Final answer:
To find the length of the longer side of the parallelogram, you can use the law of cosines.
Explanation:
To find the length of the longer side of the parallelogram, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle.
In this case, one of the diagonals is 12 meters and the other is 20 meters. The included angle is 60°.
Letting 'a' be the length of the longer side, we can set up the equation:
a^2 = 12^2 + 20^2 - 2(12)(20)cos(60°)= 304
a=17.43
If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? Check all that apply.
A. The function is inversely proportional.
B. The function is directly proportional.
C. More input results in less output.
D. More input results in more output.
Answer:
More input results in less output.
The function is inversely proportional.
Step-by-step explanation:
those two. other answer is completely wrong
If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? The correct options are A. The function is inversely proportional and C. More input results in less output.
In mathematical terms, let's consider the function as f(x), where x is the input, and f(x) is the output.
1. Option A: The function is inversely proportional.
If quadrupling the input (4x) leads to the output being one-fourth of the original output (1/4 f(x)), it implies that f(4x) = 1/4 f(x). Inverse proportionality means that as the input increases, the output decreases, and vice versa. In this case, increasing the input by a factor of 4 (4x) causes the output to reduce to one-fourth of its original value (1/4 f(x)), indicating an inverse relationship.
2. Option C: More input results in less output.
As mentioned earlier, quadrupling the input (4x) and obtaining an output of one-fourth the original (1/4 f(x)) demonstrates that increasing the input leads to a decrease in the output. When x increases, 4x (quadruple of x) will also increase, and as a result, f(4x) will be less than f(x). This aligns with the statement that more input results in less output.
It is important to understand the relationship between the input and output of a function. In this case, the given conditions indicate inverse proportionality and that increasing the input leads to a decrease in the output. Keep in mind that mathematics often deals with relationships between variables, and understanding such relationships can help solve various problems and make predictions about how a system behaves.
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If babe ruth averaged 46 home runs per year, how many home runs did he hit in 12 years
Answer:
He hit 552 home runs in 12 years
Step-by-step explanation:
To solve this problem, we will follow the steps below;
Using proportion;
Let x be the number of home runs he hits in 12 years
46 home runs = 1 year
x = 12
cross -multiply
x × 1 = 46× 12
x = 552 home runs
Therefore, he hit 552 home runs in 12 years
Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
A: 72√3 sq. units
B: 36√3 sq. units
C: 12√3 sq. units
The area of the parallelogram will be equal to 36√3 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.
Parallelogram diagram I believe down below. We must find the height and then the area using the Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A ² + B² = C²
A² + 3² = 6²
A² + 9 = 36
A² = 27
A = 3√3
Therefore the height is 3√3. Now calculate the area using A = bh
A = b x h
A = ( 12 ) x ( 3√3 )
A = 36√3
So the area is 36√3 square units.
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A car is purchased for $28,000. After each year, the resale value decreases by
35%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
Using the formula for decrement, the resale value of a $28,000 car that depreciates at a 35% rate annually for three years would be roughly $10,012.
Explanation:This question is about calculating the effects of percent decrease over a period of time. Specifically, the student is asked to calculate the value of a $28,000 car, after it undergoes a 35% percent decrease in value each year for three years. This type of problem is typically solved using the formula v = p * ((1 - r)^n), where v is the final value, p is the initial value, r is the rate of decrease, and n is the number of periods. In this case, the initial value (p) is $28,000, the rate of decrease (r) is 35% or 0.35, and the number of periods (n) is 3 years. Substituting these into the formula, we can find that the resale value after 3 years is v = 28000 * ((1 - 0.35)^3) = $10,011.75. Rounding this to the nearest dollar, we get an estimated resale value of $10,012.
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What are the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q? Round to the nearest tenth, if necessary.
Answer: The required co-ordinates of the point 'P' are (-3.5, 2.3).
Step-by-step explanation: We are to find the coordinates of point P on the directed line segment from R to Q such that P is 5/6 the length of the line segment from R to Q.
We are to find the co-ordinates of point 'P'.
The ratio in which the point 'P' dives the line segment RQ will be
[tex]m:n=5:1.[/tex]
The co-ordinates of the end-points of line segment RQ are
R(4, -1) and Q(-5, 3).
If a point 'H' divides a line segment with end points (p, q) and (s, t) in the ratio m : n, then the co-ordinates of the point 'H' are
[tex]H=\left(\dfrac{ms+np}{m+n},\dfrac{mt+nq}{m+n}\right).[/tex]
Therefore, the co-ordinates of point 'P' are
[tex]\left(\dfrac{5\times (-5)+1\times 4}{5+1},\dfrac{5\times 3+1\times (-1)}{5+1}\right)\\\\\\=\left(\dfrac{-25+4}{6},\dfrac{15-1}{6}\right)\\\\\\=\left(\dfrac{-21}{6},\dfrac{14}{6}\right)\\\\\\=(-3.5,2.3).[/tex]
Thus, the required co-ordinates of the point 'P' are (-3.5, 2.3).
