Answers
Answer:
3. -1/3 ± 2i√5 / 3
Step-by-step explanation:
3x^2 + 2x = -7
Divide through by 3:
x^2 + 2/3 x = -7/3
Completing the square:
x^2 + 2/3 x + (1/3)^2 = -7/3 + (1/3)^2
(x + 1/3)^2 = -7/3 + 1/9
(x + 1/3)^2 = -20/9
x + 1/3 = ±√(-20) / 3
x + 1/3 = ± 2√-5/3
x = -1/3 ± 2i√5 / 3
Related Questions
Let R be the region in the first quadrant bounded above by the graph of y=1−x^2 and below by the graph of y=1−√x, as shown in the figure above. What is the area of the region?
Answers
1/3
have a good day/night
If R be the region in the first quadrant bounded above by the graph of y=1−x² and below by the graph of y=1−√x then area is 1/3.
To find the area of the region bounded by the graphs of y = 1 - x² and y = 1 - √x in the first quadrant.
we need to determine the points of intersection and integrate the difference between the two functions over that interval.
To find the points of intersection, we set the two functions equal to each other:
1 - x²= 1 - √x
x²= √x
Squaring both sides again, we have:
x⁴ = x
x(x³ - 1) = 0
This equation gives us two potential solutions: x = 0 and x = 1.
To determine the limits of integration, we need to find the x-value where the two curves intersect.
Since y = 1 - √x represents the upper curve, we can set the two functions equal to each other and solve for x:
1 - x² = 1 - √x
x² = √x
x⁴ = x
Since we are only interested in the first quadrant, the solution x = 0 is not relevant.
Therefore, the only point of intersection is x = 1.
Integrating the difference between the two functions over the interval [0, 1] will give us the area of the region R:
A = ∫[0, 1] (1 - x²) - (1 - √x) dx
Expanding and simplifying the integrand:
A = ∫[0, 1] 1 - x² - 1 + √x dx
A = ∫[0, 1] -x² + √x dx
Integrating each term separately:
A = [-x³/3 + (2/3)x^(3/2)]|[0, 1]
A = [-(1/3) + (2/3)] - [0]
A = 1/3
Therefore, the area of the region R is 1/3.
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a poker hand consisting of five cards, is dealt from a standard deck of 52 cards. Find the probability that the hand contains five face cards
Answers
Answer:
56
Step-by-step explanation:
because is one times 44
a triangular prism is cut parallel from its bases, what is the shape of the cut?
Answers
Answer:
a triangle
Step-by-step explanation:
when looking at a triangular prism it is made of 4 triangles, so any way you cut it, it will be a triangle
Question 6 of 10
The graph of f(x) -13*-6 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
10+
9)
5
25-20-15-10
5 10 15 20 25
10-13-6-10-
-15+
O A 9-364-43
OB. 863)-23* +3
OC. 900---13--6
D. g(x) - 3* +2
Answers
The graph is attached.
Step-by-step explanation:
This will be an exponential function, which means it will be a smooth curve.
The y-intercept will be 35, since this is the starting population.
Since the population is increasing, the curve will increase as well.
A triangle has angle measurements of 31°, 10°, and 139º. What kind of triangle is it?
Answers
Answer:
Its a Obtuse Angled Triangle
Step-by-step explanation:
This is due to one of the angles being over 90 Degrees
The measure of the arc from A to B that does not pass through C?
A-160
B-140
C-100
D-90
Answers
Answer: C
Step-by-step explanation:
What is the 15th term of the following sequence? 0.25, 0.5, 1, 2, 4…
Answers
4,096
Solution:In this case, we have a geometric sequence.In a geometric sequence, we use multiplication/division in order to get to the next term.In this case, we multiply each term by 2.So these are the terms:0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096Hope it helps.
Do comment if you have any query.
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
Answers
Answer:
1 1/3
Step-by-step explanation:
2(8/12)=16/12=1 4/12=1 1/3
In the morning, the trip odometer in Mr. Chin's car read 47 miles. At the end of the day, the trip odometer read 114 miles. How
many miles did Mr. Chin drive that day?
Answers
Answer:
67 miles
Explanation:
initial reading: 47 milesfinal reading: 114 milesmiles travelled:
final reading - initial reading114 - 4767 milesAnswer:
67 miles
Step-by-step explanation:
An odometer measures the distance traveled by a vehicle.
To calculate the number of miles Mr Chin drove that day, subtract the reading of the odometer at the start of the day from the reading of the odometer at the end of the day.
Given information:
Starting odometer reading = 47 milesEnding odometer reading = 114 miles⇒ Number of miles driven = 114 - 47
= 67 miles
Help picture below problem 11
Answers
Answer:
B) angle B
Step-by-step explanation:
Since the question is telling you that both the triangles are essentially the same, you just have to look to see which letter of triangle ABC is in the same general place as triangle DEF.
