Roger and Trish will have completed 11/30 of the homework if they work together for 1 hour.
To solve this problem
First, we need to find their individual rates of work, which is the reciprocal of the time it takes for each to complete the homework:
Roger's rate: 1/6 of the homework per hour
Trish's rate: 1/5 of the homework per hour
When they work together, their combined rate of work is the sum of their individual rates:
Combined rate: 1/6 + 1/5 = 11/30 of the homework per hour
After working together for 1 hour, they will have completed:
11/30 * 1 = 11/30 of the homework
Therefore, Roger and Trish will have completed 11/30 of the homework if they work together for 1 hour.
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what are the answers to these questions?
The value of the points is,
(1/5, 7/5) or (0.2, 1.4)
The given equation may be simplified as follows:
x² + 14xy + 49y² = 100
(x + 7y)(x + 7y) = 100
(x + 7y)² = 10²
x + 7y = 10
This is a straight line with the equation.
y = -(1/7)x + 10/7
The minimum distance from the origin to this line is provided by a straight line that passes through the origin and which is perpendicular to the straight line.
The slope of the perpendicular line is 7 because the product of the two slopes should be -1.
The perpendicular line is of the form
y = 7x + c.
Because the line passes through (0,0), therefore c = 0.
The line y = 7x intercepts the original line when
y = 7x = -(1/7)x + 10/7
Therefore
7x = -(1/7)x + 10/7
Multiply through by 7.
49x = -x + 10
50x = 10
x = 1/5
y = 7x = 7/5
Hence, The minimum distance is
d = √(x² + y²)
= √[(1/5)² + (7/5)²]
= √2
Thus, The point is (1/5, 7/5).
So, Solution are, (1/5, 7/5) or (0.2, 1.4)
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Which statement about a dilation with a scale factor of 3 is true?
O Three is added to each side in the pre-image to find the corresponding side length in the image.
O Three is subtracted from each side in the pre-image to find the corresponding side length in the image.
Each side in the pre-image is multiplied by three to find the corresponding side length in the image.
Each side in the pre-image is divided by three to find the corresponding side length in the image.
Answer:
C is the answer
Given : dilation with a scale factor of 3
To find : Which statement is true
Step-by-step explanation:
Solution: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
if Dilation factor N then image Size is multiplied by N
if Scale factor < 1 then image get reduced
if scale factor > 1 then image get enlarged
scale factor = 1 lead to Same size image
Here is given that Scale factor of 3
=> image will be enlarged to 3 times the original image
Hence correct option is :
C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image
Answer: C
Step-by-step explanation: Edge Unit Test
soooooooooo what is x^2=-20
The value of x in the equation x² = -20 is x = 2i√5
Evaluating the equation for xFrom the question, we have the following parameters that can be used in our computation:
x² = -20
To start with, we take the square root of both sides of the equation
So, we have
√x² = √-20
When the square roots are evaluated, we have
x = √-20
Express -20 as 4 * -5
So, we have
x = √4 * -5
This gives
x = 2√-5
The expression √-5 is a complex number
So, we have
x = 2i√5
Hence, the value of x in x² = -20 is x = 2i√5
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Amanda’s new job has a 50% employer match on the first 4% of her salary contributed to her 401(k). How much was deposited in Amanda’s account if she makes $61,000 a year and she took advantage of the entire contribution match?
Answer:
$2,440 + $1,220 = $3,660
Step-by-step explanation:
If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:
$61,000 x 0.04 = $2,440
Since her employer has a 50% match on the first 4% of her salary, they would contribute:
$2,440 x 0.5 = $1,220
A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1.
What are the first 5 terms of the sequence?
The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
What are the first 5 terms of the sequence?From the question, we have the following parameters that can be used in our computation:
The sequence is generated by using gn = 2(gn-1)
Such that g1 = 1/3 and n is a whole number greater than 1.
Using the above as a guide, we have the following:
The sequence means that we multiply the current term by 2 to get the next term
So, we have the following representations
a(2) = 2 * 1/3 = 2/3
a(3) = 2 * 2/3 = 4/3
a(4) = 2 * 4/3 = 8/3
a(5) = 2 * 8/3 = 16/3
Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
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In complex numbers what is the multiplicative inverse of 2i
To find the multiplicative inverse of 2i, we need to find a complex number z such that:
(2i) * z = 1
Multiplying both sides by -i, we get:
z = -i/2
Therefore, the multiplicative inverse of 2i is -i/2.
2. Although Kevin has money, he is not spending it.
Complex or compound -complex
Answer:
complex
Step-by-step explanation:
The given sentence "Although Kevin has money, he is not spending it." is a complex sentence.
