The Venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet. Enter your answers in the boxes to complete the two-way table based on the given data.
Answers
The complete table is
Dog Not Dog Total
Cat 31 10 41
Not cat 24 7 31
Total 55 17 72
Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.
In the figure cat and dog are overlapping which means 31 people like both.
The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.
The people that like not cat not dog is 31-24=7.
The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31
The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.
Hence, the complete table is shown in attached figure for the given venn diagram.
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Related Questions
find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cm
step by step pls
Answers
Answer:
172.5cm^3
Step-by-step explanation:
* = multiply or times
volume = length*width*height
Plug in the numbers: 11.5*2.5*6 = 172.5cm^3
PLEASE HELP 80 POINTS !!!!!!!!
Answers
Answer:
Step-by-step explanation:
a) it is a reflection
b) it is vertex B"
A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units?
Answers
Answer:
X
Step-by-step explanation:
KHAN ACADEMY
Find the gradient and the intercept shown by the straight line 2x + 3y = 6
Answers
Answer:
The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.
Step-by-step explanation:
First, transform the given equation into the slope-intercept form, y = mx + b. The variable m represents slope (gradient) and the variable b represents the intercept.
2x + 3y = 6
3y = -2x + 6
y = -[tex]\frac{2}{3}[/tex]x + 2
The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.
Answer:
[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]
Step-by-step explanation:
Equation of the line in slope intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here m is the slope or gradient and b is the y-intercept.
Write the given equation in slope-intercept form.
2x + 3y = 6
3y = -2x + 6
[tex]\sf y =\dfrac{-2}{3}x +\dfrac{6}{3}\\\\ y = \dfrac{-2}{3}x + 2[/tex]
[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]
The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?
Select one:
a. 72
b. 77.5
c. 83
d. 72
Answers
Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:
A. 72 < x < 88.5.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The percentage that 978 is of 1200 is:
978/1200 x 100% = 81.5%.
Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:
Between one standard deviation below the mean and two above, which in the context of this problem is between 77.5 and 94.Between two standard deviations below the mean and one above, which in the context of this problem is between 72 and 88.5, which is option A in this problem.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Find a 49 of the sequence 70, 63, 56, 49,
Answers
Answer:
- 226
Step-by-step explanation:
ARITHMETIC SEQUENCE.
Number of term of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
First term ( a ) = 70
common difference = T2 - T1 = 63 - 70 = -7
For the 49th term
T49 = a + 48d
= 70 + 48 ( -7 )
= 70 - 336 = - 226
find the value for the given figure
Answers
Angle BDE= 30 degrees (Angles sum of triangle)
Several friends bought flowers to make table centerpieces. write the ratios of purple flowers to white flowers for each friend. bouquets of flowers purple flowers white flowers rowan 8 2 marcia 10 1 jillian 10 2 lulua 18 3 who has the smallest ratio of purple to white flowers? rowan marcia jillian lulua
Answers
The ratio for Rowan = 4:1.
The ratio for Marcia = 10:1.
The ratio for Jillian = 5:1.
The ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
Ratios are fractions in the simplest form representing the relationship between two quantities.
The ratio of purple to white flowers for each friend can be shown as:-
Rowan:
The number of purple flowers = 8
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 8/2 = 4/1.
Thus, the ratio for Rowan = 4:1.
Marcia:
The number of purple flowers = 10
The number of white flowers = 1
Thus, the fraction of purple to white flowers = 10/1.
Thus, the ratio for Marcia = 10:1.
Jillian:
The number of purple flowers = 10
The number of white flowers = 2
Thus, the fraction of purple to white flowers = 10/2 = 5/1.
Thus, the ratio for Jillian = 5:1.
Lulua:
The number of purple flowers = 18
The number of white flowers = 3
Thus, the fraction of purple to white flowers = 18/3 = 6/1.
Thus, the ratio for Lulua = 6:1.
The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.
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Answer:Its rowan
Step-by-step explanation:Mark me brainliest need award
Match each system of equations to the inverse of its coefficient matrix, A-1, and the matrix of its solution, X.
Answers
The system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X is shown in the figure.
Given that the system of equations are shown in given figure.
