The value of x in part (a) is [-3+√21]/6 and [-3-√21]/6, the value of t in part (b) is (1/5+√11/5) and (1/5-√11/10), the value of t in part (c) is 1/5 and the value of t in part (d) is 1/5-3/5i and 1/5+3/5i.
Part a. Solving for x,
1/x - 1/(x+1) = 3
(1-x+x)/x(x+1) = 3
1/(x²+x) = 3
1 = 3x²+3x
3x²+3x-1=0
Solving the quadratic by using quadratic formula,
x = [-b±√(b²-4ac)]/2a
Here,
a = 3
b = 3
c = -1
Putting all the values,
x= [-3±√(3²-4(3)(-1)]/6
x = [-3±√21]/6
We get,
x = [-3+√21]/6 and
x = [-3-√21]/6
Part b. Solving for t;
2 =√[(1+t)²+(1-2t)²]
Squaring both sides,
4 = (1+t)²+(1-2t)²
4 = 1+t²+2t+1+4t²-4t
2 = 5t²-2t
5t²-2t-2=0
Solving the equation by using quadratic formula,
t= [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = -2
Putting all the values,
t = [2±√(4-4(5)(-2))]/10
t = [2±√44]/10
We get
t = (1/5+√11/5) and (1/5-√11/10)
Part c. Solving for t;
3/√5 = √[(1 + t)² + (1 − 2t)²]
Squaring both sides,
9/5 = (1+t)²+(1-2t)²
9/5 = 1+t²+2t+1+4t²-4t
9 = 5+5t²+10t+5+20t²-20t
25t²-10t+1=0
t = [-b±√(b²-4ac)]/2a
Here,
a = 25
b = -10
c = 1
Putting all the values,
t = [10±√(100-4(25))]/50
t= [10±0]/50
t= 1/5
Part d. Solving for t;
0 = √[(1 + t)²+(1 − 2t)²]
Squaring both sides,
(1+t)² =-(1-2t)²
1+t²+2t = -(1+4t²-4t)
1+t²+2t = -1-4t²+4t
5t²-2t+2=0
Solving the equation by using quadratic formula,
t = [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = 2
Putting all the values,
t = [2±√(4-4(5)(-2)]/10
t = [2±√(-36)]/10
t = [2±6√(-1)]/10
√-1 is 'iota' or i.
t = (2±6i)/10
We get,
t = 1/5-3/5i and 1/5+3/5i
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If a Ferrari, with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes, what will its final velocity be (in km/h)?
The final velocity of the Ferrari will be 84.53 km/h. with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes.
This is a typical question from Newtonian mechanics. To solve this problem we have to convert all the given data into a standard unit like C.G.S.
Now, we will convert 10 km/h and 50 km/h by using the formula. (km/h × 5/18 = m/s )
10 km/h = 10× 5/18 = 2.78 m/s
50 km/h = 50× 5/18 = 13.89 m/sec/min = 0.23 m/s²
3 min = 3 × 60 = 180 sec. ( 1 min = 60 sec )
Now, we have to use the formula from Newton's law of motion,
v = u + at/2 .
Here, u is the initial velocity which is 2.78 m/s.a is the acceleration which is 0.23 m/s²t is the period which is 180 sec. v is the final velocity.Now we can calculate the final velocity,
v = 2.78 + (0.23 × 180)/2 = 2.78 + 20.7 = 23.48 m/s
Now, we have to calculate the velocity in km/h, which is (23.48 × 5 )/8 = 84.53 km/h. as we know (km/h = m/s ×18/5 ).
Therefore, the final velocity will be 23.48 m/s according to the given inputs and criteria.
