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Explanation:
Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.
Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.
Simple example
y = mx + b . . . . . . solve for x
In this equation, the operations performed on x are ...
multiplication by maddition of b to the productIn accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.
y -b = mx +b -b ⇒ y -b = mx
Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.
(y -b)(1/m) = (mx)(1/m) ⇒ (y -b)/m = x
Now, we have solved this literal equation for x.
_____
Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.
The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:
x + (-x) = 0
Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.
x · (1/x) = 1
When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:
(x^a)^(1/a) = x^1 = x
arcsin(sin(x)) = x
(√x)^2 = x
10^(log(x)) = x or log(10^x) = x
Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.
When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.
Example:
ax + b = cx +d . . . . . solve for x
ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)
x(a -c) = d -b . . . . . combine x-terms
x = (d -b)/(a -c) . . . . divide by the coefficient of x
Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.
More Complicated Example:
A recent Brainly problem asked for the solution to ...
T = 2π√(L/g) . . . . solve for L
Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:
[tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]
The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.
_____
Key Points
The equal sign is sacred, and its truth must be preserved at every step.Literal equations are solved the same way numerical equations are solved.Inverse operations and functions are used to "undo" operations and functions.The Order of Operations can be helpful when considering what to do first.Un automóvil consume 4 galones de gasolina al recorrer 180 kilómetros y para recorrer 900 kilómetros necesita 20 galones ¿cuántos kilómetros recorre por galón? ¿Cuantos galones consumirá en 2700 kilómetros?
Answer:
45 km por galón
60 galones en 2700 Km
Step-by-step explanation:
180 / 4
45 km por galón
900 / 45
20 galones
2700 / 45
60 galones en 2700 Km
A raffle has a grand prize of a European cruise valued at $10000 with a second prize of a Rocky Point vacation valued at $700. If each ticket costs $4 and 11000 tickets are sold, what are the expected winnings for a ticket buyer?
Answer:
- 3.027
Step-by-step explanation:
First price = 10000 ; second price = 700
Number of tickets sold = 11000
Ticket cost = $4
Probability that a ticket wins grand price = 1 / 11000
Probability that a ticket wins second price = 1 / 11000
X ____ 10000 _____ 700
P(x) ___ 1 / 11000 ___ 1/11000
Expected winning for a ticket buyer :
E(X) = Σx*p(x)
E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost
E(X) = 0.9090909 + 0.0636363 - 4
E(X) = - 3.0272728
E(X) = - 3.027
Find the value of x in each case
Answer:
x = 69
Step-by-step explanation:
m<M = x
From the triangle we know that
m<M + m<MNQ + m<MQN = 180
From the parallel lines we know that
m<MNQ = m<UQN = x
x + x + 42 = 180
2x + 42 = 180
2x = 138
x = 69
Which critical thinking issue is most relevant to the following situation:
A research journal reports that there are on average 2.773829473 TVs in homes of Endor college educators as opposed to 2.682390934 TVs in homes of Endor bank tellers.
perceived lack of anonnymity
loaded or leading question
nonresponse bias or missing data
voluntary response bias
assumed accuracy from overly precise numbers
self-interest study
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Answer:
assumed accuracy from overly precise numbers
Step-by-step explanation:
Except when counting large sums of money or considering definitions, most real-world numbers are not accurate beyond about 6 significant figures. When considering survey or sample results, the accuracy can be considerably less than that, often not even good to 3 significant figures. (Margin of error is usually some number of percentage points greater than 1.)
Expressing the given ratios to 10 significant figures substantially misstates their accuracy. (10^-9 television is less than 1 day's accumulated dust).
What is the value of 3 minus (negative 2)?
A number line going from negative 5 to positive 5.
Answer:
5
Step-by-step explanation:
3-(-2) will become positive 5. so number line will go towards positive 5.
suppose △abc≅△xyz. what is the corresponding congruent part for each segment or angle?
Answer:
See below
Step-by-step explanation:
Hi there!
We're given that ΔABC≅ΔXYZ
When two triangles are congruent, their corresponding parts are congruent
Because of that, it means vertex A in ΔABC is congruent to vertex X in ΔXYZ, vertex B is congruent to vertex Y, and vertex C is congruent to vertex Z
Since we don't have a picture of the triangles given, we can use the names of the triangles to find the corresponding parts
so, to find the corresponding congruent angle to <BCA:
B is the first letter in the angle, and the corresponding letter in ΔXYZ is Y.
C is the second letter in the angle, and the corresponding letter is Z.
