Answer:
Step-by-step explanation:
Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.
Answer:
112.5 units²
Step-by-step explanation:
Area of the shelf = ½*base*height.
The base is the distance between Z(0, 5) and Y(15, 5)
The height is the distance between X(15, 20) and Y(15, 5).
Therefore area of the shelf = ½*ZY*XY
Use the distance formula to find ZY and XY.
Distance between Z(0, 5) and Y(15, 5):
Let,
Distance between X(15, 20) and Y(15, 5):
Let,
Area of shelf = ½*15*15 = ½*225 = 112.5 units²
a farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to seperate the regions) are made up of fencing, as shown below. If the farmer has 246 feet of fencing, what are the dimensions of the region which enclose the maximal area?
The dimensions of the region which enclose the maximal area is 61.5 feet by 41 feet .
The area of a rectangle is the area occupied by the rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle which is given by [tex]AREA=L \times w[/tex] ....(1)Let the length of the rectangular plot be "L" and width be "w"
It is given that farmer wants to do fencing of 246 feet which means all the boundary will be covered which is given by
[tex]L+L+w+w+w=246\\2L+3w=246\\2L=246-3w\\\\L=\frac{246}{2} -\frac{3w}{2} \\\\L=123-\frac{3w}{2}[/tex] ...(2)
Putting the value of "L" in equation (1) , we get
[tex]A=({123-\frac{3w}{2}}) \times w\\\\A=123w-\frac{3w^2}{2}[/tex] ....(3)
Now , we are asked to find the maximum area then , put
[tex]\frac{dA}{dw}=0[/tex]
[tex]123-\frac{6w}{2} =0\\123-3w=0\\123=3w\\w=41[/tex]
Putting w = 41 in equation (3) , we will get the maximum area
[tex]A=123(41)-\frac{3(41)^2}{2} \\\\A=5043-2521.5\\\\A=2521.5[/tex]
Putting w = 41 in equation (2) , we will get the length
[tex]L=123-\frac{3(41)}{2} \\L=123-61.5\\L=61.5feet[/tex]
Hence , the dimensions will be 61.5 feet by 41 feet .
Learn more about maximum area here:
https://brainly.com/question/17004329
#SPJ9
If the number of different activities is represented by four consecutive odd integers what is the algebraic expression that represents the total number of activities they had to choose from in one day
The four consecutive odd integers are: 51 , 53 , 55 and 57.
An algebraic expression (or) a variable expression is a combination of terms by the operations such as,
addition, subtraction, multiplication, division, etc.
For example, let us have a look at the expression 5x + 7. Thus, we can say that 5x + 7 is an example of an algebraic expression.
Types of algebraic expressions may further be distinguished in the following five categories. monomial, polynomial, binomial, .trinomial. multinomial.
the expression: 3/4x + y/2 (4x + 7) By using the distributive property, the given expression can be written as,
3/4x + y/2 (4x) + y/2 (7).
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.The sum of 4 consecutive odd integers is 336, how do you find the largest integer? because odd consecutive integers differ from each other by 4. Value of x can be determined by adding up assumed terms and equating it with 336.
to know more about integers;
visit; brainly.com/question/15276410
#SPJ9
Solve. Show your work. Draw bar models to help you.
Brooke and Samuel had the same number of marbles. Brooke gave away
20 marbles and Samuel gave away 44 marbles. Brooke then had 3 times
as many marbles as Samuel. How many marbles did Brooke and Samuel each have at first?
Brooke and Samuel each had 56 marbles as represented by the bar model.
In mathematics, a bar model is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes.
To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilized.Children can determine which operations to perform or how to visualize word problems by using bar models.The concrete pictorial abstract (CPA) learning approach's pictorial stage, which deals with math mastery, centers on the bar model. However, bar models just make it simpler for students to determine which calculation needs to be made in order to answer the problem. They do not perform the calculations for the student.Let us consider that each had x marbles. Now Brooke gave away 20 marbles and Samuel gave away 44 marbles :
∴ x - 20 = 3 (x - 44)
or, x -20 = 3x - 132
or, -2x = -112
or, x = 66
Brooke and Samuel each have 56 marbles as calculated from the bar models.
