The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
Read more about simultaneous equations here:
https://brainly.com/question/148035
#SPJ1
A glass fish tank in the shape of a rectangular prism has a bace that measures 22 inches by 12 inches. Find the surface area if the height = 15 inches
Answer:
Surface Area = 2(22 x 15) + 2(12 x 15) + 2(22 x 12)
Surface Area = 660 + 360 + 528
Surface Area = 1,548 inches²
Step-by-step explanation:
Easy Points !!✅
Casey’s starting balance was $922.36. He had $256.71 in deposits and $1,317.24 in debits. What is his ending balance ?
Since starting balance is $922.36 and she deposits $256.71 and then debits $1317.24. Ending Balance will be 922.36+256.71-1317.24=$138.17 in debt.
Deposits? What do you mean?You make a deposit when you add money to your bank account. To build savings and earn interest, you should put money in a bank. For money you can withdraw at any time, a demand deposit is made. A time deposit is an investment for the long term. When you take out a loan, you might also pay a deposit as collateral.
Debit and credit mean what?In double-entry bookkeeping, debits and credits are entries made in account ledgers to record value changes brought on by business transactions. A credit entry represents a value transfer from the account, whereas a debit entry represents a transfer of value to the account.
To know more about interest visit:-
brainly.com/question/28792777
#SPJ1
A tudent council ell 48 badge for $432. Which equation repreent the relationhip of x badge to y dollar
The equation that represents the relationship of x number of badges to y dollars is y = 9x.
What is an equation?
A mathematical statement called an equation displays the equality of two mathematical expressions. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the components that make up an equation.
An equation is said to be linear if the maximum power of the variable is consistently 1.
Let the number of badges be x and the cost of x number of badges be y.
From the question, we know that for 48 badges, the cost is $432.
So the cost of one badge = 432/48 = $9
Now the cost of x number of badges = $(9x)
We mentioned in the beginning that the cost of x number of badges is y
Therefore the equation that represent the relationship of x badge to y dollars is,
y = 9x
To learn more about equations, follow the link below.
https://brainly.com/question/17145398
#SPJ4
A drum of oil has a height of 4 feet and a radius of 1.2 feet. The oil cost $22 per cubic feet. What is the cost to fill the drum of oil
The cost of oil to fill the drum with height of 4 feet and a radius of 1.2 feet will be $397.90.
What is cubic feet?An understanding of the different dimensions is necessary to truly understand cubic feet, how big a cubic foot is, and how to measure cubic feet. There are three known dimensions which include a foot measurement. The dimensions expand to include additional measurements with each new dimension.
The cubic foot is an imperial and US customary unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length. Its volume is 28.3168 L. At 60 °F, a cubic foot of water weighs 62.37 pounds. A cubic foot (abbreviated as cu ft. or cubic ft.) is an imperial unit of measurement for the volume of a space or three-dimensional object.
Given: A drum of oil has a height of 4 feet and a radius of 1.2 feet. Oil cost has been given as $22 per cubic feet.
We have to calculate the cost to fill the drum with oil.
Since formula to get the volume of the drum is V = πr²h
V = 3.14×(1.2)²×4 = 18.09 feet³
Now the cost of oil to fill the drum will be
Cost = Volume × cost = 18.09×22 = $397.90
To learn more about cubic foot refer to:
brainly.com/question/22260371
#SPJ4
Witch ones do I select
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
To know more about proportionality visit:
brainly.com/question/8598338
#SPJ1
Match the solution to its expression.
Answer:
1/3 + 1/3 = (1+1)/3 = 2/3
1) 2/3
5/7 - 2/7 = (5-2)/7 = 3/7
2) 3/7
so all you have to do is add or sub the fractions together.
1/3 + 1/3 = 2/3
5/7 - 2/7 = 3/7
for the first box is 2/3
Second box is 3/7
GOODLUCK
how do i solve this?
