Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
A: 72√3 sq. units
B: 36√3 sq. units
C: 12√3 sq. units
Answers
Parallelogram diagram I believe down below. We must find the height and then the area using Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A^2 + B^2 = C^2
A^2 + 3^2 = 6^2
A^2 + 9 = 36
A^2 = 27
A = 3√3
Therefore the height is 3√3
Now calculate the area using A = bh
A = bh
= (12)(3√3)
= 36√3
So the area is 36√3 square units.
I cannot be sure of this answer because you did not provide a diagram.
The area of the parallelogram will be equal to 36√3 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the parallelogram in a two-dimensional plane is called the area of the parallelogram.
Parallelogram diagram I believe down below. We must find the height and then the area using the Pythagorean theorem. Since the green shaded part is a 30-60-90 triangle, the base is 1/2 the hypotenuse, therefore it is 3. Now we calculate the height with it.
A ² + B² = C²
A² + 3² = 6²
A² + 9 = 36
A² = 27
A = 3√3
Therefore the height is 3√3. Now calculate the area using A = bh
A = b x h
A = ( 12 ) x ( 3√3 )
A = 36√3
So the area is 36√3 square units.
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Related Questions
Constantine picks two letters at random from the word constantinople with replacement. what is the probability that both letters picked are consonants?
Answers
P(picking a consonant) = 9/14
P(2 letters are consonants with replacement) = 9/14 * 9/14 = 81/196
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answers
One student can paint a wall in 10 minutes
another student can paint the same wall in 15 minutes.
If they paint together the wall, the result time will be
15mn - 10mn = 5 mn
proof:
let / = minute
student 1: / / / / / / / / / /
student2: / / / / / / / / / / / / / / /
x----------------------------------------x
already done
the remain time is / / / / / = five minutes
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.
Answers
For this case, we use
the cylindrical coordinates:
x² + y² = r²
dV = r dz dr dθ
The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞
θ = 0 to 2π
Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ
V = ∫ [0 to 2π] 1/18 dθ
V = θ/18 |[0 to 2π]
V = π/9
The volume of the volcano is an illustration of definite integral
The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
The graphs are given as:
[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]
The cylinder is:
[tex]\mathbf{x + y =1}[/tex]
For cylindrical coordinates, we have:
[tex]\mathbf{r^2 =x^2 + y^2}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]
[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]
Where:
[tex]\mathbf{r = 1 \to \infty}[/tex]
[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]
So, the integral is:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]
Cancel out r
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]
Integrate
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]
Expand
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]
Integrate
[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]
Expand
[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]
[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]
Cancel out 2
[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]
Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
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Find the missing length.
Answers
a^2+b^2=c^2
12^2+9^2=c^2
144+81= c^2
225=c^2
15=c
Final answer: c=15
Mason and Nora decided to swim across the river. Mason began swimming 8 seconds earlier than Nora.
Mason swam at a speed of 5 feet per second.
Nora swam at a speed of 9 feet per second.
For how many seconds had Mason been swimming at the moment when the two swimmers had swam exactly the same distance?
Answers
distance rate time
Mason d 5 t + 8
Nora d 9 t
Let me explain the values in the table. The problem says "...when the swimmers had swam exactly the same distance"; therefore, we put a d there to indicate that, although we have no idea the distance they swam, both distances were the same. The rates are easy; they are self-explanatory. The time could be a little tricky too though. If Mason began swimming 8 seconds earlier than Nora, Nora's time is t and Mason's time is t + 8, which is Nora's time with 8 seconds added to it. Because d = rt, we set up the equations like that: d = 5(t+8), and d = 9t. Because the 2 d's are the same, we set them equal to each other: 5(t+8) = 9t. Simplifying that gives you 5t + 40 = 9t and 40 = 4t and t = 10. Now put that t value of 10 into Mason's time to solve the question they are asking you: t + 8 with the substitution is 10 + 8 = 18. So Mason had been swimming for 18 seconds when they had both swam the same distance.
