Answers
[tex]\huge\bf Question:—[/tex]
[tex] \sf \longmapsto \: g=a(4− {d}^{2} )[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex] \underline{\bf \: Flip \: the \: equation:—}[/tex]
[tex] \sf \longmapsto \: −a {d}^{2} +4a=g[/tex]
[tex] \underline{\bf \: Factor \: out \: variable \: (a):—}[/tex]
[tex] \sf \longmapsto \: a(− {d}^{2} +4)=g[/tex]
[tex]\underline{ \bf \: Divide \: both \: sides \: by -d^2+4 :—} [/tex]
[tex]\sf \longmapsto \: \dfrac{a( - {d}^{2} + 4) }{ { - d ^2+ 4}^{} } = \dfrac{g}{{ - d ^2+ 4}^{}} [/tex]
[tex]\sf \longmapsto \:1 a = \dfrac{g}{{ - d^2 + 4}^{}} [/tex]
[tex]\underline{\bf Answer:—}[/tex]
[tex]\boxed{ \bf \: a = \dfrac{g}{ - d^2 + {4}^{} } }[/tex]
Answer:
[tex]\boxed{\boxed{\sf a=\cfrac{G}{4-d^2} }}[/tex]
Step-by-step explanation:
[tex]\sf G=a(4-d^2)[/tex]
Use the Distributive Property to multiply a by (4-d^2):
[tex]\sf G=4a-ad^2[/tex]
Now, we'll swap sides so that all variable terms are on the left hand side.
[tex]\sf 4a-ad^2=G[/tex]
Combine like terms:
[tex]\sf (4-d^2)\:a =G[/tex]
Divide both sides by 4-d^2:
[tex]\sf \cfrac{(4-d^2)a}{4-d^2} =\cfrac{G}{4-d^2}[/tex]
Dividing by 4-d^2 undoes the multiplication by 4-d^2.
[tex]\sf a=\cfrac{G}{4-d^2}[/tex]
_______________________________________
Related Questions
The teen club had a cupcake sale.
They sold 2/3 of their cupcakes in the morning. They sold 1/6 of their cupcakes in the afternoon. They sold 200 cupcakes altogether.
How many cupcakes were left to sell?
Answers
40. Let C be the total number of cupcakes. Then 2/3 x C + 1/6 x C = 200.
Combining , 5/6 x C = 200. So C = 240.
240–200= 40
y=1/4x−2y=−2x+3 help solve problem.
Answers
Answer:
(x, y) = (2 2/9, -1 4/9)
Step-by-step explanation:
Equate the values of y and solve for x.
1/4x -2 = -2x +3
(2 1/4)x = 5 . . . . . . . . add 2+2x to both sides
x = 20/9 = 2 2/9 . . . multiply by 4/9
y = -2(2 2/9) +3 = -4 4/9 +3 . . . . substitute for x in the second equation
y = -1 4/9
The solution is x = 2 2/9, y = -1 4/9.
Joe lost his part-time job, which reduced the net family income by 20%. His wife Janice decided to work overtime to compensate for the lost income. Other things being equal, by what percentage must her net salary increase in order to arrive at the same net family income as they had before Joe lost his job?
Answers
The percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the salary of Joe be represented by x, while the salary of Janice is represented by y.
Since the sum of the salary of Joe and Janice is the net income of the family. Therefore, the net salary when Joe had a job will be,
x + y₁ = 100%
Now, it is known that Joe lost his job, which reduced the net family income by 20%. Therefore, the net salary now will be only 80% which will be equal to the salary of Janice. Thus, we can write,
y₁ = 80%
Further, Janice decided to work overtime to compensate for the lost income. Therefore, we can write,
y₂ = 100%
Furthermore, the percentage change in salary of Janice can be written as,
Percentage Change = [(100% - 80%)/80% ] × 100%
= 20/80 × 100%
= 25%
Hence, the percentage by which Janice's net salary must be increased in order to arrive at the same net family income as they had before Joe lost his job is 25%.
Learn more about Percentages:
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An angle measures 136°. What is the measure of its supplement?
Answers
Answer:
44⁰.
Step-by-step explanation:
Its supplement = 180 - 136
= 44 degrees.
For A = {B, C, D} and B = {A, E, I, O, U}, which set is empty?