Answer:
Degree: 4
Number of terms: 4
Leading Coefficient: 4
Constant: -20
Step-by-step explanation:
1) Expand (x+3)(x-4) into x^2 - x - 12
2) Combine like terms; equation becomes 4x^4 + x^2 + 4x - 20
3) Degree is looking for the highest exponent; in this case, it's 4
4) Number of terms is looking for how many terms there are in this equation; there are 4 terms
5) Leading Coefficient is looking for the coefficient of the term with the highest exponent, so the answer is 4
6) Constant is looking for the term without a variable
Hope this helps!
The angles of a triangle measure 88°, 53°, and 39º. Which of the following could NOT be the measure of an exterior angle of the triangle?
Answer:35° being the smallest interior angle of the triangle, the exterior angle attached to it is the largest. It measures 180° - 35° = 145°.p.
Step-by-step explanation:
Help me
Please help me with both issues
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is an arithmetic operation in which a number (known as a multiplicand) is multiplied by another number (known as a multiplier) to produce a product.
In this problem, we will need to use of some mathematical operators to solve the problem
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
Learn more on multiplication here;
https://brainly.com/question/4721701
#SPJ1
What are interval examples?
An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.
Interval
An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.
Interval NotationInterval notation is a simplified way of describing a particular interval. Let’s see how it’s done.
Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.
Step 2: We use a round or square bracket on each side of the two numbers. We use:
A square bracket [ ], if we want to include the endpoints
A round bracket ( ), if we don’t want to include the endpoints
So in this example, we use:
[6, 20] if the interval includes 6 and 20(6, 20) if the interval excludes 6 and 20 (6, 20] if the interval excludes 6 but includes 20[6, 20) if the interval includes 6 but excludes 20 Types of IntervalsSo, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals
These are:
Open intervalClosed intervalHalf-open and half-closed intervalOpen IntervalThis type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.
Closed IntervalThis type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.
Half-Open and Half-Closed IntervalThis type of interval includes only one of the endpoints.
To learn more about interval:
https://brainly.com/question/10850002
#SPJ4
In case you don't see the picture:
What is the decimal form of form of -1 1/12
A. -1.083 (bar notation on 3) THE CORRECT ONE.
B -1-083 (barnotation on 83)
C -1-083 (bar notation on 083
D -1-083
Greg chose C as the correct answer. How might he have gotten that answer. !!!!!!!!!!!!!!!!
HELP ME PLEASEEEE! WHY DID GREG CHOOSE THATT.
The decimal form of the -1 1/12 is obtained by finding the sum of -1 and -1/12 (-1/12 = -0.08[tex]\overline{3}[/tex] a recurring decimal), which is the option A
A. -1.08[tex]\overline{3}[/tex]
What is a recurring decimal?A recurring decimal is a decimal that has a digit or a group of digits that is continuously repeated in the decimal.
The specified expression, -1 1/12, can be presented as follows;
[tex]-1\dfrac{1}{12}[/tex]
The value of the specified expression in decimal form is therefore;
[tex]-1\dfrac{1}{12}= -1+\left( - \dfrac{1}{12}\right)[/tex]
[tex]- \dfrac{1}{12} = -0.08\overline{3}[/tex]
The fraction -1/12, therefore consist of a recurring decimal, with the 3 in the thousandth place after the 8 being the part that repeats.
Therefore, the value of the expression, [tex]-1+\left( - \dfrac{1}{12}\right)[/tex] is -1 + (-0.08[tex]\overline{3}[/tex])
-1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]
The specified expression is therefore;
[tex]-1\dfrac{1}{12}[/tex] = -1 + (-0.08[tex]\overline{3}[/tex]) = -1.08[tex]\overline{3}[/tex]
The correct option is option A
A. -1.08[tex]\overline{3}[/tex]The option C. -1.[tex]\overline{083}[/tex] is incorrect, the correct option is option A
Learn more about recurring decimals here: https://brainly.com/question/20898146
#SPJ1
Is 2x 3y linear equation?