This is because it contains one independent clause, "he is not spending it," which can stand alone as a complete sentence. The other part of the sentence, "Although Kevin has money," is a dependent clause because it cannot stand alone as a complete sentence.
The dependent clause "Although Kevin has money" introduces a contrast or concession to the independent clause that follows it. Therefore, this sentence is an example of a complex sentence that uses a dependent clause to add meaning and complexity to the independent clause.
Please answer a) b) and c)
I’ll give 65 points
a
1.5/4
b
0.5/4
c
0.5/4
because half of 3 is 1.5
Answer:
I'm pretty sure the answer is B(
Please answer this please you will not understand how much this means 30 points
The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.
How to explain the equationWe can rewrite this equation as:
1 - sin² x = sin²x
Solving for sin x, we get:
sin x = ±✓(1/2)
Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:
sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.
sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.
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Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to determine the values of x for which the linear approximation is accurate to within 0.1. (Round your answers to three decimal places. Enter your answer using interval notation.)
sin−1(x) ≈ x
Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].
What is function?In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.
Here,
The linear approximation of sin⁻¹(x) at a = 0 is given by:
sin⁻¹(x) ≈ x
To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:
d/dx(sin⁻¹(x)) = 1/√(1-x²)
d/dx(sin⁻¹(x))|x=0 = 1
Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.
To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.
Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:
-0.099 ≤ x ≤ 0.099
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Prove the following this:The number of left cosets of a subgroup is equal to the number of its right cosets?
To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.
Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.
First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.
Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.
Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.
1. Working on a circle of radius 10cm, explain in detail how to determine the values of each of the following trigonometric expres- sions. Include a picture for each to help with your explanations.
(a) cos(5π)
(b) sin(−9π/2)
(c) sin(183π/2)
2. Approximate the value of cos π◦. Explain your reasoning. Do not use a calculator. Include a picture to help with your explanation.
The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.
The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.
The y-coordinate of this point is 1, so sin(183π/2) = sin(16,470 degrees) = 1.
How to calculate the valueIt should be noted that go find cos(5π), we first need to convert 5π to degrees. We know that π radians is equal to 180 degrees, so 5π radians is equal to 5π × (180/π) = 900 degrees. The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.
Also, to find sin(-9π/2), we first need to convert -9π/2 to degrees. We know that π radians is equal to 180 degrees, so -9π/2 radians is equal to -9π/2 × (180/π) = -810 degrees. The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.
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The frequency table below shows a student’s quiz scores. One data value in the table is missing. If the mean of the data set is 2.2, what is the score for the missing data item? A. 0 B. 1 C. 2 D. 3
Answer:
B. 1
Step-by-step explanation:
Let's use the formula for finding the mean of a set of data:
mean = (sum of all data values) / (number of data values)
We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:
2.2 = (sum of all 10 data values, including x) / 10
Multiplying both sides by 10, we get:
22 = sum of all 10 data values, including x
We can then subtract the sum of the known data values from both sides to find the missing value:
22 - (01 + 12 + 23 + 31 + 42 + 51) = x
22 - (0 + 2 + 6 + 3 + 8 + 5) = x
x = 22 - 24 = -2
However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:
If the missing score is 0:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10
2.2 = 18 / 10
2.2 = 1.8
This is not true, so the missing score cannot be 0.
If the missing score is 1:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10
2.2 = (18 + ?) / 10
22 = 18 + ?
? = 4
So the missing score is 1, and the answer is B.
Answer:
Answer is B
Total scores/total frequency =mean
54/24=2,25
If you added a score of 1
55/25=2,2
Step-by-step explanation:
hope that helps you
If someone wants to call Havana, Cuba from the United States, begins with US three digit exit code 011 followed by the two digit country code for Cuba which is 53, followed by the country code of Havana which is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone number cannot begin with 0. How many different telephone numbers are possible?
There are possible 4,782,969 different telephone numbers.
We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.
How to calculate the total number of possible telephone numbers?Using the multiplication principle to estimate the number of possible telephone numbers for each digit:
n1 x n2 x n3 x ... x nk
Here:
the first three digits are fixed: 011
The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).
The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).
Therefore, the total number of possible telephone numbers:
9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,
Therefore, 4,782,969 different telephone numbers are possible.
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The lodge has 420 skis. Predict the number of skis that are likely to be defective.
A ski lodge inspects 80 skis and discovers four that are faulty. The skis that are likely to be defective are 21.
It is assumed that there are 80 skis, four of which are faulty.
As a result, the total number of outcomes is 80.