Answers
Answer:
B is empty
Step-by-step explanation:
HELP! Due in 5 minutes
Answers
ANSWER:
the first one: 30x+48
The second one: x y^2(10 y + 15)
The third one: 30 x y - 5 x^2
Hope this helped!
sorry if im wrong. :)
GOOD LUCK!! <3
can't believe that you got me in a suit and tie I had to take a pull so I wouldn't cry
You got a line out the church door sayin' goodbye
Yeah, I believe 'em when they say you're in a better place
NAME THE SONG AND THE SINGER 50 POINTS!!!!!
Answers
Answer:
give heaven some hell by Hardy
Step-by-step explanation:
Every Thursday, Matt and Dave's Video Venture has “roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an
amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a
second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a
second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total
amount paid for these second movies will exceed $15.00?
I saw other questions for this but why is the standard deviation 0.15*sqrt of 30 and not 0.15*30 because I thought this is a linear transformation
Answers
Using the normal distribution, it is found that there is a 0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard error is [tex]s = \sigma\sqrt{n}[/tex]In this problem:
Mean of $0.47, standard deviation $0.15, hence [tex]\mu = 0.47, \sigma = 0.15[/tex]30 instances, hence [tex]n\mu = 30(0.47) = 14.1, s = 0.15\sqrt{30} = 0.8216[/tex]The probability is 1 subtracted by the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Considering the n instances:
[tex]Z = \frac{X - n\mu}{s}[/tex]
[tex]Z = \frac{15 - 14.1}{0.8216}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
1 - 0.8643 = 0.1357.
0.1357 = 13.57% probability that the total amount paid for these second movies will exceed $15.00.
A similar problem is given at https://brainly.com/question/25769446
Can you identify a parallel or perpendicular equation and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answers
The equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].
Let be a line whose equation is:
[tex]a\cdot x + b\cdot y = c[/tex] (1)
Whose explicit form is:
[tex]y = -\frac{a}{b} \cdot x +\frac{c}{b}[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable.The slope and x-intercept of the line are [tex]-\frac{a}{b}[/tex] and [tex]\frac{c}{b}[/tex], respectively.
There are two facts:
A line is parallel to other line when the former has the same slope of the latter.A line is perpendicular to other line when the former has a slope described the following form ([tex]m_{\perp} = -\frac{1}{m}[/tex]), where [tex]m[/tex] is the slope of the former.Then, the equation of the line that is parallel to [tex]2\cdot x + 5\cdot y = 10[/tex] is [tex]y = -\frac{2}{5} \cdot x + 3[/tex] and the equation of the line that is perpendicular to [tex]4\cdot x + 3\cdot y =12[/tex] is [tex]y =\frac{3}{4}\cdot x - 1[/tex].
To learn more on lines, we kindly invite to check this verified question: https://brainly.com/question/2696693
Charles wants to buy an anime book that is on sale for $14.99. Her sister kyra wants to buy a novel book for $17.99. Both of them has to pay a 7% tax. Kyra has a coupon for 15% discount. Whats the difference between the amount that each siblings has to pay?
Answers
Answer:
The difference between their total amounts is .34 cents
also it didnt look like i was supposed to count a discount for charles so i didnt :)
Step-by-step explanation:
Charles14.99 times .07 = 1.04
14.99 + 1.04 = 16.03
Kyra17.99 times .15 = 2.69
17.99 -2.69 = 15.30
15.30 times .7 = 1.07
15.30 + 1.07 = 16.37
16.37 - 16.03 = .34
Pls look at the picture for question.
Answers
Answer:
Only option A is correct
Step-by-step explanation:
Positive numbers are always greater than negative numbers no matter the quantities. Also, the greater the negative number is, the less it becomes.
Hope this helps :D
Write the equation to the line parallel to y= 3x – 5 that goes through the point (-2, -7) using any form.
Thank you!
Answers
Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 5 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , then
y = 3x + c ← is the partial equation
To find c substitute (- 2, - 7 ) into the partial equation
- 7 = - 6 + c ⇒ c = - 7 + 6 = - 1
y = 3x - 1 ← equation of parallel line
Please help me in this 4th grader question, its a homework and i was sick over the weekend
Answers
Answer:
what is your question ask then I shall answer you
Define
Rough calculating
Answers
Answer:
A rough calculation or guess is approximately correct, but not exact. roughly adverb.
Step-by-step explanation:
A recipe calls for 3/4 of a cup of flour to make 5/8 of a pound of bread
dough. How many cups of flour are needed to make 1 pound of dough?
Show your work and write your answer in simplest form.