Therefore .as a result the supplied linear equation problem's solution is shown to be a linear equation with two variables.
Define a linear equation.Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is classified as linear. The equation is written as Y=mx+b, where m denotes the slope and b
Here,
Assumed: 2x + 3Y = 0.
As a result, the following equation can be used to determine whether it is linear in two variables.
As x is the sole variable, as can be seen.
Therefore, it is a two-variable linear equation.
As a result, the supplied linear equation problem's solution is shown to be a linear equation with two variables.
To know more about linear equation visit:
brainly.com/question/11897796
#SPJ1
What is the factor of 3x² 12xy?
The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. Finally, we divide the y terms, y divided by y is 1. Therefore, the factor of 3x² 12xy is 3x².
The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. This means that the x part of the factor is 3x. Next, we divide the y terms, y divided by y is 1. This means that the y part of the factor is y. When we combine the two parts, 3x and y, we get the factor of 3x². Therefore, the factor of 3x² 12xy is 3x². This means that 3x² is a factor of 12xy, which can be seen by multiplying 3x² by 4y, which results in 12xy. This shows that 3x² is a factor of 12xy.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
PLEASE HELP ASAP, I WILL MARK YOU BRAINBLIEST <3 TYSM
The answers to each part is mentioned below.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is a straight line problem as shown in the question.
( 1 ) -(a) -
Now, 12 oz of honey will cost $5.4. So, we can write that -
1 ounce of honey will cost - (5.4/12)
Cost of 1 oz honey will be - $(0.45)
(b) -
Now, 12 oz of honey will cost $5.4. So, we can write that -
For $1, you can buy - (12/5.4) oz of honey.
Amount of honey bought in 1 dollar - 2.22 ounces
(c) -
We can write the equation as -
c = 0.45h
(d) -
The graph for this function is attached with the answer.
Therefore, the answers to each part is mentioned above.
To solve more questions on straight lines, visit the link below -
brainly.com/question/28951560
#SPJ1
What must be added to the polynomial 2x³ 3x² 8x so that it leaves a remainder 10 when divided by 2x 1?
To find the remainder 10 when dividing 2x³ 3x² 8x by 2x 1, the polynomial must be augmented with -12.
What is polynomial?A polynomial is an expression that consists of variables, exponents, and coefficients. It is a mathematical function composed of two or more terms, each of which is a number or a variable multiplied by an exponent. It can be used to represent a variety of relationships in mathematics, including equations, linear functions, quadratic functions, and more.
Therefore, the polynomial that will leave a remainder 10 when divided by 2x 1 is 2x³ 3x² 8x -12.
This is because if we divide the polynomial by 2x 1, the remainder will be the last term of the resulting polynomial, which is -12.
To know more about polynomial click-
https://brainly.com/question/15702527
#SPJ4
Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
On solving the provided question, we can say that - here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex] = [tex]4+3 = 7[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here-
from graph, x= 2
y = 1
[tex]x^2+ 3y^2 \\[/tex]
[tex]4+3 = 7[/tex]
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
A child pushes a toy car with a force of 5. 25 N a distance of 6. 5 m. The car rolls for a total distance of 32 m. How much work is done on the toy car? Need formula and the way the work is done, ASAP
The work done on the toy car is 164.4 J.
The formula for work is:
Work = force * distance
In this case, given that:
Force = 5.2 N
Distance = 32 m
So, the work is:
Work = force * distance
Work = 5.2 * 32
Work = 166.4 J
Hence, the work done is 164.4 J.
What is work vs force?Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.
Learn more work and force at: https://brainly.com/question/28039239
#SPJ4
Select the correct answer. Solve the quadratic equation by factoring.
9x -16 = 0
Answer:
x = 16/9
Step-by-step explanation:
9x -16 = 0
9x = 16
x = 16/9
Let's check
9(16/9) -16 = 0
144/9 - 16 = 0
16 - 16 = 0
0 = 0
So, x = 16/9 is correct!
