Quadilateral RUST has a vertex at R (1,5)what are the coordinates of R after after the translation (x,y) x +1 y-1 after a dual ion of 2
Answers
After applying a translation of (x, y) → (x + 1, y - 2) and a dilation with a scale factor of 3 centered at the origin, the original coordinates of R (1, 5) transform to the new coordinates (6, 9).
Let's consider the given quadrilateral RUST with vertex R at coordinates (1, 5). We need to apply a translation followed by a dilation to find the new coordinates of R.
The translation is given by the transformation (x, y) → (x + 1, y - 2), which means that we will shift the figure 1 unit to the right along the x-axis and 2 units downward along the y-axis.
To find the new coordinates after the translation, we can apply the translation to the original coordinates of R:
x' = x + 1
y' = y - 2
Substituting the original coordinates of R into these equations:
x' = 1 + 1 = 2
y' = 5 - 2 = 3
After the translation, the new coordinates of R are (2, 3).
A dilation involves resizing a figure by a certain scale factor. In this case, the scale factor is 3, and the center of dilation is the origin (0, 0).
To perform the dilation, we multiply the coordinates of the translated point R by the scale factor. Let's denote the new coordinates after dilation as (x'', y'').
x'' = scale factor * x'
y'' = scale factor * y'
Substituting the translated coordinates of R into these equations and using the scale factor of 3:
x'' = 3 * 2 = 6
y'' = 3 * 3 = 9
After the dilation, the new coordinates of R are (6, 9).
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Complete Question:
Quadrilateral RUST has a vertex at R (1,5)What are the coordinates of R after the translation (x, y) (x+ 1, y - 2),followed by a dilation by a scale factor of 3, centered at the origin?
Related Questions
You measure 38 turtles' weights, and find they have a mean weight of 62 ounces. Assume the population standard deviation is 11.9 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight.
Answers
The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is approximately 3.433 ounces.
To find the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight given that you measure 38 turtles' weights, and find they have a mean weight of 62 ounces and the population standard deviation is 11.9 ounces, you can use the formula for margin of error, which is:
Margin of Error = Zα/2 * (σ/√n)
where Zα/2 is the critical value for the desired confidence level (in this case, 90% confidence), σ is the population standard deviation, and n is the sample size.
Substituting the given values, we have:
Margin of Error = 1.645 * (11.9/√38)
≈ 3.433
Therefore, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is approximately 3.433 ounces.
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Tri-County G\$T selis 150,000 MWh per yeat of electrical power to Boulder at $80 per MWh, has fixed costs of $80.1 milion per yoar, and has varistele costs of $20 por MWh. If Tri-County has 1,000,000MW h of demand from its customers (other than Boulder), what will Tri-County have to charge to break even? Tri-County wit have to charge? to break oven. (Enter your response rounded to the nearest penny.)
Answers
Tri-County will have to charge approximately $83.1 per MWh to break even.
To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.
The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.
To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.
Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.
Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh
Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.
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I hope y'all can help me with this question!
2/6 = ?/18
Answers
Answer:
\(\frac{2}{6} =\frac{6}{18}\)
Step-by-step explanation:
Compare the denominators. Since 6 ⋅ 3 = 18 , multiply the numerator 2 by 3 to get 6
5\(5x-3y=34\\x-2y=4\)
Answers
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 20 units of protein, 15 units of vitamin A, and 10 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 5 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 5 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 5 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 8 cents per ounce, and eggs cost 12 cents per ounce.
Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken
and 0.52 ounces of tomatoes. Which of the following statements is BEST?
The serving costs about 20 cents.
The serving costs about 30 cents
The serving costs about 50 cents.
The serving costs about 40 cents.
Answers
the BEST statement is: The serving costs about 40 cents.
To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.
Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:
Cost of chicken =\(0.89 ounces * $0.40/ounce\)
Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)
Total cost = Cost of chicken + Cost of tomatoes
Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)
Total cost =\($0.356 + $0.0416\)
Total cost ≈\($0.3976\)
Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.
