Answer:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
=
[tex]\frac{ \sqrt{2} }{a + b} [/tex]
Step-by-step explanation:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
[tex](a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )[/tex]
[tex] \frac{(a - b)( {2}^{ \frac{1}{2} }) }{(a - b)(a + b)} = \frac{ \sqrt{2} }{a + b} [/tex]
Como derivar cos(2x)/tan(2x)
Use the quotient and chain rules. If
[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]
then the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]
and we can rewrite this by
• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]
• factorizing,
[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]
etc
The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1. Path Expected Duration (weeks) Variance A 10 1.21 B 8 2.00 C 12 1.00 D 15 2.89 E 14 1.44 Click here for the Excel Data File Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.) a. Graduation time? b. The end of week 15? c. The end of week 13?
The probability that the project will be completed before the graduation time is 0.6873.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event.
From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.
Also, the probability that the project will be completed before the end of week 15 will be 0.3983.
Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.
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A motorist travels from town A to town B, which are 84km apart. If he has completed 7/8 of his journey, what is the distance he has travelled?
The distance that he has traveled exists 73km 500m.
What is the distance?
Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.
Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.
To estimate the distance that he has traveled
He covered 7/8 out of 84 km
So, 7/8 × 84 = 73.5 km
The distance he has traveled = 73 km 500 m
Therefore, the distance that he has traveled exists 73km 500m.
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Determine whether or not the lines are parallel based on the
given angle measures. Explain your answer in the case.
Answer:
answer
Step-by-step explanation:
To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 76° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.
Answer:
First angle: 52°
Second angle: 26°
Third angle: 102°
Step-by-step explanation:
Let the measure of the second angle = x.
Measure of the first angle: 2x
Measure of third angle: x + 76
2x + x + x + 76 = 180
4x + 76 = 180
4x = 104
x = 26 second angle
2x = 2 × 26 = 52 first angle
x + 76 = 26 + 76 = 102 third angle
HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Write each expression in the standard form for the complex number a + bi.
1. [ 4 ( cos (7pi/9) + i sin (7pi/9))]^3
2. The complex fifth roots of 5 - 5 sqrt(3)i
1. By de Moivre's theorem,
[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]
2. First write the given number in exponential/trigonometric form.
[tex]z = 5-5\sqrt3\,i[/tex]
has modulus
[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]
and since it lies in the second quadrant of the complex plane, its argument is
[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]
So, we have
[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]
Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are
[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]
[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]
[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]
[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]
[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]
A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36-month fixed installment loan with an APR of 5.5% a) Determine Landon's finance charge. b) Determine Landon's monthly payment.
Landon's finance charge is $613.2
Landon's monthly payment is; $80.22
How to find the finance charge?
It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.
The amortization formula is:
A = Pr/(1 - (1 + r)⁻ⁿ)
where;
A is the monthly payment
P is the loan amount
r is the monthly interest rate
n is the number of months
b) Using the above formula, we can get the monthly payment as;
A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049
A = $80.22
The monthly payment amount is $80.22
a) 60 monthly payments add up to;
$80.22 × 60 = $4813.2
Since $4200 of that amount is principal, the finance charge is;
$4813.2 - $4200.00 = $613.2
Landon's finance charge is $613.2
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question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
A board, 74 cm long is cut into three pieces such as the second board is twice as long as first board and the third is 4 cm longer than second. Find length of shorter piece
Answer:
The shortest piece is the first piece and it is 14 cm long.
Step-by-step explanation:
We have three unknowns so we need 3 equations.