A is the last letter in the angle, and the corresponding letter is X
so that means <YZX is congruent to <BCA
now let's do the same for <ZYX
Z is the first letter in the angle, and the corresponding letter that's in the same place in ΔABC is C
Y is the second letter in the angle, and the corresponding letter is B
X is the last letter in the angle, and the corresponding letter is A
So that means <CBA is congruent to <ZYX
Now to find corresponding sides:
We can still use the names of the triangles, ΔABC and ΔXYZ
so to find the corresponding side to AB,
in ΔABC, AB makes up the first and second letter of the name of the triangle
The corresponding side must also make up the first and second letter of the name of the triangle
in ΔXYZ, the letters X and Y make up the first and second letter
so that means XY must be corresponding to AB
finally,
we need to find the segment congruent to YZ
in ΔXYZ, YZ makes up the second and third letter of the name of the triangle
the corresponding side must also make up the second and third letter of the name of the triangle
in ΔABC, the letters B and C make up the second and third letter in the triangle
So that means BC must be congruent to YZ
Hope this helps!
Convert the following 11110011.001 to decimal
Answer:
243.125
Step-by-step explanation:
First do the integral part
11110011
1. From left to right, starting with a zero,
2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.
The successive results are
1
3
7
15
30
60
121
243
For the decimal part, we proceed similarly but
1. From the right-most digit proceed to the left, start with a zero.
2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.
Successive results are:
0.5
.25
.125
So the final result is 11110011.001 binary is 243.125 decimal
The sum of the base and height of a triangle is 14 cm. Which of the following equations could be used to find the maximum area of the triangle?
A) A = 0.5x^2 - 15x
B) A = -0.5x^2 + 7x
C) A = -x^2 + 10x
D) A = x^2 - 10x
Answer:
B
Step-by-step explanation:
Let the base of the triangle be b and the height be h.
The sum of the base and height is 14. Thus:
[tex]b+h=14[/tex]
Recall that the area of a triangle is given by:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
From the first equation, solve for either variable:
[tex]h=14-b[/tex]
Substitute:
[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]
Distribute:
[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]
Distribute:
[tex]\displaystyle A=-0.5b^2+7b[/tex]
Let b = x. Hence:
[tex]A=-0.5x^2+7x[/tex]
Therefore, our answer is B.
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answer:
C
Step-by-step explanation:
p=20+1
Which equation can be simplified to find the inverse of
Answer:
x=y²-7hope it helps.
stay safe healthy and happy...5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
A small college has 1200 students and 80 professors. The college is planning to increase enrollment to 1450 students next year. How many new professors should be hired to keep the ratio of students to professors the same
The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
Given,
A small college has 1200 students and 80 professors.
The college is planning to increase enrollment to 1450 students next year.
We need to find how many new professors should be hired to keep the
ratio of students to professors the same.
What is meant by proportion?If the two ratios are the same then we called it that they are in proportion.
Example:
4/6 = 10/15
2/3 = 2/3
Find the ratio between the students and professors before the increase in enrollment.
= Number of students / Number of professors
= 1200 / 80
Dividing by 8
= 150 / 10
= 15 / 1
This means one professor for 15 students.
Find the number of students after the increase in enrollment.
= 1450
Find the number of new students enrolled.
= 1450 - 1200
= 250
Since the ratio between the students and professor is 15 students for one professor.
For 250 new students, the number of new professors we need is:
= 250 ÷ 15
= 16.66
This means we need around 16.66 new professors.
Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.
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You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?
$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%
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Answer:
$150 in 4%, $850 in 6%
Step-by-step explanation:
The fraction that must earn the highest rate is ...
(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85
That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.
_____
If you let x represent the amount that must earn 6%, then the total interest earned must be ...
x·6% +(1000 -x)·4% = 1000·5.7%
x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000
x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above
Polinômio (2x+6y)(4x-2y)
Answer:
I'm pretty sure it's 8x^2+20xy-12y^2
Answer:
pff don't know . sssory
Step-by-step explanation:
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
Bob had 10 more cars than Paul. Paul had 15 cars.
Answer:
Bob had 25 cars
Step-by-step explanation:
10+15=25
A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long
will it take for the projectile to reach the ground?
Answer:
Step-by-step explanation:
We will work in the y-dimension only here. What we need to remember is that acceleration in this dimension is -9.8 m/s/s and that when the projectile reaches its max height, it is here that the final velocity = 0. Another thing we have to remember is that an object reaches its max height exactly halfway through its travels. Putting all of that together, we will solve for t using the following equation.
