The length of the rectangle is 25 cm and the width is 10 cm.
How to evaluate for the length and width of the original rectangleWe shall represent the length and width of the original rectangle with x and y respectively so that the perimeter is;
2(x + y) = 70 {divide through by 2}
x + y = 35...(1)
length of new rectangle = x - 5
width of new rectangle = y + 5
area of new rectangle:
(x - 5)(y + 5) = xy + 50
xy + 5x - 5y - 25 = xy + 50
xy - xy + 5x - 5y = 50 + 25
5x - 5y = 75 {divide through by 5}
x - y = 15...(2)
add equations (1) and (2) we have;
x + y + x - y = 35 + 15
2x = 50 {divide through by 2}
x = 25
substitute 25 for x in equation (1), we have;
25 + y = 35
y = 35 - 25 {subtract 25 from both sides}
y = 10
Therefore, have the length and width of the original rectangle to be x = 25 cm and y = 10 cm respectively.
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Algebra 1 common assessment unit 2-1 SY23
Answer:
[tex]t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} [/tex]
A 2 column table with 5 rows. The first column, yards of red fabric, x, has the entries 1, 2, 3, 4. The second column, yards of blue fabric, y, has the entries 27, 26, 25, 24.
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.
The answer choices which represent equations which model the total yards of fabric Sophie will buy is; x + y = 28, 28 - x = y and 28 - y = x.
Which equations model the total yards of fabric Sophie will buy?As evident in the attached table, where x represents the yards of red fabric she buys and y represents the yards of blue fabric she buys.
It follows that the following x and y pairs are possible; (1, 27), (2, 26), (3, 25) and (4, 24).
On this note, it can be inferred that in each of the red and blue fabric pairs; x + y = 28.
Consequently, the required equations which model the total yards of of fabric Sophie will buy are; x + y = 28, 28 - x = y and 28 - y = x.
Complete question; The given answer choices are; x+y=28, 28+x=y, x-y=28, 28-x=y and 28-y=x.
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Answer:
x+y=28
28-x=y
28-y=x
What is the opposite of the opposite of point D?
In Number line, -4 is the opposite of the opposite of point D.
What does a math number line mean?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals. A number line can be used to represent every number in a sequence. Both endpoints of this line continue indefinitely.
The terms "number line" and "number grid" both refer to horizontal straight lines with numbers arranged along them at equal intervals. Some will have a defined beginning and end.
Value of D = 4
Opposite of point D = -4
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a box as a volume of 3/4 inches long 1/2 inches wide and 1/4 inches high
A train will travel 300300300 kilometer at a contant rate. 1. Write an equation that repreent the train' rate in kilometer per hour (rrr) baed on how many hour the trip take (ttt)
The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r
Define Speed :This is defined as the ratio of distance to time taken usually in kilometers per hour, miles per hour.
The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
How to write equation
Distance Saul biked = 300 kilometers
Number of hours it takes train travel = t
Speed of train travel (kilometers per hour) = r
Speed = Total distance travelled / Time taken
r = 300 / t
Equation that represents how many hours
Make t the subject of formula
r = 300 / t
cross product
r × t = 300
t = 300/r
Therefore,
The equation that represents how many hours it will take if train travel at a constant rate of r kilometers per hour speed is t = 300/r
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Consider the function f(x) = 10x² - 10x.
a. Determine, without graphing, whether the function has a minimum value or a maximum value.
b. Find the minimum or maximum value and determine where it occurs.
c. Identify the function's domain and its range.
The graph is shown below.
===================================================
Explanation:
Part A)
x² is the same as x^2
The function f(x) = 10x^2-10x is the same as y = 10x^2-10x
Compare this to the template y = ax^2+bx+c to find the following
a = 10b = -10c = 0The value of 'a' is positive, which means the parabola opens upward. Furthermore, it tells us that the graph has a lowest point. There is no highest point since both parts of the parabola go upward forever.
