Examine the figure of two parallel lines cut by a transversal.

One interior angle has a measure of 2 x plus 10 degrees; its same-interior angle has a measure of 2 x minus 30 degrees.

What is the value of x?

The exponential function representing the lifting time on day n is given as follows:

a(n) = 2^(n - 1).

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

On the first day, the time is of one minute, while the amount doubles each day, hence the parameters a and b are given as follows:

a = 1, b = 2.

We take the day one at the reference day, not day zero, meaning that the function was shifted right one unit, hence the rule is given as follows:

a(n) = 2^(n - 1).

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Yes, this collection is a set because it has a well-defined and finite number of elements, namely {2, 3, 5, 7}.

(ii) The method of describing this collection is the roster method or tabular method, where the elements of the set are listed within curly braces and separated by commas.

(iii) {2, 3, 5, 7}

In mathematics, a set is a collection of conspicuous objects or elements, taken as an object in its own right. These elements can either be numbers, letters, symbols, or even other sets. A set is defined by listing its elements or by specifying a property that its elements satisfy.

learn more about set: https://brainly.com/question/5660357

#SPJ1

The coordinates of the vertices for the image of the triangle are A(−3, 6), B(0, 10), and C(−3, 3)

From the question, we have the following parameters that can be used in our computation:

Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0)

If the preimage is translated 3 units up, then the transformation rule is

(x, y) = (x, y + 3)

Substitute the known values in the above equation, so, we have the following representation

A(−3, 3 + 3), B(0, 7 + 3), and C(−3, 0 + 3)

Evaluate

A(−3, 6), B(0, 10), and C(−3, 3)

Hence, the coordinates of the vertices for the image are A(−3, 6), B(0, 10), and C(−3, 3)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

Learn more about polynomial equation at:

https://brainly.com/question/19837586

#SPJ1

Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

Read more on perimeter of a rectangle here: brainly.com/question/28695033

#SPJ1

The missing sides of the right triangle were obtained below.

Pythagoras' theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We have that;

1) x = √26^2 - 10^2

x = 24

2) x = √20^2 + 14 ^2

x = 24.4

3) x = √50^2 - 30^2

x = 40

4) x = √15^2 + 5^2

x = 15.8

5) x = √12^2 + 20^2

x = 23.3

These are the sides that are missing.

Learn more about Pythagoras theorem:https://brainly.com/question/343682

#SPJ1

The number -0.02396 tell us about the slope of the pattern  and the value of y when x = 0 is 4.8153

Given that

y = -0.02396x + 4.8153

In the equation y = -0.02396x + 4.8153, we have

Slope = -0.02396

This means that the slope of the data is -0.02396

And as such it means that as the x values increase, the y values of the pattern decrease

We have

y = -0.02396x + 4.8153

Set x = 0

So, we have

y = -0.02396 * 0 + 4.8153

Evaluate

y =  4.8153

Hence, the value of y when x = 0 is 4.8153

Read more about linear regression at

https://brainly.com/question/10209928

#SPJ1

It will take approximately 8.6 years for the population to reach 1500.

We have,

We are given that the population is growing exponentially according to the model, P(t) = 500^(0.25t),

where t is measured in years.

We need to find the value of t when the population reaches 1500.

So we can set P(t) = 1500 and solve for t:

1500 = 500^(0.25t)

Taking the natural logarithm of both sides:

ln(1500) = ln(500^(0.25t))

Using the logarithmic identity, ln(a^b) = b ln(a):

ln(1500) = 0.25t ln(500)

Solving for t:

t = ln(1500) / (0.25 ln(500))

Using a calculator, we get:

t ≈ 8.6 years

Therefore,

It will take approximately 8.6 years for the population to reach 1500.

