Then we can write:

390 = 65t

Sοlving fοr "t", we can divide bοth sides by 65:

t = 6

Therefοre, it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

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Answer:

The answer is C i got it right i am not lieing

Step-by-step explanation:

On Wednesday the hiker had the greatest elevation of 8.74 km.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

Given, Elevation represents the distance from sea level.

Positive numbers represent elevations that are above sea level and negative numbers represent elevations that are below sea level.

We know distance is always positive so if we look through the table on Wednesday the hiker has hiked - 8.75 km,

Now modulus of - 8.75 is | - 8.75 | = 8.75, so on Wednesday the hiker has the greatest distance covered.

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Answer:

In mathematics, every integer is a rational number, hence a whole number 3 can be written as 3/1. 1/8 x 3 = 3/8 in fraction form. 1/8 x 3 = 0.375 in decimal form.

Answer:

In mathematics, every integer is a rational number, hence a whole number 3 can be written as 3/1. 1/8 x 3 = 3/8 in fraction form. 1/8 x 3 = 0.375 in decimal form.

Step-by-step explanation:

hope that helped

The diagram of water cycle is attached below.

The best describes the process occurring at U and X is Water changes from a liquid to a gas.

The process that occurs at the position of U and X is discussed when water transforms from a liquid to a gas. This is called Evaporation.

The following are the situations that should not be arisen at the location U and X:

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The sampling distribution of the sample proportion represents the probability distribution of all possible values that the sample proportion could take if we were to repeatedly take random samples from the population.

Based on the information given in the question, we know that the true proportion of employees who believe that the corporation is a great place to work is p = 0.80 (since 80% of the employees said that). Assuming that the sample size is sufficiently large (usually n ≥ 30), the central limit theorem tells us that the sampling distribution of the sample proportion is approximately normal, with mean μ = p and standard deviation

\(σ = \sqrt{} (p(1-p)/n)\)

The mean of the sampling distribution of the sample proportion is 0.80, and the standard deviation is

\( \sqrt{} (0.80 \times (1-0.80)/n)\)

If we take a random sample of size n = 100, for example, the standard deviation of the sampling distribution would be

\( \sqrt{} (0.80 \times (1-0.80)/100) = 0.040\)

The sampling distribution of the sample proportion provides important information about the variability of sample proportions that we could observe if we repeatedly took random samples from the population. Understanding this distribution can help us make more accurate inferences about the population based on the sample data.

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Answer:

225 u²

Step-by-step explanation:

The area of the larger square is 625 u². We know that area of square is the square of side. So ,

⇒ a² = 625 u²

⇒ a = √625 u²

⇒ a = 25 u .

Similarly finding the side of second square as ,

⇒ a'² = 400 u²

⇒ a' = √400 u²

⇒ a' = 20 u

If we see these are the hypontenuse and base of a right a Angled triangle formed between the square. The measure of perpendicular will be the side lenght of third square.

⇒ h² = p² + b²

⇒( 25u)² = p² + (20u)²

⇒ p² = 625 - 400 u²

⇒ p² = 225 u²

This p² is only the area of square .

Answer:

225 units

Step-by-step explanation:

Since the sum of the angles in a triangle = 180º, the 100º angle must be the vertex angle. Since the base angles of an isosceles triangle = each other, each base angle = 40º.

I hope this helps!

Answer:

C.  40

Step-by-step explanation:

180 - 100 = 80

80/2 = 40

Answer:

$4 per student

Step-by-step explanation:

If $20 was collected from 5 students, 20/5 =4.

I hope this answers your question :)

The first five terms of the sequence given the definition are -1, 0, 1, 2 and 3

To find the first five terms of the sequence {an}, we can use the recursive definition of the sequence and compute each term one by one:

a1 = -1

For n = 2, we have:

a2 = a1 + (-1)² = -1 + 1 = 0

For n = 3, we have:

a3 = a2 + (-1)³ = 0 - (-1) = 1

For n = 4, we have:

a4 = a3 + (-1)⁴ = 1 + 1 = 2

For n = 5, we have:

a5 = a4 + (-1)⁵ = 2 - (-1) = 3

Therefore, the first five terms of the sequence {an} are:

a1 = -1

a2 = 0

a3 = 1

a4 = 2

a5 = 3

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When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

When comparing the data to determine the location with the most consistent temperature, the measure of variability that should be used for both sets of data is the IQR (Interquartile Range).

This is because the IQR is a robust measure of variability that is not influenced by extreme values or outliers. Therefore, it is suitable for both symmetric and skewed distributions. Therefore, the answer is iqr, because sunny town is symmetric and iqr, because beach town is skewed.

When comparing the data to determine the location with the most consistent temperature, you should use the IQR (interquartile range) because it is a robust measure of variability that is not affected by extreme values or skewness. In this case, you should use IQR for both Sunny Town and Beach Town, regardless of their symmetry or skewness, to get a reliable comparison of their temperature consistency.

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Answer:

12 :D

Step-by-step explanation:

First we substitute all x's for -2 :)

f(-2)=−-2^3−3(-2)^2+8

Now we solve :)

f(-2)=−-2^3−3(-2)^2+8

f(-2)=− -8 −3(-2)^2 + 8

f(-2) = -8 - 3(-4) + 8

f(-2) = - 8 + 12 + 8

f(-2) = 4 + 8

f(-2) = 12 :)

f will equal 12 :)

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