The answer of the given question based on the circle is , Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
What is Circumference?Circumference is distance around edge of circular object. It is same as perimeter of circle. The circumference of a circle can be calculated using the radius of the circle, which is half the diameter.
The circumference of circle with diameter d is given :
C = πd
Using the given diameter of 14 feet, the circumference of the original garden is:
C1 = πd1 = (22/7) * 14 = 44 feet
When the diameter is doubled to 28 feet, the circumference of the new garden is:
C2 = πd2 = (22/7) * 28 = 88 feet
To find how much more fencing Henry needs to purchase to enclose the new garden, we need to subtract the original circumference from the new circumference:
C2 - C1 = 88 - 44 = 44 feet
Therefore, Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
To know more about Distance visit:
https://brainly.com/question/71956
#SPJ1
A crew painted a house. Each of the 4 crew members started with the same number of gallons of paint, and each used 12 gallons. When they were finished, there were 24 gallons left over. How many gallons did each crew
member have at the start?
Answer:
18gall
Step-by-step explanation:
Evaluate the expression without using a calculator. sin−1(cos(2)) sin^−1 (cos( − /2))
The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
Describe Algebraic Expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.
Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.
To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).
cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.
Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.
Substituting this value into the expression, we get:
sin⁻¹(0) = 0
Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
To know more about function visit:
https://brainly.com/question/30954499
#SPJ1
For this discussion post, we are going to create a linear regression model from a set of data. Suppose we get a job working for a company that provides their employees with company stock every year they work with the company. The amount of stock earned may be based on a few other variables, but all we are looking at right now is time served with the company. Here is the data we collected:
The linear regression model from a set of data is y =5.2956+4.0946*X.
What is linear regression model?A statistical tool for examining the relationship between two quantitative variables is a linear regression model. Finding the best linear relationship between the dependent variable (Y) and one or more independent variables (X) in order to forecast the value of the dependent variable based on the value of the independent variable is the objective of a linear regression study.
The regression line is determined using the formula:
y = bo + b1 X
Now, using the table we have:
sum of (x) = ∑x = 103
sum of (y) = ∑y = 480
Calculating the squares we have:
sum of (x^2)= ∑x² = 1073
sum of (y^2)= ∑y² = 22868
Multiplying the variables we have:
sum of (x*y)= ∑x*y = 4939
mean(x)= ∑x/n = 9.3636
mean(y)= ∑y/n = 43.6364
Now, the intercept is given as:
intercept (bo) = (∑y)(∑x²) - (∑x)(∑xy) / n(∑x²) - (∑x)²
Substituting the values we have:
intercept (bo) = (480)(1073) - (103)(4939) / 11(1073)-(103)^2
intercept (bo) = (515040-508717) / (11803-10609)
intercept (bo) = 5.2956
The slope is given as:
slope (b1) = n(∑xy) - (∑x)(∑y) /n(∑x²) - (∑x)²
Substituting the values we have:
slope (b1) = (11(4939) -(103)(480))/(11(1073) - (103)^2
slope (b1) = (54329-49440)/(11803-10609)
slope (b1) = 4.0946
regression equation is, y = bo + b1 X
Substituting the values we have:
y =5.2956+4.0946*X
Hence, the linear regression model from a set of data is y =5.2956+4.0946*X.
Learn more about linear regression model here:
https://brainly.com/question/29855836
#SPJ1
The complete question is:
The vector matrix -6, -3 is rotated at different angles. Match the angles of rotation with the vector matrices they produce.
Answer: Without the options for the vector matrices resulting from rotation, I cannot provide a specific matching. However, I can provide the general formula for rotating a vector by an angle of θ degrees counterclockwise as follows:
To rotate a vector with coordinates (x, y) counterclockwise about the origin by an angle of θ degrees, we use the following formula to find the new coordinates (x', y'):
x' = xcos(θ) - ysin(θ)
y' = xsin(θ) + ycos(θ)
Therefore, to obtain the vector matrix resulting from rotating the vector (-6, -3) by a certain angle of rotation, we plug in the values of x = -6 and y = -3 into the above formulas, and use the corresponding angle of rotation in degrees for θ.
Step-by-step explanation:
question is in the picture
The calculated value of the volume of the solid is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
Finding the volume of the solidTo find the volume of the solid when the region R is rotated about the horizontal line y = -1, we can use the method of cylindrical shells.
The height of each cylindrical shell will be the difference between the function y = 2x and the horizontal line y = -1, which is (2x + 1).
The radius of each cylindrical shell will be the distance from the axis of rotation (y = -1) to the function y = x².
This distance is given by (x² + 1).
The thickness of each cylindrical shell will be dx.