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Are the following triangles similar? Explain.
Answers
Answer:
yes
the sides bear a similar proportion to each other
CE = 1.67BC
CD = 1.67AC
Step-by-step explanation:
Two triangles are similar if the corresponding angels are congruent to each other and if the sides of the triangle are in proportion to each other
to determine if the triangles are similar, determine if the sides are in proportion to each other
CE = 10
BC = 6
10 / 6 = 1.67
DC = 15
AC = 9
15/9 = 1.67
The sides of the triangle are in proportion to each other, thus they are similar
Let S, T , X, and Y be subsets of some universal set. Assume that
242 Chapter 5. Set Theory
(i) S [T X [Y; (ii) S \T D;; and (iii) X S.
(a) Using assumption (i), what conclusion(s) can be made if it is known that a 2 T ? (b) Using assumption (ii), what conclusion(s) can be made if it is known that a 2 T ? (c) Using all three assumptions, either prove that T Y or explain why it
Answers
Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. A subset is a set that contains only elements that belong to a larger set, called the universal set. In this context, let S, T, X, and Y be subsets of some universal set.
Assuming that S [T X [Y, we can conclude that if a belongs to T, then a belongs to S or a belongs to X or a belongs to Y. This is because T is a subset of S [T X [Y, and any element in T must belong to at least one of these sets.
Assuming that S \T D, we can conclude that if a belongs to T, then a does not belong to S. This is because S \T is the set of elements that belong to S but not to T, and D is the empty set, meaning that there are no elements in the set. Therefore, if a belongs to T, it cannot belong to S \T, and so it must not belong to S.
Assuming that X S, we can use all three assumptions to prove that T Y. Suppose that a belongs to T. Then, using assumption (i), we know that a belongs to S or a belongs to X or a belongs to Y. But since a cannot belong to S (using assumption (ii)), we must have either a belongs to X or a belongs to Y. But since X is a subset of S (using assumption (iii)), we know that if a belongs to X, then a belongs to S. Therefore, we must have a belongs to Y. This holds for any element a in T, so we can conclude that T Y.
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Solve for x. Enter the solutions from least to greatest.
(x+7)^2 −49=0
Help plz
Answers
Answer:
x=0
Step-by-step explanation:
We can first add 49 to both sides to get (x+7)^2=49
We can then take the square root of both sides and get x+7=7
Subtract 7 to both sides and you get x=0
Answer:
\(x=-14\text{ and } x=0\)
Step-by-step explanation:
We are given:
\((x+7)^2-49=0\)
And we want to solve for x.
First, we can add 49 to both sides:
\((x+7)^2=49\)
Now, we can take the square root of both sides. Since we are taking an even root, we will need plus-minus. Hence:
\(x+7=\pm\sqrt{49}\)
Evaluate:
\(x+7=\pm7\)
Subtract 7 from both sides:
\(x=-7\pm7\)
So, we have two solutions:
\(x=-7+7\text{ and } x=-7-7\)
Evaluate:
\(x=0\text{ and } x=-14\)
So, from least to greatest, our solutions are:
\(x=-14\text{ and } x=0\)
Which is a possible way to rewrite the equation y = 3x + 3b to solve for b?