The first system of equations are
[tex]\begin{aligned}4x+2y-z&=150\\x+y-z&=-100\\-3x-y+z&=600\\\end[/tex]
By writing in matrix AX=b, we get
Coefficient matrix [tex]A=\left[\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right][/tex] and [tex]B=\left[\begin{array}{l}150&-100&600\end{array}\right][/tex]
Firstly, we will find the A⁻¹ by finding the determinant and adjoint of A and divide the adjoint with determinant, we get
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right|\\ &=4(1-1)-2(1-3)-1(-1+3)\\&=4(0)-2(-2)-1(2)\\ &=2\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}0&2&2\\-1&1&-2\\-2&3&2\end{array}\right]^T\\&=\left[\begin{array}{lll}0&-1&-2\\2&1&3\\2&-2&2\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0&-0.5&-0.5\\1&0.5&1.5\\1&-1&1\end{array}\right]\end[/tex]
For a solution Consider [A B] and apply row operations, we get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{lll1}4&2&-1&150\\1&1&-1&-100\\-3&-1&1&600\end{array}\right]\\ R_{2}&\rightarrow 4R_{2}-R_{1},R_{3}\rightarrow 4R_{3}+3R_{1}\\ &\sim \left[\begin{array}{lll1}4&2&-1&150\\0&2&-3&-550\\0&2&1&2850\end{array}\right]\\ R_{3}&\rightarrow R_{3}-R_{2}\\ &\sim \left[\begin{array}{llll}4&2&-1&150\\0&2&-3&-550\\0&0&4&3400\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}-250\\1000\\850\end{array}\right][/tex]
The second system of equations are
[tex]\begin{aligned}x+y-z&=220\\5x-5y-z&=-640\\-x+y+z&=200\\\end[/tex]
Similarly, we will find for second system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}1&1&-1\\5&-5&-1\\-1&1&1\end{array}\right|\\ &=1(-5+1)-1(5-1)-1(5-5)\\&=1(-4)-1(4)-1(0)\\ &=-8\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-4&-4&0\\-2&0&-2\\-6&-4&-10\end{array}\right]^T\\&=\left[\begin{array}{lll}-4&-2&-6\\-4&0&-4\\0&-2&-10\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.5&0.25&0.75\\0.5&0&0.5\\0&0.25&1.25\end{array}\right]\end[/tex]
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}1&1&-1&220\\5&-5&-1&-640\\-1&1&1&200\end{array}\right]\\ R_{2}&\rightarrow R_{2}-5R_{1},R_{3}\rightarrow R_{3}+R_{1}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&2&0&420\end{array}\right]\\ R_{3}&\rightarrow 5R_{3}+R_{2}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&0&4&360\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}100\\210\\90\end{array}\right][/tex]
The third system of equations are
[tex]\begin{aligned}2x+2y-z&=290\\x+y-3z&=500\\x-y+2z&=600\\\end[/tex]
Similarly, we will find for third system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}2&2&-1\\1&1&-3\\1&-1&2\end{array}\right|\\ &=2(2-3)-2(2+3)-1(-1-1)\\&=2(-1)-2(5)-1(-2)\\ &=-10\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-1&-5&-2\\-3&5&4\\-5&5&0\end{array}\right]^T\\&=\left[\begin{array}{lll}-1&-3&-5\\-5&5&5\\-2&4&0\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.1&0.3&0.5\\0.5&-0.5&-0.5\\0.2&-0.4&0\end{array}\right]\end[/tex]
get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}2&2&-1&290\\1&1&-3&500\\1&-1&2&600\end{array}\right]\\ R_{2}&\rightarrow 2R_{2}-R_{1},R_{3}\rightarrow 2R_{3}-R_{1}\\ &\sim \left[\begin{array}{llll}2&2&-1&290\\&0&-5&710\\0&-4&5&910\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}479\\-405\\-142\end{array}\right][/tex]
Hence, each system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X.
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WILL MAKE BRAINLIEST!! What type of angle is angle A?