-----------------------------
Part B)
We'll use the values of 'a' and b found earlier to get...
h = -b/(2a)
h = -(-10)/(2*10)
h = 10/20
h = 0.5
The min value therefore occurs when x = 0.5, which is the x coordinate of the vertex. The vertex being (h,k)
To find the value of k, we plug x = 0.5 into the original function.
y = 10x^2-10x
y = 10(0.5)^2-10*0.5
y = -2.5
This is the smallest the output y values can get. Therefore, it is the minimum value.
The vertex is located at (h,k) = (0.5, -2.5)
-----------------------------
Part C)
With any quadratic function, the domain is "set of all real numbers". We don't have to worry about things like...
Division by zero errors.Taking the square root of negative values.And so on.
The range is [tex]\text{y} \ge -2.5[/tex] since we found y = -2.5 to be the smallest y value possible. See part B above. So either y = -2.5 or y > -2.5
Check out the graph below. I used GeoGebra to make it, but you could use Desmos or other similar graphing tools if you prefer.
How do you calculate 2 + 3 x 7?
a. 2+3 x 7 = 2+21= 23
b. 2+7x7 = 2 + 21 = 35
C. 2+7x3 = 2 + 21 = 23
Answer:
A
Step-by-step explanation:
using BODMAS
3×7=21+2=23
Subtract (5x + 1/3) - (3x - 1/6)
The value of the mathematical expression is 2x + 1/2
How to evaluate the mathematical expression?From the question, we have the following parameters that can be used in our computation:
A mathematical expression
The mathematical statement is give as
Subtract (5x + 1/3) - (3x - 1/6)
When this is represented as an expression
We have the following representation
(5x + 1/3) - (3x - 1/6)
Open the brackets
So, we have the following representation
5x + 1/3 - 3x + 1/6
Collect the like terms
So, we have the following representation
5x - 3x + 1/3 + 1/6
Evaluate the like terms
2x + 1/2
Hence, the expression is 2x + 1/2
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PLEASE HELP WITH THIS QUESTION ASAP
Find the missing values so that the area of the product is equal to the
area of its sum.
1 yard in 6 minutes only correct answers
Answer: Depending on you mean I have answers for them so I hope one of them is for what your looking for.
A distance of 1 yard covered in 6 minutes, which would indicate a speed of 1 yard/6 minutes, or 0.17 yards per minute.A measurement of time, with the duration of an event or task being 6 minutes and the quantity or amount being 1 yard.
A quantity that is spread out over a period of 6 minutes, such as 1 yard of fabric or 1 yard of pipe being produced every 6 minutes.
A reference to a specific sport or activity, such as a football team gaining 1 yard in 6 minutes of play.
Answer:
(Rounded. Exact DP: 16) -- 0.166...7 yards/minuteStep-by-step explanation:
Use the speed formula:
[tex]s = \frac{d}{t}[/tex]
The runner travelled 1 yard in 6 minutes.
[tex]s = \frac{1\:yard}{6\:minutes}\\s = 0.166...7[/tex]
Hope this helps!
Find the 10th term in this
quadratic sequence.
2n² + 3
A.5
B.43
C. 105
D. 203
Answer:
D
Step-by-step explanation:
to find the 10th term substitute n = 10 into the rule, that is
2(10)² + 3
= 2(100) + 3
= 200 + 3
= 203
the 10th term is 203
Find Dy/Dx By Implicit Differentiation. x/y +y/x = 3y
The derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).
The given equation is x/y + y/x = 3y.
To find the derivative of y with respect to x (Dy/Dx), we will use implicit differentiation.
First, we will take the derivative of both sides of the equation with respect to x:
(1/y) * (Dy/Dx) + (1/x) * (Dy/Dx) + (y/x^2) * (Dx/Dx) = (3)(Dy/Dx)
We can simplify this expression by combining the terms with Dy/Dx and Dx/Dx:
(Dy/Dx)(1/y + 1/x + 3) = (y/x^2)(Dx/Dx)
Now we can solve for Dy/Dx by rearranging the equation:
Dy/Dx = (y/x^2)(Dx/Dx) / (1/y + 1/x + 3)
Finally, we can plug in our known values and solve for Dy/Dx:
Dy/Dx = (x/y)(Dx/Dx) / (3y - x - y)
Therefore, the derivative of y with respect to x (Dy/Dx) can be found by using implicit differentiation and is equal to (x/y)(Dx/Dx) / (3y - x - y).
