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
Witch equation can be simplified to find the inverse of y=5x^2+10
Answers
Answer:
[tex]\huge\boxed{y=\sqrt{\dfrac{x-10}{2}}\ \text{for}\ x\geq10}[/tex]
Step-by-step explanation:
[tex]y=5x^2+10\\\\\text{exchange x to y and vice versa}\\\\x=5y^2+10\qquad|\text{subtract 10 from both sides}\\\\x-10=5y^2\qquad|\text{divide both sides by 5}\\\\\dfrac{x-10}{5}=y^2\\\\y^2=\dfrac{x-10}{5}\to y=\sqrt{\dfrac{x-10}{2}}[/tex]
Writing
Tammy bought some books. She spent a total of $45 after a discount of S6 off of her total purchase. Each book cost $3. How many books did she buy?
(a) Write an equation that could be used to answer the question above.
First, choose the appropriate form. Then, fill in the blanks with the
numbers 45, 6, and 3. Let b represent the number of books.
X
5
o 16+ = 0
(b) Solve the equation in part (a) to find the number of books.
b = 0
Answers
Answer:
b=17
Step-by-step explanation:
b=(45+6)/3
b=51/3
b=17
she bought 17 books since the original price of evereything was 51 dollars before the discount of 6 dollars.
Solve x2 + 5x – 3 = 0 using the quadratic formula.
Solve (2x – 1)2 = 8 using the quadratic formula.
A) x = –1∕2 + , x = –1∕2 –
B) x = 1∕2 + , x = 1∕2 –
C) x = 1∕2
D) x = –1∕2
Answers
Answer:
d
Step-by-step explanation:
distribute two through the parentheses
=4x-2
move the constant to the right side and change its sign
=4x=8+2
=4x=10
divide both sides by 4
x=5/2
An artist paints a mural containing different-sized triangles. The area of each triangle is
given by the function A(x) = 1/2x(x – 3), where x represents the base length of the
triangle, in inches.
What is the area of a triangle with a base length of 16 inches, represented by A(16), in
square inches?
Answers
Answer:
104
Step-by-step explanation:
A(16)=1/2(16)(16-3)
A=8(13)
Area is 104 inches squared
Use logarithms to solve the equation 5^x = 3^(2x-1), giving your answer correct to 3 significant figures.
Answers
[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]
The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):
Take the natural logarithm (ln) of both sides:
ln(5^x) = ln(3²ˣ⁻¹)
Apply the logarithm rule: ln(a^b) = b * ln(a):
x * ln(5) = (2x - 1) * ln(3)
Expand the equation:
x * ln(5) = 2x * ln(3) - ln(3)
Move the terms with "x" to one side of the equation:
x * ln(5) - 2x * ln(3) = -ln(3)
Factor out "x" from the left side:
x * (ln(5) - 2 * ln(3)) = -ln(3)
Solve for "x":
x = -ln(3) / (ln(5) - 2 * ln(3))
Now, we can calculate the value of "x" using a calculator:
ln(3) ≈ 1.099
ln(5) ≈ 1.609
x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864
Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).
Learn more about natural logarithm from the link given below.
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Solve the linear system using elimination.
46) -2x+4y=-2
6x - y=28
Answers
Answer:
x = 5, y = 2
Step-by-step explanation:
just trust me, I used a calculator
Tomatoes that regularly sell for $0.55 per pound are on sale for 20% off the regular price. What is the sale price?
Answers
Answer:
$0.44
Step-by-step explanation:
lmk if you want an explanation
the students in Jake's class , 6 have visited a zoo and 6 have visited a factory 3 students have visited both a zoo and a factory . How many students have visited a zoo but not a factory ?
Answers
Answer:
3
Step-by-step explanation:
6 have visited a zoo.
6 have visited a factory.
3 visited both.
Of the 6 who visited a zoo, 3 also visited a factory.
Of the 6 who visited a factory, 3 also visited a zoo.
Here is the list of students:
3 visited a zoo but not a factory.
3 visited a factory but not a zoo.
3 visited both.
Answer: 3
A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. Testing at the 5% level the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%.
a. Calculate the p-value for this test.
b. Find the p-value for this test and draw your conclusion.
c. Suppose that the alternative hypothesis in part b had been two-sided rather than one-sided. Conduct your test using either the critical value or the p-value approach.