To learn more about bar models visit:
https://brainly.com/question/2271799
#SPJ1
What scales are equal to 3 cm to 15 m
The scale is equal to 1:500.
The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale."
if 1 cm on the map corresponds to 100 cm on actual ground then the scale of the map is given by the ration 1:100.
Scale of map is widely used in cartography and constructions.
The given condition states that 3 cm to 15 m.
We know that 1 cm =100 meters
Hence 15 meters = 15 × 100 cm =1500 cm
Therefore length on map = 1 cm
Length on ground = 1500 cm
Scale = distance on map : distance on ground
or, Scale = 3 : 1500
or, Scale = 1: 500.
Therefore the scale is 1: 500.
To learn more about scale visit :
https://brainly.com/question/13279076
#SPJ9
Complete the following descriptions with adjectives of nationality.In a normal distribution, x = 9 and z = −1.21. This tells you that x = 9 is _______ standard deviations to the left the mean
In a normal distribution, x = 9 and z = −1.21. This tells you that x = 9 is 1.21 standard deviations to the left the mean.
What is the z-score?The z-score is a mathematical measure that allows us to see how much above or below the mean a value in a distribution is in terms of standard deviation.
When the value is above or right of the mean, the z-score would be positive and when the z-score is left or below the mean, the z-score would be negative.
In this instance, x = 9 has a z-score of -1.21 which means that it is 1.21 standard deviations to the left of the mean.
Find out more on the z-score at https://brainly.com/question/25638875
#SPJ1
if you help me you will have good luck karma exists
The volume of the given three-dimensional figures are:
64ft³72ft³30ft³80ft³What is a cuboid?A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid means "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces.So, the volume of the cube: a³
(1) a³ = 4³ = 64ft³
The volume of the cuboid: whl
(2) whl = 4 × 6 × 3 = 72ft³
(3) whl = 2 × 3 × 5 = 30ft³
(4) whl = 2 × 5 × 8 = 80ft³
Therefore, the volume of the given three-dimensional figures are:
64ft³72ft³30ft³80ft³Know more about cuboid here:
https://brainly.com/question/46030
#SPJ9
I need help with this question please
20 people likes movies, such that 12 of these also like music, then the probability is just the quotient between:
Q = 12/20 = 0.6
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
How to find the probability P(movies|music)?Notice that there are 5 + 7 common elements between movies and music, and a total of 20 people likes movies, such that 5 + 7 = 12 of these also like music, then the probability is just the quotient between the numbers of total people that likes movies which we know is 20, and the people that likes movies and also music.
So the quotient between 12 and 20, that will gave us the probability we want to find.
The probability that a person likes music given that he/she lies movies is 0.6 or 60%
If you want to learn more about probability:
https://brainly.com/question/24756209
#SPJ1
Write the expression as a number in scientific notation.
quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by the quantity 4 times 10 cubed
The expression written in the simplest scientific notation is 6. 4 × 10^4
What is scientific notation?
Scientific notation can be defined as a mathematical method of presenting numbers or figures too large or small in simpler forms.
It is also termed index form or standard form
From the information given, we have that;
8 times 10 squared = 8 × 10²3.2 times 10 to the fifth power = 3. 2 × 10^54 times 10 cubed = 4 × 10³Now, substitute the values
8 × 10² × 3. 2 × 10^5 / 4 × 10³
Using the rule of exponent, we have;
25. 6 × 10^2 + 5/ 4 × 10³
25. 6 × 10^7/ 4 × 10³
Divide the numbers, we have
6. 4
Take the inverse power of the denominator
6. 4 × 10^ 7 - 3
6. 4 × 10^4
Thus, the expression written in the simplest scientific notation is 6. 4 × 10^4
Learn more about scientific notation here:
https://brainly.com/question/5756316
#SPJ1
Find the ratio created when BA is partitioned by C.