Let x = the length of the first piece
Let y = the length of the second piece
Let z = the length of the third piece.
x + y + z = 74 y = 2x z = y + 4
There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:
x + y + z = 74
x + 2x + z = 74 Combine the x terms
3x + z = 74
Next, I am going to substitute 2x in for y in the third equation above.
z = y + 4
z = 2x + 4 I am going to put both variable on the left side of the equation
z - 2x = 4
I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:
z - 2x = 4
-1(z - 2x) = 4(-1)
-z +2x = -4
I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4
z + 3x = 74
-z + 2x = -4
5x = 70 divide both sides by 5
x = 14 This is the length of the first piece.
y = 2x
y = 2(14) = 28
y = 28 This is the length of the second piece.
z = y+4
z = 28 + 4 = 32
or
x + y + z = 74
14 + 28 + z = 74
42 + z = 74 Subtract 42 from both sides.
z = 32
solve x^2 + x - 12 = 0
Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
Ali’s ate 1/3 of a pizza for lunch. Later, she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
05* Find, for y> 0, the general solution of the differential equation dy/dx=xy.
Inlyl=1/2x^2+c
Inlyl=1/2x^2-c
Inlyl=-1/2x^2-c
Inly|=-1/2x^2+c
The ODE is separable.
[tex]\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx[/tex]
Integrate both sides to get
[tex]\displaystyle \int\frac{dy}y = \int x\,dx[/tex]
[tex]\boxed{\ln|y| = \dfrac12 x^2 + C}[/tex]
But notice that replacing the constant [tex]C[/tex] with [tex]-C[/tex] doesn't affect the solution, since its derivative would recover the same ODE as before.
[tex]\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy[/tex]
so either of the first two answers are technically correct.
What is the ratio of my lawn if it is 4 meters by 4.5 meters
Answer:
The 1:n ratio is= 1 : 1.125
The n:1 ratio is= 8/9 : 1
Just the simple ratio is= 4 : 4.5
Application
I
3. Ray has a stride of about 1.4 m. He runs 9 km daily to train for a marathon. Approximately
how many strides does he need to run 9 km?
He needs to run with approximately 6429 for a distance of 9 km
How to determine the number of strides?The given parameters are:
Length of stride = 1.4 m
Distance for marathon = 9 km
The number of strides needed is then calculated as:
Number of stride = Distance for marathon/Length of stride
Substitute the known values in the above equation
Number of stride = 9km/1.4m
Convert km to m
Number of stride = 9000m/1.4m
Evaluate the quotient
Number of stride = 6428.57143
Approximate the estimate
Number of stride = 6429
Hence, he needs to run with approximately 6429 for a distance of 9 km
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In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and
130 play both the games. Find
(i) The number of pupils who play Football only,
(ii) The number of pupils who play Hockey only,
(iii) The total number of pupils in the school
Answer:370 play football and 20 play hockey
Step-by-step explanation: because 400 - 130 equals 370 for football
then hockey 150-130 equals 20
Then the total students are 420
150+400-130 equals 420
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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Function and Reasoning:
There are 60 calories in 5 ounces of a certain brand of soda.
Part A: Represent the relationship between the number of calories and the number of ounces of soda as a line in the coordinate plane below.
Part B: What is the number of calories per ounce of soda?
Part C: How does the unit rate relate to the slope of the line in the graph above? Explain your answer.
The number of calories per ounce of soda is 10
Part A: Represent the relationship between the number of calories and the number of ouncesThe given parameters are:
Calories = 50
Ounces = 5
Let the number of calories be y and the ounces be x.
So, we have:
y = kx
Substitute y = 50 and x = 5
50 = 5k
Divide by 5
k = 10
Substitute k = 10 in y = kx
y = 10x
See attachment for the graph of the relationship between the number of calories and the number of ounces
Part B: What is the number of calories per ounce of soda?In (a), we have:
k = 10
This means that the number of calories per ounce of soda is 10
Part C: How does the unit rate relate to the slope of the line in the graph above?The unit rate and the slope represent the same and they have the same value
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using
a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3;
-2 and 7+5 i are zeros;
f(2)=200
f(x) =
(Type an expression using x as the variable. Simplify your answer.)
possible
4
Answer:
f(x) = x³ -12x² +46x +148
Step-by-step explanation:
When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.