Answers
Answer:
c
Step-by-step explanation:
Marl me as brainliest answer c
The p-value for the given test is 0.0901.
Given that, a pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%.
What is a standard deviation?Standard deviation is the degree of dispersion or the scatter of the data points relative to its mean, in descriptive statistics.
Given, Mean = 3.07, μ=3%, σ =0.4% and n=64.
Hypothesis test [tex]H_{0}[/tex];μ=3 and [tex]H_{1}[/tex];μ>3
We need to test the null hypothesis against the alternative hypothesis, we reject the null hypothesis and accept the alternative hypothesis.
When x>x critical
x critical = μ+Z+σ
Z = (x-μ)/(σ/√n)
= (3.07-3)/(0.4/√64)
= (0.07)/0.05
= 1.4
α = 5 and [tex]z_{0.05[/tex]= 1.645
If Z>[tex]Z_{0.05[/tex]
1.4 > 1.645
Therefore, we do not reject null hypothesis at 5% significant level.
There is sufficient evidence that the mean impurity in concentration pills is 3% or less than 3%.
p-value
p−value=P(Z>1.4)
=1−P(Z<1.4)
=1−0.90988
=0.0901
Therefore, the p-value for the given test is 0.0901.
To learn more about the standard deviation visit:
https://brainly.com/question/14747159.
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The equation of the blue line is y=-x+ 5. Manipulate the orange line by setting the sliders so its slope, m, is -1 and its y-intercept, b, is 5. Which statement describes the system after the changes? O The lines intersect at the same point as before the changes. O The lines intersect at a different point than before the changes. O The lines do not intersect. 0 The lines overlap.
Answers
Hope that helps :)
Answer:
D
Step-by-step explanation:
a service or software application that relies on shared resources over the internet
Answers
The present year is 2014. Which year comes AFTER THE NEXT 3 years?
Answers
Answer:
2017 Pls mark me as a brainliest I really need it
Which shows two triangles that are congruent by AAS
Answers
Answer:
answer A is the correct option.
Step-by-step explanation:
The triangles ( A ) are congruent by AAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔABD
Now , AB is the common side of both the triangles
And , measure of ∠ACB = measure of ∠ADB
And , the measure of ∠ABC = measure of ∠ABD = 90°
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent
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20/50 = 30/x solve for x
Answers
Answer:
x = 75
Step-by-step explanation:
20/50 = 30/x
Divide the numbers and find x. If you plug back in 75 for x and simply, you should get the same fraction for each, 4/10.
Solve: 6 − x = −12
helpppppppppppp quickkk
Answers
Answer:
x = 18
Step-by-step explanation:
6 − x = −12
subtract 6 from both sides
- x = - 18
divide both sides by -1
x = 18
Answer:
x=18
Step-by-step explanation:
6 - x = -12
-6 -6
----------------
-x = -18
*divide by -1*
x = 18
hope this helps! :D
have a MIRACULOUS day!! <3
I’ll give brainliest!
Add 3/4 + (2^1/2) using the number line
Select the location on the number line to plot the sum
Answers
Answer: -1 3/4
Step-by-step explanation
just add the fractions together :)
(between the -2 and -1 1/2)
HELP ME PLEASEEEE I WILL GIVE BRAINLIEST
Answers
Answer: DE, EW WD
Step-by-step explanation:
It looks shortest to longest...i think its the best answer. good luck :>
What is the slope of the line?
Answers
Answer:
1/4
Step-by-step explanation:
Answer:
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
m = slope
(x_1, y_1) = coordinates of first point in the line
(x_2, y_2) = coordinates of second point in the line
Find the product of ( - 6 + 3i) and its conjugate.
product =
Submit Question
Answers
Answer:
45Step-by-step explanation:
The conjugate of the given is:
( - 6 - 3i)Find their product:
(- 6 + 3i)( - 6 - 3i) = (-6)² - (3i)² = 36 - 9i² = 36 - 9(- 1) = 36 + 9 = 45help with this question, please!
Answers
Answer:
Y Intercept: 0, 2.5
X Intercept: 3.5, 0
Explanation:
An Intercept is where a line crosses an axis. A Y Intercept is for the Y axis and the X intercept is for the X axis.