Write your answer as a ratio with a colon and no spaces. Example 10:3
The ratio of the point C on the line segment is 3 : 5
How to determine the ratio of the point C on the line segment?The line segment that completes the question is added as an attachment
On the attached line segment, we have the following points assuming that the point A is at A = 0
So, we have
A = 0
C = 3
B = 8
The above means that
AB : CB = C - A : B - C
So, we have
AB : CB = 3 - 0 : 8 - 3
Evaluate the difference
AB : CB = 3 : 5
Hence, the ratio of the point C on the line segment is 3 : 5
Read more about ratio at
https://brainly.com/question/17374569
#SPJ1
WHO EVER GETS THIS QUESTION RIGHT WILL GET 30 POINTS!
Scott was 63 ⅜ inches tall when he started seventh grade and 65 ¼ inches tall when he started eighth grade. How many inches did he grow during this time?
Please show work.
Answer: 1 inch 7/8
Step-by-step explanation: 65 1/4 inches is the same and 65 2/8 inches. its now just as simple as finding the difference.
<-----------take 8/8 or 1 away from the 65 and add it to the 2/8 65 2/8
- 63 3/8
----------------
64 10/8 <------now the equation looks like this
- 63 3/8 <----10-3 is 7 ---- 64 - 63 is 1
----------------
1 inch and 7/8
.................................................................................................................................................
Answer:
.........................................................
Step-by-step explanation:
.................................................
HELP ME PLS If f(x) = 4x+1, find
f(a+h)-f(a)/h
Answer:
it's called the difference quotient of a function
Step-by-step explanation:
f(x+h)-f(x)/h is the slope of the secant line of a function
What is the slope of the line?
Answer:
Slope = (4/5)
Step-by-step explanation:
Point 1: (-2, 0); Point 2: (3, 4)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 4 - 0 4 4
m = ----------- = ------------ = ------------ = ------
x₂ - x₁ 3 - (-2) 3 + 2 5
y - y₁ = m(x - x₁)
y - 0 = (4/5) (x - (-2)
y - 0 = (4/5) (x + 2)
y - 0 = (4/5)x + (8/5)
y = (4/5)x + (8/5)
I hope this helps!
HELP ASP I NEED TO KNOW WHATS 1+1 IS OR I MIGHT GET A B AHHHHHHH WHATEVER IS RIGHT GETS10 POINTS!!!!!! HELPPPPPPPPPP
Answer:
2
Step-by-step explanation:
2m/5=2 trial error solution please help
Answer:
(2m+5)
2
=
Use binomial theorem (a+b)
2
=a
2
+2ab+b
2
to expand (2m+5)
2
.
4m
2
+20m+25
Answer - 4m + 2 + 20m + 25
Step-by-step explanation:
help
The sum of the first and third of three consecutive even integers is 156. Find the three even integers.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $70. A season ski pass cost$450. The skier would have to rent skis with either pass $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily basis
The skier have to go for 7 days skiing in order to make the season pass less expensive than the daily basis.
Cost of daily pass = $70
Cost of season ski pass = $450
Let the cost of skiing per day = 'x'
Now we will equate the season pass plus ski rentals to daily skiing plus ski rentals :
450 + 30x = 70x + 30x
We have 30x on both sides, so those can cancel out easily :
Then we get,
450 = 70x
Dividing both sides by 70 :
x = 6.42
We can't pay for a partial day, so the skier will have to ski for at least 7 days to make the season pass cheaper than getting daily passes.
To learn more about Ski Pass visit :
https://brainly.com/question/713716
#SPJ9
15 POINTS HELP I WILL GIVE BRAINLIEST!!!!Which linear functions represent a slope of 4? Check all that apply. A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries negative 11, 1, 13, 25. On a coordinate plane, a line goes through points (0, 3) and (5, 4). A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 1, 3, 7. Column 2 is labeled y with entries negative 32, 24, 16, 8. On a coordinate plane, a line goes through points (2, 0) and (3, 4).