To find point P's coordinates, calculate weights for points R and Q using the ratio 5/6 and apply these to R and Q's coordinates based on linear interpolation.
Explanation:The question involves determining the coordinates of a point P located at a specific fraction of the distance from point R to point Q on a directed line segment. The fraction given is 5/6, meaning that point P is 5/6th the distance from R to Q. The process to find the coordinates of point P involves calculating the weights for R and Q in the form of (1 - 5/6) and (5/6) respectively and then applying these weights to the coordinates of R and Q. This method is based on the concept of linear interpolation or finding a point of division in a line segment.
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The area of a circle is 28.26 square centimeters. What is its diameter (use 3.14 for Pi)?
A bag contains three green Christmas ornaments and four gold ornaments. If you randomly pick two ornaments from the bag, at the same time, what is the probability that both ornaments will be gold? A) 4/7 B) 2/7 C) 3/7 D) none of the above
The probability of drawing two gold ornaments in a row from a bag containing three green and four gold ornaments is 2/7. This is calculated by multiplying the probability of drawing a gold ornament on the first draw, 4/7, by the probability of drawing another gold ornament from the remaining ornaments, 1/2.
Explanation:The subject matter of this problem is probability. Probability tells us how likely an event is to occur given certain conditions. In this case, we are interested in the probability of drawing two gold ornaments from a bag containing three green and four gold ornaments. To solve this problem, we have to calculate the probability of selecting a gold ornament on the first and second draw.
Start with the total amount of ornaments, which is seven (three green and four gold). The probability of drawing a gold ornament on the first pick is 4 out of 7, or 4/7. However, if you draw a gold ornament first, there will be 6 ornaments left with 3 being gold.
So, the probability of drawing another gold ornament becomes 3 out of 6, or 1/2. The probable event is happening two times in a row and we're not replacing the ornaments, so we multiply these probabilities together:
4/7 * 1/2 = 2/7
Therefore, the probability of drawing two gold ornaments in a row from this bag is 2/7, so the correct answer is B) 2/7.
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What is the equation of a line that goes through the point (0,−35)(0,−35) and has a slope of -1?
Select one:
a. y=x−35y=x−35
b. y=−x−35y=−x−35
c. y=−35x−1y=−35x−1
d. −35y=−x
Answer:
y=−x−35 (Did it on college bridge)
Step-by-step explanation:
0.9×10-1 in Standard notation
I just need to know how do I find the domain for this function Y=-4x+2
Which of the following lists some of the non-monetary factors that are taken into account when doing cost-benefit analysis
Answer:
A.
product being used by everyone
B.
the aesthetic value of nature
C.
identifying internal costs
D.
categorizing internal and external costs
Step-by-step explanation:
How would I solve this?
Which combination of compounds will create a buffer solution? a weak acid and a weak base a weak acid and its conjugate base a strong acid and its conjugate base a strong acid and a strong base
Answer:
a weak acid and its conjugate base
Step-by-step explanation:
A Buffer solution is a solution that tends to keep the pH almost constant when small amounts of acids (H +) or bases (OH-) are added, therefore, they are very useful to reduce the impact of drastic changes in (H+) and (OH-) in processes that require a specific pH. They can be prepared by dissolving in water adequate amounts of a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid.
A student scored 98 and 87 on his first two quizzes. Use a compound inequality to find the possible values for a third quiz score that would give him an average between 90 and 95 inclusive
The range of possible scores for the third quiz that would yield an average score between 90 and 95 is 85 to 100, inclusive.
Explanation:The objective is to find the range of possible scores for the third quiz that would give an average score between 90 and 95, inclusive. As per the question, the sum of the student's first two quizzes is 98+87=185. If we denote the third quiz score as 'x', then the equation could be written as (185+x)/3 = average score. Considering the lower and upper limit of the average, we form two inequalities. For the lower limit, it's (185+x)/3 >= 90, which simplifies to x >= 270 - 185, thus x >= 85. For the upper limit, it's (185+x)/3 <= 95, which simplifies to x <= 285 - 185, thus x <= 100. So, the range of scores for the third quiz that would give an average between 90 and 95 inclusive is 85 <= x <= 100.
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The polynomial 9x2+3x3y2z is what degree?
Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?
41
67
113
139
Answer: The correct option is (A) 41°.
Step-by-step explanation: Given that quadrilateral OPQR is inscribed in circle N as shown in the figure.
Also, ∠ROP = (x+17)° and ∠RQP = (6x-5)°.
We are to find the measure of ∠ROP.
Since quadrilateral OPQR is inscribed in a circle, so it is a cyclic quadrilateral.
We know that the sum of the measures of opposite angles of a cyclic quadrilateral is 180°.
So, in cyclic quadrilateral OPQR, we have
[tex]m\angle ROP+m\angle RQP=180^\circ\\\\\Rightarrow (x+17)^\circ+(6x-5)^\circ=180^\circ\\\\\Rightarrow (7x+12)^\circ=180^circ\\\\\Rightarrow 7x^\circ=168^\circ\\\\\Rightarrow x^\circ=\left(\dfrac{168}{7}\right)^\circ\\\\\Rightarrow x^\circ=24^\circ.[/tex]
Therefore, we get
[tex]m\angle ROP=(x+17)^\circ=(24+17)^\circ=41^\circ.[/tex]
Thus, the measure of angle ROP is 41°.
