Answers
Answer:
b. [tex]\frac{7+\sqrt{61} }{6} ,\frac{7-\sqrt{61} }{6}[/tex]
Step-by-step explanation:
[tex]3x^{2} -1=7x[/tex]
Quadratic equations are suppose to be written as: [tex]ax^2+bx+c=0[/tex]
so the new quadratic equation for this problem will be: [tex]3x^{2} -1-7x=0[/tex]
Now rearrange the terms: [tex]3x^{2} -7x-1=0[/tex]
Then use the Quadratic Formula to Solve for the Quadratic Equation
Quadratic Formula = [tex]x=\frac{-b±}{} \frac{\sqrt{b^2-4ac} }{2a}[/tex]
Note: Ignore the A in the quadratic formula
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
[tex]3x^{2} -7x-1=0[/tex]
a = 3
b = -7
c = -1
[tex]x=-(-7)±\frac{\sqrt{(-7)^2-4(3)(-1)} }{2(3)}[/tex]
Evaluate The Exponent
[tex]x=\frac{7±\sqrt{(49)-4(3)(-1)} }{2(3)}[/tex]
Multiply The Numbers
[tex]x=\frac{7±\sqrt{49+12} }{2(3)}[/tex]
Add The Numbers
[tex]x=\frac{7±\sqrt{61} }{2(3)}[/tex]
Multiply The Numbers
[tex]x=\frac{7±\sqrt{61} }{6}[/tex]
Related Questions
In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d.
The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.
Answers
Given:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.
I hope this helps!
Answer:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answers
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
please answer the question first
Answers
Answer:
Yes, 2.4
Step-by-step explanation:
Y is directly dependant on x, and the constant we multiply x by to get y is 2.4.
Answer:
Yes, 2,4
Step-by-step explanation:
This explains direct proportion because it shows that y equals the 2.4x which is the direct proportion
Hopes this helps
a carton of orange juice is 9 centimeters wide. 13 centimeters long and 24 centimeter is tall. if i drink one third of the fruit juice what is the volume left in the carton?
Answers
Answer: 1872cm³
Step-by-step explanation:
First and foremost, we've to calculate the volume of the carton which will be:
= Length × Width × Height
= 13cm × 9cm × 24cm
= 2808cm³
The volume that'll be left after ⅓ of the volume is drank will be:
= 2808 - (⅓ × 2808)
= 2808cm³ - 936cm³
= 1872cm³
b. If you take one spin, what is your expected value?
Answers
Answer:
3/7
Step-by-step explanation:
Expected Value:
3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7
Expected value when we take one spin = 3/7
What is the expected value?It is the sum of values multiplied by their respective probabilities.
How do we calculate the expected value after one spin?We have 2 red, 2 purple, 2 yellow, and 1 blue sector.
Total number of Sectors = 7
∴Probability of landing on red sector = 2/7
∴Probability of landing on purple sector = 2/7
∴Probability of landing on yellow sector = 2/7
∴Probability of landing on blue sector = 1/7
Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.
X 3 1 0 -1
P(X) 1/7 2/7 2/7 2/7
Expected Value = ∑X.P(X)
=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)
= 3/7
Learn more about Expected Values on
https://brainly.com/question/15858152
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what will the time be after 1 hour 5 minutes from 8:15 am
Answers
Answer:
9:20 am
Step-by-step explanation:
So, lets go over two things.
Minutes and hours.
Minutes changes the second number.
You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.
Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.
In this case. we are moving the minutes place up by 5:
15+5=20
So the minutes place is 20, and does not change the hours place since it is below 60.
Next we have a increase in hours by 2:
8+1=9
So the hours place is 9, and does not reset or change the pm/am since its below 12.
Answer:
9:20am
Hope thias helps!
Answer:
9:20 am
Step-by-step explanation:
Add 1 hour
8:15 to 9:15
Add 5 minutes
9:15 to 9:20
you spin each spinner and find the sum how many different sums are possible
Answers
Answer:
let's use a sample set.
8+8, 8+4, 8+5, 8+6, 8+7
4+8, 4+4, 4+5, 4+6, 4+7
5+8, 5+4, 5+5, 5+6, 5+7
6+8, 6+4, 6+5, 6+6, 6+7
7+8, 7+4, 7+5, 7+6, 7+7
There is 25 sums.
