The value of sin(θ - φ) = sin(A - B) in simplest form is sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800
How to determine simplest form?Use the trigonometric identity sin(α - β) = sin α cos β - cos α sin β to find sin(θ - φ), where θ = A and φ = B.
First, find cos A and sin B using the given information:
Since sin A = 53/45, use the Pythagorean identity cos² A + sin² A = 1 to find cos A:
cos² A + (53/45)² = 1
cos² A = 1 - (53/45)²
cos A = ± √(1 - (53/45)²)
Since A is a positive acute angle, take the positive square root:
cos A = √(1 - (53/45)²)
Similarly, since cos B = 29/20, use the Pythagorean identity cos² B + sin² B = 1 to find sin B:
sin² B = 1 - cos² B
sin B = ± √(1 - cos² B)
Since B is a positive acute angle, take the positive square root:
sin B = √(1 - (29/20)²)
Use the identity sin(α - β) = sin α cos β - cos α sin β to find sin(A - B):
sin(A - B) = sin A cos B - cos A sin B
= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)
Simplifying this expression:
sin(A - B) = (53/60) - √(2561)/900
Finally, use the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ to find sin(θ - φ) = sin(A - B):
sin(A - B) = sin θ cos φ - cos θ sin φ
= sin A cos B - cos A sin B
= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)
= (53/60) - √(2561)/900
Therefore, the value of sin(θ - φ) = sin(A - B) in simplest form is:
sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800
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rate of change between (-4,-12)and (2,4)
Answer: 2.667
Step-by-step explanation:
Answer:
Can you mark me brainiest.
Step-by-step explanation:
Instead of me telling you the answer I will make it easy for you go to M a th way its very easy.
Or 2.667
3x° P (2x+45)° find the x value
Since angles M and P are complementary, if m∠M = 3x - 45 and m∠P = 2x + 15, the value of x is 24
and the value of M and P are 27° and 63° respectively.
Since M and P are complimentary, that means the sum of them is = 90°
So
3x - 45 + 2x + 15 = 90
Taking like terms
3x + 2x = 90 + 45 -15
5x = 120
x = 120/5
x = 24
to find M and P
since m∠M = 3x - 45
m = 3(24) -45
m = 27°
m∠P = 2x + 15
since x = 60
P = 2(24) + 15
P = 63°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Angles M and P are complementary. If m∠M = 3x - 45 and m∠P = 2x + 15, what is the value of x? What is the measure of each angle?
At the end of the week, a paper company in Scranton, PA, determines whether they broke even, made a profit, or made a loss. The likelihood of making a profit is 0.75, whereas the probability of breaking even is 0.21. What is the likelihood that for two consecutive weeks, the company makes a profit and then makes a loss? A. 0.32 B. 0.06 C. 0.03 D. 0.16
The likelihood of profit and loss in the following week is 18.75%. The Option D is correct.
What is the probability?A probability means the branch of math which deals with finding out the likelihood of the occurrence of an event. Its measures the chance of an event happening.
To get probability of the company making a profit and then making a loss in two consecutive weeks, we need to multiply the probabilities of each event occurring.
The probability of making a profit in one week is 0.75
The probability of making a loss in the following week will be:
= 1 - 0.75
= 0.25.
So, probability of the company making a profit in one week and then making a loss in the following week is:
= 0.75 * 0.25
= 0.1875
= 18.75%.
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Find the quotient and remainder using synthetic division for
x^5
-
x^4
+
9
x^3
-
9
x^2
+
9
x
-
10
/x
-
1
The quotient is x2+9x2+9
The remainder is −1
The division of x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 will have a quotient of x⁴ + 9x² + 9 and a remainder of -1 using synthetic division.
Dividing with synthetic divisionThe procedure for synthetic division involves the following steps:
Divide.
Multiply.
Subtract.
Bring down the next term, and
Repeat the process to get zero or arrive at a remainder.
We shall divide x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 by x - 1 as follows;
x⁵ divided by x equals x⁴
x - 1 multiplied by x⁴ equals x⁵ - x⁴
subtract x⁵ - x⁴ from x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 will give 9x³ - 9x² + 9x - 10
9x³ divided by x equals 9x²
x - 1 multiplied by 9x² equals 9x³ - 9x²
subtract 9x³ - 9x² from 9x³ - 9x² + 9x - 10 will give 9x - 10
9x divided by x equals 9
x - 1 multiplied by 9 equals 9x - 9
subtract 9x - 9 from 9x - 10 will give us a remainder of -1
Therefore by synthetic division, x⁵ - x⁴ + 9x³ - 9x² + 9x - 10 divided by x - 1 will result to a quotient of x⁴ + 9x² + 9 and a remainder of -1.