Also when writing coordinates, the x coordinate comes before the y one.
Hope this helps :)
Use >,<, or = to solve
the inequality below.
4/5 1/2
Answers
Answer:
4/5 > 1/2
Step-by-step explanation:
4/5 1/2
\/
4/5 -> 8/10
1/2 -> 5/10
\/
8/10 > 5/10
\/
4/5 > 1/2
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
4/5>1/2
Step-by-step explanation:
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
4/5 = 0.8
1/2 = 0.5
Then, we compare the two decimal numbers to get the answer.
0.8 is greater than 0.5.
Therefore, 4/5 is greater than 1/2
The amount of money, y, pizzeria J makes by
selling x pizzas can be modeled by the equation
y = 14x. The relationship of the amount of money
pizzeria W makes is shown in the following graph.
Which pizzeria makes more money per pizza?
Answers
Answer:
Pizzeria J
Step-by-step explanation:
Pizzeria J makes
y = 14x
Let x = 1, for 1 pizza. Then,
y = 14 × 1
y = 14
At pizzeria J, 1 pizza costs $14.
In the equation y = 14x, the slope, 14, is the cost per pizza.
Now we find the slope of the graph for pizzeria W.
The x-axis is the number of pizzas.
For x = 1, y = 11.
The slope is 11, so the price per pizza is $11.
Answer: Pizzeria J
The Greens bought a condo for $110,000 in 2005. If its value appreciates at 6%
per year, what will the value be in 2012?
Answers
Answer:
Use the A = p(1 + r/100)^t. A is the amount after appreciation, p is the principal or starting value, r is the interest rate, and t is the time in years.
Step-by-step explanation:
Your utility company charges 14 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 150-watt light bulb for 8 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
a. The daily cost of keeping lit a 150-watt light bulb for 8 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 150-watt light bulb with a 20-watt light bulb is
(Round to two decimal places as needed.)
Answers
Answer:
P = 150 W * 60 sec/min * 60 min/hr = 540000 W-sec/hr
1 kW = 1000 W * 3600 sec = 3.6E6 W-sec
E (8 hrs) = 8 * .54E6 W-s = 4.32E6 W-sec
or E= 4.32/3.6 = 1.2 kW = .168 $/day
20/150 = .133 as much for a 20-watt bulb
For a LED bulb cost/day = .168 * .133 = $.022/da
Note 1 W = 1 Joule/sec
Which table of values represents possible solutions to
the equation y = 0.7x - 4.3?
х
49
у
30
X y
49 40
19 19
-11-12
-31-16
19 19
-11-12
-31 -26
B
Х
у
30
49
19 9
-11-12
-31 -26
Х
у
49 40
19 19
-11 -2.
-31 -16
D
Answers
Step-by-step explanation:
it will be c as shown in the photo
John is selling sets of knives and makes a 10% commission on all sales. What would his commission be on the sale of a $3250 set of knives?
Answers
5^2 x 5^2 20 80 625 425
Answers
Which graph represents y = –2x?
Answers
Answer:
B, the second one down on the first page
Step-by-step explanation:
hope this helps! :D
brainliest is immensely appreciated!! <3
15/4= simplify it please
Answers
Answer:
[tex]The \: fraction \: \frac{15}{4} \: is \: equivalent \: to \: 3 \frac{3}{4 } .[/tex]
This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denomintor (4). So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction [tex]3 \frac{3}{4} [/tex]
The fraction [tex] \frac{15}{4} [/tex]
is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.
The fraction 15/4 is equivalent to 3 3/4.
Here, we have,
To simplify the fraction 15/4, you need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (4) and divide both the numerator and denominator by the GCD.
The GCD of 15 and 4 is 1 since there are no common factors other than 1.
Dividing both the numerator and denominator by 1, we get:
(15 ÷ 1) / (4 ÷ 1) = 15/4
This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denominator (4).
So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction 3 3/4.
The fraction 15/4 is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.
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If there are 10,000 people on a space ship and 7.5 potatoes grow out of 1 potato plant. How many potato plants are we going to need per person?
Answers
This can be answered by the equation 10,000 / 7.5 = 1,333.33, so we can round to 1,333.
Hope this helps!
Answer: 1333
Step-by-step explanation: