Congruent means that the shapes, lines, angles, etc are equal and the same. In other words, it means they are identical.
A 61° angle is congruent to another 61° angle. A square with a side length of 5 inches is congruent to another square with a side of 5 inches.
Read more about congruence here:
https://brainly.com/question/16790846
A rectangle is inscribed in a circle with diameter 8cm. Find the dimensions of the rectangle such that the area would be a maximum.
Step 1. We need to find the maximum area of a rectangle inscribed in a circle.
The diameter of the circle is:
\(\begin{gathered} Diameter: \\ d=8cm \end{gathered}\)Step 2. The radius of the circle is:
\(\begin{gathered} Radius: \\ r=d/2 \\ r=8cm/2 \\ r=4cm \end{gathered}\)Step 3. The formula to find the maximum area of a rectangle inscribed in a circle with radius r is:
\(\begin{gathered} Area: \\ A=2r^2 \end{gathered}\)Step 4. Substituting the known value of r and finding the area:
\(\begin{gathered} A=2(4cm)^2 \\ \downarrow\downarrow \\ A=2(16cm^2) \\ \downarrow \\ A=32cm^2 \end{gathered}\)The maximum area is 32cm^2.
Step 5. The maximum area of a rectangle or quadrilateral inside a circle happens when the sides of the quadrilateral are equal. This means the quadrilateral is a square.
For a square the area formula is:
\(A=l^2\)Where l is the length.
Step 6. Substituting the area to find the length of the sides:
\(\begin{gathered} 32cm^2=l^2 \\ l=\sqrt{32cm^2} \\ l=4\sqrt{2}cm \end{gathered}\)Thus, the dimensions are:
\(4\sqrt{2}cm\times4\sqrt{2}cm\)Answer: The figure for which the area is maximum is the square, and the dimensions are:
\(4\sqrt{2c}m\times4\sqrt[]{2}cm\)The function f(x) = 12,000(1 + 0. 05)x models the fish population in a lake. What will the population be in 4 years? what was the population 4 years ago?.
About 14,586 will the population be in 4 years.
About 9,872 was the population 4 years ago.
Assuming an exponential function
\(f(x) = 12,000(1 + 0. 05)^x\)
(Where x is the number of years and f(x) is the population of fish in a lake.)
Put x = 4 in the function to determine the population in 4 years:
\(If, x=4,\\f(4) = 12,000(1 + 0. 05)^4\\f(4) = 12,000(1 . 05)^4\\f(4) = 12,000(1.21550625)\\f(4) = 14586.075\\f(4) = 14586approx\)
Add x = -4 to the function to determine the population four years ago:
\(If, x=-4,\\f(-4) = 12,000(1 + 0. 05)^{-4}\\f(-4) = 12,000(1. 05)^{-4}\\f(-4) = 12,000(0.8227024748)\\f(4) = 9872.429698\\f(-4) = 9872approx\)
To learn more about function visit;
https://brainly.com/question/12431044
#SPJ4
Walker invests $4,200 in a savings account earning 8% interest compounded yearly. What will the account balance be after 7 years?
Answer:
2,562
Step-by-step explanation:
8% of 4,200 is 366, 366×7=2,562
Hope This Helps!
Which translation will change figure ABCD to figure A'B'C'D'?
A. 8 units left and 6 units up
B. 6 units left and 7 units up
C. 7 units left and 5 units up
D. 5 units left and 6 units up
Answer:
Option A 8 units left and 6 units up
B. What is each piece measurement if the angle is cut into 9 equal
lengths? Kerf width is 0.125.
Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.
Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.
What is an Angle?
An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths
To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:
Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.
Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees
Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees
Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
For more questions on Measurement .
https://brainly.com/question/27233632
#SPJ8
What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
Learn more about standard deviation on https://brainly.com/question/16555520
#SPJ9
Y/7 - 1 = 8 what is y
Answer:
y = 63
Step-by-step explanation:
Reverse the equation and do (8+1) x 7 = y.
8 + 1 = 9.
9 x 7 = 63.
Show what a monomial expression looks like
Give me a monomial expression and solve it, step-by-step, thoroughly, show your work and explain with each step how your doing it
(New to this, thanks in advance for the extra help!!!)
Answer:
Refer to the step-by-step explanation.
Step-by-step explanation:
Come up with a monomial expression and solve it.
What is a monomial expression?A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.
Here are a few examples of an monomial expression:
5x-2xy²3a⁵7m³n²\(\hrulefill\)
Let's work with the monomial expression, 3x²y³z.
To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.
Plug these values into the expression:
3x²y³z
=> 3(3)²(2)³(1)
=> 3(9)(8)(1)
=> 27(8)(1)
=> 216(1)
=> 216
Thus, the expression is solved.
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
For more such questions on points, click on:
https://brainly.com/question/26865
#SPJ8
If two cubes have edges of 2 ft and 4 ft, what is the ratio of their surface areas?