Answer:
The function which has a slope of 4 will be that function or line which is going through the points (2, 0) and (3, 4).
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
In the given question is saying for the second case the line goes through points (2, 0) and (3, 4) so the slope will be
(4 - 0)/(3 - 2) = 4 hence, it will be the correct answer because it is the only line that has a slope of 4.
Answer:
On a coordinate plane, a line goes through points (2, 0) and (3, 4).
Step-by-step explanation:
-1/2 + 1/3a = 1/8 find a please
3. Estimate the value of -√90 to the nearest integer. (1 point)
A. 3
B. -5
C. 7
D. -9
4. Wei-Min makes a square quilt that has an area of 100 square inches. It has 25 square blocks,
each the same size. What is the length of each side of a block?
A. 2 inches
B. 4 inches
C. 6 inches
D. 10 inches
(1 point)
After using 25 square block, a quilt has been prepared by Wei-Min that has an area of 100 square inches. The length of each side of a block is 2 inches by calculating using concept of mensuration.
As per the question statement, Wei-Min makes a square quilt that has an area of 100 square inches and has got 25 square blocks, each the same size. We are supposed to find the length of each side of a block.
Using concept of mensuration,
Area of square quilt = 100 square inches
Number of block used = 25 square blocks
Therefore, area of each block = 100/25 = 4 square inches
As the block is a square, so each side will be equal in length.
Let's assume each side of square be "x" inches
Therefore x^2 = 4
or x = √4
or x = 2 inches
Mensuration: In the field of mathematics known as measurement, length, volume, shape, surface area, and other properties are measured for 2D and 3D objects. In other terms, it is the method of measuring based on mathematical formulas and algebraic equations.To learn more about Mensuration, click on the link given below:
https://brainly.com/question/14312097
#SPJ1
Help me out please!!
Answer:
No
Step-by-step explanation:
substitute x = - 4 and y = - 17 into the left side and compare the result obtained to the right side.
2y - 3x
= 2(- 17) - 3(- 4) = - 34 + 12 = - 22 < 12
thus (- 4, - 17 ) is not a solution of the inequality
Ninety students auditioned for the school play. One-third of thise who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal
The fraction of those who were cast got major roles is 1 / 5.
What is a fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.
Given that ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles.
The fraction will be calculated as below:-
Fraction of the students cast = 90 / 3 = 30
Fraction of the students selected for major roles = 6 / 30 = 1 / 5
Therefore, the fraction of those who were cast got major roles is 1 / 5.
To know more about a fraction follow
https://brainly.com/question/17220365
#SPJ1
Everyday I earn 5$. I am saving up for a total of 400. How many Days will it take for me reach my goal. Of 400$?
Answer:
80 days
Step-by-step explanation:
Total wanted ($400) divided by how much per day ($5)= Total amount of days
$400/$5= 80 days
Answer:
80 days
Step-by-step explanation:
Total wanted ($400) divided by how much per day ($5)= Total amount of days
$400/$5= 80 days
Which equation illustrates the associative property of addition
A. 5 + (6 + 2) = (6 + 2) + 5
B. 5 + (6 + 2) = (5 + 6) + 2
C. 5 + (6 + 2) = 5 + (2 + 6)
D. 5 + (6 + 2) = 5 + (6 + 2)
The required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the equation that represents the associative property of addition?The expression is given as
-15 + 0
The associative property of addition states that
(x + y) + z = x + (y + z)
This means that
(x + y) + z = x + (y + z) is a representation of the associative property of addition
From the list of given options, we have
5 + (6 + 2) = (5 + 6) + 2
The above is a perfect illustration of (x + y) + z = x + (y + z)
So, 5 + (6 + 2) = (5 + 6) + 2 is a representation of the associative property of addition
Hence, the required equation that is a representation of the associative property of addition is 5 + (6 + 2) = (5 + 6) + 2
Read more about expressions at
https://brainly.com/question/2364391
#SPJ1
Answer:
5 + (6 + 2) = (5 + 6) + 2
Step-by-step explanation:
The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
The rate of change of the linear relationship that between the playing time and the file size is: C. 120.