The lengths of the sides of a triangle are 6, 8, 10. Can the triangle be a right triangle? Yes or no?
Answers
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?
Answers
Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
What is unitary method?The unitary method is a technique in mathematics for solving a problem by finding the value of a single unit, I.e.,1,(by dividing) and then finding the necessary value by multiplying the single unit value.A method of solving a problem that involves first determining the value of a single unit, And then multiplying that value to determine the required value.According to the question,
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?let the number of paper be "X".$4=500$2000= 250,000Hence we can say that Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
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The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
Answers
A given line has the equation 10x + 2y = −2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Answers
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
Subtract [tex]10x[/tex] both sides
[tex]2y=-10x-2[/tex]
Divide by [tex]2[/tex] both sides
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
Step 2
Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]
we know that
If two lines are parallel. then their slope are equal
In this problem we have
[tex]m=-5[/tex]
[tex](0, 12)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]12=-5*0+b[/tex]
[tex]b=12[/tex]
the equation of the line is
[tex]y=-5x+12[/tex]
therefore
the answer is
[tex]y=-5x+12[/tex]
Two less than twice a number is the same as four times the number
Answers
-2+2x=4x
minus 2x both sides
-2=2x
divide by 2
-1=x
the number is -1
Final answer:
The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.
Explanation:
The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.
Subtract 2n from both sides: -2 = 2n.
Divide both sides by 2 to find the value of n: n = -1.
In conclusion, the number that satisfies the condition given is -1.
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2
Answers
m∠C = 85°, a= 10, c = 13
From the Law of Sines,
sin(A)/a = sin(C)/c
sin(A) = (a/c)*sin(C)
= (10/13)*sin(85°)
= 0.7663
m∠A = sin⁻¹ 0.7663 = 50°, or 130°
When m∠A = 50°, obtain
m∠B = 180° - (m∠A + m∠C) = 180 - (50+85) = 45°
Again from the Law of Sines, obtain
b = (sinB/sinC)*c = 9.2
When m∠A = 130°, obtain
m∠B = 180° - (130 + 85) = -35° (not possible)
Therefore this triangle does not exist.
Answer:
There is only one possible triangle, with
A=50°, B=45°, C=85°, a=10, b=9.2, c=13.
Final answer:
Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.
Explanation:
The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.
By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.
In the diagram, PN¯¯¯¯¯ is the perpendicular bisector of AB¯¯¯¯¯ and is also the angle bisector of ∠CPD. If m∠CPD = x, which quantity is equal to sin ∠DPB?
sin x2
sinx2
cosx2
cos x2
Answers
Since ∠CPD = x and segment PN is the angle bisector of this angle, therefore segment PN equally divides ∠CPD into two angles. Which means that:
∠CPN = ∠NPD = x / 2
Further, segment PN is also the perpendicular bisector of AB which further means that the intersection formed by PN and AB creates a right angle (90°). Therefore:
∠NPD + ∠DPB = 90°
x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
Therefore:
sin∠DPB = sin(90 – x/2) which is not in the choices
However we know that the relationship of sin and cos is:
sin(π/2 - θ) = cos θ
Where,
π/2 = 90
θ = x/2
Therefore:
sin(90 – x/2) = cos(x/2)
Answer:
cos(x/2)
The quantity which is equal to sin ∠DPB is:
cos(x/2)What is an Angle?This refers to the figure which is formed by two rays with a common endpoint.
Hence, we know that
∠CPN = ∠NPD = x / 2If we segment PN which is the bisector of AB, it would crerate angle 90 and this would give us:
∠NPD + ∠DPB = 90°x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
With this in mind, there is the relation between sin and cos, which would be:
sin(π/2 - θ) = cos θWe are aware that
π/2 = 90θ = x/2Hence,
sin(90 – x/2) = cos(x/2)
=cos(x/2)
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Melissa exercises for 20 minutes every day. She decides to increase her daily exercise time by 5 minutes each week. However, according to her doctor’s orders, she can spend no more than 45 minutes a day exercising. For how many weeks can Melissa increase her exercise time this way?