Answers
What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
Answers
The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
How to determine the domain?The function is given as
g(x) = –⌊x⌋ + 3
The above is a step function, and the domain is the set of input values it can accept
Step functions of the given form can accept any real value of x
Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
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Complete question
The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
Answer:
A
Step-by-step explanation:
Carson buys eggs and lemons at the store. he pays a total of $39.62. he pays $6.74 for the eggs. he buys 8 bags of lemons that each cost the same amount.
Answers
The algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74
According to the question,
Cost of 1 bag of lemons = $x
Cost of 8 bags of lemons = 8*x = 8x
Cost of 8 bags of lemons = Total cost - cost of the egg
8x = $39.62 - $6.74
Hence, the algebraic equation is used to determine the costs of each bag of lemons is 8x = $39.62 - $6.74.
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Which type of bacterial pneumonia is most often seen in children and young adults, is characterized by a persistent cough and low-grade fever, and is usually treated with tetracycline
Answers
The type of bacterial pneumonia is most often seen in children and young adults is; Pneumococcal infection.
What is the Type of Bacteria?The correct type of Bacterial pneumonia that is most often seen in children and young adult is called Pneumococcal infection. This is because it is a name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.
Thus, we can conclude that the type of Bacterial pneumonia here is called Pneumococcal infection.
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At 9am a car a began a journey from a point, travelling at 40 mph. at 10am another car b started travelling from the same point ai 60 mpb in the same direction as car a. at what time will car b pass car a?
Answers
Answer:
In 3h (12am)
Step-by-step explanation:
First car A Will by 10 am be 40 miles from staring point, then car B Will start going 60mph and by 11am car A Will be 80 miles from start, and car B Will be 60 miles from start in 12 am car A Will be at 120 miles and car B Will be also 120 miles
And answer is in 3h or in 12am
A scientist testing the effects of a chemical on apple yield (apples/acre) sprays an orchard with the chemical. A second orchard does not receive the chemical. In the fall, the yield is determined (number of apples harvested per acre). What is the dependent variable
Answers
Following are the dependent variables:
1. The amount of water that each orchard receives.
2. The species of trees in the orchard.
Reason:
The exercise scientist is looking for the effects of a chemical between an apple crop to which it is administered and another to which it is not, 4 options are presented, of which it is essential to count as a variable the amount of water each Orchard and tree species in the orchard, since they can generate alterations in the results, the other two variables of the exercise such as number of apples and size of the orchards are not significant and their variations do not affect the scientist's objective.
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The square root of the quantity 4 x minus 3 end quantity equals 5.
Answers
Answer:
The statement is false.
Step-by-step explanation:
Given,
[tex] \sqrt{4 \times - 3} = 5[/tex]
To Prove
Soln:
[tex] \sqrt{4 \times - 3} [/tex]=[tex]2i \sqrt{3} [/tex]
=>[tex]2i \sqrt{3} ≠5[/tex]
Hence, 2i√3 is not equal (≠) to 5.
There are 500 passengers on a train. 7/20 are men and 40% are women. the rest are children
Answers
On the train, there are a total of 125 children.
Calculating the number of childrenTotal number of passengers = 500
Out of 500 passengers, men =7/20
So, the number of men= 500* 7/20 = 175
Out of 500 passengers, women = 40%
So, the number of women passengers = 500*40/100 = 200
Therefore, the total number of men and women passengers= 175+200 = 375.
There are also children on the train. So, the rest number should be those children.
The rest number =children= 500- 375 = 125.
So, it is concluded from the above equation that there are 125 children on the train.
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PLEASE HELP IM STUCK
Answers
Step-by-step explanation:
we have
2y = 4x - 9
and we want it to look like
...x + ...y = -9
simple.
the y term is already on the left side. we need to move the x term to the same side.
what do we do ? we subtract the term we want to get rid of on one side from both sides (we always have to do changes in both sides of the equation, or we change the whole meaning of the equation).
2y = 4x - 9 | -4x on both sides
-4x + 2y = -9
and we are finished. that's it.
Answer:
-4x + 2y = -9
Step-by-step explanation:
Pre-Solving InformationWe are given the equation 2y=4x-9, and we want to convert it into standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0.
SolvingNotice how in standard form, x and y are on the same side. Currently, x and y are on different sides.