Answer:
1/4
Step-by-step explanation:
x-2y+3z=-1
-3x+6y-9z=3
2x-4y+6z=-2
Step-by-step explanation:
out of the first equation we get
x = 2y - 3z - 1
this we use in the second equation
-3(2y - 3z - 1) + 6y - 9z = 3
-6y + 9z + 3 + 6y - 9z = 3
0 = 0
this is the same equation as the first one, just multiplied by -3.
and we see the third equation is again the same one as the first just multiplied by 2.
so, there are infinite solutions.
this has not a single solution, as in the end this is just one equation with 3 variables.
what is the time signature of Chua ay songaliya
Answer:
The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are contained in each measure (bar), and which note value is equivalent to a beat.Step-by-step explanation:
The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are contained in each measure (bar), and which note value is equivalent to a beat.Answer:
2/4
Step-by-step explanation:
What is
(
3
4
)
÷
1
8
?
Answer:
1.8888888889 is the answer
Benjamin and his children went into a grocery store and he bought $18 worth of apples and bananas. Each apple costs $1.50 and each banana costs $0.90. He bought 4 more apples than bananas. Determine the number of apples, x,x, and the number of bananas, y,y, that Benjamin bought.
The number of bananas = x= 5 and
the number of apples = y = 9
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Given that the cost of 1 banana = $0.90
Cost of 1 apple = $1.50.
Total cost= $ 18
Here, x be the number of bananas and y be the numbers of apples
As the number of apples is 4 more than the number of bananas.
So, y= x+4...........(i)
Cost of x bananas = 0.9x
Cost of y apples = 1.5y
Total cost = 0.9x+1.5y
=> 18= 0.9x+1.5y
=> y=12-0.6x...........(ii)
Solving both the equations (i) as well as (ii),
x+4 = 12-0.6x
=> x=5
So, y= x+4 = 5+4=9
The number of bananas = x= 5 and
the number of apples = y = 9
To learn more about the solution of an equation from the given link
https://brainly.com/question/22688504
#SPJ1
At the beginning of March, a store bought a fancy watch at a cost of $250 and marked it up 20%. At the end of the month, the fancy watch had not sold, so the store marked it down 10%. What was the discounted price?
Answer:
$270
Step-by-step explanation:
Price after markup was 1.20($250) = $300
Price after discounting: (1.00 - 0.10)($300) = $270
A salad dressing is made by mixing lemon juice and vinegar in the ratio of 4 : 3. Vicky makes 700ml of the salad dressing. How much lemon juice does she use?
Answer:
Vicky uses 400 ml of lemon juice in the salad dressing.
Liam will spin the pointer one time. What is the probability that the pointer will land on red?
Answer:
Step-by-step explanation:
What are the other colors?
if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2
similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....
depends on how many colors are there
The equation of line c is y–5=
3
5 (x–7). Parallel to line c is line d, which passes through the point (1,
-1). What is the equation of line d? btw the 3 that's over the 5 is 3/5
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the "c" equation
\(y-5=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{5}}(x-7)\qquad \impliedby \begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\)
so line "d" is a line with a slope of 3/5 and passes through (1,-1)
\((\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{5}}(x-\stackrel{x_1}{1})\implies y+1=\cfrac{3}{5}(x-1) \\\\\\ y+1=\cfrac{3}{5}x-\cfrac{3}{5}\implies y=\cfrac{3}{5}x-\cfrac{3}{5}-1\implies y=\cfrac{3}{5}x-\cfrac{8}{5}\)
The equation of parallel line is y= -8/5x -3/5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Equation of line c is y–5= 3/5 (x–7).
Now, the parallel line to c is d whose slope will be 3/5.
Now, the line passes through (1, -1). So,
y= mx+ b
-1 = 3/5(1)+ b
-1 - 3/5= b
-8/5 =b
Thus, the equation of parallel line
y -(-1) = -8/5 ( x- 1)
y+ 1= -8/5 (x- 1)
y = -8/5x + 8/5 - 1
y= -8/5x -3/5
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
I just need helping answering this one if you will
Answer:
\(discount = \frac{1}{2} \times 39.95 \\ \: \: \: \: \: \: \: = 19.975 \\ sale \: price = 39.95 - 19.975 \\ = 19.975\)
Step-by-step explanation:
Hope that this is helpful.
To factor 4x^2-25, you can first rewrite the expression as:
a. (2x-5)^2
b. (2x)^2-(5)^2
c. (x)^2-(2)^2
d. None of the above
To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).
In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:
b. (2x)^2 - (5)^2
Using the difference of squares formula, we can factor it as follows:
(2x + 5)(2x - 5)
Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.
For such more question on factor
https://brainly.com/question/24351176
#SPJ8
Roland has built a circuit, and is using a device called an
ammeter to measure how quickly electrical current is flowing
through the circuit. He calculates that the current should be
0.180 amps, but he measures the current as 0.173 amps. What
is Roland's percent error?
Roland's percent error is approximately 3.889%.
This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.
The positive sign indicates that Roland's measured value is slightly lower than the actual value.