Answers
Answer:
Well you have to move the 3x to the same side as the y, and you do that by subtracting it. Then finally divide by 3 to get b by itself
Step-by-step explanation:
y=3x+3b
y-3x=3b
(y-3x)/3=b
Use the figure to find the exact value of the trigonometric function
Answers
In given figure we have right angled triangle,
with
Hypotenuse=5
perpendicular=3
Base=4
Apply the trignometric expression for tanΘ
\(\tan \emptyset=\frac{Perpendicular}{\text{base}}\)Substitute the value of Perendicular and base,
\(\tan \emptyset=\frac{3}{4}\)Multiply bothe side by arc(tan)
\(\begin{gathered} \arctan (\tan \emptyset)=\arctan \frac{3}{4} \\ \emptyset=\arctan \frac{3}{4} \end{gathered}\)The trignometric expression for tan2Θ is:
\(\tan 2\emptyset=\frac{2\tan \emptyset}{1-\tan ^2\emptyset}\)Put the value of Θ in the tan2Θ
\(\begin{gathered} \tan 2\emptyset=\frac{2\tan (\arctan \frac{3}{4)}}{1-\tan ^2(\arctan \frac{3}{4})} \\ \tan 2\emptyset=\frac{2\frac{3}{4}}{1-(\frac{3}{4})^2} \\ \tan 2\emptyset=\frac{\frac{6}{4}}{1-\frac{9}{16}} \\ \tan 2\emptyset=\frac{\frac{6}{4}}{\frac{16-9}{16}} \\ \tan 2\emptyset=\frac{\frac{6}{4}}{\frac{7}{16}} \\ \tan 2\emptyset=\frac{6}{4}\times\frac{16}{7} \\ \tan 2\emptyset=\frac{6\times4}{7} \\ \tan 2\emptyset=\frac{24}{7} \end{gathered}\)ANSWER : (D). 24/7
The exact value of the trigonometric function is tan2θ = 15/8.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The figure given in the question has a right-angled triangle,
As per the given triangle,
Hypotenuse = 5
Perpendicular = 3
Base = 4
Apply the trignometric expression for tanθ
⇒ tanθ = Perpendicular / Base
⇒ tanθ = 3/5 ....(i)
We know that the identity of tangent functions as
⇒ tan2θ = 2tanθ /(1 - tan²θ)
Substitute the value of tanθ = 3/5 in the above identity
⇒ tan2θ = 2(3/5)/(1 - (3/5)²)
⇒ tan2θ = (6/5)/(1 - 9/25)
⇒ tan2θ = (6/5)/(16/25)
⇒ tan2θ = (6/5) × (25/16)
⇒ tan2θ = 15/8
Therefore, the exact value of the trigonometric function is tan2θ = 15/8.
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5. Miguel has an after-school job. He works
between 15 and 25 hours each week and is paid
$12 per hour. What is an appropriate domain for
this scenario?
A. All real numbers such that 15
B. All real numbers such that 180 < x < 300
C. All real numbers
D. All real numbers such that x>0
Answers
Answer:
The domain is 15 ≤ x ≤ 25
Step-by-step explanation:
The given parameters are;
The number of hours Miguel works each week = Between 15 and 25 hours
The amount he is paid per hour = $12
Therefore, we have;
The domain is all real numbers, 'x', such that 15 ≤ x ≤ 25
The amount Miguel makes each week, 'y' is between; 12 × 15 ≤ A ≤ 12 × 25
Therefore the range is 180 ≤ y ≤ 300.
the percent of age of rajus fater is twice that of Raju. after 10 years, the sum of their ages would be 80 years. find their present age
pls fast plss
Answers
Answer:
raju is 20 years old while the father is 40 years old
Step-by-step explanation:
present : lets assume raju is x years old so the father will be 2x
after 10 yrs raju will be x+10 yrs while the father will be 2x+10 yrs
therefore :
(x+10)+(2x+10)=80
liketerms together
x+2x+10+10=80
3x+20=80
3x=80-20
3x=60
simplify
x=20 so raju is 20 years old now and the father since he is twice the age of his son he is 40 years old
Suppose that l is a tangent line to this circle which is parallel to the line y=5x+7 and has a negative y intercept. Then the point of tangency of l with this circle is.
