The expression of the length in terms of w is l = 20 - w cm
The expression of the area in terms of w is 20w - w² cm²
The greatest area that the rectangle could have is 400cm²
How to determine the values of the perimeter, length and areaIt is crucial to note that the calculating the perimeter of a rectangles is expressed as;
Perimeter = 2( l +w )
Where;
l is the length of the rectanglew is the width of the rectangleFrom the information given, the perimeter of the rectangle is 40cm
Now, substitute the value for perimeter
40 = 2( l +w )
Divide both sides by the coefficient, we have;
40/2 = 2(l + w)/2
Find the quotient
l + w = 20
Make 'l' the subject of formula
l = 20 - w cm
The formula for determining the area of a rectangle is expressed as;
Area = lw
Now, substitute the value of l as 20 -w in the formula, we have;
Area = 20- w(w)
expand the bracket
Area = 20w - w² cm²
For the greatest area;
Length = perimeter/4 = 40/ 4 = 20 cm
Width =perimeter/4 = 40/ 4 = 20cm
Area = 20(20)
Area = 400cm²
Thus, the expression of the length is l = 20 - w cm
Learn more about rectangles here:
https://brainly.com/question/25292087
#SPJ1
PLS ANSWER THIS MATH PROBLEM!!
For the linear function y = 2/3x + 1 given in this problem, we have that:
a) The slope is of 2/3 and the intercept is of 1.
b) The y-intercept is marked at y = 1 on the y-axis.
c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.
d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.
How to we graph the linear function?In slope-intercept format, a linear function is defined as follows:
y = mx + b.
For this problem, the function is:
y = 2/3x + b.
Hence:
The slope is of m = 2/3, meaning that when the input x increases by 3, the output y increases by 2.The intercept is of b = 1, meaning that the graph of the function crosses the y-axis(vertical axis), at y = 1.From the intercept, we know that point (0,1), which has x = 0 and y = 1, is part of the graph of the function.
Considering the concept of the slope, of change in y divided by change in x, we have that:
y + 2 = 1 + 2 = 3.x + 3 = 0 + 3 = 3.Hence point (3,3) also belongs to the graph of the given function. Given two points, we can graph a line passing through them, hence the graph is given at the end of the answer, and represents the function y = 2/3x + 1.
A similar problem, also about linear functions, is given at https://brainly.com/question/24808124
#SPJ1
What is the ratio of blue paint to total paint in the mixture?
The ratio of blue paint to the total paint in the mixture is 5:8.
How is a ratio calculated?Ratios contrast two figures by ordinarily dividing them. The term "antecedent" refers to the dividend and "consequent" to the divisor. A ratio in mathematics demonstrates how many times one number is present in another.It is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is expressed as a/b or a: b.Given:
In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.
Total paint in the mixture = 10+6 = 16
Ratio of blue paint to total paint = 10/16 = 5/8
Therefore, the required ratio is 5:8.
To learn more about ratios visit:
https://brainly.com/question/23724140
#SPJ9
Use numerals instead of words.
Explain how to compare the products of two expressions without multiplying the numbers.
Since 40 x (951-686) can be rewritten as * 5x (951-686), the value of 40 x (951-686) is
of 5 x (951-685).
Since 40 x (951-686) can be rewritten as 5x (951-686), the value of 40 x (951-686) is 8 times as value of 5 x (951-685).
In what ways does multiplication compare?A multiplicative comparison compares two expressions so that they are produced when one is multiplied by a certain number.
You must be able to distinguish between the given expressions in order to do that.
So the expression 40 x (951-686) can be rewritten as 5 x (951-686), the value of 40 x (951-686) is 8 times of the expression 5 x (951-685) as we can notice here.
Without engaging in a complicated multiplication process we have to comprehend the two expressions to find the difference between the respective products.
To know more about the multiplication of expressions visit:
https://brainly.com/question/14615643
#SPJ9
PLEASE HELP ME I MISSED CLASS BECAUSE I WAS SICK AND I DONT I UNDERSTAND
Answer:
see explanation
Step-by-step explanation:
(a)
the angles shown are alternate interior angles and are congruent
(c)
since they are congruent , then
27x - 5 = 130 ( add 5 to both sides )
27x = 135 ( divide both sides by 27 )
x = 5
(d)
then
27x - 5 = 27(5) - 5 = 135 - 5 = 130
Find the equation of the exponential function that goes through the points (0,3) and (3,375).