To calculate Roland's percent error, we can use the formula:
Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100
Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:
Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100
Simplifying the expression within the absolute value:
Percent Error = (|-0.007| / 0.180) \(\times\) 100
Since the absolute value of -0.007 is 0.007, we have:
Percent Error = (0.007 / 0.180) \(\times\) 100
Calculating the division:
Percent Error = 0.03889 \(\times\) 100
Percent Error = 3.889%.
For similar question on percent error.
https://brainly.com/question/28771966
#SPJ8
Triangle DEF is similar to a triangle ABC. What is the slope of the line that passes through the hypotenuse of the Two similar triangles?
Answer:
D. Slope is 1
Step-by-step explanation:
Start at any point on the line. Go up 1 (rise of 1). Go right 1 (run of 1). You're on the line again.
slope = rise/run = 1/1 = 1
IM NOT SURE HOW TO SOLVE THIS CAN SOMEBODY HELP ME
Answer:
The y-intercept is the point (0, 128).
The x-intercepts are the points (-4, 0) and (-8, 0).
As x → ∞, y → ∞.
As x → -∞, y → -∞.
Step-by-step explanation:
To find the y-intercept, substitute 0 for x and solve for y.
P(x) = (x + 4)²(x + 8) P(0) = (0 + 4)²(0 + 8)P(0) = (4)²(8)P(0) = 16 * 8 P(0) = 128The y-intercept is (0, 128).
To find the x-intercept, substitute 0 for y and solve for x.
0 = (x + 4)²(x + 8)Set the first term, (x + 4)², equal to 0.
0 = (x + 4)²0 = x + 4 -4 = xx = -4Set the second term, (x + 8), equal to 0.
0 = x + 8 -8 = xx = -8The x-intercepts are the point (-4, 0) and (-8, 0).
Look at the degree and leading coefficient of the polynomial to determine the end behavior, and therefore you can determine how y behaves as x gets closer to infinity.
Since the degree of the polynomial is odd (3) and the leading coefficient is positive, the graph falls to the left and rises to the right.
So, as x → ∞, y → ∞ and as x → -∞, y → -∞.
If you want to verify this, plug the equation into your calculator and look at the graph. How does it behave as you look at negative x-values? How about for positive x-values?
At the end of the year, company A paid a dividend of 3,000 VND/share. Speed
constant annual dividend growth of 5%.
The current selling price of stock A is VND 60,000/share.
Definition of cost of common equity
Answer:
all u do is take 3000×5%=150
What is the equivalent ratio for 4
The equivalent ratios are 8: 6 and 12:9.
Equivalent ratios:Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.
Here we have 4:3
To find equivalent ratios, we can multiply both terms by the same number.
Multiplying by 2
=> 4 × 2 : 3 × 2
=> 8 : 6
Multiplying by 3
=> 4 × 3 : 3 × 3
=> 12: 9
Therefore,
The equivalent ratios are 8: 6 and 12:9.
Learn more about Equivalent ratios at
https://brainly.com/question/29250986
#SPJ1
Complete Question
What is the equivalent ratio for 4: 3
Jada has read 7/10 of a book. The book has 80 pages. How many more pages does she need to read before she is done with the book?
Answer:
24 More Pages
Step-by-step explanation:
7/10=0.7=70%
70% of 80 = 56
80 - 56 = 24
24 More Pages
Answer: 24 pages
Step-by-step explanation:
7 x
10 80
560=10x
÷10 ÷10
56=x
56 pages already read
80-56=24
24 pages left
Give the answer in its simplest form
Answer:
1/52
Step-by-step explanation:
as there is only one of the three of clubs,
total possible outcomes= 52
favourable outcome= 1
P(getting a three of clubs) = total outcome/ favourable outcome
= 1/52
hope this helps
the dice was thrown 35 times and following numbers were obtained prepare frequency table51423266142545361526254132141626333
This table shows the frequency of each number obtained after throwing the die 35 times
How to prepare frequency tableTo prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.
Numbers: 1, 2, 3, 4, 5, 6
Frequency: 5, 14, 6, 4, 5, 1
Based on the given numbers, the frequency table would look like this:
Number | Frequency
1 5
2 14
3 6
4 4
5 5
6 1
This table shows the frequency of each number obtained after throwing the die 35 times.
Learn more about frequency table at https://brainly.com/question/27820465
#SPJ1
Twenty less than a number is more than twice the same number . Find the smallest possible value of the number.
The smallest possible value of the number that is an integer is -21
Determining the value of a numberFrom the question, we are to determine the smallest possible value of the number
From the given information, we have that
"Twenty less than a number is more than twice the same number"
Let the number be x
Then,
we can write that
x - 20 > 2x
Now, we will solve for x
x - 20 > 2x
-20 > 2x - x
-20 > x
Therefore,
x < -20
The possible integers are -21, -22, -23, -24, -25, -26, ...
Then,
The smallest integer is -21
Learn more on Determining a number here: https://brainly.com/question/13966934
#SPJ1
Evaluate the follow problems. Show your work
Answer:
Step-by-step explanation:
7) 13-24:(8-2)*1^3=
13-(24:6)*1=
13-(4*1)=
13-4=9
8)( -81:9)*4+8^2=
(-9*4)+64=
-36+64=28