Answers
A. The equation of a tangent line to the circle through the point (- 6 , 8) is y = 0.75x + 12.50
B. The point of tangency of L with the circle is (9.81 , - 1.96).
The full question is in the attachment. The equation of a tangent line to the circle with radius r centered at the origin through the point (p , q)
r = 10 p = - 6 q = 8px + qy = r²
- 6x + 8y = 10²
8y = 6x + 100
y = 6/8x + 100/8
y = 3/4x + 25/2
y = 0.75x + 12.50
The equation line y = mx + c has the slope or the gradient m. If two lines are parallel, the two lines have the same slope.
y = 5x + 7
m = 5m of L = 5 because parallelThe tangent line L to the circle with the gradient m and radius r
\(y \:=\: mx \pm r \: \sqrt{1 \:+\: m^2}\)
\(y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 5^2}\)
\(y \:=\: 5x \pm 10 \: \sqrt{1 \:+\: 25}\)
\(y \:=\: 5x \pm 10 \: \sqrt{26}\)
Because L has a negative y-intercept, it means when x = 0, y is negative. So the equation L
\(y \:=\: 5x \:+\: 10 \: \sqrt{26}\)
The point x of tangency of L with the circle
x² + y² = r²
x² + (5x - 10 √26)² = 10²
x² + 25x² - 100√26 x + 2,600 = 100
26x² - 100√26 x + 2,500 = 0
a = 26b = - 100√26c = 2,500\(x_{1.2} \:=\: \frac{-b \pm \sqrt{b^2 \:-\: 4ac}}{2a}\)
\(x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{(- 100 \sqrt{26})^2 \:-\: (4 \times 26 \times 2,500)}}{2 \times 26}\)
\(x_{1.2} \:=\: \frac{100 \sqrt{26} \pm \sqrt{260,000 \:-\: 260,000}}{52}\)
\(x \:=\: \frac{100 \sqrt{26}}{52}\)
\(x \:=\: \frac{50 \sqrt{26}}{26}\)
x = 50/26 × √26
x = 9.81
The point y of tangency of L with the circle
\(y \:=\: 5x \:+\: 10 \: \sqrt{26}\)
\(y \:=\: 5 \times \frac{50 \sqrt{26}}{26} \:+\: 10 \: \sqrt{26}\)
\(y \:=\: \frac{250 \sqrt{26}}{26} \:+\: \frac{260 \sqrt{26}}{26}\)
\(y \:=\: \frac{- 10 \sqrt{26}}{26}}\)
y = - 10/26 × √26
y = - 1.96
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find the support and confidence of this transaction
A = I2, B = I3
Let 1 = {1,, I, I...... 1.} be a set of items, where I, denotes an item ID. Consider the transaction database D, defined in the table below: Transaction ID List of Items in the Transaction T₂ I, I,
Answers
For confidence interval: support of the association rule A to B is 0.5 and the confidence of the association rule A to B is 0.5.
For Support and confidence of the association rule A - B
To determine the support and the confidence of the association rule A → B, where A = {1, }, B = {1}, we use the formulas given below:
Support(A → B) = frequency of (A, B) / N
Confidence(A → B) = frequency of (A, B) / frequency of A
where N is the number of transactions in the database.
To find the frequency of (A, B) and the frequency of A.
Thus Frequency of (A, B) = 1
Since there is only one transaction in the database where both A and B occur, the frequency of (A, B) is 1.
Frequency of A = 2
The itemset {1, } occurs in two transactions T₁ and T₂.
Hence, the frequency of A is 2.
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ind the 94th term of the arithmetic sequence -26,−37,−48
Answers
The 94th term of the arithmetic sequence -26,−37,−48 is -1049.
How to calculate the value?It is important to note that an arithmetic sequence is calculated by using the formula:
a + (n - 1)d
where a = -26
d = -37 + 26 = -11
Therefore, the 94th term will be:
= a + (n - 1)d
= -26 + (94 - 1) × -11
= -26 + (93 × -11)
= -26 - 1023
= -1049
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with a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Answers
The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b)
This is incomplete question
Complete question is this:
With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?
Only use models that produce values of r = 1Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line Maximize the size of the residualsFind the best fit line that crosses the y- axis at x = 0Choose the correct option:
Now, According to the question:
Hence, The aim when choosing the model parameters:
Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line
The correct option is (b).