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Determine whether each function is linear. write yes or no. explain.
can someone please help me with this question?
Answer:
yes, it is linear
Step-by-step explanation:
the x is +3 to each one, and the y is -1 to each one, this keeps it linear
How can I learn 5 tables easily?
"Complete table of 5" refers to a multiplication table containing all products of the number 5 multiplied by integers from 1 up to a specified maximum value.
Write a complete table of 5.Here is an example of 5 complete tables:
5x1=5
5x2=10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30
5 x 7 = 35
5x8=40
5 x 9 = 45
5 x 10 = 50
In this example, the maximum multiplier value is 10, but a full table of 5 can continue with any number of rows. This table will help you remember the facts about multiplication by 5 and identify patterns for multiples of 5.
Note that if you're looking for a way to compute the product, you can use a loop or function that takes the maximum value of the multiplier as input and outputs the full table of 5.
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What is the following quotient?
√96/√ 8
O 2√3
O 4
O 2√√22
O 12
The distances between some planets are given below.
Planet Q
Planet Q is 3.5 × 10° km from planet P.
Planet R is 1.2 × 10? km from planet P.
The shortest distance between planet Q and planet R is 1.64 * 10⁷ km
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:
hypotenuse² = adjacent² + opposite²
From the diagram, QR is the shortest distance between planet Q and planet R. Hence using Pythagoras:
QR² = QP² + PR²
QR² = (3.6 * 10⁶)² + (1.6 * 10⁷)²
QR = 1.64 * 10⁷ km
The shortest distance is 1.64 * 10⁷ km
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What are the properties of algebra?
The algebra properties are as follows: associative property , distributive property, identity property, inverse property.
As given in the question,
Properties of the algebra are as follow:
1. Associative property :
Let a, b, c be the three expressions
a. For addition:
( a + b ) + c = a + ( b + c )
b. For multiplication :
a × ( b × c ) = ( a × b ) × c
2. Distributive property:
Let a, b, c be the three expressions
For multiplication over addition:
a ( b + c ) = ab + ac
3. Identity property:
a. For addition:
a + 0 = a
b. for multiplication :
a × 1 = a
4. For inverse
For addition:
a + ( -a ) = 0
For multiplication:
a × ( 1 /a) = 1
Therefore, the four properties of the algebra are associative property , distributive property, identity property, inverse property.
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Carey's extreme sports is an ecommerce store specializing in selling extreme sports products.
The products include equipment, apparel, and other items related to extreme sports. Founded in 2015 in Arizona, US, the company has grown from a high-end sports gear equipment company into a national extreme sports brand with operations in 50 States and close to 1000 employees working for the company. The world of Carey's Extreme has traditionally conjured up images of inclusivity, sophistication, and elegance, attracting both wealthy and not-so-wealthy crowds, including college students.
Based on the Pareto analysis, the set of brands which contributes most to the profit , i.e., about 80% is Adidas , Hyperlite ,mongoose , Schwinn and aquaronotman.
Pareto analysis is based on the idea that 80% of a project's benefit can be achieved by doing 20% of the work . In bigger business firms it is taken as a powerful tool for quality maintenance and decision-making .We can say that ,it is a method used for getting the required facts and information needed for setting priorities.
Thus , we can say that it is a technique used in business decision-making, but it also be used in welfare economics . It is based on the "80-20 rule." Pareto analysis, as a decision-making technique, statistically distinguishes a small number of input factors , either good or undesirable that have the largest impact on an output.
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Does (0, 5) make the equation y = x + 5 true?
A right triangle has coordinates A (4,6) , B (4, 12) and C (8, 6) . Write the coordinates of the triangle after a dilation of 12 .
The coordinates of the triangle after dilation are A'(48, 72), B'(48, 144) and C'(96, 72).
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Assume that the dilation is about the origin.
When a point (x, y) is dilated with k, then new coordinates are (kx, ky).