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Triangle TUV is dilated by a scale factor of 2.5
The coordinates of V' include the following: V' (-5, -10).
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.
This ultimately implies that, the dimension (size) or side lengths of the dilated geometric object would increase or decrease depending on the scale factor applied.
In this scenario an exercise, we would dilate the coordinates of V at (-2, -4) by applying a scale factor of 2.5 that is centered at the origin as follows:
V (-2, -4) → V' (-2 × 2.5, -4 × 2.5) = V' (-5, -10).
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5x3y ( 2x + 3y - 4 )
The simplified form of 5x³y (2x + 3y - 4) will be 10x⁴y + 15x³y² - 20x³y.
Given that:
Expression, 5x³y (2x + 3y - 4)
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Simplify the expression, then we have
5x³y * 2x + 5x³y * 3y - 5x³y * 4
10x⁴y + 15x³y² - 20x³y
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
The answer is C. Mean, because Desert Landing is symmetric.
What is distributions?A distribution refers to the pattern of how data is spread out or distributed across different values or intervals. It is a way to describe and analyze the shape, center, and spread of a set of data.
According to question:To determine the location with the most consistent temperature, we need to measure the variability of the temperature data in both locations. The measure of variability that is appropriate for this purpose is the Mean, which measures the spread of the middle of the data.
The answer is C. Mean, because Desert Landing is symmetric. depending on the shape of the distributions. If the temperature data in Desert Landing is symmetric, then the Mean would be appropriate to measure the spread of the data. If the temperature data in Sunny Town is skewed, then the Mean would also be appropriate to measure the spread of the data. However, if the temperature data in either location is not skewed, then the range would not be an appropriate measure of variability.
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(h) Three meals per day are provided by the hotel. The hotel will charge a total of $9,240 for all meals for the entire group. What is the cost of meals for each person?
Answer:
$3,080 for each person
Step-by-step explanation:
9,240 / 3 = 3,080
How to solve this question!
All the values of a 12-sided die will be represented by two 6-sided die. The probability of rolling a 7 on the 12-sided die is 1/12 and rolling a sum of 7 on the two 6-sided dice will be 1/6.
The 12-sided die which is dodecahedral consists of numbers up to 12. The 6-sided die consists of numbers up to 6. The suggestion of using two 6-sided dice instead of a 12-sided die will make a difference in the probabilities of a specific outcome.
Although, using a pair of 6-sided dice and adding their scores will represent all the values or outcomes you can get in a 12-sided die but still there will be a difference in the probabilities.
If we find the probability of rolling 7 on the 12-sided die, then it will be 1/12.
But, in the case of two 6-sided dice, we will obtain the sum of 7 in 6 outcomes which are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of outcomes, in this case, is 36.
Therefore, the probability of rolling a sum of 7 on the two 6-sided dice will be 6/36 = 1/6.
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What is the least common denominator of -2x/x-1 + x+3/x^2-1 =
The least common denominator will be (x-1)(x²-1).
When two or more fractions have the same denominators, they are termed as the common denominators.
The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.
For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.
The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.
Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,
So,
-2x/x-1 + x+3/x²-1
Taking the LCM,
-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).
Hence the least common denominator will be (x-1)(x²-1).
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Graph slope =-3 y-intercept=4
Answer:
Step-by-step explanation:
slope intercept: y = mx + b
where m is the slope and b is the y-intercept
Equation: y = -3x + 4
Since y-intercept is given, then we have the first point of the line as (0,4)
Let's find the value of x when y is 0
y = -3x + 4
0 = -3x + 4
3x = 4
x = 4/3
(4/3,0) ---second point
Since there are two points/coordinates already then we can now plot/graph.
How do I solve for this?
The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
Writing the trigonometry function in terms of the otherFrom the question, we have the following parameters that can be used in our computation:
First = tan(θ)
Second = cos(θ)
The basis trigonometry identity is
sin²(θ) + cos²(θ) = 1
Divide through the equation by cos²(θ)
So, we have
tan²(θ) + 1 = 1/cos²(θ)
Subtract 1 from both sides
tan²(θ) = - 1 + 1/cos²(θ)
Take the square root of both sides
tan(θ) = √[-1 + 1/cos²(θ)]
Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
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Please help asap !!! I will give points !!!
