Answer:
[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]
You can choose the level of precision as desired from the above
Step-by-step explanation:
The area of an equilateral triangle of side a
is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]
We are given A = 243
Plugging in values we get
[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]
Switch sides so [tex]a^2[/tex] term is on the left
[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]
Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]
Divide by [tex]\sqrt{3}[/tex] both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]
Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]
Miguel Rodriguez borrowed $200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.3%
Answer:
simple interest is $6.8
Miguel pay the amount to Julio at the end of 6 months was $206.8
Step-by-step explanation:
Given : Miguel Rodriguez borrowed $200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8%.
To Find : a) How much will the interest amount to?
b) What amount must Miguel pay Julio at the end of 6 months?
Solution :
Formula for simple interest :
Where rate is in decimal
Time is in years
So, rate of interest = 6.8 % = 0.068
Time = 6 months = 6/12=0.5
Principal = $200
Thus= 200x0.068x0.5=6.8
What is the size, in degrees, of the missing angle?
45
65°
Explain how you would solve negative x = 9 algebraically what inverse operation ?should be used is there an invisible number in front of x ?if so what is it? if not how do you solve this?
The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.
Solving the equation "negative x = 9" algebraicallyTo solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.
First, we notice that "negative x" means "-x", so we can rewrite the equation as:
-x = 9
To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:
-x + x = 9 + x
Simplifying the left-hand side by canceling out the "-x" and "+x", we get:
0 = 9 + x
We can further simplify this equation by subtracting 9 from both sides:
0 - 9 = 9 + x - 9
-9 = x
So the solution to the equation "negative x = 9" is "x = -9".
There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.
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In the coordinate plane, rhombus LMNO has vertices L(– 4,1), M(0,4), N(5,4), and O(1,1), and rhombus WXYZ has vertices W(– 9,– 1), X(– 1,– 7), Y(9,– 7), and Z(1,– 1). Select the sequence of transformations that can be applied to LMNO to show that it is similar to WXYZ.
On solving the provided question, we can say that Area of Rhombus is 24 cm²
What is Rhοmbus?A rhombus is an equal-sided quadrilateral in Euclidean plane geοmetry. The term "equilateral triangle" alsο refers to a quadrilateral whose sides are of the same length. A parallelοgram has a unique variation knοwn as a rhombus. In a rhombus, the οpposite sides and angles are parallel and equal.
A rhombus's diagοnal is split in half by a right angle, and each of its sides is the same length. Rhombic diamοnds and diamonds are other names for rhοmbuses. The length οf every side is the same. Diagοnals are equal in a rhοmbus. At a 90° angle, parallel lines split in half, 180 degrees is the sum of adjacent angles.
By distance formula
BD = [tex]\sqrt{(-2-4)^2 + (-1-5)^2}[/tex]
BD = [tex]\sqrt{36 + 36}[/tex]
BD = 6√2
similarly,
AC = 4√2
and, Area = 1/2 × (product of diagonals)
Area of Rhombus = 1/2 × 6√2 × 4√2 = 24 cm²
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Based on the scatter plot above, which three statements are true?
A
The graph shows a positive association.
B
The graph shows a negative association.
C
As the cost of a t-shirt increases, the # of t-shirts sold increases.
D
As the cost of a t-shirt increases, the # of t-shirts sold decreases.
E
There is a linear association shown.
F
There is a nonlinear association shown.
G
There is no correlation shown on the scatter plot.
The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.
What is a nonlinear?A nonlinear system is one in mathematics and science where the change in the output is not proportional to the change in the input. Since the majority of systems are fundamentally nonlinear, engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems. A nonlinear equation is one in which the highest degree of any term is two or more. For instance, 3x2. + 2x + 1 = 0, 3x + 4y = 5, is an example of a nonlinear equation since equation 1 has the greatest degree of 2, while equation 2 involves variables x and y. Anything connected to a line is considered linear. To construct a line, one uses all of the linear equations. Unable to form a straight line is a non-linear equation. With a fluctuating slope value, it resembles a graphed curve.To learn more about nonlinear refer to:
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Task
You put two targets in the field. The coordinates for target 1 (6 Points)
The coordinates for target 2 (4 points). See the figure below.
Informe the coach
You asked the players to shoot the ball on the targets 4 times. You added that if
they hit one of the targets, they get the target points.
Test 1:
Messi shot the ball. His ball followed the path of the equation where x is the target
points:
3(3x-4)= 24
6.8 (2.3x + 5.7) = 132.6
Test 2:
Ronaldo shot the ball. His ball followed the path of the equation where y is the
target points.
2/3 (6y - 18) = -16.4. : 2 times
8.2 (x/2 - 5) = - 16.4. : 2 times
Answer:
Step-by-step explanation:
3/2*2/3(6y)=30*3/2
6y=45
6y/y=45/y
y=7.5
Which equation best represents the curve of best fit for this data?
