Answers
Answer:
a) 4 cm
b) 5 cm
Step-by-step explanation:
a) Area of a rectangle = width x length
From inspection, the width of this rectangle is 2 cm and the length is 8 cm
⇒ area of the rectangle = 2 x 8 = 16 cm²
A square has 4 sides of equal measure.
Let the side of a square = [tex]x[/tex]
Therefore, the area of a square = [tex]x \times x = x^2[/tex]
If the square has the same area as the rectangle, then
[tex]x^2=16[/tex]
Square root both sides: [tex]x = \sqrt{16} =\pm4[/tex]
Since the length of a side cannot be negative, [tex]x=4[/tex] only
So the side length of the square = 4 cm
b) Perimeter of a rectangle = 2 x length + 2 x width
⇒ perimeter of the rectangle = (2 x 8) + (2 x 2) = 20 cm
Since the side lengths of a square are equal, and a side length = [tex]x[/tex]
Perimeter of a square = 4 x [tex]x[/tex] = 4[tex]x[/tex]
If a square has the same perimeter as the rectangle, then
[tex]4x=20[/tex]
Divide both sides by 4: [tex]x=20 \div 4 = 5[/tex]
side length of this square = 5 cm
Answer:
a)4cm b)5cm
Step-by-step explanation:
a)
[tex]Solution,\\\\Length(l)=8cm\\\\Breadth(b)=2cm\\\\Now,\\\\Area=l*b\\\\Area=8cm*2cm\\\\Area=16cm^{2}[/tex]
Area of the rectangle is 16cm².
When,
Area of the rectangle is equal to the area of the square then,
Area of square=16cm²
Now,
→Length=√Area
→Length=√16cm²
→Length=4cm
b)
[tex]Solution,\\\\Length(l)=8cm\\\\Breadth(b)=2cm\\\\Now,\\\\Perimeter=2(l+b)\\\\Perimeter=2(8cm+2cm)\\\\Perimeter=2(10cm)\\\\Perimeter=20cm[/tex]
The perimeter of rectangle=20cm
When,
The perimeter of the rectangle is equal to the perimeter of the square then,
The perimeter of square=20cm
Now,
Length=Perimeter/4
Length=20cm/4
Length=5cm
Related Questions
what is the area of this trapezoid. Enter your answer in the box.
Answers
Answer:
[tex]352\ ft ^2[/tex]
Step-by-step explanation:
The formula for the area of a trapezoid is:
[tex]A=\frac{b_1+b_2}{2}*h[/tex]
In this case [tex]b_1 b_2[/tex] represent the two bases of the trapezoid.
We can plug in the given lengths into the equation:
[tex]A=\frac{13+31}{2}*16=\frac{44}{2}*16=22*16=352\ ft^2[/tex]
Answer:
352 ft
Step-by-step explanation:
to do area of a trapezoid you do: (a+b) *h/ 2
a would be 13 b would b 31 and h would be 16 : (13+31) * 16/2
now you will have 44*16/2
now you have 704/2
your final answer is 352
Keith correctly determined the area of this parallelogram by adding the areas of the triangles and rectangle. How did Keith determine the area? Enter your answer by filling in the boxes. Keith determined that the area of the rectangle is m² and that the area of each triangle is m². He added the areas of the two triangles and the rectangle for a total area of m².
Answers
Answer:
Keith determined that the area of the rectangle is 56 m²
and that the area of each triangle is 14 m². He
added the areas of the two triangles and the rectangle for a total
area of 84 m².
The area of the parallelogram will be the area of two triangles and a rectangle
Area of a parallelogramA parallelogram is a two dimensional shape with equal opposite sides.
The opposite sides of a parallelogram are congruent. In order to find the area of the parallelogram!l, the formula of a parallelogram can be applied or the shape divided into 3 parts.
The 3 is made up of 2 triangles and a rectangle to have;
Area of the parallelogram = area of the two triangles + area of rectangle.