The value of p when q is 2 is 1
What is inverse variation?Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
This means that has x increases y will decrease and vice versa.
If p is inversely proportional to q , then p = kq
when p = 2, q = 4
2 = k4
k = 2/4
k = 1/2
When q = 2
p = 1/2 × 2
p = 1
Therefore the value of p is 1
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Write the equation of the conic section shown below.
The vertex form of the equation of a parabola is equal to y + 1 = - (1 / 12) · (x - 2)².
How to determine the equation of a parabola in vertex form
In this problem we need to determine the equation of a parabola, this can be done by knowing the distance between vertex and focus and the coordinates of the focus. The vertex form of the equation of the parabola is:
y - k = [1 / (4 · p)] · (x - h)²
Where:
h, k - Coordinates of the vertex.p - Distance of the focus with respect to vertex.If we know that (h, k) = (2, - 1) and p = - 3, then the equation of the parabola in vertex form is:
y + 1 = - (1 / 12) · (x - 2)²
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Answer:
[tex](x-2)^2=-12(y+1)[/tex]
Step-by-step explanation:
From observation of the given diagram, we can see that the graphed conic section is a vertical parabola that opens downwards, with a vertex at (2, -1) and a focus at (2, -4).
The equation of a vertical parabola in standard form is:
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a vertical parabola}\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k + p)$\\\end{minipage}}[/tex]
Given the vertex is (2, -1):
[tex]h = 2[/tex][tex]k = -1[/tex]Given the formula for the focus is (h, k+p), then:
[tex]\begin{aligned}(h, k+p)&=(2, -4)\\(2,-1+p)&=(2,-4)\\\\\implies -1+p&=-4\\p&=-4+1\\p&=-3\end{aligned}[/tex]
To write the equation of the graphed conic section, substitute the found values of h, k and p into the standard formula:
[tex](x-2)^2=4(-3)(y-(-1))[/tex]
[tex](x-2)^2=-12(y+1)[/tex]
Therefore, the equation of the graphed conic section is:
[tex]\boxed{(x-2)^2=-12(y+1)}[/tex]
Seward Elementary School plans to sell friendship bracelets. The bracelets can be purchased from three
companies.
Company C charges $27 for 15 bracelets, plus a flat rate of $18 for shipping any number of bracelets.
Let n be a number of bracelets, and let t be the total cost in dollars.
For Company C, write an equation for the total cost in dollars t in terms of the number of friendship
bracelets n.
t=
In +
Answer:
Step-by-step explanation:
For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:
t = 27n + 18
In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.
asap 100 points step by step what is the value of x in x. in x/-9=0
Answer: x = 0
Step-by-step explanation:
Anything divided by 0 equals 0
Multiply -9 to the other side
x = 0 × -9
Anything Multiplied by 0 equals 0
x = 0
an expression is given -2y+3/2x+7/4 which are equivelent to the given expression
The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -2y+ 3/2x + 7/4
On simplifying , we get
A = ( -4y + 3 )/2x + 7/4
Taking LCM on both sides , we get
A = ( -16y + 12 + 7 ) / 8x
Hence , the expression is A = ( -16y + 12 + 7 ) / 8x
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Triangle BCD with vertices B(-2, 3), C(8, 7), and D(-1,-5): y = x
B' (-3, 2); C'(7,8); D'(-5,-1)
B' (-3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,8); D'(-5,-1)
B' (3,-2); C'(7,-8); D'(-5,-1)
Answer:
(c) B'(3, -2); C'(7, 8); D'(-5, -1)
Step-by-step explanation:
Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.
ReflectionThe reflection in the line y = x has the effect of swapping the x- and y-coordinates:
(x, y) ⇒ (y, x)
No sign changes are involved.
The reflected coordinates are ...
B'(3, -2); C'(7, 8); D'(-5, -1)
<95141404393>
Andrea tossed a fair number cube with faces numbered 1 through 6 a total of 30 times. The number 4 came up 8 times. How do Andrea’s results compare to the expected probability of getting the number 4 on 30 tosses?
a. The outcome of 4 occurred 3 more times than expected.
b. The outcome of 4 occurred 3 less times than expected.
c. The outcome of 4 occurred 2 more times than expected.
d. The outcome of 4 occurred 2 less times than expected.
The outcome of 4 occurred 3 more times than expected. This is the resulting probability. Therefore, the correct option is option A.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which anything is probable to happen is basically what probability means. The outcome of 4 occurred 3 more times than expected.