Answer:yes
Step-by-step explanation:
Name two pairs of suplimentary angles. need ASAP PLSS IM BEGGING
angle BCE and angle CEF
b
angle BFE and ang BCE
c
angle CBF and angle CEF
d
angle CBF and angle BFE
In the given figure angle CBF and angle CEF are supplementary angles. So Option C is correct.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Given that,
A figure which contains one trapezium BCEF
And in this portion angle CBF and angle BCE are opposite angles
and opposite angles are supplementary angles,
Hence, the pairs of angles are ∠CBF & ∠CEF
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What is a common factor for the two fractional terms
5
8
The terms can be written as (5)
05
-100 100
y
(x) and (11)
11
8
x and.
(x) (y).
xy?
Answer:
Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0), which is not in the given options, so none of the options are the correct answer.
Can someone please help me with the problem below
The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.
What is area of square ?
Area of square can be defined as the square of given side.
Given ,
Let's assume that the side length of the original square is 's'. The perimeter of the original square is then 4s and its area is s².
The perimeter of the dilated square will be 4 times longer than the original square, so it will be 4 * 4s = 16s.
The area of the dilated square will be 4 times greater than the original square, so it will be 4^2 * s² = 16s².
Here s is 12
so ,
16s = 16 * 12 = 192
16s*s = 16 * 12 * 12 = 2304
Therefore, The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.
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Which of the contexts below represents linear growth?
A music service has a fixed monthly cost and charges $0.35 for each downloaded
song.
An elevator descends at a rate of 32 feet per second.
OA town's population shrinks at a rate of 9.4% every year.
The amount of a certain medication in a person's bloodstream decreases by 1/4
every day.
The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".
What is linear Growth:A linear growth function has a constant slope, increases by a consistent amount over time, and is represented graphically as a line.
In other words, when a quantity rises in proportion to another factor or variable in a connection it is said to be a linear growth.
Let's check the given option to check whether it is linear growth or not.
1. A music service has a fixed monthly cost and charges $0.35 for each downloaded song.
Here there is a fixed cost and the cost will increase when the number of songs is increased
Let's say the constant charge is 'y' and the number of songs is 'x' then the equation that can represent the situation is
=> f(x) = y + x(0.35)
Here there is a constant increase in cost
∴ The given situation can represent Linear growth.
2. An elevator descends at a rate of 32 feet per second.
Here descends indicated the elevator decreases in speed of the elevator at a point the elevator speed will be zero
∴ It doesn't show the linear growth
3. OA town's population shrinks at a rate of 9.4% every year.
Here the town's population is shrinking means It doesn't show any growth
∴ It doesn't show the linear growth
4. The amount of certain medication in a person's bloodstream decreases by 1/4 every day.
Here, the person's bloodstream decreases by 1/4 every day.
∴ It doesn't show the linear growth
Therefore,
The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".
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can you please write out how you got the below answer?
Answer:
degree 2 and 10
Step-by-step explanation:
the degree of a polynomial is the value of the largest exponent of the variable.
r(x) = 10x² + 4x - 7
has largest exponent 2
this is a polynomial of degree 2
the leading coefficient is the coefficient of 10x²
that is leading coefficient is 10
Reactive Power VARS Apparent Power VA CD True Power W
a. Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit.
b. Apparent power is the power is the total power delivered to an AC electrical circuit
c. True power is the power lost in a resistive load in an AC electrical circuit.
What is power?Power is the rate at which work is done.
a. What is reactive power VARS?Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit. The reactive power is given by
P' = IVsinФ where
I = current in circuit, V = voltage in circuit and Ф = load angleb. What is apparent power VA?Apparent power is the power is the total power delivered to an AC electrical circuit. The apparent power is given by
S = IV where
I = current in circuit, V = voltage in circuit c. What is true power W?True power is the power lost in a resistive load in an AC electrical circuit. The true power is given by
P' = IVcosФ where
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∠A=6x−35 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 35, degrees, end color #11accd ∠ � = 3 � + 5 3 ∘ ∠B=3x+53 ∘
73 degrees is the equivalent meausure of m<A
Solving line geometryFrom the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:
m∠A + m∠B = 180
Given the following
∠A = 6x - 35
∠B = 3x + 53
Substitute the given parameters
6x - 35 + 3x + 53 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Determine the measure of <A
<A = 6x - 35
<A = 6(18) - 35
<A = 108 - 35
<A = 73 degrees
Hence the measure of angle A from the given diagram is 73 degrees
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Identify the error in generating and expression equivalent to 4 + 2x - 1/2(10 - 4x). Then the correct the error
The error in the expression 4 + 2x - 1/2(10 - 4x) is the missing parentheses.