In this case angle B is in the same general spot as angle E, so therefore B is your answer.
Hope this helps you :)
The selling price of a textbook is
$
158.75
.
If the markup is
25
% of the bookstore's cost, what is the bookstore's cost of the textbook?
Answers
Answer:
198.43. dollars is the answer
Given: -7x<-21 choose the solution set
Answers
Answer:
x > 3
Step-by-step explanation:
The only thing you need to do is just divide both sides by -7
-7x/-7<-21/-7
x>3
I hope this helped!! Good luck (:
Cherokee Manufacturing Company established the following standard price and cost data.
Sales price
Variable manufacturing cost
Fixed manufacturing cost
Fixed selling and administrative cost
$12.00 per unit
$ 7.20 per unit
$3,600 total
$1,200 total
Cherokee planned to produce and sell 2,000 units. Actual production and sales amounted to 2,200 units.
Required
a. Determine the sales and variable cost volume variances.
b. Classify the variances as favorable (F) or unfavorable (U).
d. Determine the amount of fixed cost that will appear in the flexible budget.
e. Determine the fixed cost per unit based on planned activity and the fixed cost per unit based on actual activity.
Answer is not complete.
Answers
Assuming the Actual production and sales amounted to 2,200 units.The sales and variable cost is:2400 F; $1,440 UF.
Sales and variable cost volume variancesa. Sales and variable cost volume variances
Sales =(Actual units sold -Budgeted units sold)× Budgeted price per unit
Sales=(2200-2000)×$12.00 per unit
Sales=26,400-$24,000
Sales=2400 F
Variable=(Actual units sold -Budgeted units sold)× Budgeted price per unit
Variable=(2200-2000)×$7.20 per unit
Variable=$15,840-$14,400
Variable=$1,440 UF
b. Sales=2400 F
Variable=$1,440 UF
d. Fixed cost
Fixed manufacturing cost $3,600
Fixed selling and administrative cost $1,200
e. Master budget Flexible budget
Fixed manufacturing cost $3,600 $3,600
Fixed selling and administrative cost $1,200 $1,200
Tota fixed cost $4,800 $4,800
Cost per units $2.4 $2.18
($4,800 /2000) ($4,800/2200)
Therefore the sales and variable cost is:2400 F; $1,440 UF.
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Help picture below 3 problems easy will give brainlest
Answers
Answer:
7. 64
22. 12.9
12. 22
Step-by-step explanation:
x = 154 154 - 90 = 64
15% of 86 is 12.9
A triangle's angles must all add up to 180.
90 + 68 = 158 180 - 158 = 22
A toy boat is bobbing on the water.
Its distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) from the floor of the lake as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, when the boat is exactly in the middle of its oscillation, it is 1\text{ m}1 m1, start text, space, m, end text above the water's floor. The boat reaches its maximum height of 1.2\text{ m}1.2 m1, point, 2, start text, space, m, end text after \dfrac{\pi}{4}
4
π
start fraction, pi, divided by, 4, end fraction seconds.
Find D(t)D(t)D, left parenthesis, t, right parenthesis.
Answers
An equation for a toy boat is bobbing on the water is in the sinusoidal form which we can write as, D(t) = 0.2 sin2t +1
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, D(t) = acos2t +b
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given information,
Equation of bobbing, D(t) = a sinbt + d
By graph we can say that it is compressed two times,
So, value of b will be, 2
At t =0, height from the floor is 1 m
1 = a sin(2×0) + d
d = 0
At t =π/4, height from the floor is 1.2 m
1.2 = a sin(2×π/4) + 1
a = 0.2
By graph we can say that it is compressed two times,
So, value of b will be 2
Hence, An equation is D(t) = 0.2 sin2t +1
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Re-write the quadratic function below in Standard Form
y=2(x+2)(x−4)
Answers
Answer:
Standard form:
y=2x^2-4x-16
find the factors of 45
Answers
Answer:
1, 3, 5, 9, 15, 45
Step-by-step explanation:
Factors of a number is when two or more numbers are multiplied to give you your original number. Here, it's 45.
The factors of 45:
1 x 45 = 45
3 x 15 = 45
5 x 9 = 45
1, 3, 5, 9, 15, 45
Hope this helps!
Two boys san around a track that is 400 meters long. Miguel ran around the track three
times in 240 seconds. Joseph ran around the track three times in 200 seconds. What was the
difference between the speeds of the two boys?
A.
1 meter per second
5 meters per second
B.
C.
6 meters per second
D.
11 meters per second
Answers
Using proportions, it is found that the difference between the speeds of the two boys was of:
A. 1 meter per second.
What is a proportion?A proportion is a fraction of a total amount. Following this concept, velocity is distance divided by time.
In this problem, Miguel ran 1 lap = 400 meters each 240/3 = 80 seconds, hence his speed is given by:
sM = 400/80 = 5 m/s.