Thus, the volume of the solid can be expressed as:
V = ∫[0,2] (x² + 1) - (2x + 1) dx
Hence, the expression is (d) V = ∫[0,2] (x² + 1) - (2x + 1) dx
Read more about volume at
https://brainly.com/question/11942113
#SPJ1
Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?
In statistics, critical value is value that is used to determine whether to reject null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
To know more about Null hypothesis visit:
brainly.com/question/30404845
#SPJ1
Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
The annual profits for a company are given in the following table, where x represents the number of years since 2005, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2016, rounded to the nearest thousand dollars.
The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars.
What is data in mathematics?Data in math is information that is organized and analyzed to help draw conclusions and make predictions. It can be numerical, or it can be non-numerical, such as words or images. Data can be collected through experiments, surveys, or other methods. Data analysis helps mathematicians to uncover patterns, relationships, and trends that could not be seen through traditional methods. Data can be used to solve problems, make decisions, or create models to help explain the behavior of a system.
x y
0 1150
1 1550
2 1850
3 2150
4 2500
Linear regression equation:
y = 442.86x + 1150
Projected profit for 2016 (in thousands of dollars):
7,427.
The linear regression equation that represents the given set of data is y = 442.86x + 1150, where x represents the number of years since 2005 and y represents the profit in thousands of dollars. Using this equation, the projected profit for 2016 (in thousands of dollars) can be calculated to be 7,427. This shows that the company's profits are expected to increase steadily over time.
It is important to note that the linear regression equation is just a model of the data and may not accurately predict the actual profits in 2016. Other factors such as economic conditions, competition, and market trends can all affect a company's profits and should be taken into consideration when making any predictions.
To know more about data click-
http://brainly.com/question/14592520
#SPJ1
Consider the two-node circuit shown below:
The node voltages V₁ and V₂ (in volts) satisfy the following system of equations:
15V₁ = 7V₂ + 60
3V₂ + 10 = 3V₁
a) Write the system of equations in the matrix form AV-B, where V = [V1, V2]
b) Find V₁ and V₂ using the matrix algebra method. Perform all matrix computations and show all steps.
a) The system of equations can be written in the matrix form AV-B as: | -3 3 | | V2 | | -10 |
b) V1 = 369/22 volts and V2 = -51/22 volts.
What is matrix?A matrix is a rectangular array of numbers or symbols, arranged in rows and columns. Matrices are often used in mathematics, science, engineering, and other fields to represent and manipulate data, perform operations, and solve equations. The size of a matrix is determined by the number of rows and columns it contains, and is usually written in the form "m x n", where "m" is the number of rows and "n" is the number of columns. Matrices can be added, subtracted, multiplied, transposed, and inverted, and can be used to represent a wide range of mathematical objects, including systems of linear equations, transformations, and graphs.
a) The system of equations can be written in the matrix form AV-B as:
| 15 -7 | | V1 | | 60 |
| | x | | = | |
| -3 3 | | V2 | | -10 |
b) To solve for V1 and V2 using matrix algebra, we can use the inverse of matrix A as follows:
AV = B
V = A⁻¹B
First, let's find the inverse of matrix A:
A = | 15 -7 |
| -3 3 |
To find the inverse of A, we need to calculate the determinant of A:
det(A) = (15)(3) - (-7)(-3) = 66
Then, we can find the inverse of A as follows:
A⁻¹ = (1/det(A)) x | 3 7 |
| 3 15 |
Now, we can solve for V by multiplying A⁻¹ and B:
| V1 | | 3 7 | | 60 | | 369/22 |
| | = | | x | | = | |
| V2 | | 3 15 | |-10 | | -51/22 |
Therefore, V1 = 369/22 volts and V2 = -51/22 volts.
To know more about matrix visit:
https://brainly.com/question/27929071
#SPJ1
Rewrite in simplest terms: 4(0.7n-6n-0.3)-0.4n
Answer:
21.6n-1.2
Step-by-step explanation:
=2.8n-24n-1.2-0.4n
=21.6n-1.2
Look at the image provided below
The density of nitrogen in the space will be 3.13 kg/m³
What is density?Density is the ratio of mass to volume of a substance. It is measured in kg/m³.
The volume of the shade part = volume of the cone- volume of the hemisphere
volume of the hemisphere = 2/3 πr³
= 2/3 × 3.14 × 40³
= 401920/3
= 133973.33m³
volume of the cone = 1/3 πr²h
= 1/3 × 3.14 × 40²× 500
= 2512000/3
= 837333.33 m³
volume of the shaded part = 837333.33-133973.33 = 703360m³
The density of the space = 2200000/703360
= 3.13kg/m³.
learn more about density from
https://brainly.com/question/1354972
#SPJ1
A landscaper has enough concrete paving stones to create a patio with an area of at most 250 square feet. The landscaper wants the length of the patio to be six feet longer than three times the width.