What is parentheses?Parentheses are a sort of punctuation mark that is used to separate or distinguish content inside a phrase. They frequently assist to clarify the meaning of a statement by adding information. Parentheses can also be used to denote a break or to divide items in a list.
Error in the given question: Missing parentheses
Corrected expression: 4 + 2x - 1/2(10 - 4x)
How can the error be corrected?The problem may be fixed by ensuring that the proper syntax is used when declaring variables. If the variable is a string, for example, it should be stated as "var myVariable ='string value';". If it is an integer, define it like "var myVariable = 42;".
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Please see attached photo thanks
The single payment 2 years from now will be of $13,287.26
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.
To calculate investments or debts with compound interests.
Where:
V(n) is the value of the debt after n years,
R is the annual interest rate,
t is the number of times the debt is going to be compounded annually,
n is the number of years the debt is going to be compounded,
P is the principal amount being owed.
we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.
Then you have that t = 4, because the debt is compounded quarterly.
We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.
And finally we have that R = 7.74.
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 2,370 / (1 + 7.74/365)(365)^(2)
P = $13,287.26
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PLS HELP!!!
Find the vertices of the image of △ABC under the transformation (x, y) ⟶ (x − 3, y + 1) followed by a dilation centered at the origin with scale factor 2.
The coordinates of the image of triangle ABC are A''(x, y) = (- 4, 2), B''(x, y) = (0, 0) and C''(x, y) = (2, 4).
How to determine the vertices of the image of a triangle
Triangles are generated by the location of three distinct points on Cartesian plane. In this problem we find the representation of a triangle, whose vertices are listed below:
A(x, y) = (1, 0), B(x, y) = (3, - 1), C(x, y) = (4, 1)
We need to apply the following rigid transformations:
Translation
(x, y) → (x - 3, y + 1)
Dilation centered at the origin with scale factor 2
(x, y) → (2 · x, 2 · y)
Now we proceed to determine the coordinates of the image:
Translation
A'(x, y) = (- 2, 1), B'(x, y) = (0, 0), C'(x, y) = (1, 2)
Dilation
A''(x, y) = (- 4, 2), B''(x, y) = (0, 0), C''(x, y) = (2, 4)
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Kara earns 9.75 per hour plus 15.50 in tips each night. If she works for 5 2/5 hours four nights this week how much money will she earn
Answer: $272.60
Step-by-step explanation:
9.75x5.4= 52.65
52.65+15.50=68.15
68.15x4=272.6
-4x+7x=4(x+2)-(x+8)
The best way to figure out if there is a solution to the equation:
--> solve this whole thing algebraically
Let's solve:
[tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]
If we get this kind of circumstance:
--> where the left/right part of the equation are equal and cannot be
solved further
---> the solution is all real numbers
Answer: solution is all real numbers
A. 600 square inches
B. 768 square inches
C. 648 square inches
D. 792 square inches
Answer:
Step-by-step explanation:
area of pole=75×8=600 square inch
area if sign=12×12+1/2×12×4
=144+24
=168 square inches
total area=600+168
=768 square inches
When the price of almond milk is $3 per half gallon the quantity demanded of
oat milk is 20,000 half gallons. When the price of almond milk is $5 per half
gallon the quantity demanded of oat milk is 30,000.
Calculate the cross-price elasticity of demand for almond milk and oat milk.
Based on your calculation, what type of goods are almond milk and oat milk?
Answer:
Step-by-step explanation:
The cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. In other words, it shows how the demand for one good changes in response to changes in the price of another good. The cross-price elasticity of demand is a useful concept for understanding the relationship between two goods and can provide valuable information for firms in making pricing and marketing decisions.
The formula for cross-price elasticity of demand is as follows:
Cross-price elasticity of demand = (Percentage change in quantity demanded of good A) / (Percentage change in price of good B)
In this case, we are calculating the cross-price elasticity of demand between almond milk and oat milk. To do this, we first need to calculate the percentage change in quantity demanded of oat milk and the percentage change in price of almond milk.
Percentage change in quantity demanded of oat milk = (30,000 - 20,000) / 20,000 = 0.5
Percentage change in price of almond milk = ($5 - $3) / $3 = 0.67
Next, we use these values to calculate the cross-price elasticity of demand:
Cross-price elasticity of demand = 0.5 / 0.67 = 0.74
A positive cross-price elasticity of demand indicates that the two goods are substitutes. This means that as the price of one good increases, the demand for the other good increases. A cross-price elasticity of demand between 0 and 1 indicates that the two goods are weak substitutes. In this case, a cross-price elasticity of demand of 0.74 suggests that almond milk and oat milk are weak substitutes. This means that if the price of almond milk were to increase, the demand for oat milk would increase to some extent, but not by a significant amount.
