Answer:
To find the height of the plane, we need to use trigonometry. Let's call the height of the plane "h". We can use the given angle of 57° and the opposite side (height) to the angle to find the adjacent side (distance traveled east) using the tangent function:
tan(57°) = h / distance traveled east
We can rearrange this equation to solve for h:
h = distance traveled east x tan(57°)
To find the distance traveled east, we need to use the given distance of 322 miles and the direction traveled. Since the plane is traveling at a 57° angle northeast, we can split this into two right triangles, one facing northeast and the other facing southeast, as shown below:
N
|
|
|\ 57°
|
\
The distance traveled east is the adjacent side of the southeast-facing right triangle, which can be found using the cosine function:
cos(57°) = distance traveled east / 322
We can rearrange this equation to solve for the distance traveled east:
distance traveled east = 322 x cos(57°)
Now we can plug in this value for the distance traveled east into the equation for the height of the plane:
h = distance traveled east x tan(57°)
h = (322 x cos(57°)) x tan(57°)
Using a calculator, we can evaluate this expression to find:
h ≈ 389.4 miles
Therefore, the height of the plane to the nearest mile is 389 miles.
Determine the quotient and remainder when (2a^(3)+7a^(2)+2a+9) is divided by (2a+3). Use long division or synthetic division
The remainder is -21 and the quotient is 6a2-18a+21.
What is synthetic division?Synthetic division is a method for dividing polynomials by monomials. It is a simplified form of the long division of polynomials, and is useful when the divisor is a monomial. The method involves arranging the coefficients of the dividend in a row, and then dividing each term by the divisor .
To determine the quotient and remainder when (2a3+7a2+2a+9) is divided by (2a+3), you can use either long division or synthetic division.
Using long division:
÷2a+3
2a3+7a2+2a+9
-6a2 (2a3 ÷ 2a = 6a2)
-18a (7a2 ÷ 2a = 3a2 = 18a)
-21 (2a+9 ÷ 2a+3 = -2a+12 ÷ 2a+3 = -21)
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A rectangular region has an area of 299 square miles. The length of the region is 10 miles longer than its width. Find the length and width of the region.
Answer:
Let's represent the width of the region by "w". According to the problem, the length of the region is 10 miles longer than the width, so we can represent the length as "w + 10".
The formula for the area of a rectangle is:
Area = Length x Width
So we can write an equation for the area of this region:
299 = (w + 10) x w
Expanding the right side, we get:
299 = w^2 + 10w
Now we can rearrange this equation into standard quadratic form:
w^2 + 10w - 299 = 0
We can solve for "w" by using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 10, and c = -299. Plugging in these values, we get:
w = (-10 ± sqrt(10^2 - 4(1)(-299))) / 2(1)
w = (-10 ± sqrt(1180)) / 2
w = (-10 ± 34.351) / 2
We can ignore the negative solution, since the width of the region cannot be negative. So the width is:
w = (-10 + 34.351) / 2
w = 12.176
We can round the width to the nearest mile, since we can't have a fractional width. So the width is approximately 12 miles.
Now we can use the equation we derived earlier to find the length:
299 = (w + 10) x w
299 = (12 + 10) x 12
299 = 22 x 12
So the length is 22 miles.
Therefore, the width of the region is approximately 12 miles and the length is 22 miles.
HELP PLS HURRY...............................................................................
Answer:
C) - 1/10--------------------------------
Given two points:
[tex](-3, -7/2}) \ and \ (2, -4)[/tex]Find the slope of the line containing these points.
Slope equation:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]Substitute coordinates and find the slope:
[tex]m=(-4-(-7/2))/(2-(-3))=(-4+7/2)/(2+3)=(-1/2)/5=-1/10[/tex]Answer:
-1/10
Step-by-step explanation:
To find:-
The slope of the line passing through the points (-3,-7/2) and (2,-4) .Answer:-
We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;
[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]
where ,
(x1,y1) and (x2,y2) are the coordinates of the two points.Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .
So on substituting the respective values, we have;
[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]
[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]
[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]
[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]
[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]
Hence the slope of the line is -1/10 .
David wants to build a pen for his goat. He wants the area of the pen to be 48 square feet. If the length and width of the pen are both whole numbers. What could be the perimeter of the pen. Alright I can’t figure it out please help
If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.
To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.
Using this method, we can find all the possible length and width pairs:
1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8
Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:
perimeter = 2(length + width)
For each pair, we can plug in the values for length and width to get the perimeter:
1 x 48: perimeter = 2(1 + 48) = 98
2 x 24: perimeter = 2(2 + 24) = 52
3 x 16: perimeter = 2(3 + 16) = 38
4 x 12: perimeter = 2(4 + 12) = 32
6 x 8: perimeter = 2(6 + 8) = 28
Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.
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Which point would be included in the region shaded to show the half-plane greater than the line?
The point that would be included in the region shaded to show the half-plane greater than the line is the point that lies above the line.
In order to determine which point is included in the region shaded to show the half-plane greater than the line, we can use the following steps:
1. Identify the equation of the line.
2. Plug in the x and y values of the point into the equation of the line.
3. If the result is greater than the constant term in the equation of the line, then the point is included in the region shaded to show the half-plane greater than the line.
For example, if the equation of the line is y = 2x + 1, and the point is (2,5), we can plug in the x and y values into the equation:
5 = 2(2) + 1
5 = 5
Since the result is equal to the constant term in the equation of the line, the point (2,5) is included in the region shaded to show the half-plane greater than the line.
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Estimate the quotient 5,692 divided by 5
Let \( T_{1} \) and \( T_{2} \) be linear transformations given by \[ \begin{array}{l} T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2}
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
M=\left[\begin{array}{cc}
3 & 6 \\
5 & -2
\end{array}\right]
\]
and
\[
M=\left[\begin{array}{cc}
8 & 4 \\
5 & 2
\end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
M_{1}M_{2}=\left[\begin{array}{cc}
43 & 2 \\
-10 & 4
\end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.
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sandra contributed $400, jaclyn $600 and alecia $1000. they agreed that the profit would be divided among them based on how each person give as capital.how much percentage of the capitol did jacklyn contribute
The total percentage of capital contributed by Jacklyn is 30%
The total capital contributed by Sandra, Jaclyn, and Alecia is:
$400 + $600 + $1000 = $2000
To find the percentage of capital contributed by Jacklyn contributed,
Percentage contributed by Jaclyn = (Jaclyn's contribution / Total capital) x 100
= ($600 / $2000) x 100
= 30%
Therefore, Jacklyn contributed 30% of the capital.
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calculate the ground distance if the map distance is 20 cm write your answer in kilometers
The ground distance, given the map distance and the scale, would be 5 kilometers.
How to find the distance?If the scale on a map is 1:25,000, it means that one unit of distance on the map represents 25,000 units of distance on the ground. If the map distance is 20 cm, we can find the ground distance as follows:
Convert the map distance from centimeters to kilometers:
20 cm = 0.2 m = 0. 0002 km
Find the ground distance using the scale:
Ground distance = Map distance / Scale
Ground distance = 0. 0002 km / ( 1 / 25,000 )
Ground distance = 0.0002 km x 25,000
Ground distance = 5 km
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The full question is:
The scale on a map is 1:25,000. Calculate the ground distance if the map distance is 20 cm write your answer in kilometers
Mipl Analyze a Problem Without calculating, is the product of 7 and 5(3)/(4) greater than or less than 35 ? Explain.
The product is less than 35.
To analyze this problem without calculating, we can look at the factors involved in the product. The first factor is 7, and the second factor is 5(3)/(4).
The second factor, 5(3)/(4), is less than 5 because it is the product of 5 and a fraction less than 1.
When we multiply 7 by a number less than 5, the result will be less than 35.