Therefore, the correct option is option A.
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Need help on this!!!!!!!!
A. The greatest number of packages that can fit the truck is 24000
B. The volume of the part that is filled is 375 cubic feet
A. How to determine the greatest number of packagesGiven that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
Also, we have
Package = 1/4 foot cube
So, we have
Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)
Evaluate
Number of packages = 24000
This means that the greatest number of packages is 24000
B. How to determine the volume of the part that is filledRecall that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
So, we have
Volume = (8 * 6 1/4 * 7 1/2)
Evaluate
Volume = 375
Hence, the volume is 375 cubic feet
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A football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +
2.4 a) How high is the football after 1 second? b) For how long is the football more than 30 m high? c)
What is the maximum height of the football?
After 1 second the football is 24.5 meters.
Given that, a football is catapulted into the air so that its height h, in meters, after t seconds is h = -4.9t² +27t +2.4
a) Here, t=1
Now, h =-4.9(1)²+27(1)+2.4
= -4.9+27+2.4
= 24.5 meters
b) Given that, h=30 meter
30=-4.9t² +27t +2.4
30+4.9t²-27t-2.4=0
4.9t²-27t+27.6=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√4701)/49, (135−√4701)/49
Decimal Form:
t=4.15436405…, and 1.35584002...
c) To find maximum height, set h=0
-4.9t² +27t +2.4=0
Factor and set each factor equal to zero.
Exact Form:
t=(135+√19401)/49, (135−√19401)/49
Decimal Form:
t=5.59770352…,−0.08749943…
Therefore, after 1 second the football is 24.5 meters.
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Determine the values of k for which the equation has no solutions:
|2x + 7|-k≤5
Ok> 5
Ok < 5
Ok < -5
Ok> -5
The expression has no solution when k < - 5.
Hence, option B is correct.
The given inequality is
|2x + 7|-k ≤ 5
We know that,
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.
A function with absolute values is another name for it.
No matter what input was provided to this function, the outcome is always favorable.
Now adding k both sides of inequality,
⇒ |2x + 7| ≤ 5 + k
When we take value of k less than -5
Then the expression |2x + 7| becomes negative.
Since it always gives absolute value,
Therefore,
There is no any solution when k < -5.
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1. How does the author support her argument that
some modern voting laws might be intended to
prevent minorities from exercising their civil rights?
Cite evidence from the text in your response.
PAMENT
The author references a couple of situations that occured in the country and are occuring presently, justified by laws, which reduces the ability of social minorities to vote.
How does the author pose her argument?The author of this article cites several laws passed in states that make it harder for minorities, especially blacks, to vote regularly. He said that even after an amendment was passed allowing blacks to vote, he passed other laws preventing blacks from voting, such as requiring voter education.
These laws were enacted with increasing force until the passage of the Civil Rights Act in the 1960s.
Every year since civil rights, different laws have been passed making it harder for blacks, women, the working class, and homosexuals to vote among other members of social minorities. Many of these laws are still in effect.
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. Out of 250 randomly selected people who rode a jet 'ski, 90% wore life vests. Out of 275 randomly selected
boaters, 85% wore life vests. For a two proportion 95% confidence interval, find the margin of error. Use at least
two decimal places.
The margin of error for the two-proportion 95% confidence interval is 0.0662.
The margin of error for a two-proportion 95% confidence interval can be calculated using the following formula:
ME = z√(p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂)
where ME is the margin of error, z is the z-score corresponding to the level of confidence (in this case 1.96 for a 95% confidence interval), p₁ and p₂ are the sample proportions, and n₁ and n₂ are the sample sizes.
Using the given information, we have:
Sample 1: n₁ = 250, p₁ = 0.90
Sample 2: n₂ = 275, p₂ = 0.85
Level of confidence: 95%
Substituting these values into the formula, we get:
ME = 1.96√[(0.90×0.10 / 250) + (0.85 × 0.15 / 275)]
ME = 0.0662
Therefore, the margin of error for the two-proportion 95% confidence interval is 0.0662.
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Look at the shape below.
*image uploaded **
Sharon says that this shape can be classified as a square, a rectangle, and quadrilateral. Explain why Sharon is correct. Include all 4 classifications with a reason why it is correct.
Sharon is correct in classifying the shape as a square, rectangle, and quadrilateral.