Learn more about exponential growth here:

https://brainly.com/question/12490064

#SPJ1

Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

To learn more about the amount of air to fill a basketball

https://brainly.com/question/20592924?referrer=searchResults

https://brainly.com/question/16606259?referrer=searchResults

The surface area of the right square pyramid with the given base area and slant height would be = 221cm²

To calculate the surface area of the right square pyramid, the formula that should be used would be given below as follows. That is;

Surface area = a²+ 2al

where;

a² = area of base = 169cm²

a = side length of base = √169 = 13

l = slant height = 13 cm

S.A = 169+ 2(13×13)

= 169 + 52

= 221cm²

Learn more about area here:

https://brainly.com/question/28470545

#SPJ1

The quadratic equation has only one solution if m = 14

For a quadratic equation:

ax² + bx + c = 0

The discriminant is:

D = b² - 4ac

If the discriminant is zero, then the quadratic has only one solution, here we have the equation:

2x² - 28x + 7m = 0

Then the discriminant is:

D = (-28)^2 - 4*2*7m

Now we need to solve:

(-28)^2 - 4*2*7m = 0

784 - 56m = 0

Solving that for m:

784/56 = m

14 = m

Learn more about quadratic equations at.

https://brainly.com/question/1214333

#SPJ1

The domain of this relation is [0, 5].

The range of this relation is [-4, 3].

No, this relation is not a function.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graphs shown in the image attached above, we can reasonably and logically deduce the following domain and range for graph 4:

Domain = [0, 5].

Range = [-4, 3].

Read more on domain here: brainly.com/question/9765637

#SPJ1

The mean of the data set is 3.33.

The variance of the data set is 0.47.

We have,

To find the mean of the data set,

We need to add up all the numbers and divide by the total number of values:

Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9

= 3.33 (rounded to two decimal places)

To find the variance,

We need to first find the squared difference between each value and the mean:

(2 - 3.33)^2 = 1.11

(2 - 3.33)^2 = 1.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

Next, we need to find the average of these squared differences:

Average of squared differences

= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9

= 0.47 (rounded to two decimal places)

Thus,

The mean of the data set is 3.33.

The variance of the data set is 0.47.

Learn more about mean here:

https://brainly.com/question/23263573

#SPJ1

The solution for integrals are -1/3 (2 + cos² (x))[tex]^\frac{3}{2}[/tex]  +C

If we are finding the following integral below

∫ (√2 + (cos x)² / secx × cscx) dx instead of ∫ (√(2 + cos²x)) / (secx × csc) dx

then

secx = 1/cosx and cscx = 1/sinx

∫ (√(2 + cos²x)) × sinx × cosx dx

givn that sin²x + cos²x = 1

sin²x = 1 - cos²x

u = cosx,

du = -sinx dx.

-∫ (√u) / (2sinxcosx) du.

-√u + C.

When you substitute the original equation into the result

1/3 (2 + cos²x)^(3/2) + C.

Find more exercises on  finding integral;

https://brainly.com/question/27745537

#SPJ1

The information from the histogram are as follow,

Students exercised for 4 or more hours are 14.

Students exercised for 9 or fewer hours are 13.

Mean of the data = 7.3.

median of the data = 6.33.

The histogram provides information about the distribution of hours students spent exercising in a week.

The number of students who exercised 4 hours or more,

= adding up the counts in the first and second bins.

= 9 + 5

= 14 students

The number of students who exercised 9 hours or fewer,

= adding up the counts in the first and second bins

= 9 + 4

= 13 students

The mean hours of exercise is not provided by the histogram

use the formula,

Mean = Σ[tex]x_{i} y_{i}[/tex] / N

where

[tex]x_{i}[/tex] is the midpoint of the ith bin

[tex]y_{i}[/tex] is the frequency of the ith bin

N is the total sample size

Mean = [(2)(4)  + (7)(9) + (12)(5)] / 18

          = 7.3

The median hours of exercise is not provided by the histogram.

Median = L + ( (n/2 – F) / f ) × w

where

L=The lower limit of the median group

n = The total number of observations

F = The cumulative frequency up to the median group

f =The frequency of the median group

w = The width of the median group

median = 5 + ( ( 14/2 - 4 ) /9 × 4

             = 6.33

Therefore, from the histogram the number of students exercised for ,

4 hours or more are 14.

9 hours or fewer are 13.

mean = 7.3

Median = 6.33

learn more about histogram here

brainly.com/question/9696858

#SPJ1

The total cost of the meal is $65.50, with tip included.