Positive outcomes = 4
Let [tex]E_{1}[/tex] represent the event of selecting a faulty. As a result, the likelihood of selecting a defective ski is expressed mathematically as follows.
[tex]E_{1}[/tex] = Favorable case of defective / Total number of skis
= 4 / 80
= 1 / 20
=0.05
Skis will be discovered in 5% of cases.
So, the event of choosing a defective is 4 / 80.
If the total number of skis is 420, then the number of defective skis will be:
4 / 80 × 420
= 1/20 × 420
= 21
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Correct question:
A ski lodge inspects 80 skis and finds 4 to be defective. The lodge has 420 skis. Predict the number of skis that are likely to be defective.
What are the first 4 terms of the arithmetic sequence in the graph?
ANSWER: 2, -2,-6,-10
just took the test
By looking at the y-values of the points, we can see that the first four terms are.
2, -2, -6, -10
How to identify the first four terms?We know that the x-value of each of the points is the index of the term, so:
x = 1 is the first term
x = 2 is the second term.
And so on.
The y-value will be the actual value of the term.
Here we can see 4 points graphed, these are:
(1, 2), (2, -2), (3, -6), (4, -10)
Then the values of the first four terms of the sequence are:
2, -2, -6, -10
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A sum of money raised in a show was distributed to Charities A, B and C. Charity A received of the total amount Charities B and C received. Charity C received of the otal amount Charities A and B received. a) What fraction of the total amount of money did Charity B receive? p) Charity B received $88 000. How much money was raised in the show? a)
The total money raised is (15/7) * $88,000 = $188,571.43.
How to solvea) Let x be the total amount raised.
Charity A received (1/3)(x - A), Charity C received (1/4)(x - C). We have A = (1/3)(B+C) and C = (1/4)(A+B).
Solving these equations, we find B's share to be 7/15 of the total amount.
p) Since Charity B received $88,000, which is 7/15 of the total amount, the total money raised is (15/7) * $88,000 = $188,571.43.
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what is twenty-five divided bye four?
Answer: The answer is 6.25
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
What is the sine of 0?
The sine of angle θ is given as follows:
sin(θ) = -8/17.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The point in this problem has the coordinates given as follows:
(15/17, -8/17).
Hence the trigonometric ratios are given as follows:
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Find the volume of the solid obtained by rotating the region underneath the graph of the function over the given interval about
the y-axis.
f(x)=√x² +9, [0,2]
(Use symbolic notation and fractions where needed.)
The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³
Given data ,
The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis
The formula for Area under definite integral is
∫ₐᵇ f ( x ) = f ( b ) - f ( a )
Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x
The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)
Using these expressions for r and h, we can write the volume of each cylindrical shell as:
V(x) = 2πx[f(x + Δx) - f(x)]Δx
V = ∫₀² 2πx[f(x + Δx) - f(x)]dx
As Δx approaches zero, this integral becomes:
V = ∫₀² 2πx√(1 + (f'(x))²) dx
where f'(x) is the derivative of f(x), which is:
f'(x) = x/√(x² + 9)
Substituting this expression for f'(x) into the integral, we get:
V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx
This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:
V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx
V = [4/5 π(x² + 9)^(5/2)]₉¹³
V = 44.46 units³
Hence , the volume of the solid is 44.46 units³
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The Soule's live on a corner lot. Often, children cut across
their lot to save walking distance. The diagram to the right
represents the corner lot. The children's path is
represented by a dashed line. Approximate the walking
distance that is saved by cutting across their property
instead of walking around the lot.
...
The walking distance that is saved by cutting across the lot is
feet.
X
15 feet
x+3
Answer:
The walking distance that is saved by cutting across the lot is approximately 18 feet.
26 less than twice a number is 4. Find each number
Answer:
15
Step-by-step explanation:
Let's call the number we try to find "[tex]x[/tex]"
In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:
[tex]2x - 26 = 4[/tex]
Now we can solve for x by isolating it on one side of the equation.
First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".
[tex]2x = 4 + 26[/tex]
Then we add
[tex]2x = 30[/tex]
finally, we isolate the x by dividing each side with 2
2x ÷ 2 = 30 ÷ 2
x = 15
The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8
Think about prime numbers and composite numbers.list all the digits that are the last digit of at least one prime number.
Answer:
1,3,5,7,9
Step-by-step explanation:
0 can't be, let's take 10 or 20 or 30 for example, not a prime number.
1 can be because let's take 11, 31 as example, they're prime numbers.
2, 4, 6, 8 can't be the answer because they have factors
The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59
Rewrite the given formula relating the area of a square to the length of its diagonal to solve for d. The 2nd screenshot is the formula sorry for the poor sc
Answer:
\( A=\frac{d^2}{2} \).