[tex]v=v_0+at[/tex]
BUT we do not have the upwards velocity of the projectile, we only have the "blanket" velocity. Initial velocity is different in both the x and y dimension. We have formulas to find the initial velocity having been given the "blanket" (or generic) velocity and the angle of inclination. Since we are only working in the y dimension, the formula is
[tex]v_{0y}=V_0sin\theta[/tex] so solving for this initial velocity specific to the y dimension:
[tex]v_{0y}=35sin(35)[/tex] so
[tex]v_{0y}=[/tex] 2.0 × 10¹ m/s
NOW we can fill in our equation from above:
0 = 2.0 × 10¹ + (-9.8)t and
-2.0 × 10¹ = -9.8t so
t = 2.0 seconds
This is how long it takes for the projectile to reach its max height. It will then fall back down to the ground for a total time of 4.0 seconds.
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
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Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
help pls I need it badly
9514 1404 393
Answer:
22
Step-by-step explanation:
For calculators without a cube root key, you can use the 1/3 power. The attached shows the quotient to be about 22.
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 18 trees from this forest. The researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is normal. For this sample what is the margin of error for her 99% confidence interval
Answer:
The margin of error for her confdence interval is of 0.3757.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Standard deviation of 0.55 meters.
This means that [tex]s = 0.55[/tex]
What is the margin of error for her 99% confidence interval?
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]
[tex]M = 0.3757[/tex]
The margin of error for her confdence interval is of 0.3757.
Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.
What is the margin of error for small samples?Suppose that we have:
Sample size n < 30
Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Degree of freedom = n-1Then the margin of error(MOE) is obtained as
Case 1: Population standard deviation is knownMargin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]
where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance
For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.
Then, by the given data, we get:
[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18
The degree of freedom is n-1 = 17
Level of significance = 100% - 99% = 1% = 0.01
The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)
Thus, margin of error for 99% confidence interval for considered case is:
[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]
Thus, the margin of error for the given condition is 3.28 approximately.
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The cardinal number of {200, 201, 202, 203, ..., 1099}
Answer:
I have not been able to answer it sorry
An air conditioning system can circulate 310 cubic feet of air per minute. How many cubic yards of air can it circulate per minute? The air conditioning system can circulate about cubic yards of air per minute.
Answer:
310/[tex]3^{3}[/tex] = 310/27 =11.48
Step-by-step explanation:
Answer:
310/ = 310/27 =11.48
Step-by-step explanation:
Suppose you want to have $800,000 for retirement in 20 years. Your account earns 8% interest. How much would you need to deposit in the account each month?
Answer:
$40,000
Step-by-step explanation:
this the workings above
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
HELP ASAP I WILL GIVE BRAINLIST
Find the length of an arc of a circle with a 8-cm radius associated with a central angle of 240 degrees. Give your answer in exact and approximate form to the nearest hundredth. Show and explain your work
Answer:
33.51 cm
Step-by-step explanation:
240/360 = 2/3 (Arc length is 2/3 of the total circumference)
C = 2[tex]\pi[/tex]r ( Calculate the total circumference)
C = 2(8)[tex]\pi[/tex]
C = 50.265
2/3(50.265) (Take 2/3 of the circumference. times 2 divide by 3)
33.51
Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.
The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
The arc length in approximate form is 33.49 radians.
What is the formula for arc length?[tex]s = r\times \theta[/tex]
where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.
How to convert angle from degrees to radians?Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]
For given question,
We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.
[tex]r=8~cm,~\theta=240^{\circ}[/tex]
First we convert angle in radians.
[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]
Using the formula of the arc length,
[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]
The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]
Substitute the value of [tex]\pi = 3.14[/tex]
So, the arc length would be,
[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians
Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
the arc length in approximate form is 33.49 radians.
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log2(6x) – log2 (x)-2
Answer:
xlog(64)−xlog(2)−2
Step-by-step explanation:
Simplify 6log(2) by moving 6 inside the logarithm.
log(2^6)x − log(2)x − 2
Raise 2 to the power of 6.
log(64)x − log(2)x − 2
Reorder factors in log(64)x − log(2)x −2.
In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice.
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Answer:
5/8
Step-by-step explanation:
The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.
Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.
The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.
4b^2+300=0 this is a quadratic equation that I am trying to solve including any solutions with imaginary numbers I will include a picture
Answer:
b= 5i square root of 3
b = -5i square root of 3
Step-by-step explanation:
4b^2+300=0
4b^2 = -300
b^2 = -75
b = square root of -75
b = -75^1/2
^1/2 means square root
b = 25^1/2 * 3^1/2 * i
b= 5i square root of 3
b = -5i square root of 3