Factored formGiven the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...
f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))
Rearranging a bit, this is ...
f(x) = (x +2)((x -7) -5i)((x -7) +5i)
The latter two factors are recognizable as the factors of the difference of squares, so this is ...
f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)
Standard formMultiplying the factors, we have ...
f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)
f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property
f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms
Again I need help, If you tell me the answer that would be very nice! ,
Find the surface area of the composite figure :
The surface area of the given two rectangular prism is given as follows:
498 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and height h is given as follows:
S = 2(lw + wh + hl).
For this problem, there are two prisms, with dimensions given as follows:
l = 12 cm, w = 7 cm, h = 7 cm.l = 2 cm, w = 7 cm, h = 2 cm.Hence the surface area of the figure is the combined surface area of each figure, hence:
S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².
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Please solve this now. Everything is attached in the file. You need to provide a full solution. Thanks
Based on the requirements for FICA and Medicare tax, the amount to be withheld in March for FiCA is $685.10 and for Medicare is $160.23.
The amount to be withheld in December of FICA is $523.90 and for Medicare is $160.23.
How much is to be withheld for FICA?In March, the amount to be withheld is:
= 11,050 x 6.2%
= $685.10
To find out the amount withheld in December, find out the earnings up to that point:
= 11,050 x 12
= $132,600
FICA can only be withheld on the first $130,000 so the amount of FICA In December is:
= 6.2% x ( 11,050 - (132,600 - 130,000))
= $523.90
What amount will be withheld for Medicare?The amount will be the same for both March and December as Medicare is for all earnings:
= 11,050 x 1.45%
= $160.23
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A 12-yard-long pipe is cut into three equal sections. Two of the resulting sections are cut in half, and one of the halves is cut into thirds. If two pipe sections are chosen and combined end to end, what is the difference between the longest possible and shortest possible combinations? (Note: 1 yard = 3 feet)
Answer:
14ft
Step-by-step explanation:
12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.
Find the last number of the following series
10 8 16 13 39 35
1)75
2)100
3)130
4)140
The answer is 4) 140.
If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.
10 - 2 = 88 × 2 = 1616 - 3 = 1313 × 3 = 3939 - 4 = 35The next step, according to the pattern, would be to multiply 4.
35 × 414030% of what number is
165
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
Will mark brainliest
The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.
Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.
So we have
[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]
60% of people who purchase sports cars are men. If
10 sports car owners are randomly selected, find
the probability that exactly 7 are men.
The probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men. This can be obtained by using binomial distribution formula.
Calculate the required probability:This question can be solved using binomial distribution formula.
The formula for binomial distribution is the following,
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
where,
n = number of trials(or the number being sampled)
x = number of success desired
p = probability of getting a success in one trial
q = 1 - p = probability of getting a failure in one trial
Here in the question it is given that,
⇒ 60% of people who purchase sports cars are men
This statements clearly means that probability of men purchase sports cars is 60%.
⇒ P(men purchasers) = p = 60% = 0.6
From this we can find the probability of women who purchase sports cars,
⇒ P(women purchasers) = q = 1 - p = 1 - 0.6 = 0.4
So we can find the probability that exactly 7 are men out of 10 sports car owners who are randomly selected
It is a binomial case with n = 10
By using the formula for binomial distribution we get,
P(X = 7) = ¹⁰C₇ × 0.6⁷ × 0.4³
P(X = 7) = 120 × 0.0279936 × 0.064
P(X = 7) = 0.21499
P(X = 7) = 0.215
Hence the probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men.
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Astrid is looking for a job at a call center. Call center A offers her $15 per hour and call-center B offers her $.25 per minute.
Which place offers a higher wage?
Answer: They are the same
Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.
Relate ratios in right triangles
Consider right triangle ADEF below. Which Expressions are equivalent to cos(E)?
Answer:
B
Step-by-step explanation:
Cos is the adjacent side over the hypotenuse. The adjacent side to <E is side ED. The hypotenuse is side EF. ED/EF. They do not go right out and give you this choice, but you see that B says the same thing.
(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball x) and the number of minutes he
plays volleyball (y) every day. (5 points)
Part B: How much time doos Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball (or 25 minutes
longer than he plays volleyball? Explain your reasoning. (2 points)