Here, in this question we need to find the percentage Value, to find the total cost of the meal plus the tip, Carter needs to multiply the cost of the meal by a factor of 1 + the tip percentage, which is 1 + 31% = 1.31.

So, the number Carter should multiply the cost of the meal by to find the total plus tip in one step is 1.31.

For example, if the cost of the meal was $50, then the total cost including the tip would be addition of cost of meal and tip.

Total cost = Cost of meal + Tip

Total cost = $50 + 31% of $50

Total cost = $50 + $15.50

Total cost = $65.50

To know more about Percentage:

https://brainly.com/question/29630127

#SPJ1

There are 24 ways to pick two green marbles first and one red marble last.

The probability of picking a green marble on the first draw is 4/10, and then 3/9 on the second draw since there are only 3 green marbles left out of 9 total marbles remaining.

The probability of picking a red marble on the third draw is 4/8 since there are 4 red marbles left out of 8 total marbles remaining.

So the probability of picking two green marbles first and one red marble last is (4/10) x (3/9) x (4/8) = 2/45.

To calculate the number of ways to pick two green marbles first and one red marble last, we need to use combinations.

There are [tex]^4C_2[/tex] = 6 ways to choose two green marbles from four, and there are 4 ways to choose one red marble from four.

So there are 6 x 4 = 24 ways to pick two green marbles first and one red marble last.

To learn more on Combinations click:

https://brainly.com/question/19692242

#SPJ1

Don would take 1500 minutes to fill the 1000-gallon water tank using the 2-gallon bucket.

If the capacity of the water tank is 1000 gallons and Don uses a bucket that can hold 2 gallons to fill the tank, we can calculate the number of buckets Don needs to fill the tank.

Let's assume the number of buckets Don needs to fill the tank is represented by 'n'.

Capacity of the tank = 1000 gallons

Capacity of each bucket = 2 gallons

Number of buckets needed to fill the tank, n = Capacity of the tank / Capacity of each bucket

n = 1000 gallons / 2 gallons

n = 500

So, Don needs 500 buckets, each holding 2 gallons, to fill the 1000-gallon water tank.

Given that it takes Don 3 minutes to fill the bucket with water and pour it into the tank, the total time taken by Don to fill the tank would be the product of the number of buckets (500) and the time taken to fill each bucket (3 minutes).

Total time taken to fill the tank = Number of buckets × Time taken to fill each bucket

Total time taken = 500 × 3 minutes

Total time taken = 1500 minutes

To know more about gallon here

https://brainly.com/question/31702678

#SPJ1

Answer:

Option 2 is correct. The function is increasing on the set of all positive real numbers.

This is correct. If M is a subset of N and N is a subset of P, then, M is a subset of P.

This follows from the transitivity of the subset relation. In set theory, the transitive property states that if a relation applies between elements A and B, and between elements B and C, then it also applies between elements A and C.

For the subset relation, if M is a subset of N (M ⊆ N), this means that every element in M is also an element of N. Similarly, if N is a subset of P (N ⊆ P), every element in N is also an element of P.

Read more on subsets here:https://brainly.com/question/13265691

#SPJ1

The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

To know more about substitution:

https://brainly.com/question/30284922

#SPJ1

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

The ordered pair that would represent the coordinates of vertex D' is given as follows:

D'(4u, -3u).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = u.

The coordinates of each vertex are multiplied by y, hence the ordered pair that would represent the coordinates of vertex D' is given as follows:

D'(4u, -3u).

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

The logarithm equations and corresponding x-value are

[tex]log_{2}x=5[/tex] has x=32

[tex]log_{10}x=3[/tex] then x=1000

[tex]log_{4}x=2[/tex] then x=16

[tex]log_{3}x=1[/tex] then x=1

We know that [tex]log_{a}x=b[/tex]

Then [tex]x=a^b[/tex]

(1) [tex]log_{2}x=5[/tex]

x=2⁵

=32

So [tex]log_{2}x=5[/tex] has x=32

(2) [tex]log_{10}x=3[/tex]

Then  by using the above property of logarithmic function we have:

x=10³

x=1000

So [tex]log_{10}x=3[/tex] then x=1000

(3) [tex]log_{4}x=2[/tex]

x=4²

x=16

so  [tex]log_{4}x=2[/tex] then x=16

(4) [tex]log_{3}x=1[/tex]

x=1³

=1

So  [tex]log_{3}x=1[/tex] then value  x=1

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

The list represents the ages of students in a gymnastics class.