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Find the coordinates of the vertex of the following parabola algebraically. Write your
answer as an (x, y) point.
y=x²-8x + 24
Answers
Answer:
\((4,8)\)
Step-by-step explanation:
\(y=x^2-8x+24 \\ \\ y=(x^2-8x+16)+24-16 \\ \\ y=(x-4)^2+8\)
So, the vertex is \((4,8)\).
Does anyone know which answer it is in the image? Doesn’t require any work
Answers
Answer:
b
Step-by-step explanation:
Answer:
It's the second one
PLEASE HELP!❤️
If 12% of a number is 6, find 4% of that number.
Answers
Answer:
1.5
Step-by-step explanation:
37,5*0.12=6
37.5*0.04=1.5
Suppose that f(1) = 1, f(4) = 5, f '(1) = 3, f '(4) = 3, and f '' is continuous. find the value of 4 1 xf ''(x) dx.
Answers
Answer: b
Step-by-step explanation:
I think
what is the answer to two plus two divided by 3 times 6
Answers
Answer:
8
Step-by-step explanation:
2 + 2 = 4
4 / 3 = 1.3
1.3 x 6 = 8
Step 2: 4/3
Step 3: 1.3 x 6= 7.8
Gold is sold by the troy ounce (31.103 g). What is the volume (in cm3) of 7 troy ounces of pure gold
Answers
To determine the volume of 7 troy ounces of pure gold, we need to know the density of gold. The density of gold is commonly expressed in grams per cubic centimeter (g/cm³).
The average density of gold is approximately 19.3 g/cm³.
Given that 1 troy ounce is equal to 31.103 grams, we can calculate the volume of 7 troy ounces of gold using the density formula:
Volume = Mass / Density
Mass of 7 troy ounces of gold = 7 troy ounces * 31.103 g/troy ounce = 217.721 grams
Volume = 217.721 g / 19.3 g/cm³ ≈ 11.28 cm³
Therefore, the volume of 7 troy ounces of pure gold is approximately 11.28 cm³.
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One mechanic services 4 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 4 working days, and broakdowns tend to Poisson distribution. The mechanic can handie an average of one repair job per day. Repairs follow a negative exponential distribution: a) On the average, how many machines are waiting for service? The average number of machines waiting for service is (Round your response to three decimal places.)
Answers
Therefore, the average number of machines waiting for service is 0.083 (rounded to three decimal places).
To calculate the average number of machines waiting for service, we can use the concept of the M/M/1 queue, where arrivals follow a Poisson distribution and service times follow a negative exponential distribution.
In this case, the arrival rate (λ) is 1 breakdown every 4 working days, and the service rate (μ) is 1 repair job per day.
The utilization factor (ρ), which represents the system's utilization, can be calculated as ρ = λ/μ = (1/4)/(1) = 1/4.
The average number of machines waiting for service (Lq) can be calculated using the formula Lq = ρ² / (1 - ρ).
Plugging in the values, we have Lq = (1/4)²/ (1 - 1/4) = 1/12.
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is a transformation involving the addition, subtraction, multiplication, or division of or by a constant.
Answers
Yes, a transformation can involve the addition, subtraction, multiplication, or division of or by a constant. In fact, these operations are commonly used in mathematical transformations.
For example, adding a constant to each value in a set of data is a common way to shift the entire set of values up or down. Multiplying each value in a set of data by a constant is a common way to stretch or shrink the data. Subtraction and division can also be used in transformations, depending on the context. However, it is important to note that not all transformations involve these operations.
Some transformations may involve more complex operations, such as exponentiation or logarithmic transformations. So, the short answer is yes, but the long answer is that it depends on the specific transformation being used.
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The larger the , Group of answer choices the larger the differences between the expected frequencies. the less likely our data represent . the more likely our data represent the model. the less likely our data represent the model.
Answers
The larger the group of answer choices, the less likely our data represent the model due to larger differences between the expected frequencies.
Based on the terms provided, we want to know the relationship between the size of a group of answer choices, differences between expected frequencies, and how likely the data represents a model.
The larger the group of answer choices, the larger the differences between the expected frequencies, and the less likely our data represent the model.