Why Sharon is correct in her classificationThe shape satisfies the criteria for each classification: it has equal sides and right angles, making it a square; it has right angles, making it a rectangle; and it has four sides, making it a quadrilateral. Therefore, the shape can be accurately described and categorized using all four classifications.
Moreover, as a quadrilateral, this shape satisfies the general criteria of having four sides. Its defined boundaries encompassing an enclosed area are emblematic of a quadrilateral.
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Please help with this 8-9
Answer:
8) b. 15 m²
9) c. 63.5 ft²
Step-by-step explanation:
Area of composite figure:
8) To find the area of the composite figure, we have to add the area of rectangle, area of the top triangle and the area of the below triangle.
Rectangle:
length = 3m
width = 2.5 m
[tex]\boxed{\text{\bf Area of rectangle = length * width}}[/tex]
= 3 * 2.5
= 7.5 m²
Area of triangle:
[tex]\boxed{\text{\bf Area of triangle =$ \dfrac{1}{2}*base*height$}}[/tex]
Triangle1:
base = 3 m ; height = 1.5 m
[tex]\sf Area \ of \ triangle1 = \dfrac{1}{2}*3*1.5[/tex]
[tex]= 2.25 \ m^2[/tex]
Triangle2:
base = 3 m ; height = 2.5 + 1 = 3.5 m
[tex]\sf Area \ of \ triangle2 = \dfrac{1}{2}*3*3.5[/tex]
= 5.25 m²
Area of the figure = 7.5 + 2.25 + 5.25
= 15 m²
_______________________________________________________
9) To find area of the given area, add the area of rectangle1 and area of rectangle2.
length = 5 ft ; width = 5.5 ft
Rectangle1:
Area of rectangle1 = 5 * 5.5
= 27.5 ft²
Rectangle2:
length = 8ft
width = 10 - 5.5
= 4.5 ft²
Area of rectangle2 = 8 * 4.5
= 36 ft²
Area of the given figure = area of rectangle1 + area of rectangle2
= 27.5 + 36
= 63.5 ft²
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3
Write an equation to determine the area, A, of the patio that will be painted.
A. A = (x + 18)(x + 35)
B. A = (x + 15)(x + 25) + 30
C. A = (x + 5)(x + 22)
D. A = (x + 25)(x + 15) − 30
The correct equation to determine the area, A, of the patio that will be painted is,
D. A = (x + 25)(x + 15) - 30
We have to given that;
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted.
Here, rectangle with a length of x plus 25 and width of x plus 15 with a rectangle.
And, in the bottom right corner labeled bench that has a length of 10 and width of 3.
Hence, Area of rectangle is,
A = (x + 25) (x + 15)
And, Area of bottom right corner is,
A = 10 x 3
A = 30
Thus, The equation to determine the area, A, of the patio that will be painted is,
⇒ A = (x + 25)(x + 15) - 30
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what value of X makes the model true?
The value of x is -1 which makes the model true
The equation from the given model will be 5x+6=1
We have to find the value of x
5x+6=1
Subtract 6 from both sides
5x=-5
Divide both sides by 5
x=-1
Hence, the value of x is -1 which makes the model true
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Given rhombus ABCD, find the area if mZABC = 60° and AE = 2.
The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;
Area = 8·√3
What is the area of a plane figure?The area of a plane figure is the two dimensional space occupied by the figure on a plane.
The measure of the angle ABC, m∠ABC = 60°
The length of the segment AE = 2 units
The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;
BE = ED, m∠AEB = 90°
m∠ABE = 30°
sin(30°) = AE/AB
sin(30°) = 2/AB
AB = 2/(sin(30°)) = 4
AB = 4
BE = √(4² - 2²) = √(12) = 2·√3
Therefore; AC = 2 + 2 = 4
BD = 2·√3 + 2·√3 = 4·√3
The area of a rhombus = (1/2) × The product of the length of the diagonals
Therefore;
Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3
The area of the rhombus = 8·√3
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HELP ME PLEASE I DON’T UNDERSTAND!!
3a. 60
3b. 4
3c. It means that the individual speeds of the trucks are pretty close to the mean.
4. The temperature is not very consistent.
5. The values in the data set are close together, and the mean is pretty consistent.
6. Evelyn and Nova are correct
Pls give brainliest
Answer:
3a. 60
3b. 4
3c. represents the difference in speed from the mean, or data is close to mean
4. The temps are not consistent, data varies a lot
5. It means that the data does not vary much, data is basically exactly the same as the mean.
6. evelyn, nova