What is a Linear Function?A linear function can be described as a function whose graph is represented as a straight line graph on a coordinate plane with all its points plotted on the graph.
A linear function is modelled by the equation which is expressed in slope-intercept form as .f(x) = mx + b.
The "m" in the equation represents the rate of change of the function, which can also be called the slope of the graph while "b" represents the y-intercept where the line intercepts or crosses the y-axis.
What is the Rate of Change of a Function?The rate of change of a linear function = the slope = change in y / change in x.
Use two pairs of values from the table to find the rate of change, say, (2, 240) and (5, 600):
Rate of change (m) = (600 - 240) / (5 - 2)
Rate of change (m) = (360) / (3)
Rate of change (m) = 120
Therefore, the rate of change of the linear relationship that between the playing time and the file size is: C. 120.
Learn more about the rate of change on:
https://brainly.com/question/1509153
#SPJ1
Answer:
120
Step-by-step explanation: when i took the test it was right
karen tiene 60100 soles ,compro 23 cocinas,28 televisores y 15 refrigeradoras.cuantos nuevos soles le quedan a un.
The amount that will be left based on the information will be 60100 - 23s - 28t - 14r.
How to calculate the value?Total number of soles = 60100
From the information, she bought 23 stoves, 28 television, and 14 refrigerators.
Therefore, the amount that will be left based on the information will be:
= 60100 - 23s - 28t - 14r
where s = stove
t = television
r = refrigerator
Therefore, the amount that will be left based on the information will be 60100 - 23s - 28t - 14r.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
Ganesh spends 60% of his income every month and saves Rs 11120 in a month. Find his monthly income and expenditure.
Monthly income and expenditure of Ganesh will be-16680
Let Ganesh's monthly income be x
The problem can be solved using linear equation
The amount of 60% of his salary is spent which can be written as 60% of x or 0.6x
The amount of money saved by Ganesh = total salary - amount spent
= x - 0.6x
= 0.4x
The amount of savings made by Ganesh as per the question = 11120
Lets equate both the equation
0.4x = 11120
x = (11120 × 100)/ 40
x = 27800
Hence, Ganesh's monthly salary comes out to be 27800
Ganesh's monthly expenditure = 0.6 x= 0.6 × 27800 =16680
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line
To know more about linear equation - https://brainly.com/question/13738061
#SPJ9
If Curtis needs 18 gallons of green paint in all, how many gallons of yellow paint will he need to keep the ratio of colors the Curtis is mixing paint to make a certain shade of green to paint props for the school play. The table shows how much of each color he mixes to get the shade he needs?
Answer:
Step-by-step explanation:
Answer:
the table shows how much of each
Step-by-step explanation:
Solve 2x +2y=4
2x+4y=66
The solution of the system of equation are as follows:
x = -29y = 31How to solve system of equation?The system of equation can be solved as follows;
2x + 2y = 4
2x + 4y = 66
subtract equation(i) from equation(ii)
4y - 2y = 66 - 4
2y = 62
divide both sides by 2
y = 62 / 2
y = 31
Therefore, substitute the value of y in equation(i)
2x + 2(31) = 4
2x + 62 = 4
2x = 4 - 62
2x = -58
divide both sides by 2
x = -58 / 2
x = - 29
learn more on system of equation here: https://brainly.com/question/28680208
#SPJ1
Three students at a local community college ran for the position of Treasurer for the Student Government Association. The results of the election are shown below. Sherry Smith 36% Lakeisha Miller 29% Adrian Zargoza 31% If Sherry Smith received 600 votes, how many total votes were cast? Round your answer to the nearest whole number
Using proportions, it is found that 1,667 total votes were cast.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Sherry Smith received 36% of the votes, which is equivalent to 600 votes, hence:
0.36x = 600
x = 600/0.36
x = 1,667.
1,667 total votes were cast.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1