Answer:
Step-by-step explanation:
9x = 16
x = 16/9
The four-digit numeral $3AA1$ is divisible by $9$. What digit does $A$ represent?
When a four-digit number is divisible by nine and is written as 3AA1, the digit A stands for 7.
Properties of 9-divisible numbersA number is itself divisible by nine if the total of its digits is also nine digits.
Multiples in mathematics are the outcomes of multiplying an integer by a certain number. a multiple of 9 is a number that divides by nine.
By utilizing the aforementioned attribute, we can
3 + A +A +1 = 9, OR 18, OR 27
4 + 2A = 9, OR 18, OR 27
using 18
2A = 18 - 4
2A = 14
A = 7
therefore we can say that the number is 3771
Learn more about division at:
brainly.com/question/25289437
#SPJ1
What is the difference between the high and low temp in the thermometer?
*
Captionless Image
The difference between the two given temperature values is 24 °F
How are Kelvin, Celsius, and Fahrenheit related?We have got an equation that can relate these three units of measurement of temperature, as given below:
c/5 = (F - 32)/9= (K - 273)/5
where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.
The given parameter the lowest temperature = -3 °F
the highest temperature = 21 °F
To determine the difference between the two given temperature values.
The range or difference between the two given temperature values is calculated as follows;
Range = highest - lowest
Range = 21 °F -(-3 °F)
Range = 24 °F
Thus, the difference between the two given temperature values will be 24 °F
Learn more about temperature scale here:
https://brainly.com/question/2919967
#SPJ1
Solve for x 3 /11 = x /3 Give your answer as a fraction in its simplest form.
Answer: x 33/5
Step-by-step explanation:
Answer: 9/11
Step-by-step explanation:
Step 1: Cross-multiply.
3/11 = x/3
(3)*(3) = x*(11)
9 = 11x
Step 2: Flip the equation.
11x = 9
Step 3: Divide both sides by 11.
11x/11 = 9/11
x = 9/11
The lateral urface area of cone A i equal to the lateral urface area of cylinder b
A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.
We know that the formula for the lateral surface area of cone:
Area = π × radius × slant height
and the formula for the lateral surface area of cylinder:
Area = 2π × (radius) × (height)
Here we have been given a cone A with radius r and slant height 2h.
Using the above formula, the lateral surface area of cone A would be:
A1 = π × r × 2h
A1 = 2π × r × h ..................(1)
Also, we have been given a cylinder B with radius r and height h.
Using the above formula, the lateral surface area of cylinder A would be:
A2 = 2π × r × h ..............(2)
From (1) and (2) we can observe that,
A1 = A2
Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.
Learn more about the lateral surface area here:
https://brainly.com/question/28122860
#SPJ4
Luciana is adding water to a pool at a constant rate. Before she added any water the pool had 12. 000 gallons of water Luciana is adding 9 gallons of water each minuto Which equation roprosents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes? A m = Dw+ 12,000 B W = m + 12. 000 С W = 12,000m + 9 D W = 12. 000 - 9m
The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
What is a linear equation?
A linear equation is an equation that can be written in the form of
y = mx + b
Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.
Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.
Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
To learn more about the linear equation, visit:
https://brainly.com/question/12788590
#SPJ4
The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
Option (D) is correct.
What is a linear equation?
A linear equation is an equation that can be written in the form of
y = mx + b
Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.
Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.
Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.
To learn more about the linear equation, visit:
brainly.com/question/12788590
#SPJ4
What is the size of the augmented matrix for the linear system?
The augmented matrix, however, is a two-by-four matrix because it also contains the constants.
What do you meant by augmented matrix for the linear system?The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.
In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.
For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.
To learn more about augmented matrix for the linear system visit:
brainly.com/question/13512085
#SPJ4
Answer:
What is the size of the augmented matrix for the linear system?