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Which of the following lines best fits the data shown in the scatter plot? 10 9 8 7 6 1 2 3 4 5 6 7 8 9 x Line a A С Line c Line b B. D None of the lines fit the data well
Scatter drawing plot
Use the Multiplication Property of One to rewrite the statement.8+1=x1) = 0
We need to isolate on the equation
[tex]8+(z\times1)=0[/tex]since any number multiplied by one is the same, then z times 1 is z, so we can write
[tex]8+z=0[/tex]Now, we can add -8 to both side and get
[tex]8-8+z=-8[/tex]since 8 - 8 is zero, we have
[tex]z=-8[/tex]then, z is equal to -8.
The graph of g(x) shown below has the same shape as the graph of f(x)=x2 but it is shifted right by 5 units write the equation for g(x)please help me!! :(
f(x)= x^2
To shift 5 units to the right subtract 5 to x .
g(x)= (x-5)^2
7 is added to 11 divided by a number r write the algebraic expression
Answer: 7+(11/r)
Step-by-step explanation:
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)
2) [tex]\angle X=\angle X[/tex] (reflexive property)
3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)
718-119x+719 for x =0
please simplify and find the value
The length of a rectangle is double its width. If the rectangle has a perimeter of 138cm, find its length (in cm).
Answer:
length = 46cm
Step-by-step explanation:
The length of a rectangle is double its width. If the rectangle has a perimeter of 138cm, find its length (in cm).
p = 2l + 2w
when l = 2w, substitute in to equation:
138 = 2(2w) + 2w
138 = 4w + 2w
138 = 6w
divide both sides by 6:
138/6 = 6w/6
so width = 23cm
and we know that length = 2 width so:
length = 23cm × 2
length = 46cm
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-2, 3); y=-3/4x+4
Answer:
y=4/3x+17/3
Step-by-step explanation:
Perpendicular lines have reciprocal negative slopes, find the slope of the new line:
-3/4 --> m = 4/3
Write line in point slope form:
y-3 = 4/3(x+2)
Distribute:
y-3=4/3x+8/3
Simplify:
y=4/3x+17/3
A store generates Monday through Thursday sales of $150, $125, $75, and $180. What sales on Friday would give a weekday average of $150?
Answer:
mi cola es grande
Step-by-step explanation:
uhh
An architect notices that the scale on a blueprint he is using has been torn off. However, he sees that a 12.5-ft. wall that has been built is 5 in. long on the blueprint. What is the scale for this blueprint?
A. 1 in. : 2.5 ft.
B. 1 in. : 25 ft.
C. 1 in. : 62 ft.
D. 1 in. : 62.5 ft.
Answer it is c because when you multiply 12 x 5 you get 60 right so round up to the nearest number 62 an u can't subtract or divide you won't get a or b
help l need help with this
Answer:
Step-by-step explanation:
Answer: Y = 3x + 3
Simply plug in points on graph calculator.
Answer:
Step-by-step explanation:
I think it might be y=3/1+6 ??? i might be wrong
I'll give brainliest!
Answer:
The answer is A
write the missing power of 10 in the exponential form…….*0.006=0.6
Answer:
10 to the second power
[tex]10^2[/tex]Explanation:
Let the unknown value be x
The given expression can be rewritten as:
[tex]x\times0.006=0.6[/tex]Express as a fraction;
[tex]\begin{gathered} x\times\frac{6}{1000}=\frac{6}{10} \\ \frac{6x}{1000}=\frac{6}{10} \\ \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 6x\times10=6\times1000 \\ 60x=6000 \\ x=\frac{6000}{60} \\ x=100 \\ x=10^2 \end{gathered}[/tex]Hence the required unknown number in the exponential power of 10 is 10^2
ANSWERS ASAPP
i got a 57 in this class
Answer:
Y=-1/4x+-6
Step-by-step explanation:
convert the line to slope intercept form
x is the slope and the last thing is the y intercept
What is the x-coordinate for point A? TO B (9.9) Sixta- 9 8 7 6 5 4 3 2. 1 A (9.3) 1 0 1 2 3 4 5 6 7 8 9 10
EXPLANATION
The coordinate for point A is x=9
Mental Math Using the slope formula, find the slope of the line through the points (0,0) and (3,6).Use pencil and paper. Explain how you can use mental math to find the slope of the line.