Select the statement that accurately describes the situation and justifies a possible width of the patio.
A.
A possible width is 10 feet because w = 10 satisfies 3w2 + 6 ≥ 250.
B.
A possible width is 11 feet because w = 11 satisfies 3w2 + 6w ≥ 250.
C.
A possible width is 8 feet because w = 8 satisfies 3w2 + 6w ≤ 250.
D.
A possible width is 9 feet because w = 9 satisfies 3w2 + 6 ≤ 250.
Answer:
C
Step-by-step explanation:
+) L = 3W + 6
+) L×W = (3W + 6)×W = 3W² + 6W ≤ 250
VERY EASY BASICALLY FREE <333
You should be very familiar with the informal use of probability. We make most of our decisions based on what we feel is likely, or unlikely, to happen.
Think of a time when you made a decision based on what you felt would probably happen. Did it turn out the way you thought it was likely to?
Let's say you're trying to decide whether or not to invest in a certain stock. You've analyzed the company's financial reports and economic indicators, but you're still uncertain about the stock's future performance. Based on your intuition and experience with the stock market, you estimate that there is a 70% chance that the stock's value will rise in the next six months.
Was your investment effective?You decide to invest based on that probability, and six months later the stock has actually gone up in value. Your decision turned out to be a good one, but that doesn't necessarily mean your probability estimate was accurate. The stock could have gone down in value just as easily, despite your assessment of its likelihood of going up.
Therefore, even when we make decisions based on probability, there is always a level of uncertainty involved and the outcome may not always line up with our initial estimates. However, taking the time to consider the likelihood of different outcomes can help us make more informed decisions and better manage risk.
Find out more about probability at:
https://brainly.com/question/24756209
#SPJ1
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used.
2
one half
4
one fourth
Answer: there all divided by 2
so it's 2
BELLRINGER:
In the function below, b is a constant. If f (2) = 0, what is the value of f(-1)?
f(x)=3/2 x + b
Answer:
-9/2
Step-by-step explanation:
f(x) = 3/2x + b
f(2) = 0
Find out what the variable b is.
3/2(2) + b = 0
3 + b = 0
Subtract 3 from both sides.
b = -3
f(-1) = 3/2(-1) - 3
f(-1) = -4.5
-4.5 = -9/2
k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
A card is dealt from a complete deck of fifty-two playing cards (no jokers). Use probability rules (when appropriate) to find the probability that the card is as stated. (Count an ace as high. Enter your answers as fractions.)
What is
both under a 3 and above an 8
The probability of the card is as stated at 7/52, which simplifies it to 1/8.
What is probability?Probability is the study of the possibility that an event or phenomenon will occur. It can be expressed numerically as a number between 0 and 1, where 1 implies a certain outcome of an event and 0 denotes an inconceivable chance of occurrence.
There are four cards that are under a 3 (the 2, the Ace, the King, and the Queen) and four cards that are above an 8 (the 9, the 10, the Jack, and the Queen). However, the Queen is both above an 8 and under a 3, so we need to subtract one from the total count.
Therefore, the number of cards that are either under a 3 or above an 8 is 4 + 4 - 1 = 7.
Therefore, the probability that the card is as stated is 7/52, which simplifies it to 1/8.
Learn more about probability, here:
https://brainly.com/question/29862517
#SPJ1
the equation for a projectile's height versus time is h(t)=-16t^2+v0t+h0 a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. what is the maximum height, in feet, the ball will attain?
round to the nearest whole foot
Therefore, the maximum height the ball will attain is 221.875 feet.
We are given the equation for the height of a projectile as a function of time:
[tex]h(t) = -16t^2 + v0t + h0[/tex]
where v0 is the initial velocity, h0 is the initial height, and t is the time. We are also given that a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Therefore, we can plug in the values of v0 and h0 into the equation:
[tex]h(t) = -16t^2 + 120t + 2[/tex]
To find the maximum height, we need to find the vertex of this parabola. The x-coordinate of the vertex is given by:
[tex]t = -b/2a[/tex]
where a = -16 and b = 120. Substituting these values, we get:
[tex]t = -120/(2(-16)) = 3.75 seconds[/tex]
To find the corresponding maximum height, we can plug this value of t back into the equation:
[tex]h(3.75) = -16(3.75)^2 + 120(3.75) + 2 = 221.875 feet[/tex]
Therefore, the maximum height the ball will attain is 221.875 feet.