Step-by-step explanation:
Area of Square by Applying Formula for the Diagonal
We can use the relationship between diagonal length d and the side a length of a square to find its area A. So, the formula for area of square using diagonal is \( A=\frac{d^2}{2} \).
Abel starts walking from Point A at a speed of 4 km/h, 2 hours later, from Point A,
Jack rides his bicycle at 8 Km/h along the same route.
a) When will Jack overtake Abel?
b) How far will they have travelled by the time Jack overtake Abel?
Answer:
a) In 2 hours
b) 16 km
Step-by-step explanation:
Let's first find out how far Abel has traveled in 2 hours. We can use the formula:
distance = speed x time
distance = 4 km/h x 2 h = 8 km
So when Jack starts cycling, Abel has already covered 8 km.
Now, let's say it takes Jack t hours to catch up to Abel. During this time, Abel has continued walking for t + 2 hours. So we can write:
distance covered by Abel = distance covered by Jack
4 km/h x (t + 2 h) = 8 km/h x t
Simplifying this equation, we get:
4t + 8 = 8t
4t = 8
t = 2
So Jack will overtake Abel after 2 hours of cycling. To find out how far they will have traveled, we can use the formula:
distance = speed x time
distance = 8 km/h x 2 h = 16 km
Therefore, when Jack overtakes Abel, they will have traveled 16 km in total.
One factor of this polynomial is (x+8) x2+5x2-11x+104
The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13
What is a polynomial?A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.
The possible polynomial in the question is; x³ + 5·x² - 11·x + 104
The factor of the polynomial is; (x + 8)
The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.
The other steps of synthetic division can then be presented, summarily as follows;
Therefore;
-8 | 1[tex]{}[/tex] 5 -11 104
| [tex]{}[/tex] -8 24 104
1 -3 [tex]{}[/tex] 13 0
The factors of the polynomial
The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13
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Can Anyone HELP?
The length of the base of an isosceles triangle is 4 inches less than the length of one of the two equal sides of the triangles. If the perimeter is 32, find the three sides of the triangle. If x represents one of the equal sides of the triangle, then which equation can be used to solve the problem?
A. 2x - 4 = 32
B. 3x + 4 = 32
C. 3x - 4 = 32
Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:
x + x + (x - 4) = 3x - 4
We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:
3x - 4 = 32
Adding 4 to both sides gives:
3x = 36
Dividing by 3 gives:
x = 12
Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.
So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.
The correct equation to solve the problem is (C) 3x - 4 = 32.
Plot the foci of this ellipse.
The equation of the ellipse derived as is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.
The equation of foci is
F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)
What is an ellipse?An ellipse is described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.
We can write the equation of an ellipse as:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) = the center of the ellipse,
a = the semi-major axis,
and b = the semi-minor axis.
The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).
we know also the formula to find the foci of an ellipse is:
F₁ = (h - √(a^2 - b^2), k)
F₂ = (h + √(a^2 - b^2), k)
The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:
2a = √((x - h + √(a^2 - b^2))^2 + (y - k)^2) + √((x - h - √(a^2 - b^2))^2 + (y - k)^2)
Simplifying, we then can write the equation of the ellipse as:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
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Kadeesha borrowed some money from her friend in order to help buy a new video
game system. Kadeesha originally borrowed $120 and agreed to pay back her friend
$8 per week. Make a table of values and then write an equation for L, in terms of t,
representing the amount Kadeesha owes her friend after t weeks.
Number of Weeks Amount of Money Owed
0
1
2
3
You must answer all questions above in order to submit.
attempt 1 out of 2
An equation for L, in terms of t, representing the amount Kadeesha owes her friend after t weeks is L = 8t + 120.
The table of values is as follows;
Number of Weeks Amount of Money Owed
0 $120
1 $128
2 $136
3 $144
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the amount of money that Kadeesha borrowed originally and the number of weeks respectively, and then translate the word problem into a linear equation as follows:
Let the variable L represent amount of money that Kadeesha owed.Let the variable t represent number of weeks.Since Kadeesha originally borrowed $120 and agreed to pay back her friend $8 per week, a linear equation which can be used to model the total amount of money that Kadeesha owed is given by;
L = 8t + 120
When t = 0, the value of L is given by;
L = 8(0) + 120
L = $120.
When t = 1, the value of L is given by;
L = 8(1) + 120
L = $128.
When t = 2, the value of L is given by;
L = 8(2) + 120
L = $136.
When t = 3, the value of L is given by;
L = 8(3) + 120
L = $144.
Read more on equation here: brainly.com/question/18912929
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