What’s the volume of the rectangular prism in cubic meters
Answers
Answer:
Volume of the prism=60m3
Step-by-step explanation:
Volume of any prism=height*width*length
Volume of the prism=3m*5m*4m=60m3
Volume of the prism=60m3
help pls
Draw a line segment AB=8cm. Construct angle BAC=angle ABC=60 DEGREE.
Now draw the angular bisector of each angle of angle ABC.
pls help
Answers
Answer:
Step-by-step explanation:
Bisection implies dividing a given segment into equal haves by construction. So that in the given question, angle ABC would be divided into equal parts.
After drawing segment AB to given length, use a compass to construct the required angle ABC. Then use the ends of the arc for the angle to bisect the angle.
The construction to this question is herewith attached to this answer for more clarifications.
Write the equation of the line that passes through the points (6,-6)
and (7,-4) Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
9514 1404 393
Answer:
y +6 = 2(x -6)
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -(-6))/(7 -6) = 2/1 = 2
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Using the slope we found and the first point, the equation is ...
y +6 = 2(x -6)
Consider a two-station production line in which no inventory is allowed between stations (i.e., the stations are tightly coupled). Station 1 consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely (i.e., potential production is determined by the roll of a single die). Station 2 consists of a single machine that has a potentialdaily production of eitther three or four units both which are equally likely (i.e. it produces three units if a fair coin comes up heads and four units if ir comes up tails).
Required:
a. Compute the capacity of each station (units per day). Is the line balanced (do both stations have the same capacity)?
b. Compute the expected throughput of the line. Does this diifer from a.?
c. Suppose a second identical machine is added to station 1 and station 2. What is the expected throughput of the line. How does this compare to previous throughput.
Answers
Answer:
a) Capacities : station 1 = 3.5 , station 2 = 3.5
Both stations have the same capacity
b) 3.5 ( it does not differ from a )
c) The value will double i.e. 3.5 * 2 = 7
Step-by-step explanation:
a) compute the capacity of each station and show if the line is balanced
for station 1
Units : 1 ,2 ,3, 4 ,5, 6
probabilities : 1/6 ( same value for all units )
for station 2
units : 3, 4
probabilities : 1/2 1/2
Capacity of station 1= ( 1/6 * 1 ) + ( 1/6 *2 ) + ( 1/6 *3) + (1/6 *4) + (1/6*5) + (1/6*6 )
= 3.5
Capacity of station 2 = ( 1/2 * 3 ) + ( 1/2 * 4 )
= 3.5
∴ both stations have the same capacity
B) Expected throughput of the line
= Min( capacity of station 1 , capacity of station 2 )
= 3.5 ( It does not differ from a )
C) When an additional identical machine is added to both stations the expected throughput of the line will be doubled
i.e. expected throughput = ( 3.5 ) * 2 = 7
An aerodynamic 1,000 kg car takes about 270 newtons of force to maintain a speed of 25 m/s. how much horsepower is required from the engine to maintain this speed?
Answers
Answer:
9.05 horse power
Step-by-step explanation:
Given:
Force = 270 Newton
Speed = 25 m/s
Power = Force * velocity
Power = 270 Newton * 25 m/s
Power = 6750 watt
Recall:
1 horse power = 746 watts
Hence, required horsepower is :
6750 watt / 746 watt
9.048 hp
9.05 horse power
The two way table shows information about preferred drinks of some people how many males drank only coffee
Answers
Answer:
73% The two-way table shows information about the preferred drinks of some people. b a How many males drank only coffee? b What is the probability that any person is male and only drinks coffee? 73% The two-way table shows information about the preferred drinks of some people
A plane left Kennedy airport on Tuesday morning for an 630mile 5 hour trip for the first part of the trip the average speed was 120 mph for the remainder of the trip the average speed was 130 mph how long did the plane fly at each speed
Answers
Answer:
The plane travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \rm mph[/tex] and [tex]\text{$3$ hours}[/tex] at an average speed of [tex]130\; \rm mph[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the number of hours that the plane travelled at an average speed of [tex]120\; \rm mph[/tex].
Given that the trip is [tex]5\; \text{hours}[/tex] long in total, the plane would have travelled at an average speed of [tex]130\; \rm mph[/tex] for [tex](5 - x)\; \text{hours}[/tex].
The plane would have travelled [tex]120\, x[/tex] miles after [tex]x\; \text{hours}[/tex] at an average speed of [tex]120\; \rm mph[/tex]. Likewise, the plane would have travelled [tex]130\, (5 - x)\; \text{miles}[/tex] after [tex](5 - x)\; \text{hours}[/tex] at an average of [tex]130\; \text{mph}[/tex].
