Two parallel lines are cut by transverse as shown suppose

We have two points and we have to find the line that includes them both.

The points are: (3,4) and (7,2).

We can start with a point-slope equation of the line, using the point (3,4):

We now have to find the value of the slope m. We can find it by replacing the 2nd point, (7,2), in the equation:

Now, we can write the equation of the line as:

We can graph this line and verify if it includes both points:

Both points are included.

Equation of the line: y = -(1/2)*x + 11/2

If P(A) is 0.64, then P(A') is 0.36. P(A) is probability of occurrence of event A.

This question pertains to Probability principles. Probability is a measure of the possibility of an event occurring. Many occurrences cannot be foreseen with absolute accuracy. We can only anticipate the likelihood of an event occurring using it.

A is an occurrence in this context. A' denotes the event's complement.  

For example, if Event A is getting heads on a coin toss, then Event A' is getting tails.

This demonstrates one thing:

A ∪ A' = U, here U is the universal set.

P ( U) = 1

P (A) + P(A') = 1

0.64 + P (A') = 1

P(A') = 1 - 0.64

P (A') = 0.36

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Answer:

Step-by-step explanation:

The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation h(x) = -1/2(x -3)² + 4

The given graph is a quadratic graph. Given the function of the blue parabola expressed as:

f(x) = -1/2x²

The blue graph shows a upward translation by 4 units and horizontal translation by 3 units to have the equation

h(x) = -1/2(x -3)² + 4

Note that the upward translation will be positive while the horizontal shift to the right will be negative

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The solution of the function 3f(1) - 4g(-2)  is -19.

The functions can be solved as follows;

f(x) = 7x - 4

g(x) = 11 - x²

Therefore, let's solve the composite function as follows:

A composite function is generally a function that is written inside another function.

Hence,

3f(1) - 4g(-2) = ?

f(1) = 7(1) - 4 = 7 - 4 = 3

g(-2) = 11 - (-2)² = 11 - 4 = 7

Therefore,

3f(1) - 4g(-2) = 3(3) - 4(7) = 9 - 28 = -19

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The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

The pattern that this system detects is a four-digit number that is divisible by 3.

1. The system starts by taking an input of a four-digit number.

2. It then checks if the last digit of the input number is divisible by 3.

3. If it is, the system continues to check if the sum of the remaining three digits is divisible by 3.

4. If this turns out to be true, the system will output a signal indicating that the input number is divisible by 3.

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The mean and standard deviation for 30 multiple-choice questions for the number of correct answers is Mean(μ) = 6 and Standard deviation(σ) = 2.19.

What is mean?

A collection of values are averaged to form the mean. The total points were divided by the total scores. When population samples are tiny, the mean is sensitive to extreme scores. For example, if two students in a class of 20 earned significantly higher than the rest, the mean will be skewed higher than the other students' scores might suggest. When using means, larger sample sizes are preferable.

Define standard deviation.

In statistics, a measure of variability known as the standard deviation ( standard deviation ) is frequently used. It demonstrates how different things are from the norm. (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide variety of values.

Given: number of questions(n) = 30, p = \(\frac{1}{5}\), q = \(\frac{4}{5}\)

Mean μ = n*p

            = 30  *\(\frac{1}{5}\)

         μ = 6

Standard deviation σ = \(\sqrt{n*p*q}\)

                                   = \(\sqrt{30*\frac{1}{5}*\frac{4}{5}}\)

                                   = \(\sqrt{4.8}\)

                                σ = 2.19

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The difference between 301 and 134 is 167

What is difference?

Difference in mathematics means subtracting one number from another.

According to the question, we were asked to subtract 134 from 301

301 -134

= 167

Hence the difference between 301 and 134 is 167

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The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

because 2 and 3 are all prime factors

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

If angle f is 50 degrees and cuts it to 75 degrees

Find the difference between the two numbers

75-50 = 25

Divide by the correct value

25/50 = 1/2

Change to percent form

50%

Answer:

13.9534883721

Step-by-step explanation:

12/(0.9-0.04)=12/0.86=13.9534883721

Measures of center describe the middle or typical value of a data set, while measures of variation describe how spread out the data is; the mean is a measure of center, the range is a measure of variation, and the median is also a measure of center.

What are measures of center and variation and how are they used to describe a data set?

The following statements are true:

The following statement is false:

The following statement is ambiguous or incorrect:

The question is incomplete; the full question is provided below -

Data sets can be described using measures of centre and variance.

Choose ALL truthful statements about these measurements.

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The measure of side TR is given as follows:

TR = 6.7.

Similar triangles are triangles that share these two features listed as follows:

As the triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:

TR/35 = 5/26.

Hence the length of side TR is given as follows:

TR = 35 x 5/26

TR = 6.7.

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On doubling 1 and 3/4 cup, what we get is 7/2 cups which is roughly equal to 3 and 1/2 cups

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The number at the top of the line is referred to as the numerator. It indicates the number of equally sized portions that were picked from the total or collection. The number below the line is referred to as the denominator. It displays the total number of equal portions into which integral elements split or the total number of the identical objects in a collection.

When the total is divided into equal pieces, parts we take is a fraction. When doubled it becomes whole again. If a cake is cut into eight equal pieces and one piece is placed on every plate, every plate is said to hold 1/8 of a cake.

How to solve?

1 3/4 =7/4

7/4 +7/4 = 7/2 = 3 1/2

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With a speed of 0.013 m/s, the snail would need to traverse 174 km in about 3718 hours.

The term "distance" refers to the length or space across two points as well as objects. It is a tangible quality that can be quantified in a variety of ways, including in metres, kilometres, miles, or feet. The distance formula in mathematics, which is derived first from Pythagorean theorem, can be used to determine the separation in space or in a plane between two points. In a plane, for instance, the distance that separates (x1, y1) and (x2, y2) is represented by: D is equal to sqrt((x2 - x1)2 + (y2 - y1)2) .Sqrt stands for the square root function.

given

We can apply the following formula to resolve this issue:

Time = Speed / Distance

(0.013 m/s) x (3600 s/h) x (1 km/1000 m) = 0.013 m/s

0.013 m/s = 0.0468 km/h

The snail moves at a speed of 0.0468 km/h.

The snail must go 174 km in how many hours, according to the question. The following values can be entered in the formula above:

Distance times speed equals 174 km / 0.0468 km/h, or 3717.94 hours.

To the nearest hour, we round:

duration: 3718 hours

With a speed of 0.013 m/s, the snail would need to traverse 174 km in about 3718 hours.

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Answer:

d

Step-by-step explanation:

d is .04 percent plz mark branliest

Answer:

Slope is 14

Step-by-step explanation:

prove me wrong

Answer:

2/3

Step-by-step explanation:

Gradient of line

= (y1-y2) /(x1-x2)

= (3-(-1))/(4-(-2))

= (3+1)/(4+2)

= 4/6

= 2/3

Answer:

  7.7 seconds

Step-by-step explanation:

Put the given height into the formula and do the arithmetic.

  t = √(290.57/4.9) = √59.3 ≈ 7.7 . . . seconds

The object will take 7.7 seconds to hit the ground.

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

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Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Given:

it is given that population in 2010 is 6.9 billion and its growth rate is 1.1% per year.

Find:

we have to find the population in the years 2011,2012,2013,

Explanation:

The following table shows the population growth

Calender year Number of years after 2010 Projected Population

2010 0 6.90 billion

2011 1 6.97 billion

2012 2 7.05 billion

2013 3 7.13 billion