To know more about height visit:
https://brainly.com/question/10726356
#SPJ1
On the Y axis we have the profit from the trucking company and on the X axis we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
!!i’ll give brainlist!!
Tim is taking the path shown to bike to Greg's house. Tim travels an average speed of 15 mi/hr.
Determine how much time it will take Tim to get to Greg's house. (You may use decimals here)
Answer:
Road:
Distance to Greg's house = 3.2 + 1.7 =
4.9 miles
Time to get to Greg's house =
(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)
Shortcut:
Distance to Greg's house:
[tex] \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 [/tex]
Time to get to Greg's house:
(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)
The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)
Consider 8 = − 2/3x. 1 Which is the BEST first step to take when solving the given equation?
Compute the following
(a) Calculate the scalar projection and projection of (5,3) onto (7,-2)
(b) Interpret this projection graphically
The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.
The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
What is graph?Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.
(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:
Projection = (A⋅B)/|B|
In this case, the scalar projection of (5,3) onto (7,-2) is:
Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
= (35 - 6)/53
= 29/53
Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:
Projection Vector = (A⋅B/|B|²)B
In this case, the projection vector of (5,3) onto (7,-2) is:
Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
= (35 - 6)/53 ⋅ (7,-2)
= (29/53)⋅(7,-2)
= (203/53, -58/53)
(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:
First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).
Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).
This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
To know more about graph click-
http://brainly.com/question/19040584
#SPJ1
2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
Read more about set at
https://brainly.com/question/24462379
#SPJ1
Use the formula z = x-μ/σ
and the given information to find the missing piece of information
1. Given x = 75, μ = 80, o = 5, find z.
The missing piece of information z-score is -1.
Explain information
Information refers to data or knowledge that has been transmitted or received. It can be expressed in different forms, including numerical data, text, images, or sound. The information serves as a basis for understanding, analysis, and decision-making. It can be processed and analyzed using mathematical methods and tools such as statistics, probability, and data analysis. The effective management and utilization of information are essential for progress and innovation in many fields, including science, technology, and business.
According to the given information
Using the formula z = (x - μ) / σ, we can plug in the given values and calculate:
z = (75 - 80) / 5
z = -1
Therefore, the z-score is -1.
To know more about z-score visit
brainly.com/question/15016913
#SPJ1
The volume of a pyramid whose base is a right triangle is 108 units^3
. If the two legs of the right triangle measure 8 units and 9 units, find the height of the pyramid.
According to the question the volume formula to find the height of the pyramid is 9 units.
What is formula?Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.
The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h
108 = (1/3) × 36 × h
108 = 12 × h
h = 9 units
To learn more about volume of a pyramid
https://brainly.com/question/17615619
#SPJ1
Solve x to make A||B
Answer:
x = 7
Step-by-step explanation:
if A and B are parallel , then
4x + 14 and 3x + 21 are alternate angles and are congruent , that is
4x + 14 = 3x + 21 ( subtract 3x from both sides )
x + 14 = 21 ( subtract 14 from both sides )
x = 7
For A and B to be parallel then x = 7
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
Please help me with this problem
The area of the poster in square meters is 0.014 m².
How to calculate the areaIt should be noted that to convert the area from square centimeters to square meters, we need to divide by 10,000 (since 1 square meter is equal to 10,000 square centimeters).
The area of the poster is:
14 cm × 10 cm = 140 cm²
To convert this to square meters, we divide by 10,000:
140 cm² ÷ 10,000 = 0.014 m²
Therefore, the area of the poster in square meters is 0.014 m².
Learn more about area on;
https://brainly.com/question/2607596
#SPJ1
Heather has a rectangular poster that is 14 centimeters long and 10 centimeters wide. What is the area of the poster in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
John is making his pasta dish. his mom eats 1/12 of pasta and his brother eats 1/6 of pasta. How much of pasta is left over?
Answer:
1/4 of the pot is left.
Step-by-step explanation:
Let x be the total amount of pasta in the pot.
Then the amount of pasta her mother got= 1x/12
The amount of pasta her brother got= 1x/6
The total amount of pasta he serve= 1x/12 + 1x/6
First, convert them into like fractions, then
The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4
Hence, 1/4 of the pot is left over.
Step-by-step explanation:
Mom: 1/12
Brother: 1/6
1/6 × 2/2 = 2/12
2/12 + 1/12 = 3/12
12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left
you are opening an ice cream shop. The new equipment and ice cream for the shop will cost $6,000. The supplier requires a down payment of 25% of the total cost at the time of purchase. What is the balance you owe after making the down payment?
Answer:
$4500
Step-by-step explanation:
Find out 25% of $6000. 25/100 × 6000 = 1500
6000 - 1500 = 4500