Answers
Answer:
[tex]\huge\boxed{\sf 1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}[/tex]
Step-by-step explanation:
[tex]\displaystyle \underline{Given \ that:}\\\\\frac{5}{8} \ pound \ of \ dough = \frac{3}{4} \ cup\ of \ flour\\\\Multiply \ 8 \ to \ both \ sides\\\\5 \ pounds \ of \ dough = \frac{3}{4} \times 8 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 3 \times 2 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 6 \ cups \ of \ flour\\\\Divide \ both \ sides \ by \ 5\\\\1 \ pound \ of \ dough = \frac{6}{5} \ cup \ of \ flour\\\\\boxed{1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}\\\\[/tex]
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807At TGI Fridankay's you order a drink for $2.99, an appetizer for $9.99, the cajun chicken pasta for $11.50, and a dessert for $7.99. You had amazing service and know that you are going to tip your waiter 20%! The waiter also gave you a 10% coupon to use. There is also a 7% sales tax on the bill. What is your total bill after the tip, discount, and tax?
Answers
The total bill after the tip, discount, and tax is $37.76.
The total cost of the order is reduced by the coupon and increased by the tax paid and tip.
Total cost of the items bought = cost of the drink + appetizer + Cajun + dessert
$2.99 + $9.99 + $11.50 + $7.99 = $32.47
Value of the tip = 20% x $32.47 = $6.49
Cost of the items after the coupon: (100% - 10%) x $32.47
90% x $32.47
0.9 x $32.47 = $29.22
Cost of the items after the tax: (1.07) x $29.22 = $31.27
Total cost of the items = $31.27 +$6.49 = $37.76
To learn more about taxes, please check: https://brainly.com/question/25311567
Need help fast worth 20 points
Select the correct answer.
Which set of absolute values is compared correctly
OA. 1-10] < |-5| < |17| < 151
OB. 1-5| > |-10| > |-12| > |17||
OC. |10| > |-15] > [-5| > 12||
OD. |-101 < [12] < |-15| < |17||
Answers
Answer:
i think its b.
Step-by-step explanation:
correct me if im wrong. and it was worth 10 points instead of 20.
A farmer has 220 bushels of apples to sell at roadside stand. She sells an average of 14 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days.The total change in the number of bushels has for sale is ???, please answer as a fraction
Answers
Answer:
Step-by-step explanation:
He has sold (16+1/4) bushels/day x 5 days = (16 x 5) + (1/4 x 5) = 80 + 5/4 = 81 + 1/4 = 81.25
The change in the number of bushels is 140 - 81.25 = 58.75 or 58 and 3/4 bushels
In other words, he has 58.75 (or 18 and 3/4) bushels remaining and has sold 81.25 (or 81 and 1/4) bushels
The label on a 4-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to test the claim on the label.
(a) Develop the appropriate null and alternative hypotheses.
a) H0: μ = 1
b) Ha: μ ≠ 1
a) H0: μ > 1
b) Ha: μ ≤ 1
a)H0: μ ≥ 1
b) Ha: μ < 1
a) H0: μ < 1
b) Ha: μ ≥ 1
a) H0: μ ≤ 1
b) Ha: μ > 1
(b)What is the type I error in this situation? What are the consequences of making this error?
a) It is claiming μ < 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.
b) It is claiming μ > 1 when it is not. This error would claim that the product is not meeting its label specification when it really is meeting its specification.
c) It is claiming μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
d) It is claiming μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
(c) What is the type II error in this situation? What are the consequences of making this error?
a) It is concluding μ > 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.
b) It is concluding μ ≤ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
c) It is concluding μ ≥ 1 when it is not. This error would miss the fact that the product is not meeting its label specification.
d) It is concluding μ < 1 when it is not. This error would conclude that the product is not meeting its label specification when it really is meeting its specification.
Answers
Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.
NO LINKS!!
Answers
Answer:
(x -1)²/64 -(y -4)²/80 = 1foci (-11, 4) and (13, 4)Step-by-step explanation:
The standard form of a hyperbola whose transverse axis is horizontal is ...
(x -h)²/a² -(y -k)²/b² = 1 . . . . center (h, k); transverse axis 2a; conjugate axis 2b
The distance between the two vertices is given as (9 -(-7)) = 16 = 2a, so the value of a is 8 and we have the partial equation ...
(x -1)²/8² -(y -4)²/b² = 1
Filling in the given point value gives us an equation for b².
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 80
So, the equation is ...
(x -1)²/64 +(y -4)²/80 = 1
__
The distance between the foci is 2c, where c² = a² +b².
c² = 64 +80 = 144 = 12²
c = 12, so the foci are at ...