-------

8, 8, 8, 9, 9, 10, 10, 10, 11, 12

If another student of age 10 joins the class, how is the mean affected?

The mean will remain the same at 10.

The mean will increase to about 10.2.

The mean will decrease to about 9.

-------

8 + 8 + 8 + 9 + 9 + 10 + 10+ 10 + 11 + 12

= 95

95 ÷ 10

=9.5

8 + 8 + 8 + 9 + 9 + 10 + 10 + 10+ 10 + 11 + 12

= 105

105 ÷ 11

= 9.54.....

The difference in volumes for the two cylinders is given as follows:

A. 61π mm³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

For Cylinder 1, the parameters are given as follows:

r = 0.5 x 8 = 4 mm, h = 10 mm.

Hence the volume is given as follows:

V = π x 4² x 10

V = 160π mm³.

For Cylinder 2, the parameters are given as follows:

r = 0.5 x 6 = 3 mm, h = 11 mm.

Hence the volume is given as follows:

V = π x 9² x 11

V = 99π mm³.

Hence the difference is given as follows:

160π mm³ - 99π mm³ = 61π mm³.

More can be learned about the volume of a cylinder at brainly.com/question/9554871

#SPJ1

The area of the rectangle is 81 square units. (option a)

To find the area of a rectangle, we need to know its length and width. We can determine these values by looking at the difference between the x-coordinates and the y-coordinates of the vertices.

In this case, we have the following coordinates: (-4,5), (5,5), (-4,-4), and (5,-4).

The length of the rectangle is the difference between the x-coordinates of the left and right vertices:

=> 5 - (-4) = 9.

The width is the difference between the y-coordinates of the top and bottom vertices:

=> 5 - (-4) = 9.

To find the area of the rectangle, we multiply its length by its width:

=> 9 x 9 = 81.

So, the correct answer is the (a), 81 square units.

To know more about rectangle here

https://brainly.com/question/8663941

#SPJ1

There is no solution from the given matrix equation.

In a two by two matrix equation system, two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. It implies that the first matrix is 2×2 and the second matrix is 2×1.

Given that:

[tex]\left[\begin{array}{cc}6&4\\9&6\end{array}\right] \left[\begin{array}{c}x\\y \end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]

We multiply each row in the first matrix by each column in the second matrix, so we get:

[tex]\left[\begin{array}{c}6x+4y\\9x+6y\end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]

Then, we can express it as a system of linear equations:

6x + 4y = 1 --- (1)

9x + 6y = 3 --- (2)

Here, we decided to use the substitution method to solve the system of equations.

From equation (1)

x = 1/6 - 2y/3

Replace the value of x into equation (2) and solve for y, we get:

9(1/6 - 2y/3) + 6y = 3

By solving it, we get:

3/2 = 3

Thus, since 3/2 = 3 is not a true solution, then we can conclude that there is no solution.

Learn more about solving matrix equations here:

https://brainly.com/question/27929071

#SPJ1

The value of x from the given isosceles triangle is 5.6 units.

Given that, the measure of equal sides of an isosceles triangle is 6 units and the base measures 5.9 units.

Draw perpendicular bisector to base, so we get halves as 5.9/2 =2.95

Let the length of perpendicular bisector be x.

By using Pythagoras theorem, we get

6²=2.95²+x²

36=8.7025+x²

x²=36-8.7025

x²=27.2975

x=5.2 units

We know that, sinθ=Opposite/Hypotenuse

sin68°=5.2/x

x=5.6 units

Therefore, the value of x from the given isosceles triangle is 5.6 units.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ1