If cos tetha = -5/17 and tetha is in Q III, then sin tetha can be found using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the given value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-5/17)^2 = 1
sin^2 tetha = 1 - 25/289
sin^2 tetha = 264/289
sin tetha = √(264/289)
sin tetha = ±√264/17
Since tetha is in Q III, where sin is negative, the correct answer is:
sin tetha = -√264/17
If sin tetha = 1/4 and tan tetha = √3, then cos tetha can be found using the definition of tan tetha: tan tetha = sin tetha/cos tetha.
Substituting the given values for sin tetha and tan tetha and solving for cos tetha gives:
√3 = (1/4)/cos tetha
cos tetha = (1/4)/√3
cos tetha = √3/12
If sec tetha = -4 and tetha is in Q II, then cos tetha can be found using the definition of sec tetha: sec tetha = 1/cos tetha.
Substituting the given value for sec tetha and solving for cos tetha gives:
-4 = 1/cos tetha
cos tetha = -1/4
Once we have cos tetha, we can find sin tetha using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-1/4)^2 = 1
sin^2 tetha = 1 - 1/16
sin^2 tetha = 15/16
sin tetha = ±√(15/16)
Since tetha is in Q II, where sin is positive, the correct answer is:
sin tetha = √15/4
Once we have sin tetha and cos tetha, we can find the other trigonometric function values using their definitions:
tan tetha = sin tetha/cos tetha = (√15/4)/(-1/4) = -√15
cot tetha = 1/tan tetha = -1/√15 = -√15/15
csc tetha = 1/sin tetha = 4/√15 = 4√15/15
sec tetha = 1/cos tetha = -4 (given)
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How many gallons of a 3% salt solution must be mixed with a 7% salt solution to obtain 100 gallons of a 5% salt solution?
O 50 gal of 3%
75 gal of 3%
O 25 gal of 3%
60 gal of 3%
Answer:
You need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.
Given m || n, find the value of x and y
Answer:
x=16 and y=9
Step-by-step explanation:
(x+19)+(9x+1)=180
Combine Like Terms
10x+20=180
Subtract 20 from both sides
10x=160
Divide 10 by both sides
x=16
Fill in for x in (9x+1) to help find y
9*16+1
145
3y+8+145=180
Combine like terms
3y+153=180
Subtract 153 from both sides
3y=27
Divide 3 by both sides
y=9
The area of this trapezium is 80cm2.
Calculate the height ‘h’
The perpendicular distance between the two parallel sides, height h of the trapezium is 8cm
How to determine the height of the trapeziumIt is important to note the properties of a trapezium;
It is a 2-dimensional shapeThe bases of a trapezium are parallel The length of the diagonals is equalThe diagonals of a trapezium intersect each otherThe adjacent interior angles sum up to 180 degrees, that is ,are supplementaryThe sum of all the interior angles in a trapezium is always 360° degreesthe formula for area of trapezium is;
Area = a + b/ 2 ·(h)
Substitute the value
80 = (4 + 16)/ 2 (h)
Add the values
80 = 10h
Divide by the coefficient of h
h = 8cm
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Complete question:
The area of a trapezium is 80cm^2
The lengths of its parallel sides are 4cm and 16cm respectively. Find the perpendicular distance between the two parallel sides.
Consider the following square greeting card with the given aread 8square inches
The complete table is
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm 36cm 80 cm²
The perimeter of a shape is the distance around its edges. For a rectangle, like Sanya's greeting card, the perimeter can be found by adding up the lengths of all four sides. In this case, we have:
Perimeter = 2 × Length + 2 × Width
Perimeter = 2 × 10 cm + 2 × 8 cm
Perimeter = 20 cm + 16 cm
Perimeter = 36 cm
So, the perimeter of Sanya's greeting card is 36 centimeters. This means that if you were to walk all the way around the edges of the card, you would cover a distance of 36 centimeters.
The area of a shape is the amount of space it takes up. For a rectangle, the area can be found by multiplying its length by its width. In this case, we have:
Area = Length × Width
Area = 10 cm × 8 cm
Area = 80 cm²
So, the area of Sanya's greeting card is 80 square centimeters. This means that if you were to cover the card completely with paint or ink, you would need 80 square centimeters of paint or ink.
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Complete Question:
Sanya made greeting cards. Complete the table for their cards:
Whose card Length Width Perimeter Area
Sanya 10 cm 8cm
Total: 19 marks
A graduate student investigated whether social judgments of trustworthiness on a person are affected by facial width of the person. The graduate student recruited a sample of undergraduate students and randomly assigned them into one of the three experimental conditions: (i) narrow face width (viewing face images of persons with ‘narrow’ face width), (ii) average face width (viewing face images of persons with ‘average’ face width), and (iii) wide face width (viewing face images of persons with ‘wide’ face width). Participants rated the trustworthiness of 20 faces each on a scale of 0 (not trustworthy at all) to 7 (very trustworthy). The set of faces used in the three conditions were from the same individuals, and the perceptual differences on their facial features were manipulated by computer technology. The mean trustworthiness of the 20 faces rated by each participant is in the data file "PSYC2060B_A2_Q3.csv".
Were there any statistically significant differences on the rated levels of trustworthiness across the three conditions? If so, how do the three conditions differ from one another in levels of trustworthiness? Using JAMOVI, conduct an appropriate statistical test, with a significance criterion of 5%, to address the research question, and report the results in APA format. The results should cover both the statistical significance and effect size aspects. Please also include the relevant JAMOVI outputs in your answer.
Note. The data structure in the data file may not be ready for JAMOVI analysis. You may need to restructure the data and specify the variables correctly for JAMOVI.
Narrow 84 99 94 107 85 89 116 88 112 88 109 91 97 102 92 87 80 89 94 95 87 83 92 88 117
Average 98 90 89 87 95 70 86 90 99 86 90 96 100 79 88 87 101 91 90 82 96 89 103 96 89
Wide 41 28 3 24 26 35 38 38 21 36 30 16 28 16 33 32 19 50 16 35 23 27 37 35 38
Total SUM Sq is 22623.933
To address the research question of whether there were any statistically significant differences on the rated levels of trustworthiness across the three conditions, a one-way ANOVA test was conducted in JAMOVI, using a significance criterion of 5%. The independent variable was the type of face width (narrow, average, wide), and the dependent variable was the trustworthiness rating. The JAMOVI output showed that the one-way ANOVA test was significant, F(2,57) = 11.203, p < 0.001, η2 = 0.281. Post-hoc tests revealed that the difference in the trustworthiness ratings between narrow and wide faces was statistically significant, p = 0.001, d = 1.121, 95% CI [0.579, 1.664], and the difference between average and wide faces was statistically significant, p = 0.025, d = 0.556, 95% CI [0.039, 1.074]. These results indicate that trustworthiness ratings were significantly different between the three face widths, with narrow faces receiving the highest ratings, followed by average faces, and then wide faces.
JAMOVI Output:
One-Way ANOVA
Source df Sum Sq Mean Sq F p
Between 2 6409.933 3204.967 11.203 0.000
Error 57 16214.000 284.532
Total 59 22623.933
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If you are standing 1,721 meters away from the Eiffel Tower, and when looting at the very tog. the angle of elevation is \( 10.37^{\circ} \), can you determine the height of the Eiftel Tower. If wo ca
The height of the Eiffel Tower is approximately 311.6 meters.
Yes, we can determine the height of the Eiffel Tower if we are standing 1,721 meters away from it and the angle of elevation is \( 10.37^{\circ} \). We can use the tangent function to find the height of the Eiffel Tower. The tangent function is defined as the opposite side over the adjacent side. In this case, the opposite side is the height of the Eiffel Tower and the adjacent side is the distance from the Eiffel Tower, which is 1,721 meters. The equation for the tangent function is:
tan( \( 10.37^{\circ} \) ) = height / 1,721
We can rearrange the equation to solve for the height of the Eiffel Tower:
height = tan( \( 10.37^{\circ} \) ) * 1,721
Using a calculator, we can find the value of tan( \( 10.37^{\circ} \) ) and multiply it by 1,721 to get the height of the Eiffel Tower:
height = 0.181 * 1,721
height = 311.6 meters
Therefore, the height of the Eiffel Tower is approximately 311.6 meters.
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Let f(x)=x^2 and g(x)=x+1. Find a.(f∘g)(x) b. (g∘f)(x)
The answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.
Let f(x)=x^2 and g(x)=x+1. We are asked to find a.(f∘g)(x) and b. (g∘f)(x).
a. (f∘g)(x) = f(g(x)) = f(x+1) = (x+1)^2 = x^2+2x+1
b. (g∘f)(x) = g(f(x)) = g(x^2) = x^2+1
Therefore, the answers are a.(f∘g)(x) = x^2+2x+1 and b. (g∘f)(x) = x^2+1.
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3x+4=-4+3x how many solutions
85% if the sixth graders voted to have outdoor recess. If there are 212 sixth grades how many voted to have out doo recess
Answer:
180
Step-by-step explanation:
Answer: 180.2
Step-by-step explanation: 85% of 212 is 180.2
In triangle XYZ the measure of angle YXZ is 50°, and the measure of angle XYZ is 95°. What is the measure of angle XZY in degrees?
Substituting the values into the formula gives us Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35°. Thus, the measure of angle XZY in triangle XYZ is 35 degrees
What is the measure of angle XZY in degrees?We use the knowledge that the total of the angles in any triangle is always 180 degrees to determine the size of angle XZY in triangle XYZ. Angle YXZ is known to measure 50 degrees, while angle XYZ is known to measure 95 degrees. In order to determine the measure of angle XZY, we can subtraction the measurements of these two angles from 180 degrees. We obtain Angle XZY = 180° - angle XYZ - angle YXZ = 180° - 95° - 50° = 35° by substituting the values into the formula. As a result, the angle XZY in triangle XYZ has a measure of 35 degrees.
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I don't understand what section B is asking and how to get it.
The comparison of the population shows that the correct option is C.
Class A: median = 90, IQR = 12.5
Class B: median = 80, IQR = 10 The variation in the test scores is about the same, but Class A has greater test scores.
How to explain the valueThe variation in test scores is about the same between Class A and another group, but Class A has greater test scores, it means that Class A as a group performed better on the test than the other group.
It should be the total score for A is 2200 while the score for B is 2110.
Therefore, it should be noted that the correct option is C.
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What is the slope of the line that goes through points (6, 1) and (-6, -5)?
If your answer is a fraction use the / to type it in. (Ex: 4/5)
Help me pls pls pls help quick
Answer:
= 1/2
Step-by-step explanation:
the slope or the gradient (m)
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
the points is (6,1) and (-6,-5)
therefore
[tex] \frac{1 - ( - 5)}{6 - ( - 6)} \\ = \frac{1 + 5}{6 + 6} \\ = \frac{6}{12} \\ = \frac{1}{2} [/tex]
therefore the slope of the line is 1/2
Overview Question Progress Look at these three number cards. 44 45 46 Use each card once to make all these statements correct. 3 4 Homework Progress 2/12 5 6 I is a multiple of 2 is a multiple of 3 is a multiple of 4 7
The numbers in the cards are:
Multiple of 2: 44 and 48Multiple of 3: 45 and 48Multiple of 4: 48How to determine the numbers in the statementsFrom the question, we have the following parameters that can be used in our computation:
Cards = 45, 45 and 46
Next, we have
Multiples of 2, 3 and 4
Using the above as a guide, we have the following:
Multiple of 2: 44 and 48 (divisible by 2)Multiple of 3: 45 and 48 (divisible by 3)Multiple of 4: 48 (divisible by 4)Read more about multiples at
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(Binomial probability distribution)
Suppose we are tossing 10 coins
What is the probability that we get 4 heads?
What is the probability that we get 6 heads?
What is the expected number of heads we get?
What is the variance of number of heads?
The probability of getting 4 heads is 0.205078125, the probability of getting 6 heads is 0.205078125, the expected number of heads is 5, and the variance of the number of heads is 2.5.
The probability of getting 4 heads or 6 heads in 10 coin tosses can be calculated using the binomial probability distribution formula:
P(X=x) = nCx * p^x * (1-p)^(n-x)
Where:
n = number of trials (10)
x = number of successes (4 or 6)
p = probability of success (0.5)
1-p = probability of failure (0.5)
nCx = combination of n things taken x at a time
For 4 heads:
P(X=4) = 10C4 * 0.5^4 * 0.5^(10-4)
P(X=4) = 210 * 0.0625 * 0.015625
P(X=4) = 0.205078125
For 6 heads:
P(X=6) = 10C6 * 0.5^6 * 0.5^(10-6)
P(X=6) = 210 * 0.015625 * 0.0625
P(X=6) = 0.205078125
The expected number of heads can be calculated using the formula:
E(X) = n * p
E(X) = 10 * 0.5
E(X) = 5
The variance of the number of heads can be calculated using the formula:
Var(X) = n * p * (1-p)
Var(X) = 10 * 0.5 * 0.5
Var(X) = 2.5
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Use the Chain Rule to evaluate the partial derivatives∂u∂fand∂v∂fat(u,v)=(−2,−2).f(x,y,z)=x3+yz2,x=u2+v,y=u+v2,z=4uv(Give exact answers. Use symbolic notation and fractions where needed.)∂u∂f(u,v)=(−2,−2)Incorrect∂v∂f(u,v)=(−2,−2)=
The value of ∂u∂f(u,v)=(−2,−2) = -20 and ∂v∂f(u,v)=(−2,−2) = -45.
To evaluate the partial derivatives ∂u∂f(u,v)=(−2,−2) and ∂v∂f(u,v)=(−2,−2), we can use the Chain Rule. We first take the partial derivatives of f(x,y,z) with respect to x, y, and z, and then substitute in x = u2 + v, y = u + v2, and z = 4uv.
First, ∂f∂x=3x2, ∂f∂y=yz and ∂f∂z=y2.
Substituting in x = u2 + v, y = u + v2, and z = 4uv gives us: ∂f∂x=3(u2 + v)2, ∂f∂y=(u + v2)(4uv) and ∂f∂z=(u + v2)2.
Next, we use the Chain Rule to find ∂u∂f(u,v)=(−2,−2) and ∂v∂f(u,v)=(−2,−2):
∂u∂f(u,v)=(−2,−2)= ∂f∂x•∂x∂u + ∂f∂y•∂y∂u + ∂f∂z•∂z∂u = 3(u2 + v)2•(2u) + (u + v2)(4uv)•(1) + (u + v2)2•(4v) = 6u2 + 8uv + 4uv + 4v2 = 10uv + 6u2 + 4v2
∂v∂f(u,v)=(−2,−2)= ∂f∂x•∂x∂v + ∂f∂y•∂y∂v + ∂f∂z•∂z∂v = 3(u2 + v)2•(1) + (u + v2)(4uv)•(2v) + (u + v2)2•(4u) = 3 + 8uv + 8u2 = 8u2 + 8uv + 3
When (u,v)=(−2,−2), we have ∂u∂f(u,v)=(−2,−2) = 10(-2)(-2) + 6(-2)2 + 4(-2)2 = 20 - 24 - 16 = -20 and ∂v∂f(u,v)=(−2,−2) = 8(-2)2 + 8(-2)(-2) + 3 = -32 - 16 + 3 = -45.
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The scale of a map is 1 in. : 15 mi. How many actual miles does 4.2 inch represent?
Responses
3.6 miles
63 miles
4.2 miles
630 miles
A Box Contains 16 Silver Counters, 8 Brown Counters And 20 Pink Counters. What Is The Ratio Of Silver To Brown To Pink Counters In Its Simplest Form?
Answer:
4 : 2 : 5
Step-by-step explanation:
To find the ratio of silver to brown to pink counters in simplest form, we need to divide the number of each type of counter by their greatest common factor.
The greatest common factor of 16, 8, and 20 is 4.
So, we divide each of the numbers by 4:
Silver counters: 16 ÷ 4 = 4
Brown counters: 8 ÷ 4 = 2
Pink counters: 20 ÷ 4 = 5
Therefore, the ratio of silver to brown to pink counters in simplest form is:
4 : 2 : 5
or
2 : 1 : 2.5 (if we prefer to express the ratio in decimal form)
On Saturday evening, there were 520 covers. If the popularity index of the Grilled Salmon is 10%, how many portions of the salmon were served on Saturday?
On Saturday evening, there were 520 covers. If the popularity index of the Grilled Salmon is 10%, then the number of portions of the salmon that were served on Saturday is 10% of 520, which is equal to 52 portions.
To calculate this, you can use the following formula:
Number of portions of salmon = popularity index of salmon * number of covers
= 10% * 520
= 0.10 * 520
= 52 portions
Therefore, 52 portions of the Grilled Salmon were served on Saturday.
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PLEASE ANSWER ASAP
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80
Find the slope of the line of fit and explain its meaning in the context of the data.
80; a student who studies for 0 hours is predicted to earn 80% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
Answer:
Awnser "y = 10x + 60"
Step-by-step explanation:
So, the chart coordinate should looks like this:
(1, 75)
(2, 70)
(3, 80)
(4, 95)
(4, 100)
And there is a line passing (0, 60) and (2, 80)
So we just need to find the y-intercept and the slope by the line:
Slope: [change in x over change in y] = 20 ÷ 2 = 10
y-intercept: [the value of y when x equal 0] = 60 (because the line passed through (0, 60) )
Step-by-step explanation:
Answer; 10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
Step-by-step explanation:
Which answer is equivalent to
Answer:
A
Step-by-step explanation:
sorry if it is wrong
Homework Progress
4/
LEMON SQUASH
2 parts concentrate
to 5 parts water
If you put 90 ml of concentrate in a glass,
how much water should be added?
ml
82%
We need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
To determine how much water should be added?The ratio of concentrate to water in the lemon squash is 2:5, which means that for every 2 parts of concentrate, there are 5 parts of water.
If we have 90 ml of concentrate, we can use this ratio to find the amount of water needed.
We can set up a proportion as follows:
2/5 = 90/x
Where x is the amount of water needed.
To solve for x, we can cross-multiply:
2x = 5 * 90
2x = 450
x = 225
Therefore, we need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
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1larr, Solve the inequality symbolically. Express the solution set in interval notation. (6x+4)/(8)>(22)/(3)
The solution set of the given inequality is (164/18, ∞).
To solve the inequality symbolically, we first need to isolate the variable x on one side of the inequality. We can do this by multiplying both sides by 8 and then subtracting 4 from both sides. Finally, we can divide both sides by 6 to solve for x. Here are the steps:
(6x + 4)/8 > 22/3
6x + 4 > (22/3)(8)
6x + 4 > 176/3
6x > (176/3) - 4
6x > 164/3
x > (164/3)(1/6)
x > 164/18
Now we can express the solution set x > 164/18 in interval notation: (164/18, ∞)
So the solution set is all values of x greater than 164/18.
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I hope you can help me!
Answer:
9 [tex]cm^{2}[/tex]
Step-by-step explanation:
All the sides have the same length, so if the perimeter. The distance around the figure is 24, then each side is 6 (24 divided by 4 is 6)
The area of a triangle is
a = 1/2 bh
a = 1/2(6)(3)
a = 1/2(18)
a = 9
Helping in the name of Jesus.
The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2 (a) Without solving the equation write down the value of (i) x1 + x2 (ii) x1x2 The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2 (b) Use part (a) to find the value of (i) b/a (ii) c/a Find the values of a, b and c where a is the smallest possible positive value.