Answers
45-20 = 25 minutes.
Now we know that each week she increases her time by 5 minutes. Therefore, we have to find how many 5's can fit in the 25 minute difference.
25/5 = 5 weeks
Melissa increases 5 minutes every week for 5 weeks until she reaches her limit of 45 minutes.
I hope that helps!
Answer:
at most 5 weeks
Step-by-step explanation:
HELP if f(x)=-14x-2, then f^-1(x)=?
Answers
[tex]f(x) = -14x - 2 [/tex]
[tex]y = -14x - 2 [/tex]
[tex]x = -14y - 2 [/tex]
[tex]x+2 = -14y [/tex]
[tex]-14y = x+2 [/tex]
[tex]y = -\frac{x+2}{14} [/tex]
[tex]f^{-1}(x) = -\frac{x+2}{14} [/tex]
please help on b (left of c) and c !!!
rewrite each of the following expressions so that your answer has no negative or fractional exponents
Answers
remember
[tex](ab)^c=(a^c)(b^c)[/tex]
and
[tex]x^\frac{m}{n}=\sqrt[n]{x^m}[/tex]
and
[tex](x^m)^n=x^{mn}
and
[tex]x^0=1[/tex] for all real numbers x
and
[tex]x^{-m}=\frac{1}{x^m}[/tex]
b.
[tex](x^5y^4)^\frac{1}{2}=((x^5)^\frac{1}{2})((y^4)^\frac{1}{2})[/tex]=
[tex](x^\frac{5}{2})(y^\frac{4}{2})=(\sqrt{x^5})(\sqrt{y^4})=x^2y^2\sqrt{x}[/tex]
c.
x^0=1
so
that (x^-3y)^0=1
because exponents first in pemdas
so we are left with
x^2y^-1
[tex]x^2y^{-1}=(x^2)(y^{-1})=(x^2)(\frac{1}{y^1})=\frac{x^2}{y}[/tex]
The area of one circle is 4 times as large as a smaller circle with a radius of 3 inches. the radius of the larger circle is
Answers
As the area of other circle is four times greater than small one
So the area of larger circle will be= 4(9π)=36π
So the radius will be
area=π r^2
36π=π(r^2)
r^2=36
√r^2=√36
r=6 inchs
ANSWER IS THAT THE RADIUSOF LARGER CIRCLE WILL BE
6 INCHES
What is the circumference of this circle, in millimeters? use 22/7 for pi
r = 49
Answers
Answer: circumference = 308mm
Step-by-step explanation: the formula for the circumference of a circle is given by
C=2πr
Given that r=49mm
Pi=22/4
C=2*22/7*49
C=44*7=308mm
In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.
Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8 A. x = 2, y = 1 B. x = 5, y = 6 C. x = 3, y = −1 D. x = −1, y = 2
Answers
(-1, 2) verifies the 2 equations Answer D
because :
3(-1)+5(2) = 7...right
6(-1)-(2) = -8...... right
How do I solve this? (Geometry)
Answers
circle to the midpoint of a side of the triangle.
Now draw a line from the center to the vertex
of that side. You now have a right triangle with
a base angle of 30º, side adjacent to that angle
of 3, and hypotenuse = r, the radius of circle. So,
cos 30º = 3/r, r = 3.46, the diameter
is twice that, 6.92 round to 6.9
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is
a-36
b-18
c-288
d-5
Answers
A ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answers
You get : [tex]-16t^2-4t+70[/tex] which can be further simplified to [tex]8t^2+2t-35[/tex] if you divide all of the numbers by -2.
Here you can use the quadratic formula again!
You get the numbers to be : 1.97 and -2.22
I had made a mistake to think that negative numbers can be included but in these questions, you can't have negative numbers as your answer. So the correct answer is 1.97!