Option (A) is CORRECT.
It wont let me post a picture of the angles but they are verticle angles and the equations are (3x+8), (5x-40) and it says find m ABC.
The choices are 24, 56, 80, 90
Answer:
the answer is 24 i hope this helps ...
How many gallons of gas is in my tank?
F(180) = x/30
= 180/30 = 6 gallons of gas is needed
The area of a rectangular wall of a barn is 300 square feet. its length is 10 feet longer than twice its width. find the length and width of the wall of the barn.
L
* W = 300 sq ft
Length is 10 ft greater than twice the width.
L = 2W + 10
Substituting
(2W+10)*W = 300
2W^2 + 10W = 300
Divide both sides by 2
W^2 + 5W = 150
W^2 + 5W - 150 = 0
Factor
(W +15)(W -10) = 0
Roots are W=-15 and W=10.
A negative width is impossible, so W=10
L = 2W + 10
L = 2(10) + 10
L = 30
length = 30 feet, width = 10 feet
Check: 30*10 = 300
To find the dimensions of the barn wall, we first expressed the given information as an equation using the formula for area. After simplifying and factoring the quadratic equation, we determined the width to be 10 feet and the length to be 30 feet.
Explanation:The question involves finding the length and width of a rectangular wall when given the area and a relationship between the length and width. We know the area of the wall is 300 square feet and that the length is 10 feet longer than twice the width. Let's denote the width as 'w' and the length as 'l'. The relationship between them can be expressed as l = 2w + 10. Using the formula for the area of a rectangle, which is A = l * w, we substitute the given area and the relationship between length and width to create an equation: 300 = (2w + 10) * w.
Solving this quadratic equation:
Expand the right side: 300 = 2w^2 + 10wMove all terms to one side: 2w^2 + 10w - 300 = 0Divide by 2 to simplify: w^2 + 5w - 150 = 0Factor the quadratic: (w + 15)(w - 10) = 0Find the roots: w = -15 or w = 10 (since width can't be negative, w = 10)Substitute w back into the relationship to find l: l = 2(10) + 10 = 30Therefore, the width of the wall is 10 feet, and the length is 30 feet.
So the cube root of 312 lies
Which property of addition is shown in the equation below?
c + di + 0 + 0i = c + di
commutative propertyinverse propertyidentity propertyassociative property
Answer:
C. identity property
Step-by-step explanation:
The cross section of a square pyramid taken perpendicular to the base that passes through the top vertex produces which two-dimensional shape?
Note: Use all lowercase letters in your answer to receive credit.
Answer:
triangle.
Step-by-step explanation:
given: a square pyramid
to find : shape of cross section made when a plane perpendicular
to base and passes through top vertex.
when a plane cuts the square pyramid perpendicular to base and passes through top vertex we get a cross section made by its two equal slant height and side of the square.
therefore, we get a triangle or more specifically isosceles triangle.
picture is attached.
The population of Glendale this year is 3,200 more than half of last year’s population. The population this year is 26,300. Which equation could be solved to find last year’s population?
Evaluate the expression 2(8 - 4)^2 - 10 / 2
Answer:
27
Step-by-step explanation:
2(8 - 4)^2 - 10/2
Using the order PEMDAS, or parenthesis, exponents, multiplication, division, addition, subtraction, we will start with the parenthesis, or 8-4.
2(4)^2 - 10/2
Next is exponents.
2(16) - 10/2
And then multiplication.
32 - 10/2
Then division.
32 - 5
Finally, subtraction.
27
Therefore, the answer is 27.
What are the limitations of determining a function’s average rate of change by examining the function’s graph?
The limitations of determining a function's average rate of change by examining the function's graph include incomplete information, the need for tangent lines, and limited interval-specific data.
Explanation:When determining a function's average rate of change by examining the function's graph, there are several limitations to consider.
The graph may not provide enough information about the function's behavior between plotted points, leading to an inaccurate estimation of the average rate of change.A curved graph may require the use of tangent lines to calculate the instantaneous rate of change, which may not accurately represent the average rate of change.The graph may not show the function's behavior in different intervals or at certain points, making it difficult to determine the average rate of change for specific intervals or points.These limitations highlight the importance of understanding the limitations of graph analysis and considering alternative methods, such as calculus, to accurately calculate the average rate of change of a function.
What's the circumference of a circular swimming pool with a diameter of 20 feet
circumference = Diameter x PI
using 3.14 for PI
3.14 x 20 = 62.8 feet
The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the last step
Answer:
AXxaXax
Step-by-step explanation:
PLZ ASAP, I NEED HELP ASAP
When 8668/25+4141/9-5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of the mixed number, plz give the right answer
Thanks
4(3h+7)/4+h for h=-2
Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal? A. $4000.00 B. $4214.41 C. $4508.64 D. $4448.13