Learn more on parallelogram here: https://brainly.com/question/17028028
I NEED EXTREME HELP GUYSSSS
Answers
Answer:
-18
Step-by-step explanation:
-5/4(12) + -3 = -18
Which expressions are equivalent to 2 ln a 2 ln b - ln a? Check all that apply. Ln ab2 - ln a ln a 2 ln b ln a2 ln b2 - ln a 2 ln ab ln ab2.
Answers
Equivalent expressions are expressions with same simplified form. Equivalent expressions for the given expression are;
Expression 2: [tex]\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)[/tex]Expression 3: [tex]\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)[/tex]Expression 5: [tex]\ln(ab^2)[/tex]What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = log_a(c)[/tex]
Some properties of logarithm are:
[tex]log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1\\\\ log_a(b) + log_b(c) = log_a(c)[/tex]
Log with base e = 2.71828.... is written as [tex]\ln(x)[/tex] simply.
The expression given is [tex]2\ln(a) + 2\ln(b) - \ln(a)[/tex]
We get its simplified form as
[tex]2\ln(a) + 2\ln(b) - \ln(a) = \ln(a) + \ln(b^2) = \ln(ab^2)[/tex]
Simplifying given expressions:
Expression 1: [tex]\ln(ab^2) - \ln(a) = \ln(ab^2/a) = \ln(b^2)[/tex]This isn't same as simplified form of original
. Thus , this expression is not equivalent to the given expression.
Expression 2: [tex]\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)[/tex]This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.
Expression 3: [tex]\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)[/tex]This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.
Expression 4: [tex]2\ln(ab) = \ln((ab)^2) = \ln(a^2b^2)[/tex]This isn't same as simplified form of original expression. Thus , this expression is not equivalent to the given expression.
Expression 5: [tex]\ln(ab^2)[/tex]This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.
Thus, equivalent expressions for the given expression are;
Expression 2: [tex]\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)[/tex]Expression 3: [tex]\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)[/tex]Expression 5: [tex]\ln(ab^2)[/tex]Learn more about equivalent expressions here:
https://brainly.com/question/10628562
Answer:
B,C, and E is correct. Next answer is C and D.
Step-by-step explanation:
Express in partial fraction
[tex] \frac{ {4x}^{2 - } 47x + 141}{x {}^{2} + 13x + 40} [/tex]
Answers
Step-by-step explanation:
There is one possible way:
(4x² - 47x + 141)/(x² + 13x + 40) = (4x² + 4*13x + 4*40 - 47x - 52x - 160 + 141)/(x² + 13x + 40) =4 - (99x + 19)/(x² + 13x + 40)No further simplification
Answer:
basic polynomial division.put 4 in quotient,subtract with the dividend the multiplicative integer, then what in the remainder. stays a remainder.partial fraction is the sum of polynomial, decomposition, with a simple denominator.answer: [tex]4+\frac{-99x-19}{x^2+13x+40}[/tex]What are the values of x and y in the figures shown? show your work.
Answers
Answer:
unknown numbers
Step-by-step explanation:
letters are used for unknown numbers
Answer:
Step-by-step explanation:
2 [ x + ( x + 2y )] = 28
2x + 2y = 14
x + y = 7
x = 7 - y
x ∈ ( 0 , 7 )
y ∈ ( 0 , 7 )
What is the equation of the line that passes through the points (6,6) and (9,8)?
Answers
Answer:
[tex]y=\frac{2}{3}x+2[/tex]
Step-by-step explanation:
The equation for a line is:
y=mx+b
m=slope
b=y-intercept
x,y=(x,y) coordinate pair
Start by finding the slope. The equation for slope is...
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Plug in the given coordinates into the equation
[tex]Slope=\frac{8-6}{9-6}=\frac{2}{3}[/tex]
Now, we can use the slope and an x,y coordinate pair to find the y-intercept...
y=mx+b
6=2/3(6)+b
6=12/3+b
6=4+b
Subtract 4 from both sides
b=2
Therefore the equation is...
[tex]y=\frac{2}{3}x+2[/tex]
Abha has lovely black hair that has 36 inches long. She asks the hairdresser to
cut off one-sixth of the total length of her hair. How long will Abha’s hair
measure after hair cut?