B) 2x3
Identify the values for the elements in the augmented matrix:
a11 = 3
a12 = 7
a13 = 20
a21 = 1
a22 = -4
a23 = 9
Step-by-step explanation:
Marcy made a lane change when. A car was in her side mirror blind spot. She missed the car but immediately crashed into the car ahead of her, causing damage. After Marcy filed the insurance claim, she was notified that her premium for full insurance would increase by 35% what is Marcy new yearly premium if her premium before the accident was $2,140
Peter insurance company is raising his rates after he files a claim . He pays $75 per month and his insurance is set to increase by 30% . What will Peters new monthly premium be ?
Kevin purchases a truck for $35,000 with a down payment of $4,300 . The monthly payment factor is 0.01933. What is the monthly payment for the truck ?
On solving the provided question, we can say that By percentage, the amount that will be covered in the insurance = $749
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a the fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
By percentage.,
35% 0f 2140 =
35/100 X 2140 = 0.35*2140 = $749
the amount that will be covered in the insurance = $749
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
Tyler is flying a kite on 100 feet spring how high is it above the ground if the horizontal distance between Tyler and the kite is 600 feet
If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.
Pythagorean theoremPythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.
The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.
Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
We apply the Pythagorean Theorem to determine the kite's height, h
the problem can solve if the kite is 60feet
[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]
h =80 ft (we take the positive solution since the height can not be negative number)
The kite is 80 ft above the ground.
To learn more about Pythagoras Theorem visit:
https://brainly.com/question/343682
#SPJ1
Three vertices of parallelogram ABCD are A(-3,1), B(5, 7) and C(6, 2). Find the coordinates of vertex D
The coordinates of vertex D in the parallelogram ABCD are (7,-3).
What is the relation of vertex in a parallelogram?In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.
The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]
So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]
The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]
So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]
To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.
The coordinates of vertex C are (6, 2)
So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]
Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).
To know more about parallelogram visit: https://brainly.com/question/1563728
#SPJ4
In 2010, the population of a city was 191,000. From 2010 to 2015, the population grew by 3.9%. From 2015 to 2020, it fell by 3.3%. To the nearest 100 people, what was the population in 2020?
Answer:
The population by 2020 is 191,900
Step-by-step explanation:
Given that;
population 2010 (population in 2010): 191000
the population grew from 2010 to 2015: by 3.9%
so, population by 2015 = [tex]191000(1 + \frac{3.9}{100})[/tex]
= [tex]191000(1 + 0.039)[/tex]
= [tex]191000(1.039)[/tex]
= [tex]198449[/tex]
the population drop from 2015 to 2020: 3.3%
so, population by 2015 = [tex]198449(1 - \frac{3.3}{100})[/tex]
= [tex]198449(1 - 0.033)[/tex]
= [tex]198449(0.967)[/tex]
= [tex]191,900.183[/tex]
A ball is thrown upward and its height after seconds can be described by formula 5.6. Find the maximum height the ball will reach.
The maximum height reached by the ball is 20 units at 1.2 unit time.
What is Maxima and Minima ?The extrema of a function are the maxima and minima. The highest and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, throughout its full range.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
The equation is given as
h = [tex]-10t\x^{2} + 24t + 5.6[/tex]
Differentiating both side with respect to t we get
[tex]\frac{dh}{dt} = -20t + 24[/tex]
To reach maximum value [tex]\frac{dh}{dt} = 0[/tex]
⇒20t = 24
⇒ t = 1.2
So the maximum height reached = [tex]-10 *(1.2)\x^{2} + 24*1.2 + 5.6 = 20[/tex]
To learn more about Maxima and minima refer to :
https://brainly.com/question/14384831
#SPJ4
How can you differentiate best time worst time and average time of an algorithm?
You can differentiate best time, worst time and average time of an algorithm like this:
Best time = fastest completion time with optimal inputs.
Worst time = slowest completion time, with pessimistic inputs.
Average time = arithmetic mean
What is Average case?The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.
There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.
Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.
Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.
What is average case complexity
https://brainly.com/question/30004574
#SPJ4