Given the points (0,0) and (3,6)
slope = y2 - y1 / x2 -x1
x1= 0, y1 = 0 , x2= 3, and y2 = 6
slope = 6 - 0 / 3 - 0
slope = 6 / 3
slope = 2
the answer is 2
The lines shown below are parallel. If the green line has a slope of 5, what isthe slope of the red line?.O A.OB. 55O C.C. -//OD. -5(1)→
The slope of the red line is 5. The correct answer is option B. 5
Two parallel lines, always have the same slope. Since the green and red line are parallels and the green line has slope 5, the slope of the red line is also 5.
There are 6 roses in a vase of 14 flowers. The rest are daisies. What is the ratio of all flowers in the vase to daisies?
Given:
There are 6 roses in a vase of 14 flowers.
Required:
To find the ratio of all flowers in the vase to daisies.
Explanation:
The total number of daisies in the vase are
[tex]\begin{gathered} =14-6 \\ =8 \end{gathered}[/tex]So the ratio of all flowers in the vase to daisies is,
[tex]14:8[/tex][tex]7:4[/tex]Final Answer:
[tex]7:4[/tex]Name The Transformations Y=(x+3)^2-5
Answer: move three units to the left, and 5 units down would be the answer to it
Step-by-step explanation: hope i helped
Emily is a sales representative. She receives 7% commission on all sales. At the end of the year she receives a bonus of 5% of her commission. If Emily's sales for the year total $412,454, calculate: 1) 7% Commission on Sales 2) 5% Bonus on Commission 3) Total Gross Pay for the year 4) Monthly Income
start by calculating the 7% of all the sales
[tex]\begin{gathered} \text{Comission}=(0.07)\cdot412,454 \\ \text{comission}=28,871.78 \end{gathered}[/tex]Calculate the bonus from the comission
[tex]\begin{gathered} \text{Bonus}=(28,871.78)\cdot(0.05) \\ \text{Bonus}=1,443.59 \end{gathered}[/tex]The total gross pay will be the addition between the comission and bonus
[tex]\begin{gathered} G.\text{ Income=28,871.78+1,443.59} \\ G\text{. income=30,315.37} \end{gathered}[/tex]The monthly income will be the division between 12 months of the year
[tex]\begin{gathered} \text{Monthly income} \\ \frac{30,315.37}{12}=2526.28 \end{gathered}[/tex]Determine which expression is equivalent to the expression 5 over 4 times g minus 3 minus 7 over 12 times g minus the expression one over 3 times g plus 15. negative 1 over 3 times g plus negative 18 negative 4 over 12 times g plus negative 12 4 over 12 times g plus negative 18 16 over 12 times g plus negative 12 (BEST ANSWER WILL GET BRAINLIST)
The expression that is equivalent to the expression illustrated is 1/12g - 18.
What is an expression?It should be noted that an expression is used to show the relationship between the variables.
The expression will be illustrated as:.
= 5/4g - 3 - 7/12g - (1/3g + 15)
= 5/4g - 3 - 7/12g - 1/3g - 15
= 5/4g - 7/12g - 1/3g - 3 - 15
= 15/12g - 7/12g - 4/12g - 18
= 1/12g - 18
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what are the correct answers for each blank using the dropbox's provided for each blank?Dropbox 1: Congruent, Similar, Not congruent or similarDropbox 2: Proportional, Not proportional, CongruentDropbox 3: Proportional Not proportional, Congruent
The pair of triangles shown are similar because the sides are proportional and corresponding angles are congruent.
A random sample of 89 observations produced a mean x = 25.4 and a standard deviation s = 2.4.a. Find a 95% confidence interval for u.b. Find a 90% confidence interval for H.c. Find a 99% confidence interval for u.a. The 95% confidence interval is O.(Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)
The formula for the confidence interval is;
Where:
[tex]undefined[/tex]Given:
The mean is 25.4, the sample size n is 89, the standard deviation s is 2.4.
a. For the 95% confidence interval, the z-score for a 95% interval is 1.96.