Therefore, the product of 7 and 5(3)/(4) is less than 35.
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Find two numbers that multiply to -24 and adds to 2
Answer:
6 and -4
Step-by-step explanation:
Let the first number be n.
Other number= [tex]\frac{-24}{n}[/tex]
Their sum= 2
n + [tex]\frac{-24}{n}[/tex]= 2
[tex]\frac{n^{2-24} }{n}[/tex]= 2
n²-24= 2n
You can solve this problem in either of these 2 ways:
i) Square Completion method:
n²-2n = 24
Half of the coefficient= [tex]\frac{2}{2}[/tex] =1
Its square= 1²= 1
n²-2n+1= 24+1
(n-1)²= 25
n-1= [tex]\sqrt{25}[/tex]
n-1= ±5
If n-1= 5,
n= 5+1
n= 6
If n-1= -5,
n= -5+1
n= -4
∴ the numbers are 6 and -4
ii) Equation Method:
n²-24= 2n
n²-2n-24= 0
a= 1,
b= -2,
-b= 2,
c= -24
n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a
n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1
n= 2±[tex]\sqrt{4+96}[/tex]/2
n= 2±[tex]\sqrt{100}[/tex]/2
n= 2±10/2
If n= [tex]\frac{2+10}{2}[/tex],
n= [tex]\frac{12}{2}[/tex]
n= 6
If n= [tex]\frac{2-10}{2}[/tex],
n= [tex]\frac{-8}{2}[/tex]
n= -4
∴ the numbers are 6 and -4
The cost to repair a computer was $190. This included $115 for parts and $25 per hour for labor. How many hours of labor were required to fix the computer? hr
Total 3 hours of labor were required to fix the computer.
To find the number of hours of labor required to fix the computer, we can use the following equation:
Total cost = Cost of parts + (Cost of labor per hour × Number of hours of labor)
We can rearrange this equation to solve for the number of hours of labor:
Number of hours of labor = (Total cost - Cost of parts) ÷ Cost of labor per hour
Plugging in the given values:
Number of hours of labor = ($190 - $115) ÷ $25
Number of hours of labor = $75 ÷ $25
Number of hours of labor = 3 hr
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Christopher needs to order some new supplies for the restaurant where he works. The restaurant needs at least 775 spoons. There are currently 355 spoons. If each set on sale contains 10 spoons, write and solve an inequality which can be used to determine
�
s, the number of sets of spoons Christopher could buy for the restaurant to have enough spoons.
According to the inequality, Christopher would need to purchase 35 + 10s 75 sets of spoons to ensure that the restaurant has enough of them.
Why does inequality matter?According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller proportion of what they earn than do poorer households, concentrated earnings lower the amount of demand for goods and services. The economy may suffer if low-income families have fewer possibilities.
There are already 355 spoons available, but the eatery needs at least 75. Each set that is for sale includes 10 spoons.
Let s be the representation of each set. It will be demonstrated by:
35 + (10 × s) ≥ 75
35 + 10s ≥ 75
Collect like terms
10s ≥ 75 - 30
10s ≥ 45
Divide
s ≥ 45/10
s ≥ 4.5
The restaurant must have at least 5 sets.
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Answer: 10s + 355 >=755
s>=42
Step-by-step explanation:
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with same friend. His height could be modeled by the equation [tex]h= -16x^{2}+16x+480[/tex] , where t is the time in seconds and h is the height in feet.
After how many seconds, did Jason hit the water? Step by step.
Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.
After how many seconds, did Jason hit the water?We know that the height of Jason is modeled by the quadratic function:
h = - 16x² + 16x + 480
The water is at h = 0, so we need to solve the quadratic equation:
0 = - 16x² + 16x + 480
If we divide all the right side by 16,we will get:
0 = (- 16x² + 16x + 480)/16
0 = -x² + x + 30
Now we can use the quadratic formula to get the solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]
We only care for the positive solution, which is:
x = (-1 - 11)/-2 = 6
Jason will hit the water after 6 seconds.