Answers
30 inches long
Step-by-step explanation:
divide 36 by 1/6
this gives you six
subtract 6 from 36
there is 30 inches of hair left
At the ice cream shop, there are 11 shakes sold for every 6 malts. What is the ratio of malts to shakes?
Answers
Answer:
Step-by-step explanation:
The question reads malts to shakes. You must keep it that way.
Malts / shakes = 6/11
I genuinely have no idea
Answers
Answer:
10/13/17
15/15/22
Step-by-step explanation:
I may of made some mistakes but I tried, I hope this helps you.
giving 10 points and brainliest to the best correct answer, and explain it please.
Answers
Answer:
200,000 x 1.09^14 =668345.4054
So, 668,345
Hope this helps!
please need it like now
Answers
Answer:
A. (10, 3)Step-by-step explanation:
Given:
f⁻¹(x) = (x - 1)/3Find f⁻¹(10):
f⁻¹(10) = (10 - 1)/3 = 9 / 3 = 3Ordered pair is (10, 3)
Put 10 in f^{-1}(x)
10-1/39/33The pair is (10,3)
What is 5/12 as the product of a whole number and a fraction
Answers
Answer:
0.4 is the whole number 5/12 is the fraction
Step-by-step explanation:
Here are scores for two softball teams for seven innings. Each team's total score is the sum of the numbers in its row. Rosie's Riveters beat The Susan Bees by how many runs?
Answers
Answer:
The Susans Bees lost by 3 points.Step-by-step explanation:
Rosie's Riveters has 13 points in all.
The Susans Bees have 10 points in all.
13 - 10 = 3.
Write an equation where a number is added to a variable, and a solution is -8. b. Write an equation where a number is multiplied by a variable, and a solution is . 5. The markings on the number line are evenly spaced. Label the other markings on the number line.
Answers
1. 3 + x = -8 | × = -11
2. 2.5 times x = 5 | x = 2
Solve.
y = 6x − 9
y = x + 1
Answers
Answer:
(2, 3)
Step-by-step explanation:
y=y
6x-9=x+1
5x-9=1
5x=10
x=2
y=2+1
y=3
Simplify the expression -2(-3m + 10)
Answers
Answer:
6m-20
Step-by-step explanation:
you have to use the distributive property
-2(-3m+10)
-2(-3m) -2(10)
-2 times -3m = 6m
-2 times 10 = -20
=6m-20
HELPPPP PLS HURYYYYY !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
-1/10
Step-by-step explanation:
welp it is going down to the right so you know it is a negative slope only leaving the last 2
100 is your y and 1000 is your x
100/1000
and make it negative
-1/10
Answer:
1/10
Step-by-step explanation:
For this problem, since we are finding slope, we can use rise/run.
the "rise", or height, of the mountain is 100 meters
the "run", or length, of the mountain is 1000 meters
rise/run
100/1000
simplify:
1/10
function f(x) = (x +2)(x + 6) is shown
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Answers
Answer:
2nd one
Step-by-step explanation:
I just need the points
(6x-4)•(5x-3)
find area and perimeter in feet
Answers
*IMPORTANT* This < means up words i just don't know how to write it
Answer:
30 x < 2 - 38x + 12
Step-by-step explanation:
1- Multiply
2- Calculate
Multiply
3- Collect like terms
To become a member at an art museum costs $60. If
you are a member art lessons will cost $2 for each
class. If you are not a member lessons will cost $6
each. Which system of equations would be used to
solve for how many lessons it would take member and
nonmemeber to cost the same.
Answers
Answer:
10
Step-by-step explanation:
If your not a member it would cost 6 member lessons because 60 by 6=10
6=1 lesson
12=2 lessons
18=3 lessons
24= 4 lessons
30=5 lessons
36=6 lessons
42=7 lessons
48=8 lessons
54=9 lessons
60=10 lessons
If your are ready and member the 30 because 2$ if for 1 lesson so 30 lessons x 2$ each is 30.
