9 - 6(x+1) = 2(x-4) + 27
Answers
1) Use the distributive property to multiply −6 by x + 1
9−6x −6 = 2(x−4) +27
2) Subtract 6 from 9 to get 3
3−6x =2(x−4) +27
3) Use the distributive property to multiply 2 by x−4
3−6x =2x−8 +27
4) Add −8 and 27 to get 19
3−6x = 2x +19
5) Subtract 2x from both sides
3−6x −2x = 19
6) Combine −6x and −2x to get −8x
3−8x = 19
7) Subtract 3 from both sides
−8x= 19−3
8) Subtract 3 from 19 to get 16
−8x = 16
9) Divide both sides by −8
x= 16/-8
10) Divide 16 by −8 to get −2
x=−2
Hope this helps :D
Related Questions
Solve for the two possible values of X: (3x – 14) (8x + 13) = 0
Answers
Since the right side is 0, so equate each factor by 0 and find the values of x
Put 3x - 14 = 0 and 8x + 13 = 0
3x - 14 = 0
Add 14 to both sides
3x - 14 + 14 = 0 + 14
3x = 14
Divide both sides by 3
\(\frac{3x}{3}=\frac{14}{3}\)\(x=\frac{14}{3}\)This is the first value of x
Let us do the same with other factor
8x + 13 = 0
Subtract 13 from both sides
8x + 13 - 13 = 0 - 13
8x = - 13
Divide both sides by 8
\(\frac{8x}{8}=-\frac{13}{8}\)\(x=-\frac{13}{8}\)This is the second value of x
So the two values of x are
\(\frac{14}{3},-\frac{13}{8}\)Part B: Write a rule for determining the sign of the product when multiply negative integer
Answers
): Please can someone help me with these questions , im stressed out already pls! Thank you
Answers
Answer:
15. k=21 answer 21
16. r=-11 answer -11
17. m= 26
18. p=17
3.) Forty percent of a number is equal
to one-half the number decreased by
15. Which one can be used to
determine the number?
A 40x = – 15
B 40x > 2x – 15
C 0.40x< - 15
D 0.4x =x/2-15
Answers
D
0.4 multiplied by x would give you the percentage and putting x over 2 would give you half of that number
a door was rolled 60 times. it landed on one-11 times, two-9 times, four-12 times, five-12 times, and six - 8 times. How many times was there rolled in there 60 times?
Answers
The die was rolled 7 times in there 60 times if it is landed on one-11 times, two-9 times, four-12 times, five-12 times, and six - 8 times.
What is meant by probability?Probabilities are mathematical explanations of the probability of an event occurring or of a proposition being true. The probability of an event is expressed as a number between 0 and 1, where 0 often indicates impossibility and 1 generally indicates certainty.
Given,
Number of times a die rolled=60
And also given that it landed on,
One --- 11 times
Two -----9 times
Four -----12 times
Five -----12 times
Six -------8 times
Total number of times the die was landed on is 52 times.
Therefore, total number of times a die was rolled=60
S0, 52+x=60
x=7
Therefore, the die was rolled 7 times in there 60 times.
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Which of the following is not a function?
Answers
Answer:
D is not a function
Step-by-step explanation:
A function is a relation where the x values or domain do not repeat in this case the d repeats itself so it would be D
What is the missing degree measure of the third angle of the triangle below?
46°
56°
68°
90°
Answers
Answer:
56 degrees
Step-by-step explanation:
Hello there!
Remember the sum of the angles in a triangle is equal to 180
so to find the missing angle we subtract the given angles from 180
180 - 34 - 90 = 56
so we can conclude that the measure of the missing angle is 56 degrees
Note: the little square at the bottom left of the triangle indicates that the angle is a right angle. The measure of a right angle is 90 degrees so thats where the 90 came from
Answer:
third angle Δ = 56°hope it help you
An iguana is about 42 cm. at birth and increases in length at an approximate rate of 12% per week. Write the function which models the growth. Use X for the number of weeks and y for the length of the iguana.