The plane has travelled [tex]630\; \text{miles}[/tex] in total. In other words:
[tex]120\, x + 130\, (5 - x) = 630[/tex].
Solve this equation for [tex]x[/tex]: [tex]x = 2[/tex].
In other words, the plane has travelled for [tex]\text{$2$ hours}[/tex] at an average of speed [tex]120\; \text{mph}[/tex]. It would have travelled for [tex](5 - x)\; \text{hours} = (5 - 2)\; \text{hours} = 3 \; \text{hours}[/tex] for the other part of the trip (at an average speed of [tex]130\; \text{mph}[/tex].)
(I+ tan square theta)(1-sin square theta)
Answers
Answer:
1
Step-by-step explanation:
Formulas used:
[tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]
[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]
Answer:
[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]
The rectangle was rotated 360° around its center, point
C. Vertex D traces the path of a circle and lands back
Which best explains why the rotation represents an
isometric transformation?
upon itself.
y
O The angle at point D remained a right angle.
O The rectangle did not change shape or size.
O Point C remained the center of the rectangle.
5
D
4
Point C did not remain the center of the rectangle.
3
2+
1
с
+
1
43 -2 -11
2
3
4.
-2+
-3+
Answers
Answer:
O The rectangle did not change shape or size.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Isometric transformation is a transformation that preserves the shape and size of the figure. Types of isometric transformations are reflection, translation and rotation.
The rectangle represents an isometric transformation because the rectangle did not change shape or size.
Here is some record keeping from a coffee shop about their paper cups. Cups are delivered 2,000 at a time. day change Monday +2000 Tuesday -125 Wednesday -127 Thursday +1719 Friday -356 Saturday -782 Sunday 0 2. How many paper cups are left at the end of the week?
Do only number 2
Answers
Answer:
2329
Step-by-step explanation:
2000 - 125 - 127 + 1719 - 356 - 782 = 2329
HELP PLEASE! What is BD??
Answers
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
Simplify the following expression
7-5/6 × 7-7/6
Answers
[tex]\longrightarrow{\blue{ 0 }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex]7 - ( \frac{5}{6} \times 7) - \frac{7}{6} [/tex]
[tex] = 7 - \frac{35}{6} - \frac{7}{6} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for the denominators.
The L. C. M is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{7 \times 6}{1 \times 6} - \frac{35}{6} - \frac{7}{6} [/tex]
Now that the denominators are equal, we can add/subtract them.
[tex] = \frac{42- 35 - 7}{6} [/tex]
[tex] = \frac{42 - 42}{6} [/tex]
[tex] = \frac{ 0}{6} [/tex]
[tex] = 0[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Please help me with #26-28
Answers
Answers:
26) probability = 1/427) probability = 0.058828) probability = 0.157=================================================
Work Shown:
26)
1/2 = probability of an odd number, since half of the numbers are odd
1/2 = probability of tails
(1/2)*(1/2) = 1/4 is the probability of both events happening at the same time
----------------------------
27)
13/52 = probability of pulling out one club
12/51 = probability of pulling out a second club, assuming the first one is not put back
(13/52)*(12/51) = 156/2652 = 1/17 = 0.0588 is the probability of pulling two clubs in a row (without replacement).
----------------------------
28)
11/27 = probability first person has blonde hair
10/26 = probability second person has blonde hair (cannot reselect the first person again)
(11/27)*(10/26) = 110/702 = 55/351 = 0.157 is the probability of selecting two people with blonde hair
f(x)=x^2+2x-4 and g(x)=3x+1 find
Answers
Answer:
Step-by-step explanation:
[tex]f(x)=x^2+2x-4\\g(x)=3x+1\\\\g\circ f(x)=g(f(x)=3(x^2+2x-4)+1=3x^2+6x-11[/tex]
Answer:
g(f(x)) = 3x^2 + 6x - 11.
Step-by-step explanation:
Replace the x in g(x) by f(x):
g(f(x)) = 3(x^2 + 2x - 4) + 1
= 3x^2 + 6x - 12 + 1
= 3x^2 + 6x - 11.