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Manuel’s final exam has true/false questions, worth three points each, and multiple choice questions, worth four points each, let x be the number of true/false questions he gets correct, and let y be the number of multiple choice questions he gets correct. He needs more than 82 points on the exam to get an A in the class. Using the values and variables given, right in equality describing it.
Answer: Let T be the number of true/false questions on the exam, and let M be the number of multiple choice questions on the exam.
Then, the total number of points Manuel can earn on the exam is:
3T + 4M
We know that Manuel needs more than 82 points on the exam to get an A in the class. Therefore, we can write the following inequality:
3x + 4y > 82
where x is the number of true/false questions Manuel gets correct, and y is the number of multiple choice questions Manuel gets correct.
Step-by-step explanation:
On the standard (x, y) coordinate plane below, which of the following quadrants contain all of the points found on the line –3x + 5y = 15 ?
The quadrants that contain all the points found on the linear function -3x + 5y = 15 are given as follows:
Quadrant 1.Quadrant 2.Quadrant 3.How to obtain the quadrants of the linear function?The linear function for this problem is defined as follows:
-3x + 5y = 15.
In slope-intercept format, it is given as follows:
5y = 3x + 15
y = 0.6x + 3.
The features of the line are given as follows:
Increasing line due to the positive slope -> passes through the first quadrant.Positive intercept -> Means that the line passes though the 2nd quadrant and the 3rd quadrant.More can be learned about linear functions at https://brainly.com/question/24808124
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Rewrite the quadratic function in standard form. f (x) = x2 - 8x + 23 Get Hint Enter Your Step Here 7 4
The quadratic function in standard form of f (x) = x2 - 8x + 23 is (x) = (x - 4)2 + 7.
The quadratic function given is f (x) = x2 - 8x + 23. To rewrite this function in standard form, we need to complete the square for the x terms. Standard form for a quadratic function is f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
f (x) = 1(x2 - 8x) + 23
Step 2: Take half of the coefficient of the x term, square it, and add it inside the parentheses. In this case, half of -8 is -4, and -4 squared is 16.f (x) = 1(x2 - 8x + 16) + 23 - 16
Step 3: Simplify the constant term outside of the parentheses.f (x) = 1(x2 - 8x + 16) + 7
Step 4: Factor the quadratic inside the parentheses.f (x) = 1(x - 4)2 + 7
Step 5: Simplify the coefficient of the quadratic term, if necessary. In this case, the coefficient is 1, so there is no need to simplify further.The final answer is f (x) = (x - 4)2 + 7, which is the standard form of the given quadratic function.
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Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.
PART A
Viet describes the probability of each number being called first. Quinn describes the probability of any particular letter being called first. Compare the probabilities.
Comparing the two probabilities, we can see that the probability of any particular letter being called first (1/5) is five times greater than the probability of any particular number being called first (1/75). This is because there are five letters and only one number will be called first.
What is the probability about?Viet's description of the probability of each number being called first can be determined as follows. There are 75 numbers in the set, and each number has an equal chance of being called first. Therefore, the probability of any particular number being called first is 1/75.
Quinn's description of the probability of any particular letter being called first can be determined as follows. There are five letters in the set, and each letter has 15 numbers associated with it. Therefore, the probability of any particular letter being called first is 15/75 or 1/5.
Comparing the probabilities, we can see that the probability of any particular letter being called first is greater than the probability of any particular number being called first. This is because there are fewer letters (5) than numbers (75), so the probability of selecting a particular letter is higher than the probability of selecting a particular number.
Therefore, Quinn's probability of any particular letter being called first is greater than Viet's probability of any particular number being called first.
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See transcribed text below
TOPIC
7
MID-TOPIC PERFORMANCE TASK
Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.
Letter
Numbers
B - 1-15
1 -16-30
N-31-45
G- 46-60
O- 61-75
PART A
Viet describes the probability of each number being called first. Quinn describes the probability of any particular letter being called first. Compare the probabilities.