The equation of the exponential function that goes through the points (0,3) and (3,375) is y = 5(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (0,3) and (3,375).
The equivalent equations are;
375 = ab^3
3 = ab^0
From equation2;
a= 3
Substitute into equation 1;
375 = 3b^3
b^3 = 375/3
b^3 = 125
b = 5
Determine the equation
y = 3ab^x
y = 3(5)^x
This gives the required exponential equation
Learn more on exponential function here: https://brainly.com/question/2456547
#SPJ1
1677/203 as a reduced fraction
This is an improper fraction since the absolute value of the numerator (1677) is greater than the absolute value of the denominator (203). We can say that this fraction cannot be reduced.
1 over 6 divided by 6 divided by 6
Answer:
1/216
Step-by-step explanation:
[tex] \frac{1}{6} \div 6 \div 6[/tex]
[tex] \frac{1}{6} \div \frac{6}{1} \div \frac{6}{1} [/tex]
[tex] \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} [/tex]
[tex] \frac{1}{216} [/tex]
Reduce 36/60 to simplest terms
Answer:
3/5
Step-by-step explanation:
You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.
Answer:
3/5
Step-by-step explanation:
You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.
Can someone help me with the answer
The area of triangle ABC is 17.5 or 35/2
To solve this, we need to know the base and height of the triangle.
In this case, the base is the side AB, and the height is the side BC
Now we can count the units to get the lenght of the sides:
AB is 7 units long
BC is 5 units long.
Now we can use the formula for the area of a triangle:
[tex]A=\frac{bh}{2}[/tex]Where A is the area, b is the base and h is the height.
Putting the values of b and h:
[tex]A=\frac{7\cdot5}{2}=\frac{35}{2}=17.5[/tex]Then the area is 35/2 or 17.5 square units
Solve systems using inverses:
Solve the system:
4x - 5y + z = 9 6X + 8y - Z=27 3x – 2y + 5z = 40
(?, ?, ?)
Answer:
Step-by-step explanation:
4 x - 5 y + z = 9z = - 27 + 6 x + 8 y3 x
Write a system that would produce the graph below
Answer:
2x -y ≥ -53x +y < 10x +2y > 0Step-by-step explanation:
You want a system of inequalities that will define the area within the triangle with vertices (-2, 1), (1, 7), and (4, -2), including only the left side.
Linear equationsAn equation through points (x1, y1) and (x2, y2) can be written as ...
(y2 -y1)x -(x2 -x1)y = x1·y2 -x2·y1
Removing any common factor from the coefficients, and making sure the leading coefficient is positive will put this in standard form.
For points (-2, 1) and (1, 7), the equation of the line can be ...
(7 -1)x -(1 -(-2))y = (-2)(7) -(1)(1)
6x -3y = -15 . . . simplify
2x -y = -5 . . . . . divide by 3 (shading is right of the solid line)
For points (1, 7) and (4, -2), the equation of the line can be ...
(-2 -7)x -(4 -1)y = (1)(-2) -(7)(4)
-9x -3y = -30 . . . simplify
3x +y = 10 . . . . . . divide by -3 (shading is left of the dashed line)
For points (4, -2) and (-2, 1), the equation of the line can be ...
(1 -(-2))x -(-2 -4)y = (4)(1) -(-2)(-2)
3x +6y = 0 . . . simplify
x +2y = 0 . . . . divide by 3 (shading is right of the dashed line)
InequalitiesIn each of the above equations, the x-coefficient is positive. This means the equal sign can be replaced with > when shading is right of the line, and with < when shading is left of the line.
There will be an "or equal to" symbol when the line is solid.
This means our inequalities are ...
2x -y ≥ -53x +y < 10x +2y > 0the linear equation 3x- 4y =7 has:
a, unique solution
b, two solutions
c, infinitely many solutions
d,no solution
The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.
Given that,
The linear equation is 3x+4y=7
Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.
There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.
The x and y are positive integers so it is a unique solution.
Therefore, The solution to the equation 3x+4y=7 is unique.
To learn more about linear equation visit: https://brainly.com/question/13738061
#SPJ1
Suppose you buy a phone for $750 and sign up for a one-year service contract that costs $110 per month. What is the total cost you will pay over the length of the contract?
Answer:
$2070
Step-by-step explanation:
→ Find the total cost of 12 months
750 + ( 12 × 110 ) = 2070
Which is a function?