Convex angles help me
Answers
Answer:
C, D, F
Step-by-step explanation:
Shape A is not a polygon; it has a line that doesn't connect anywhere. Even if it is a polygon, it would be concave. Shape B is a concave polygon, shape E is also a concave polygon, shape G and H are also concave polygons. Only shapes C, D, and F are convex polygons. Concave polygons are shapes that cave in, and convex polygons are caves that don't cave in.
Pls help I’m need to get my grade up
Answers
Answer:
38
Step-by-step explanation:
So, we know the formula is:
D=rt or D=r*t
We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.
Here are the two sets we can look at:
t=2, d=76
t=3, d=114
Lets plug these in and solve:
76=r*2
Divide both sides by 2 to get r alone:
38=r
Now lets check if this is true by pluggin in 38 for r in the second set, and seeing if it works:
D=r*t
114=38*3
=
114=114
So 38 is our answer.
Hope this helps!
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answers
Answer:
A
Step-by-step explanation:
Because the angles must add to 180 we can see the misssing angle is 69
This means that answer is either A or C
Using SOH we can solve for side CD
sin(21)=x/18
18sin(21)=x
x=6.45
If CD= 6.45 this means that the answer is A
Please help me I don’t understand …
Answers
Answer:
X=90°
Y=58°
Z=32°
Step-by-step explanation:
X=180°-90°=90°
Y=180°-90°-32°=58°
Z=180°-58°-90°=32°
Answer:
x = 90°, y = 58°, z = 32°
Step-by-step explanation:
The angles in a square = 90° , then
x = 90° ( adjacent angle )
The sum of the 3 angles in a triangle = 180° , then
x + y + 32° = 180° , that is
90° + y + 32° = 180°
y + 122° = 180° ( subtract 122° from both sides )
y = 58°
y + 90° + z = 180° ( straight angle )
58° + 90° + z = 180°
148° + z = 180° ( subtract 148° from both sides )
z = 32°
A study examines the relationship between educational preparation and scores on a cultural competency exam. Subjects included are nurses with an associate's degree, nurses with a baccalaureate degree, nurses with a master's degree, and nurses with a doctoral degree. In this example, cultural competency is measured at what level?
a. Dependent variable
b. Independent variable
c. Outcome
d. Significant variable
Answers
Answer:
b. Independent variable
Step-by-step explanation:
Understanding the definition of variables is necessary to grasp the notion of independent and dependent variables. The attributes or sorts of features of specific occurrences or things are specified as variables.
Independent variables are variables that are modified or altered by researchers and the consequences of these modifications are evaluated and compared.
The term dependent variable relates to a sort of variable that assesses how the independent variable(s) impact the test results.
From the given information:
Education level is the predictor since we understand that nurses' education levels are closely correlated with their cultural competence scores. By applying the concept of the logistic regression model and using education level as an independent variable(predictor), we can simply predict their cultural competency. Thus, cultural competency is measured by using the independent variable.
If f(x) = x2 – 2x, find:
f(-3) = [?]
Answers
9514 1404 393
Answer:
15
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
f(-3) = (-3)² -2(-3) = 9 +6
f(-3) = 15
15
Step-by-step explanation:
f(-3)=(-3)^2 - 2(-3)
= 9 + 6 = 15
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
Answers
Answer:
Step-by-step explanation:
We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is
[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to
[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.
the volume of a cylinder is 44cm3. find the volume of another cylinder of the same height and double the base radius
Answers
Answer:
[tex]Volume \ of \ other\ cylinder = 176 \ cm^3[/tex]
Step-by-step explanation:
Let the volume of cylinder Vₐ = 44cm³
Let radius of cylinder " a " be = rₐ
Let height of cylinder " b" be = hₐ
[tex]Volume_a = \pi r_a^2 h_a\\\\44 = \pi r_a^2 h_a[/tex]
Given cylinder " b ", Radius is twice cylinder " a " , that is [tex]r_b = 2 r_a[/tex]
Also Height of cylinder " b " is same as cylinder " a " , that is [tex]h_b = h_a[/tex]
[tex]Volume_b = \pi r_b^2 h_b[/tex]
[tex]= \pi (2r_a)^2 h_a\\\\=4 \times \pi r_a^2 h_a\\\\= 4 \times 44\\\\= 176 \ cm^3[/tex]
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
Answers
9514 1404 393
Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
[tex]9^x-1=2[/tex]
You can use logarithms, or your knowledge of powers of 3 to solve this.
[tex]9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}[/tex]
Using logarithms, the solution looks like ...
[tex]x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}[/tex]