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. 1.97 is the time taken by the ball to hit the ground.
What is Distance?Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given that a ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t²
Now we can take h=0
h=-16t²+70-4t
-16t²+70-4t
Divide by 2
-8t²-2t+35
Now apply quadratic formula
a=-8, b=-2, c=35
t=-b±√b²-4ac/2a
t=2±√-2²-4(-8)(35)/2(-8)
t=2±√4+1120/-16
we get t= 1.97 and t= -2.22
You get the numbers to be : 1.97 and -2.22
We do not consider negative values. So the correct answer is 1.97
Hence 1.97 is the time taken by the ball to hit the ground.
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Calculate the upper and lower limit for a 95% confidence interval about this mean. a family needs a new car, but isn't sure they can fit the payment into their budget. a sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. if the upper limit of a 95% confidence level is below $100, the family can afford to buy the car. standard error = (standard deviation)/(square root of sample size) upper limit (dollars and cents) lower limit (dollars and cents)
Answers
To find the upper and lower limits of a 95% confidence interval for the given data, calculate the standard error, use the multiplier of 2, and apply the formula Sample mean ± Multiplier * Standard error.
To calculate the upper and lower limit for a 95% confidence interval, we use the formula: Confidence interval = Sample mean ± Multiplier * Standard error. For this case, the sample mean is $94 and the standard deviation is $10. The standard error is calculated as $10 / √36 = $10 / 6 ≈ $1.67.
With a 95% confidence level, the multiplier is approximately 2. Therefore, the upper limit would be $94 + 2($1.67) = $94 + $3.34 ≈ $97.34, and the lower limit would be $94 - $3.34≈ $90.66.
i need help find the volume of this hexagon based pyramid!
please write steps and its ok to have more than one person answering
Answers
V = (1/3)*Bh
where
B is area of the base
h is height
We know the height to be 27 in. The missing information is the area of the hexagonal base. So, let's focus on this shape as drawn in the attached picture. The area of any given polygon is one-half the product of its apothem and perimeter:
B = (1/2)*aP
The apothem is a line drawn from the center of the polygon and projected down to the center of its base. So, an apothem is a perpendicular bisector denoted by the red line. Each interior angle of a hexagon is equal to 60° because one revolution divided by 6 sides is: 360/6 = 60°. When an apothem is drawn, it makes a right angle with an angle of 30° and a base of half of 23 inches. Using the pythagorean theorem, the apothem is equal to:
tan 30° = (23/2) ÷ a
a = 23*sqrt(3)/2 in
The perimeter is the sum of all sides of the polygon. Assuming the hexagon is regular, all its sides are equal measuring 23 inches. So, the perimeter is equal to:
P = 23(6) = 138 in
So, the area of the base is equal to:
B = (1/2)(23*sqrt(3)/2 in)(138 in)
B = 1,374.3823 in²
So, we can finally solve for V:
V = (1/3)(1,374.3823 in²)(27 in)
V = 12,369.44 in³
A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..
Answers
The area of a square is calculated by the formula:
A = l²
As A = 75 ft², we have:
75 = l²
l = √75
Now, note that: 75 = 3 . 25 = 3 . 5²
So:
l = √(3 . 5²) = √3 . √(5²)
l = 5√3 ft
Now, we can assume √3 = 1.73
l ≈ 5 * 1.732
l ≈ 8,7 ft (Note that I have already put it in the nearest tenth)
OK :)
Subtract: (2x2 − 7x + 5) − (−6x2 − 4x − 2)
Answers
2x^2 - 7x + 5 + 6x^2 + 4x + 2 =
8x^2 - 3x + 7 <==
Answer:
8x^2 - 3x + 7
Step-by-step explanation:
I took the test.