Therefore, we first need to get x and y on the same side.
We can do this by subtracting 4x from both sides.
2y = 4x - 9
-4x -4x
_____________
-4x + 2y = -9
As indicated by the -9 on the left side, we have solved the question, and are now done.
Hence, the answer is -4x + 2y = -9.
52 = -5x - 3 i need help with a math test and this one question i do not understand
Answers
Answer:
x=-52/5-i3/5Step-by-step explanation:
[tex]52 = - 5x - 3i...given \: expression \\ - 5x - 3i = 52...switch \: sides \\ - 5x - 3i + 3i = 52 + 3i...add \: 3i \: to \: both \: sides \\ - 5x = 52 + 3i...simplify \\ \frac{ - 5x}{ - 5} = \frac{52}{ - 5} + \frac{3i}{ - 5} ...divide \: both \: sides \: by \: - 5 \\ x = \frac{ - 52}{5} - i \frac{3}{5} ...simplified[/tex]
Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?
Answers
Answer:
Step-by-step explanation:
70 = x/4
x = 4 cos 70 = 1.37m
x = 4 cos 80 = 0.69m
The range is ( 0.69m, 1.37m)
The range of distances from the wall (x) that the foot of the ladder placed to fall within the safety guidelines is between 0.7052 meters and 1.456 meters.
To determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines, use trigonometry.
Let's assume the distance from the wall to the foot of the ladder is x meters the ladder is 4 meters long.
The angle between the ladder and the ground is given to be between 70° and 80°. Let's consider the extreme cases for each angle:
When the ladder makes an angle of 70° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 70° = 20°.
When the ladder makes an angle of 80° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 80° = 10°.
Now, use trigonometry to calculate the range of distances (x) from the wall:
For the first case (θ = 20°):
tan(20°) = Opposite / Adjacent
tan(20°) = x / 4
x = 4 × tan(20°)
For the second case (θ = 10°):
tan(10°) = Opposite / Adjacent
tan(10°) = x / 4
x = 4 × tan(10°)
Now, let's calculate the values:
x ≈ 4 × 0.3640 ≈ 1.456 meters (rounded to three decimal places) - for the first case.
x ≈ 4 × 0.1763 ≈ 0.7052 meters (rounded to four decimal places) - for the second case.
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35. A can of popcorn is to be packed in a box for shipping as shown. The can is 18 inches tall and has a radius of 7 inches. The box is 19 inches tall and has a square base with sides of length 15 inches. All empty space around the can is to be filled with packing material. How many cubic inches of packing material will be needed?
Answers
The amount of packing material is 1506 cubic inches
How to determine the amount of packing material?The given parameters are:
Can
Radius, r = 7 inches
Height, h = 18 inches
Box
Base dimension, l = 15 inches
Height, h = 19 inches
The volume of the can is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V_1 = 3.14 * 7^2 * 18[/tex]
[tex]V_1 = 2769[/tex]
The volume of the box is
[tex]V =l^2h[/tex]
So, we have:
[tex]V_2 =15^2 * 19[/tex]
[tex]V_2 =4275[/tex]
The amount of packing material is;
Amount = V2 - V1
This gives
Amount = 4275 - 2769
Evaluate
Amount = 1506
Hence, the amount of packing material is 1506 cubic inches
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Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 72 degrees and the low temperature of 62 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Answers
The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.
Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.
We know that temperature is the intensity of the heat present around us.
We know that,
Maximum temperature=72 degrees,
Minimum temperature=62 degrees, which occurs at t=3 hours
Now we can write the equation as:
D(t)=A cos(ct)+B
Where A, c, B are constants.
We have a minimum at t=3 a minimum means cos(ct)=-1
then we have that D(3)=A cos(c*3)+B
=A*(-1)+b
=35°
Here we solve that ,
Cos(c*3)=-1
this means that
c*3=-1
c*3=π
c=π/3
We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1
D(t)=0=A(t)+B=72
With this we can find that values of A and b
-A+B=62
A+B=72
B=67
A=5
Equation will be D(t)=5 cos{(π/3)t}+67°.
Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..