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}
Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
Step-by-step explanation:
Each value of x corresponds to only one value of y, making the relation a function.
The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!!)
We can see that the value of k is -3, then the line is:
y = -3*x + 4
By finding two points of the line, we can graph the line like in the image you can see below.
How to sketch a graph of the line?
Here we have the following linear equation:
y = k*x + 4
We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.
-2 = k*2 + 4
Solving this, we can find the value of k.
-2 - 4 = k*2
-6 = k*2
-6/2 = k = -3
So the value of k, the slope of the line, is k = -3.
Then the line is:
y = -3*x + 4
If we evaluate in x = 1, we get:
y = -3*1 + 4 = 1
So, at this point we know that the line passes through points (1, 1) and (2, -2).
Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
The image shows a quadrilateral inscribed in a circle. 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 -7 -10 -11 -12 -12-11-10 9 8 7 012 3 4 5 6 7 8 9 10 11 12 hat is the value of x ? A 23.1 B 21.1 C 25.1 D 22.6 E 19.1
We have a quadrilateral inscribed in a circle.
The quadrilateral is a trapezoid.
When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle C+m\angle B=180\degree \\ 4x+(4x+11)=180 \\ 8x=180-11 \\ 8x=169 \\ x=\frac{169}{8} \\ x=21.125 \\ x\approx21.1 \end{gathered}[/tex]Answer: x = 21.1
Wat 8x3 to get a answer
Answer:
24
Step-by-step explanation:
2yd - 1ft = _____yd ______ft?
Answer: 1yd 2ft
Explanation
s we have a subtraction, we have to have the same units. Thus, in order to do so we have to consider that 1 yd = 3ft:
[tex]\frac{3ft}{1yd}[/tex]Then, converting 2yf to ft:
[tex]2yd\cdot\frac{3ft}{1yd}=6ft[/tex]Now, we can make the subtraction:
[tex]6ft-1ft=5ft[/tex]Finally, we can convert 3 ft to one yd:
[tex]3ft\frac{1yd}{3ft}=1yd[/tex]and we have 2 ft left.
Tickets for the monster truck rally cost $12 for children and $20 for adults. Last
night 400 total tickets were sold for a total of $6000. Use c for the child tickets and
a for adult tickets. If one of the equations for this system is a + c = 400, write
the second equation for this system below.
Answer:
500
Step-by-step explanition
12-children
20-adults
400 sold for 6000
c-children were
500
What is the volume??
what is volume answer the volume is your topic for to day
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is 70% pure fruit juice?
20 of the 65 percent pure fruit juice, 10 of the 90 percent pure fruit juice.
What is percentage ?A fraction that is parts out of 100 is referred to as a percentage.100% is the totality. The percentages that make up a whole add up to 100%.When representing a percentage as a number, the % symbol is used. A decimal, fraction, mixed number, integer, or other type of number can be used.In a grid of 100 squares, shading can be used to represent a percentage.
First, we define our variables: let x be the number of pints of the first fruit drink (65% pure fruit juice), and y be the number of pints of the second fruit drink (90%pure fruit juice).
We know that there are 30 total pints of the mixture. Thus:
x+y=30
We also know that 90%of those 30 pints will be pure fruit juice, and all of the pure fruit juice will come from xor y.
For x pints of the first juice, there is .65x pure fruit juice. Similarly, for ypints of the first juice, there is .90y pure fruit juice. Thus, we get:
.65x+.90y=30 ×0.7
Now we solve. First I'll get rid of the decimals in the second equation by multiplying by 100:
65x+90y=2100
Multiply the first equation by 65 on both sides to be able to cancel out one of the terms:
65x+65y=1950
Subtract the second equation from the first equation:
25y=250
y=10
Thus, we need 10 pints of the second fruit juice (90%pure fruit juice). This means that we need 30−10=20 pints of the first fruit juice (65% pure fruit juice).
To learn more about percentage visit :
brainly.com/question/28269290
#SPJ9
Write an expression for the amount of money (in nickels) in n dollars.
PLEASE HELP ITS DUE IN AN HOUR
An expression for the amount of money (in nickels) in n dollars is 20n nickels.
How many nickels are in a dollar?A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.
To write an expression for the amount of money (in nickels) in n dollars,
Convert the n dollars to nickels.