A(4, 6) after dilation become (4 × 12, 6 × 12) = A'(48, 72)
B(4, 12) after dilation become (4 × 12, 12 × 12) = B'(48, 144)
C(8, 6) after dilation become (8 × 12, 6 × 12) = C'(96, 72)
Hence the coordinates after undergone dilation are A'(48, 72), B'(48, 144) and C'(96, 72).
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expand and simplify (x+9) (x+3)
The expression (x+9) (x+3) in the simplified expanded form will be x² + 12x + 27.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (x+9) (x+3)
Simplify the expression, then we have
⇒ (x+9) (x+3)
⇒ x (x+3) + 9(x+3)
⇒ x² + 3x + 9x + 27
⇒ x² + 12x + 27
The expression (x+9) (x+3) in the simplified expanded form will be x² + 12x + 27.
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At Laura's summer camp, there were 200 boys and 16 counselors. At this rate, how many boys should be at camp with 20 counselors?
The number of boys who should be at camp with 20 counselors will be 250 boys.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
At Laura's summer camp, there were 200 boys and 16 counselors. Then the rate is given as,
Rate = 200 / 16
Rate = 12.5 boys per counselor
At this rate, the number of boys should be at camp with 20 counselors will be given as,
⇒ 12.5 x 20
⇒ 250 boys
The number of boys is 250 boys.
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Anothony says that the expression abc has three terms because it uses three different variables. Critique Anothony's reasoning and explain whether he is correct.
According to the mathematical notations, we can say that in this case, Antonhy's reasoning is incorrect, because the expression abc is only one term and not three as he stated.
What are the terms of an expression?It corresponds to a term that has letters and numbers, which are separated only if there is a mathematical sign between them, such as the plus or multiplication sign, for example, to be an expression of three terms, the expression should be like this:
a x b x cTherefore, we can consider that the term abc corresponds to a monomial, as it is only one term in an expression, and not three as supposed by Anthony.
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I need help with these questions. Please help.
Would this be correct anyone?!
Answer:
The answer would be g(x) = -4|x| - 3
Step-by-step explanation:
With transformations involving translating an absolute value function down, the translation would be outside the absolute value and is negative (since we're moving the entire graph down). As the transformation occurs after the graph is already reflected, the translation will not be affected by the reflection.
help help helpppppppp
Answer: 6
Step-by-step explanation: you subtract the one time fee($16) from the 100 then divide the rest by the cost of a one month membership($14)
How do you solve a table of values?
A table of values basically lists the values of y for the given line given the values of x.
Explain the method to solve table of values?A table of values is a graphic organizer or chart that enables you to choose two or more points from which to make your graph.
Here is an illustration of a table of values for the equation y = 2x + 1.
Put x = 0, y = 1
Put x = 1, y = 3
The method to solve table of values are-
Making a table of values allows you to graph a line using a slope-intercept form equation. To determine the coordinate point's corresponding y-values, choose a few x values and enter those values into the equation. Create a graph and plot the points. To draw the line, join the points together.To know more about the table of values, here
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Answer:
Table of Values of a Function displays the table of values for the given function.
Step-by-step explanation:
How To solve the table of Values:The procedure to use the table of values of a function calculator is as follows:
Step 1: Making a table of values allows you to graph a line using a slope-intercept form equation.
Step 2: To determine the coordinate point's corresponding y-values.
Step 3: Choose a few x values and enter those values into the equation.
Step 4: Create a graph and plot the points.
To draw the line, join the points together.
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If x -y =5 , xy =24 then the value of x^2+y^2 will be
Full steps and explanations pls
Answer:
x² +y² = 73
Step-by-step explanation:
x - y = 5 ; xy = 24
[tex]\sf \boxed{\bf x^2 + y^2 = (x -y)^2 + 2xy}[/tex]
= 5² + 2*24
= 25 + 48
= 73
Reason:
x² + y² = (x - y)² + 2xy
= x² + y² - 2xy + 2xy {(x - y)² = x² +y² - 2xy}
= x² + y²
How do you factor polynomials ?
Answer:I often do is just see how many terms in there if is only have two that will be Binomial, if it was three therm I will just think that probably trinomial, only have one that will be the monomial, more than 3 term i will think it just polynomials.