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Diagram 1 shows a tangent to a circle, centre O. Find x and y; 40° y Diagram 1
Answers
Answer:
x = 80 , y = 50
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact is 90°
given the angle between the tangent and the chord is 40° , then
angle inside triangle = 90° - 40° = 50°
the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then
y = 50°
the sum of the 3 angles in the triangle = 180° , then
x = 180° - 50° - 50° = 180° - 100° = 80°
Answer:
x = 80°
y = 50°
Step-by-step explanation:
the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.
that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.
the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.
one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.
since both leg angles must be equal (as described above), y = 50° too.
and as the sum of all angles in a triangle must be 180°, that gives us for x
180 = 50 + 50 + x
x = 180 - 50 - 50 = 80°
which of thw following equations has roots x=-1, x=-2, and x=3i, and passes through the point (0,36)?
Answers
Answer:
C. f(x) = 2x⁴ +6x³ +22x² +54x +36
Step-by-step explanation:
You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.
Y-interceptThe given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.
Rule of signsDescartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.
Given rootsThe given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.
f(x) = 2x⁴ +6x³ +22x² +54x +36
Which equation represents this number sentence?
Nine more than the quotient of a number and 3 is 21.
n3+9=21
fraction n over 3 end fraction plus 9 equals 21
3n+9=21
fraction 3 over n end fraction plus 9 equals 21
n+93=21
fraction numerator n plus 9 end numerator over 3 end fraction equals 21
9n+3=21
Answers
The equation which represents the number sentence given in the task content is; n/3 + 9 = 21.
Which equation correctly represents the number sentence?According to the task content, it follows that the sentence given is; Nine more than the quotient of a number and 3 is 21.
Since, the quotient of a number and 3 can be written as; n/3.
Consequently, the correct equation is; n/3 +9 = 21.
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2sin^2(x)+sin(2x)=2
please help!!
Answers
[tex]2sin {}^{2} (x) + sin(2x) = 2 \\ 2sin {}^{2} (x) + 2sin(x)cos(x) = 2 \\ sin {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^{2} (x) + sin(x)cos(x) = 0[/tex]
[tex]cos(x)( - cos(x) + sin(x)) = 0[/tex]
[tex]cos(x) = 0 \\ x = \frac{\pi}{2} + k\pi \\ \\ sin(x) = cos(x) \\ x = \frac{\pi}{4} + k\pi[/tex]
Triangle E D F is shown. Angle E D F is 43 degrees and angle D F E is 82 degrees. The length of D F is 15.
What is the measure of angle E?
m∠E =
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
Answers
Part 1
Angles in a triangle add to 180 degrees, so
[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]
Part 2
By the Law of Sines,
[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]
Answer:
What is the measure of angle E?
m∠E =
✔ 55
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
✔ 12.49
Step-by-step explanation:
Please someone help me, I don't get it
Answers
Answer:
a) x = 1.5 and x = -0.3
b) x = -8 and x = 5
Step-by-step explanation:
a)
The given equation follows the general structure: ax² + bx + c = 0.
Therefore, if a = 5, b = -6, and c = -2, you can substitute the values into the quadratic formula and solve for "x".
b)
Another way of solving polynomials is through factorization. After rearranging the equation to fit the general structure of a quadratic (as seen above), you can factor by asking yourself the question, which 2 numbers multiply to "c" (-40) and add to "b" (3)? The answers will make up your factors.
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1. }[/tex]
[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]
[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]
[tex]\huge\textbf{Simplify that as well:}[/tex]
[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + 3x = 40}[/tex]
[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]
[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]
[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]
[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]
[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 5\ or\ x = -8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PR=
Help me please thanks so much
Answers
Formula: U*V=R*T
3*1=4*x
3=4x
x=3/4
Hope it helps!
Answer:
[tex]\sf PR =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Intersecting chords theorem:It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.
TP * PR = UP * PV
4 * PR = 3 * 1
[tex]\sf PR = \dfrac{3}{4}[/tex]
A gym class has $12$ students, $6$ girls and $6$ boys. The teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. If the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys
Answers
Answer:
2700
Step-by-step explanation:
*6*10*9/4!*4*4*6*5/4!