1 dollar = 20 nickels
So, n dollars = 20n nickels
The required expression for the amount of money (in nickels) in n dollars is 20n nickels.
To learn more about conversions of money visit:
https://brainly.com/question/4365026
#SPJ13
Which of the following shows a correct way of simplifying 6+(3-5x)
Answer: 9 - 5x
Step-by-step explanation:
6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x
Suppose
f
(
x
)
f
(
x
)
is an nth order polynomial, with a leading coefficient of 1. Find the compact expression
f
(
n
)
(
x
)
f
(
n
)
(
x
)
. That is, what is the solution (in terms of n) if you take the derivative to respect of
x
x
some n times?
Answer:
Hi
Step-by-step explanation: how are you doing
What is the slope of a line that passes through the points: (3, 1) and (-2, 2)? Please no links, and get to the point quickly.
Answer:
-1/5 is the slope
Step-by-step explanation:
the equation
y2-y1 over x2-x1
What percent of 240 is 132? pls I need it now
Answer:
55%
Step-by-step explanation:
Answer:
55%
132 is 55% of 240
Step-by-step explanation:
Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?
Group of answer choices
1/2 cup of broccoli per beef
1 and ½ cup of broccoli per beef
2/3 pound of broccoli per beef
5/4 cup of broccoli per beef
Proportionately, the number of cups of broccoli needed for a pound of beef is B. 1 and ½ cups of broccoli per beef.
What is proportion?Proportion refers to the numerical quantity or relationship of one variable to another, which are set equal to each other.
Proportions, like ratios, use fractional values because they show the quantity of one variable in another.
We state proportions in fractions, decimals, or percentages.
The proportion of 3/4 pound of beef to broccoli = 9/8 cups of broccoli
3/4 pound = 0.75 pound
9/8 cups = 1.125 cups
The number of cups of broccoli for a pound of beef = 1.5 cups (1.125/0.75)
1.5 cups = 1½ cups
Thus, given the proportional relationship presented, for a pound of beef, Tyler would need 1½ cups of broccoli.
Learn more about proportions at https://brainly.com/question/870035
#SPJ1
Use inductive reasoning to find a pattern for the answer then use the pattern to guess the result of the final calculation and perform the operations to see if your answer is correct
Given:
1 = 1²
1 + 3 = 2²
1 + 3 + 5 = 3²
1 + 3 + 5 + 7 = 4²
1 + 3 + 5 + 7 + 9 = 5²
1 + 3 + 5 + 7 + 9 + 11 = ___
Let's find the answer and determine the pattern.
Here, we have:
1 + 3 = 4
Now, write the sum as a perfect square:
4 = 2²
For the third equation:
1 + 3 + 5 = 9
Now, write the sum as a perfect square:
9 = 3²
This means the result will be the sum written as a perfect square.
Thus, we have:
1 + 3 + 5 + 7 + 9 + 11 = 36
Now, let's write the sum (36) as a perfect square:
36 = 6²
Therefore, we have:
1 + 3 + 5 + 7 + 9 + 11 = 6²
• ANSWER:
6²
Evaluate the expression: No 4m2 when m = 3
We solve as follows:
[tex]f(3)=4(3)^2\Rightarrow f(3)=36[/tex]The solution is 36.
Find the coefficient of the x^2 term in the expansion of (5x-2)^6 //Series and sequences precalculus
We need to expand the term:
[tex](5x-2)^6[/tex]This seems like a colossal task, we would need to multiply (5x-2) 6 times. However, we can use a useful tool that is called the 'Pascal's triangle'
I'll paste an image of it above
We will use it in this way:
Each one of the rows, represent the n in the term:
[tex](x+y)^n[/tex]So, if we have the expression (x+y) we will pay attention to the upper row, if we have (x+y)^2 we will need the second row, and so on.
In our case, we need the 6th row.
Now, usually a term of the form
[tex](x+y)^6=ax^6+bx^5y+cx^4y^2+dx^3y^3+ex^2y^4+fxy^5+gy^6[/tex]As we say, look at the 6th row of the triangle, the numbers a, b, c,..., and g are given there!
[tex]\begin{gathered} a=1 \\ b=5 \\ c=10 \\ d=10 \\ e=5 \\ f=1 \end{gathered}[/tex]And we need the term that corresponds to x^2, we need the number e=5!
So, after the expansion, the coefficient of the term x^2 will be equal to 5