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 6
A =
37.68 sq. units
113.04 sq. units
226.08 sq. units
Answers
Area of a circle = [tex] \pi r^{2} [/tex] = [tex]3.14 * 6 * 6 = 3.14 * 36 = 113.04 [/tex] sq. units.
Hence, the answer is B.
Answer: 113.04 sq. units
I need to know the solution
Answers
For the second one, get x by itself as a whole number. Multiply each side by 8. You get x=16. The answer is x=16. Hope this helps! ;)
and
c. x=16
you can also get an app that is called script calculator that helps with that
A kayaker spends a morning paddling on a river. She travels 9 miles upstream and 9 miles downstream in a total of 6 hours. In still water, she can travel at an average speed of 4 miles per hour. What is the average speed of the river's current in miles per hour?
A) 1 mi/h
B) 2 mi/h
C) 3 mi/h
D) 1.5 mi/h
Answers
When the karayaker moves upstream or against the current, his speed would be 4 - y. Further, if he moves downstream or with the current, the total speed would be 4 + y. The time utilized for the travel is equal to the ratio of the distance and the speed.
Total time = 9/(4 - y) + 9/(4 + y) = 6
We multiply the equation by (4-y)(4+y)
9(4-y) + 9(4 + y) = 6(4-y)(4+y)
Simplifying,
72 = 96 - 6y²
Transposing all the constants to only one side of the equation and rearranging,
6y² = 96 - 72
y² = 4
y = 2
Hence, the speed of the river's current is 2 miles/hr. The answer is letter B.) 2 miles/hour.
Average speed is the ratio of the total distance traveled to the total time taken. The average speed of the river's current is 2 mi/h.
What is Average speed?Average speed is the ratio of the total distance traveled to the total time taken.
As we know that the total time taken by the boat to travel upstream and downstream is 6 hours. And the distance traveled by Kayaker is 9 miles, each time while going upstream and downstream.
We know that when the boat is traveling upstream the water current will try to resist the boat, therefore, the speed of the boat while going upstream is (4-x), where x is the speed of the boat. Similarly, the speed of the boat when going downstream will be (4+x), as the water stream will try to provide a push to the boat. Therefore, the total time taken by the Kayaker can be written as,
Total Time
= Time taken while going upstream + Time taken while going downstream
[tex]\rm 6 = \dfrac{Distance\ upstream}{Speed\ upstream} + \dfrac{Distance\ Downstream}{Speed\ Downstream}[/tex]
[tex]\rm 6 = \dfrac{9}{(4+x)} + \dfrac{9}{(4-x)}[/tex]
Taking the LCM,
[tex]6 = \dfrac{9(4+x)+9(4-x)}{(4+x)(4-x)}\\\\6\times (4+x)(4-x) = 9(4+x)+9(4-x)\\\\6(16-x^2) = 36+9x+36-9x\\\\96 - 6x^2 = 72\\\\-6x^2 = 72-96\\\\6x^2 = 24\\\\x^2 = 4\\\\x =2[/tex]
Hence, the average speed of the river's current in miles per hour is 2 mi/h.
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Which value is in the domain of f(x)?
A.) –7
B.) –6
C.) 4
D.) 5
Answers
f(x) = -2x + 3 0<x <= 4
hope that helps
Answer:
C) 4
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]
The function is defined on two intervals.
The first interval is
[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].
[tex]-7[/tex] does not belong to any of these intervals.
[tex]-6[/tex] does not also belong to any of these intervals.
[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].
Hence 4 is in the domain of f(x).
[tex]5[/tex] does not also belong to any of the intervals.
Therefore the correct answer is C.
A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
Answers
The expression for total price of selling the T-shirts is 15T
Profit = Total cost of selling - Total cost of buying
Profit = 15T - (20+9T)
Profit = 15T - 20 - 9T
Profit = 6T - 20
To make profit ≥150
6T - 20 ≥ 150
6T ≥ 170
T ≥ 170/6
T ≥ 28.3
The minimum number of T-shirts needed is 29 T-shirts