9 inches of ribbon is needed for wrapping one present. How many presents can be wrapped with 8 yards of ribbon?
9 presents
16 presents
32 presents
45 presents
First, we need to convert 8 yards to inches since the measurement of ribbon needed for one present is given in inches.
1 yard = 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches)
So, 8 yards = 8 x 36 = 288 inches.
To find out how many presents can be wrapped with 288 inches of ribbon, we divide the total length of ribbon by the length needed for one present:
Number of presents = Total length of ribbon ÷ Length of ribbon needed for one present
Number of presents = 288 ÷ 9
Number of presents = 32
Therefore, 32 presents can be wrapped with 8 yards (288 inches) of ribbon.
Hence, the answer is 32 presents.
Answer: c(32
Step-by-step explanation:
If figure QRST is reflected across the x-axis and then translated 3 units down which of the following will be the coordinates for point R?
To find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.
What are coordinates ?
Coordinates are numerical values that specify the position or location of a point in a given space. In mathematics, coordinates are often expressed as ordered pairs or triplets of numbers, which correspond to the distances of the point from a set of fixed reference points or axes.
Without seeing the figure QRST, it is not possible to give the exact coordinates for point R after the reflection and translation. However, we can use some general knowledge about the effects of reflection and translation on the coordinates of a point.
When a figure is reflected across the x-axis, the x-coordinates of all its points remain the same, but the y-coordinates are negated. That is, if a point has coordinates (x, y) before the reflection, its coordinates after the reflection will be (x, -y).
When a figure is translated down by 3 units, the y-coordinates of all its points are decreased by 3. That is, if a point has coordinates (x, y) before the translation, its coordinates after the translation will be (x, y - 3).
Therefore, to find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.
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Subtract the ratiunal expressi answer in its fully factored for (m^(2)+4m-12)/(m^(2)-64)-(m^(2)+11m+24)/(2m^(2)-128)
The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.
The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.
(m^(2)-64) = (m+8)(m-8)
(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)
The common denominator is 2(m+8)(m-8).
Now we can rewrite the two expressions with the common denominator and subtract them:
[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]
= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]
= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]
= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]
= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]
So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
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i need help with this
The value of x and y in the line segment are 6 and 6.5 units repsectively.
How to find length of line segment?The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .
Using the information in the diagram let's find the value of x and y in the diagram.
Therefore,
2x + 1 = x + 7
2x - x = 7 - 1
x = 6 units
Therefore,
3y - 8 = y + 5
3y - y = 5 + 8
2y = 13
divide both sides by 2
y = 13 / 2
y = 6.5 units
Therefore,
x = 6 units
y = 6.5 units
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Anyone help wit this
The value of x is equal to 10.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a line segment is intersected by a straight line which is parallel to the third (3rd) side of the line segment, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
21/(x - 3) = 27/(x - 1)
By cross-multiplying, we have the following:
21(x - 1) = 27(x - 3)
21x - 21 = 27x - 81
27x - 21x = 81 - 21
6x = 60
x = 60/6
x = 10.
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simplify using trig identities
(cos2x-1) / (sin2x)
As a result, the formula is (cos 2x - 1) / (2 sin x cos x)
What are an equation and an expression?A mathematical expression shows the worth of something by combining numbers, factors, and functions. A mathematical assertion known as an equation involves setting two expressions equivalent to one another.
We can start by using the identity:
cos 2x = cos² x - sin² x
We can rearrange this to get:
cos² x = cos 2x + sin² x
Substituting this into the expression we want to simplify, we get:
(cos² x - sin² x - 1) / (sin 2x)
We can then use the identity:
sin 2x = 2 sin x cos x
Substituting this into the expression, we get:
(cos² x - sin² x - 1) / (2 sin x cos x)
We can simplify the numerator using the identity:
cos² x - sin² x = cos 2x
Substituting this into the expression, we get:
(cos 2x - 1) / (2 sin x cos x)
Therefore, the simplified expression is:
(cos 2x - 1) / (2 sin x cos x)
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e synthetic division and the Remainder Theorem to evaluate P(C). P(x)=3x^(3)+15x^(2)-10x+9,c=2
P(2) = 73.