(x, y) = (1 ±12, 4) . . . . . . . 12 units either side of the center
The foci are (-11, 4) and (13, 4).
_____
Additional comment
The steps are ...
use the given information to fill in as much of the equation as you can.use any given points or additional information to find the unknown values in the equationdetermine any additional information asked for (foci, asymptotes, ...)The relevant relations are ...
2a = length of transverse axis (distance between vertices)
2b = length of conjugate axis (distance between co-vertices)
±b/a = slope of asymptotes, which are lines through the center
2c = distance between foci, where c² = a² +b²
The equation is (x -h)²/a² -(y -k)²/b² = 1 for a hyperbola that opens horizontally with center (h, k). Swapping variables x and y will give a hyperbola that opens vertically. If the figure opens vertically, the asymptotes will have slope ±a/b.
The distances from a point to the foci have a constant difference of 2a.
Rewrite in simplest terms: (4x + 4) - (-4x - 9)
Answer:
Submit Answer
Answers
Answer:
8x+13
Step-by-step explanation:
do you need this part?
Approximately what portion of the box is shaded blue?
A.2/3. B.9/10
C.3/5
Answers
Help help help help math
Answers
Answer:
158
Step-by-step explanation:
We know the supplement of angle 6 is 22, due to the fact that they are corresponding angles. Simply subtract 22 from 180 to get the answer. 180-22=158
Answer:
158 degrees
Step-by-step explanation:
Angle 6 has a same side interior relationship with the 22 degrees, so the sum of these angles are equal to 180 degrees.
To find the missing angle, subtract 180 by 22 degrees.
180-22= 158
What is the possible degree of a polynomial if it has a root of -3 with multiplicity of 2 and, a root of 4 with a multiplicity of 1?
Answers
Answer:
3rd degree
Step-by-step explanation:
factors are
a(x + 3)(x + 3)(x - 4)
polynomial is
a(x² + 6x + 9)(x - 4)
a(x³ + 2x² - 15x - 36)
where (a) could be any real number
The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of seven hours. Suppose we select a random sample of 125 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours
Answers
There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours
Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation,n=sample\ size[/tex]
Given that μ = 20, σ = 7, n = 125.
For x = 19.25:
[tex]z=\frac{19.25-20}{7/\sqrt{125} } =-1.20\\\\\\For\ x=21:\\\\z=\frac{21-20}{7/\sqrt{125} } =0.62[/tex]
From the normal distribution table, P(-1.20 < z < 0.62) = P(z < 0.62) - P(z < -1.2) = 0.8849 - 0.1151 = 0.7698 = 77%
There is a probability of 77% that the mean of this sample is between 19.25 hours and 21.0 hours
Find out more on z score at: https://brainly.com/question/25638875
Please help me prove that RST is congruent to RUT!
Answers
Answer:
See image
Step-by-step explanation:
On line 3, the reason is filled in that "All right angles are congruent" so kind of working backwards, the statement must say that two right angles are congruent. Use the angles in the previous two statements. Line 4 has the statement completely filled in, the reason is bc it is given in the list of given statements beside the diagram. Line 5 says that RT is congruent to itself. That is reflexive property, like a reflection in a mirror. Same ~= same.
You can see from the markings on the image that you have Angle-Side-Angle, which is one of several ways that we can show that triangles are congruent. ASA is what is shown in statements 1-5. See image.
3] What is - 2y + 10 + 2y - 8 simplified?
a) – 4y + 18
C) 18
b) 4y + 2
d) 2
Expressions
Answers
Answer:
d. 2
Step-by-step explanation:
-2y +10+2y-8
10-8. ( -2y+2y = 0)
2
Answer:
d) 2
Step-by-step explanation:
We can first combine like terms
-2y + 2y = 0
Now, our expression is simply 10 - 8, which is 2
So, the answer is
d) 2
How is the series 9 + 13+ 17+ ... + 149 represented in summation notation?
Answers
Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=0}^{35} (9 + 4k)[/tex]
but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k-1=0}^{35+1} (9 + 4(k-1))[/tex]
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=1}^{36} (5 + 4k)[/tex]
What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1)
y = -¼x - 1/2
y = ¼x + 2
y = -¼x + 4
y = ¼x - 1
Answers
Answer:
last one
Step-by-step explanation:
Stuck on this, need help on this.
Answers
Answer:
Domain: (-∞ , ∞)
Range: y <= 8 [8 , -∞)
Step-by-step explanation:
x = 2
f(x) = 8
x<=2
f(x) <=8