In conclusion, the cross-price elasticity of demand provides valuable information for firms in making pricing and marketing decisions. A positive cross-price elasticity of demand indicates that two goods are substitutes, while a cross-price elasticity of demand between 0 and 1 suggests that they are weak substitutes.
On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4).
Which is an x-intercept of the graphed function?
(0, 4)
(–1, 0)
(4, 0)
(0, –1
The x-intercepts are (-2, 0), (-1, 0), (1, 0), and (2, 0).
What is meant by the x-intercept?
The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y coordinate equals zero, is the x-intercept for any curve.
The x-intercepts are the points where the graph meets the x-axis.
Which means that the coordinate of y will be zero.
It is given in the question that the graphed function will meet the x-axis at 4 points which are (-2, 0), (-1, 0), (1, 0), and (2, 0)
Therefore the x-intercepts of the function will be: (-2, 0), (-1, 0), (1, 0), and (2, 0).
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Answer: B) (-1,0)
Step-by-step explanation:
Just took the test on edge
A study found that a student's GPA, g, is related to the number of hours worked each week, h, by the equation
g = - 0.0007h? + 0.012h + 3.04. Estimate the number of hours worked each week for a student with a GPA of 2.21.
Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.
h = (g - 3.04) / (0.012 + 0.0007)
Plugging in the GPA of 2.21, we get:
h = (2.21 - 3.04) / (0.012 + 0.0007)
h = -4.83 hours
Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.
if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then___
if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.
All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.
if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.
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answers please just need help Thank you
Answer:
162π - 324 (exact) or 184.938
Step-by-step explanation:
You probably don't even need help on this one anymore, its just the same as the previous one I helped you with.
Diameter = a^2 + b^2 = c^2 = 18^2 + 18^2 = c^2
√648 = c (this is exact) so radius is √648/2
Area of square = lw = 324
Area of circle = (√648/2)^2π = (648/4)π = 162π
Area of shaded region = 162π - 324 (exact) or 184.938
To find 15+32,
Kayla adds the ones.
Then she adds the tens.
Then she adds the ones and tens.
5+2=7
1+3=4
7+4=11
Do you agree with Kayla? Yes or No.
Explain by showing your thinking using drawings, numbers, or
words.
Answer:
no
Step-by-step explanation:
15+32 you would first add the tens
5+2=7
then the ones
1+3 =4
you're answer would then be 47 as the ones come before the tens
Chris buys a new car for $24000, if he pays $1200 in taxes, what is the effective tax rate?
Answer:
Step-by-step explanation:
The effective tax rate is the amount of tax paid as a percentage of the total purchase price. To calculate the effective tax rate, you can divide the amount of tax by the total purchase price and multiply the result by 100 to get the answer as a percentage.
In this case, the effective tax rate would be:
(1200 / 24000) * 100 = 5%
So Chris's effective tax rate on the purchase of his car is 5%.
The confidence interval for a population proportion is (0.61, 0.81). What the the sample proportion and the margin of error.
The margin of error for the confidence interval for a population is 0.71 ± 0.1.
What is margin of error?The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.
The margin of error is given as:
MOE = U - L / 2
MOE = 0.81 - 0.61 / 2
MOE = 0.2 / 2
MOE = 0.1
The interval is:
Interval = P ± 0.1
Interval = (0.61 + 0.1) ± 0.1
Interval = 0.71 ± 0.1
Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.
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PLEASE HELP!!
i think it wants it in the form of
m = y2-y1
——————
x2-x1
but i could be wrong please please please help if you can it’s greatly appreciated
a) Two different ways.
x = ln(32)/ln(2)
2^x = 2^5
b) Only the natural logarithm way can be used.
c) x = 3.58
How to solve the equation?We want to solve:
2^x = 32
in two ways.
The first way is trivial, apply the natural logarithm to both sides:
ln(2^x) = ln(32)
x = ln(32)/ln(2)
The second way is the next one:
2^x = 32
The right number can be written as:
4*8 = 32
Now we can factorize the left side:
4*8 = (2*2)*(2*2*2) = 2^5
Replacing that we get:
2^x = 2^5
So we know that x = 5.
b) The second way can't be used to solve:
2^x = 12
Because 12 has a factor different than 2.
c) Using the natural logarithm way:
x = ln(12)/ln(2) = 3.58
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please help geometry asap giving brainliest for whoever gives me the correct answers!!
The value of the segment in the geometry of the triangle is 17.5.
What is triangle?A triangle is a sort of polygon with three sides, as was said in the introduction. The vertex of a triangle is where two of its sides meet at an angle. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
If a line is parallel to one side of the triangle and intersects the other two sides, then it divides the side into segments of proportional length.
Thus,
12 / (12 + 14) = 15 / (15 + x)
12(15 + x) = 15(26)
180 + 12x = 390
12x = 210
x = 17.5
Hence, the value of the segment in the geometry of the triangle is 17.5.
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