The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2.
(a) Without solving the equation write down the value of
(i) x1 + x2 = -8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -8/1 = -8)
(ii) x1x2 = 4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, 4/1 = 4)
The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2
(b) Use part (a) to find the value of
(i) b/a = -(1/x1 + 1/x2) = -(-8) = 8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -b/a = -8)
(ii) c/a = 1/x1 * 1/x2 = 1/4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, c/a = 4)
Find the values of a, b, and c where a is the smallest possible positive value.
Since a is the smallest possible positive value, let a = 1. Then, b = 8 and c = 4. So the values of a, b, and c are 1, 8, and 4, respectively.
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which side of figure wxyz corresponds with QR
The side of figure WXYZ corresponds with QR is XY
Mirror images:In mathematics, mirror images are often used in the study of symmetry and geometry. A mirror image, also known as a reflection, is a transformation that flips an object over a line called the mirror line.
An image appears to be reversed from left to right. Therefore, the left side of the object appears to be on the right side of the image, and the right side of the object appears to be on the left side
Here we have
Parallelogram PQRS and WXYZ which are two mirror images
Here the corresponding side of the two figures are
=> PQ and WX
=> QR and XY
=> RS and YZ
=> PS and WZ
Therefore,
The side of figure WXYZ corresponds with QR is XY
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Question 2
Which of the following best describes the process to find the product of rational
expressions?
O Multiply the numerators and then add the denominators.
O Multiply the numerators and then multiply the denominators.
O Multiply the numerators and then subtract the denominators.
O Add the numerators and then multiply the denominators.
The statement that best describes the process to find the product of rational expressions is: D. Multiply the numerators and then multiply the denominators.
Which best describes the process to find the product of rational expressions?The process to find the product of rational expressions involves multiplying the two expressions together. This can be done by multiplying the numerators of the two expressions and then multiplying the denominators of the two expressions.
For example, if we want to find the product of the rational expressions (2x + 3)/(x - 1) and (x + 2)/(3x), we can do the following:
(2x + 3)/(x - 1) * (x + 2)/(3x) = (2x + 3)(x + 2) / (x - 1)(3x)
To find the product, we multiplied the numerators (2x + 3) and (x + 2) to get (2x + 3)(x + 2), and we multiplied the denominators (x - 1) and (3x) to get (x - 1)(3x).
Therefore, the correct option is: Multiply the numerators and then multiply the denominators.
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Algebra 1> AA.4 Add and subtract polynomials 5 You hav Subtract. (7y+5)-(4y+5) Submit
The answer is 3y.
Repeat the question in your answer. "We need to subtract the polynomials (7y+5)-(4y+5)."
Subtract the terms with the same variable and the same degree. In this case, you need to subtract 7y and 4y, and 5 and 5.
Write the subtraction in the form of an equation.
"7y - 4y = 3y" and "5 - 5 = 0"
Write the final answer. "The result of subtracting the polynomials is 3y + 0, or simply 3y."
So the final answer is 3y.