This is because a larger group of answer choices increases the complexity of the dataset, which may lead to more significant deviations from the expected frequencies, ultimately making it less likely that the data represents the given model.
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Mr. Baral has a stationery shop. His annual income is Rs 640000. If he is unmarried, how much income tax should he pay? find it
Answers
Mr. Baral has to pay Rs 64000 as an annual income tax at an interest of 10% for his stationary shop.
From the question, we have given that if he is unmarried and his income is between Rs 5,00,001 to Rs 7,00,000, he has to pay an annual interest of 10%.
Given annual income in Rs = 640000.
The annual income tax rate he has to pay at = 10%
So, to find out the income tax from the annual income we have to find out the 10% of 640000.
Income tax = 640000/100 * 10 = 64000
From the above analysis, we can conclude that Mr. Baral has to pay 64000 rs of income tax annually.
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Given question is not having enough information, I am writing the complete question below:
Use it to calculate the income taxes. For an individual Income slab Up to Rs 5,00,000 0% Rs 5,00,001 to Rs 7,00,000 10% Rs 7,00,001 to Rs 10,00,000 20% Rs 10,00,001 to Rs 20,00,000 30% Tax rate For couple Tax rate 0% Income slab Up to Rs 6,00,000 Rs 6,00,001 to Rs 8,00,000 Rs 8,00,001 to Rs 11,00,000 20% Rs 11,00,001 to Rs 20,00,000 30%
a) Mr. Baral has a stationery shop. His annual income is Rs 6,40,000. If he is unmarried, how much income tax should he pay? 10%
Solve the following system of equations graphically on the set of axes y= x -5 y=-/x -8
Answers
Answer:
(-3/2, -13/2)
Step-by-step explanation:
To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.
To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.
To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.
The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:
x - 5 = -x - 8 2x = -3 x = -3/2
Then, we can plug this value of x into either equation to find the corresponding value of y:
y = (-3/2) - 5 y = -13/2
So the solution to the system of equations is (-3/2, -13/2).
Solve on the interval [0,2pi):
2 sin^2 x-3 sin x + 1 = 0
Answers
Answer:
How do you solve #2sin^2x+3sinx+1=0# and find all solutions in the interval #[0,2pi)#?
Trigonometry Trigonometric Identities and Equations Solving Trigonometric Equations
Answer:
Explanation:
We may identify this as a quadratic equation in #sinx# and factorise it as a trinomial to obtain the solutions as
#(2sinx+1)(sinx+1)=0##thereforesinx=-1/2 or sinx=-1##therefore x= (7pi)/6 or (11pi)/6 or (3pi)/2#Help me please new topic
Answers
Answer:
B?
Step-by-step explanation:
Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than kayla’s biking speed. Find kayla’s biking speed
Answers
When Kayla rode her bike home from college one weekend, her biking speed is 15 miles per hour
Speed is defined as the ratio between the distance and the amount of time an object traveled.
speed = distance/time
If the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed, we have:
average speed of the bus = 10 mph + biking speed
let x = biking speed
y = average speed of the bus
y = 10 + x
Covering the same distance of 75 miles, calculate the time it took her riding the bus and the bike.
time = distance/speed
time riding the bus = 75 miles/(10 + x)
time riding the bike = 75 miles/x
If it took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike
time riding the bus = time riding the bike - 2
75 miles/(10 + x) = (75 miles/x) - 2
75/(10 + x) = (75 - 2x)/x
Multiplying both sides by x(10 + x),
x(10 + x)[75/(10 + x)] = x(10 + x)[(75 - 2x)/x]
75x = 750 - 20x + 75x - 2x^2
2x^2 + 20x - 750 = 0
x^2 + 10x - 375 = 0
(x - 15)(x + 25) = 0
x = 15 ; x = -25
Since we cannot have negative amount of time, choose x = 15.
Hence, Kayla's biking speed is 15 miles per hour.
Learn more about speed here: https://brainly.com/question/6504879
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