To evaluate P(C) using synthetic division and the Remainder Theorem, we will follow the following steps:
Set up the synthetic division table with the value of C on the left and the coefficients of P(x) on the right.
Bring down the first coefficient to the bottom row.
Multiply the value of C by the first coefficient in the bottom row and place the result in the next column.
Add the values in the second column and place the result in the bottom row.
Repeat steps 3 and 4 for the remaining columns.
The last value in the bottom row is the remainder. According to the Remainder Theorem, this is the value of P(C).
Therefore, P(2) = 73.
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A recipe calls for mixing 8/5 cups of blueberries and 7/5
cups of strawberries. The mix is divided equally among 18 items. What fraction of a cup is used for each item?
3 cups of fruit mix is divided equally among 18 items.
Each item will contain 1/6 cup of fruit mix.
How to find out what fraction of a cup is used for each item ?First we need to divide the total amount of fruit mix by the number of items.
The total amount of fruit mix is :
8/5 cups of blueberries + 7/5 cups of strawberries
= (8/5 + 7/5) cups
= 15/5 cups
= 3 cups
So, 3 cups of fruit mix is divided equally among 18 items.
To find the fraction of a cup used for each item, we need to divide 3 cups by 18:
Copy code
3 cups ÷ 18 = 1/6 cup
Therefore, each item will contain 1/6 cup of fruit mix.
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True or False with explanation (e.g. a piece of the Invertible Matrix Theorem) or a counterexample. All matrices aren×n. - (a) If the equationAx=0has only the trivial solution, thenAis row equivalent to the identity matrix. - (b) If the columns ofAspanRn, then they are linearly independent. - (c) IfATis not invertible, then neither isA. - (d) If there is a matrixDwithAD=I, thenDA=Ialso.
(a) If the equation Ax=0has only the trivial solution, then A is row equivalent to the identity matrix is True.
(b) If the columns of Aspan Rn, then they are linearly independent is True.
(c) If AT is not invertible, then neither is A is True.
(d) If there is a matrix D with AD=I, then DA=I also is True.
If the equation Ax=0 has only the trivial solution, then the matrix A has a pivot in every column and is therefore row equivalent to the identity matrix.
If the columns of A span Rn, then they are linearly independent because if they were not, there would be a nontrivial linear combination of the columns that equals the zero vector, which would contradict the fact that they span Rn.
If AT is not invertible, then it has a nontrivial null space, which means that there is a nonzero vector x such that ATx=0. This implies that xTA=0, which means that x is in the null space of A. Since A has a nontrivial null space, it is not invertible.
If there is a matrix D with AD=I, then DA=I also because the inverse of a matrix is unique and both AD and DA must be equal to the inverse of A.
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It! Add and Subtract Polynomials idd or subtract the polynomials. ((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5)) (2a^(2)b^(2)+3ab^(2)-5a^(2)b)-(3a^(2)b^(2)-9
The polynomial that need to be added is
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
To add or subtract polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
First, let's add the first two polynomials:
((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5))
= (2/5)a^(4) + (-6 + 9/4)a^(3) + (-5/6 + 2/3)a^(2) + (1/2 + 5/3)a + 1 - 8/5
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5
Now, let's subtract the third polynomial from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - (2a^(2)b^(2)+3ab^(2)-5a^(2)b)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b
Finally, let's subtract the last term from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b - (3a^(2)b^(2)-9)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
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HELP THIS IS DUE TOMMOROW USE ANY STRATEGIE
Answer: what is ur questions?
Step-by-step explanation:
Fill in the missing number.
18 - ____ = 30