Therefore, the 95% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.96\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.96\frac{2.4}{\sqrt[]{89}} \\ CI=24.90<\operatorname{mean}<25.90 \end{gathered}[/tex]Answer: (24.90, 25.90)
b. For the 90% confidence interval, the z-score for a 90% interval is 1.645.
Therefore, the 90% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.645\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.645\frac{2.4}{\sqrt[]{89}} \\ CI=24.98<\operatorname{mean}<25.82 \end{gathered}[/tex]Answer: (24.98, 25.82)
c. For the 99% confidence interval, the z-score for a 99% interval is 2.576.
Therefore, the 99% confidence interval is;
[tex]\begin{gathered} CI=25.4-2.576\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+2.576\frac{2.4}{\sqrt[]{89}} \\ CI=24.74<\operatorname{mean}<26.06 \end{gathered}[/tex]Answer: (24.74, 26.06)
Two-eighths of the movies in Beth's collection are
action movies. Another of the movies are come
What fraction of Beth's movies are either action
movies or comedies?
The answer is ..
Action movieswrite an email as if
you wanted to set up
an interview with
someone
Answer:Dear Mikey,
I saw your progress on how to serve the best food and we wanted to see if you could help us or join our company if you want.
Call 923-456-2483
Sincerely Johns Bagel Company
Step-by-step explanation:
Two standard 6-
sided dice are
rolled. How would
you describe the
following events
of having their
sum be EVEN OR
GREATER THAN 9?
The probability of having an even or a number greater than 9 is 2/3.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.
The sample space of two 6-sided dice would be 36
Of this 36, there would be 18 which would have an even sum.
There would be 6 with a sum greater than 9.
The probability of having an even or a number greater than 9 = (18/36) + (6/36) = 24 / 36 = 2/3
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Answer:
5/9
Step-by-step explanation:
You want the probability that a roll of 2 dice will produce a sum that is even or greater than 9.
EvenHalf the numbers on each die are even. Their sum will be even when the dice show ...
even + even . . . . p = (1/2)(1/2) = 1/4
odd + odd . . . . . . p = (1/2)(1/2) = 1/4
So, the 36 possible outcomes will produce an even sum (1/4) +(1/4) = 1/2 of the time. That is, there are 1/2(36) = 18 outcomes with an even sum.
Greater than 9The sums that are greater than 9 are 10, 11, 12. Of these, 10 and 12 are outcomes that are even, so are already counted.
The sum 11 can be made two ways: 6 +5 or 5 +6.
So, "or greater than 9" adds 2 outcomes to the 18 we have already counted.
Final tallyThe final tally of outcomes of interest is ...
18 + 2 = 20 . . . . of 36 possible outcomes
That is ...
P(even or >9) = 20/36 = 5/9
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Suppose that a population has a mean of 200 and a standard deviation of 26. a. Compute the standard error of the sample mean for a sample size of 10.
Given:
Mean = 200
Standard deviation = 26
a) Find the standard error for a sample size of 10:
[tex]E=\frac{\sigma}{\sqrt{N}}[/tex]Substitute the values:
[tex]E=\frac{26}{\sqrt{10}}=8.22[/tex]Answer: 8.22
order the following number from smallest to largest. 25, 10, -15, 0, -5
Answer:
-15, -5, 0, 10, 25
Step-by-step explanation:
Answer:-
15, -5, 0, 10, 25
Least -> greatest
Step-by-step explanation:
Find the values of the variables so that the figure is aparallelogram.
Answer:
The image is given below as
From the image above, we can deduce that
[tex]\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}[/tex]From the image also, we will have that
[tex]\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}[/tex]Hence,
The value of x= 64°
The value of y = 116°