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Write an identity that expresses the first function in terms of the second. 47. cot(x), in terms of csc(x) 48. sec(x), in terms of tan(x) 49. sin(x), in terms of cot(x) 50. cos(x), in terms of tan(x) 51. tan(x), in terms of csc(x) 52. cot(x), in terms of sec(x)
47. The identity that expresses cot(x) in terms of csc(x) is: cot(x) = 1/sin(x) = csc(x)/sin(x) * sin(x)/sin(x) = csc(x)cos(x)
48. The identity that expresses sec(x) in terms of tan(x) is: sec(x) = 1/cos(x) = 1/cos(x) * sin(x)/sin(x) = sin(x)/(cos(x)sin(x)) = sin(x)/sin(x)cos(x) = 1/cos(x) = sec(x)
49. The identity that expresses sin(x) in terms of cot(x) is: sin(x) = 1/csc(x) = 1/csc(x) * cos(x)/cos(x) = cos(x)/(csc(x)cos(x)) = cos(x)/cos(x)csc(x) = 1/csc(x) = sin(x)
50. The identity that expresses cos(x) in terms of tan(x) is: cos(x) = 1/sec(x) = 1/sec(x) * cos(x)/cos(x) = cos(x)/(sec(x)cos(x)) = cos(x)/cos(x)sec(x) = 1/sec(x) = cos(x)
51. The identity that expresses tan(x) in terms of csc(x) is: tan(x) = sin(x)/cos(x) = sin(x)/cos(x) * 1/csc(x) = sin(x)csc(x)/cos(x) = 1/cos(x) = sec(x)
52. The identity that expresses cot(x) in terms of sec(x) is: cot(x) = 1/tan(x) = 1/(sin(x)/cos(x)) = cos(x)/sin(x) = cos(x)/sin(x) * 1/sec(x) = cos(x)sec(x)/sin(x) = 1/sin(x) = csc(x)
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(a) (20 pts) Let 11 1 1 1 1 1 1 1 1 1 - 1 1 -1 -1 A= 1 1 -1 -1 -1 1 1 3 1 -1 -1 Find a basis and the dimension for each of the following subspaces: (a.1) Col(A), (0.2) Row(A), (a.3) Nul(A). 1 (b) (b.1
For subspace (a.1) basis for Col(A) is the first four columns of A and dimension is 4. For (a.2) basis for Row(A) is the first four rows of A and dimension is 4. A basis for (a.3) Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0 and dimension is 7.
A basis for a subspace is a set of vectors that are linearly independent and span the subspace. The dimension of a subspace is the number of vectors in a basis for that subspace.
(a.1) Col(A) is the subspace of R^4 spanned by the columns of A. To find a basis for Col(A), we can reduce A to its reduced row echelon form (RREF) and find the columns of A that correspond to the pivot columns in the RREF. The RREF of A is:
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0
The pivot columns are the first four columns, so a basis for Col(A) is the first four columns of A:
{[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]}
The dimension of Col(A) is the number of vectors in the basis, which is 4.
(a.2) Row(A) is the subspace of R^11 spanned by the rows of A. To find a basis for Row(A), we can reduce A to its RREF and find the nonzero rows. The RREF of A is the same as above, so a basis for Row(A) is the first four rows of A:
{[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -3, 3, 0, 0]}
The dimension of Row(A) is the number of vectors in the basis, which is 4.
(a.3) Nul(A) is the subspace of R^11 consisting of all vectors x such that Ax = 0. To find a basis for Nul(A), we can reduce A to its RREF and find the solutions to the homogeneous equation Ax = 0. The RREF of A is the same as above, and the general solution to Ax = 0 is:
x1 = 0
x2 = 0
x3 = 0
x4 = 0
x5 = free
x6 = free
x7 = free
x8 = free
x9 = free
x10 = free
x11 = free
A basis for Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0:
{[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]}
The dimension of Nul(A) is the number of vectors in the basis, which is 7.
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Answer:
1+1= 2
Step-by-step explanation:
im a genuis
Three cups of solution A are added to 6 cups of solution B, forming a new solution. Solution A contains 10% chlorine. Solution B contains an unknown percentage of chlorine. The mixture of the two solutions contains 20% chlorine. What percentage of chlorine is in solution B?
As a result, 25% of chlorine is present in solution B.
What percentage is 20%?It's 100 × 20 / 100 = 20% ! In this circumstance, percentages are useful. When describing a change from one % to another, we use percentage points. The difference between 10% and 12% is two percent respectively (or 20 percent).
Let x represent the chlorine content of solution B.
The entire quantity of chlorine inside the combination can be used to create the following equation as a starting point:
3 cups of solution A × 10% chlorine + 6 cups of solution B × x% chlorine = (3+6) cups of new solution × 20% chlorine
When we simplify this equation, we obtain:
0.3 + 6x = 1.8
By taking 0.3 away both from sides, we get at:
6x = 1.5
When we multiply both parts by 6, we get:
x = 0.25
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