Hope it helps have a great day
Simplify each expression. Type your answer into the box. (8 – 4)2 x |4 – 8| =
Answers
Answer:
-32
Step-by-step explanation:
First you have to solve the numbers in the parenthesis which would be (8-4)= 4 then there is a 2 that you have to multiply which would be 4x2=8, then you have to solve the other parenthesis (4-8)=-4 so then you end up with 8x-4 which equals -32
Answer:
-8
Step-by-step explanation:
what is the probability of flipping a coin 6 times and getting all heads
Answers
1/64 please mark brainiest
Please help, is this right? I’ll mark as brainliest.
Answers
Answer:
yes
Step-by-step explanation:
Which system of equations has exactly one solution? O 2x - 4y = 8 X+y = 7 3x+y=-1 6x+2y = -2 3x + 3y = 3 -6x-6y=3 О 3x-2y = 4 -3x+2y = 4
Answers
Answer:
3x+y=-1
6x+2y=-2
Step-by-step explanation:
x=(-1-y)/3
Dale uses a calculator to figure out the total cost of a $23 aquarium. Including sales tax, the total is $23.23. What is the sales tax percentage?
Answers
well, we know the aquarium is 23 bucks, the total is 23.23 or namely the tax is 0.23.
if we take 23 to be the 100%, whas is 0.23 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 23&100\\ 0.23&x \end{array}\implies \cfrac{23}{0.23}=\cfrac{100}{x}\implies 23x=23\implies x=\cfrac{23}{23}\implies x=\stackrel{\%}{1}[/tex]
Tammy is saving money in a bank that charges a fee if the account is inactive for an extended period of time. The equation y=2000(0.64)^x represents the value, , of one account that was left inactive for a period of years. Which statement below is true?
A. 0.64 is the percent of money in the account after years
B. 2000 is the -intercept, it is the amount of money in the account initially
C.0.64 is the percent of money in the account initially
D.2000 is the -intercept, it is the amount of money in the account after years
The size of a certain cell is 4.75 x 10^-7m.Another cell is 1.2 x 10^4times larger. How large is the larger cell in scientific notation?
A. 5.7 x 10-^3
B. 4.95 x 10-^11
C. 4.95 x 10-^28
D. 5.7 x 10^3
Use elimination, substitution or graphing to solve for the following system of equations: y=1/2x "-4"
x+4y=4
What is the end behavior of the function shown in the graph above?
A. As x approaches 0 , y approaches 15 .
As y approaches 0 , x approaches 25 .
B.As x approaches infinity symbol , y approaches 0 .
As y approaches infinity symbol , x approaches -infinity .
C. As x approaches infinity symbol , y approaches 0 .
As y approaches infinity , x approaches - infinity .
D. As x approaches infinity, y approaches 0.
As y approaches infinity x approaches infinity.
Find the average rate of change for the function f(x)=3.2 + 25Using the intervals of x=2 to x=6
Show ALL your work to receive credit
Answers
2000 is the y-intercept, it is the amount of money in the account initially.
Exponential functionAn exponential function is in the form:
y = abˣ
where a is the initial value of y, b is the multiplier, y, x are variables.
Let y represent the amount in the bank after x years.
Given the function y=2000(0.64)ˣ
Hence:
a = 2000, b = 0.64
0.64 = 1 + x
x = -0.36 (36% decrease)
2000 is the y-intercept, it is the amount of money in the account initially.
Find out more on Exponential function at: https://brainly.com/question/12940982
Question
Which number line represents the solution to the inequality 5 − 3x ≤ 11?
Answers
The measure of KJL= ?°.
The measure of NJM= ?°.
The measure of MJL= ?°.
Answers
kjl= 80°
njm= 25°
mjl=75°
check:
25+75+80=180°
John is planning to invest in the stock market. He will deposit $20 every month into his savings account, plus his dad likes the idea and will give him a starting capital of $100 towards his goal. Which equation can be used to find y, John's total savings after x months?
Answers
Answer:
100+20x I think
Step-by-step explanation:
he starts at 100 then he adds 20 a month and the x would represent the number of months.