Joseph ran 400 metters each 200/3 = 66.67 seconds, hence his speed is given by:
sJ = 400/66.67 = 6 m/s.
The difference is given by:
6 m/s - 5 m/s = 1m/s.
Hence, option A is correct.
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In an invasion game such as Soccer, Football, or Handball, how can you tell which team is offense and which team is defense?
Answers
Answer:
The easiest way to determine whose offense or defense would be to check where the players are positioned at. Obviously, the main goals of Soccer or Football are in the back meaning people who are defending the goal are most likely to be behind the teammates who are offensive (common sense).
Step-by-step explanation:
please fast answer guys are in doing correct answer guys
multiply 998752×15
divide 22 table 15253435
add 22222+89997+45567+10130
sub 99999-45678
Answers
Answer:
i think that to many but the answer is 5
Step-by-step explanation:
qwerty
a room is 15ft x 17ft and is 10 ft tall. if you were going to paint all four walls, with one coats of paint, how many square feet would you have to cover. if a gallon of paint covered 800 sq feet, how many gallons of paint would you have to buy?
Answers
Answer:
15 x 17 x 10 ft = __
Step-by-step explanation:
MMultiply the numbers and divided by 800. That should lead you! :D
solve for x and y please
Answers
Answer:
Step-by-step explanation:
The 2 triangles are similar so corresponding sides are in the same ratio.
3/x = 6/16
6x = 48
x = 8.
9/y = 6/16 = 3/8
3y = 72
y = 24.
Answer:
y = 24 mx = 8 musing proportional equation:
[tex]\rightarrow \sf \dfrac{AC}{CE} = \dfrac{DB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{9}{6} = \dfrac{y}{16}[/tex]
[tex]\hookrightarrow \sf 9(16)} = {6y}[/tex]
[tex]\hookrightarrow \sf y = 24[/tex]
====================
[tex]\rightarrow \sf \dfrac{AE}{CE} = \dfrac{EB}{DE}[/tex]
[tex]\hookrightarrow \sf \dfrac{3}{6} = \dfrac{x}{16}[/tex]
[tex]\hookrightarrow \sf 3(16)} = 6x[/tex]
[tex]\hookrightarrow \sf x = 8[/tex]
If 5,x,125 are in continued proportion, find valueee of xxxxx.....
Answers
Answer:
[tex] \pmb{SOLUTION:-}[/tex]
5,x,125 are in continued proportion,Then,
[tex] \displaystyle{ \frac{5}{x} = \frac{x}{125} }[/tex]
[tex]5 \times 125 = {x}^{2} [/tex]
[tex] {x}^{2} = 625[/tex]
[tex]x = \sqrt{625} [/tex]
[tex]x = 25[/tex]
Answer:
a₂ = ±25Step-by-step explanation:
5, x, and 125 are part of a geometric progressionWhat we know :
a (first term) = 5aₙ (final term) = 125n (number of terms) = 3Finding the common ratio (r)
aₙ = arⁿ⁻¹125 = (5)(r)³⁻¹25 = r²r = ± 5Finding x
x is the 2nd term of the progressiona₂ = ara₂ = 5(±5)a₂ = ±25How do you know when terms can be combined?
A. They are the same size
B. They have the same exponent
C. They have the same number
D. They have the same variable and exponent
Answers
Answer:
C. They have the same number
Find the surface area
Answers
=4 x π x 11^2
=4 x π x 121
=484π or 1520.530844cm^2
Peter earns each hour for the first 40 hours he works each week. For every hour, he works after 40 hours he earns $12 each hour last week, Peter earned $444. Which equation could be used to find the number of hours, h, during which Peter earned $12 last week?
Answers
Answer:
5
Step-by-step explanation:
I said so THATS WHY
Please help me I am so bad at math
Answers
(f ◦ g)(x) is the composition of f(x) with g(x), equivalently
(f ◦ g)(x) = f(g(x))
To get f(g(x)), replace every instance of x in the definition of f(x) with g(x):
f(x) = -x + 7 ⇒ f(g(x)) = f(√(x - 3)) = -√(x - 3) + 7
Madison and Declan are training for a lifeguard test Madison swims 2/5 mile in 3/8 hour. Declan swims 7/10 mile in 1/5 hour who swims faster
Answers
Answer:
Declan!
Step-by-step explanation:
V(Madison)=S/t=2/5÷3/8=16/15 mile/hour
V(Declan)=7/10÷1/5=7/2 mile/hour
16/15 < 7/2
explain how the model for 3/5 - 1/2 9s is different from the model for 3/5 - 3/10
Answers
The model is different because it has different denominator and numerator
find the mean absolute deviation of the set of data
1,4,7,8,10
Answers
Answer: MAD= 2.8
Step-by-step explanation: start by finding the mean of the data set. find the sum of the data values, and divide the sum by the number of data values.