Answers
We were given that:
The iguana is 42cm at birth
It increases by 12% every week; r = 12% = 0.12
The number of weeks is represented by ''x'' & the length of the Iguana is represented by ''y''
This function is represented by the expression below:
\(\begin{gathered} f\mleft(x\mright)=a\mleft(1+r\mright)^x \\ where\colon r=growth.rate \\ a=initial.length \\ f\mleft(x\mright)=y \\ \Rightarrow y=a(1+r)^x \\ y=a(1+r)^x \\ a=42,r=0.12 \\ \text{Substituting the variables into the equation, we have:} \\ y=42(1+0.12)^x \\ y=42(1.12)^x \\ \\ \therefore y=42(1.12)^x \end{gathered}\)What is the value of i 20 1? 1 –1 –i i
Answers
Answer:
The expression "i 20 1" is not well-defined and requires more context to determine its meaning. It is possible that "i" refers to the imaginary unit, while "20" and "1" could be operands or arguments for a mathematical operation or function. Without knowing the specific operation or function, it is impossible to determine the value of the expression. The list of options provided (1, -1, -i, i) are also not applicable without further information.
Find the perimeter.
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
1 37/364 am sure it is helpful
What are binary integer variables?
a. Variables with any two values, a and b.
b. Variables with values 0 and 1.
c. Variables whose sum of digits is 2.
d. Variables with values between 0 and 1.
Answers
Binary integer variables are variables whose values consist of two values, 0 and 1.
Correct answer will be :- b. Variables with values 0 and 1.
These values are also known as bits, which are represented as 0 and 1 in computers. Binary integer variables are used in computing as a way to represent numbers, characters, and instructions. Binary integer variables are used to represent information in digital systems, because they can be used to represent any value with a single bit.
For example, a single bit can represent a number, letter, or instruction. Binary integer variables are also used in computer programming, as they can be used to represent boolean values, such as true and false. Additionally, they can be used to represent various types of data, such as numbers, characters, and images.
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charlie wakes up in the night and looks at his 12-hour digital watch. the time he sees can be read as a three-digit number. he remarks:"the digits add to six and, if you divide the number by six, the answer is a prime." what time could it be?
Answers
12345678765432123456543212345432
Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0).
Answers
The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).
How is this determined?Given by: The midpoint of the two points is:
M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)
The following vector runs between the two points:
V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)
The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.
The normal vector is then provided by:
N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)
The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:
(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2
The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.
12(x - 2) = -8(y - 2) = 4(z + 1) + 2
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What 2 whole numbers is the square root of 75 between?
Answers
Answer:
8 and 9
Step-by-step explanation:
a car passes through the point (1,3)..it's gradient=2x-1/x². Find the equation of the line
Answers
Answer:
y = -1/2x - 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Determine known variables
Slope = -1/2 (m = -1/2)
y-intercept - (0, -3), so b = -3
Step 2: Write in known variables
y = -1/2x - 3
This is really to guitar out, 1+1
Answers
Answer:
2
Step-by-step explanation:
1 pizza slice and add another pizza slice :)
What method of characterization does the following character description use?
Oh! But he was a tight-fisted hand at the grindstone, Scrooge! a squeezing, wrenching, grasping, scraping, clutching, covetous, old sinner! Hard and sharp as flint, from which no steel had ever struck out generous fire; secret, and self-contained, and solitary as an oyster. The cold within him froze his old features, nipped his pointed nose, shrivelled his cheek, stiffened his gait; made his eyes red, his thin lips blue; and spoke out shrewdly in his grating voice. A frosty rime was on his head, and on his eyebrows, and his wiry chin. He carried his own low temperature always about with him; he iced his office in the dog-days; and didn’t thaw it one degree at Christmas. from:
Answers
Answer:
The author is intending the character to be mean, old, and snobby. He also hates Christmas
Step-by-step explanation:
He does this by comparing the character to other objects.
in a set of scores with a mean of 100 and a standard deviation of 15, what raw score is represented by a z score of 2.00?a.115b.100c.70d.130
Answers
The raw score represented by a z score of 2.00 is 130 (option d).
What is the raw score corresponding to a z score of 2.00?A z score, also known as a standard score, measures the distance between a particular raw score and the mean of a distribution in terms of standard deviations. In this case, the given set of scores has a mean of 100 and a standard deviation of 15. A z score of 2.00 indicates that the raw score is two standard deviations above the mean.
To find the corresponding raw score, we can use the formula:
Raw Score = (Z Score × Standard Deviation) + Mean
Plugging in the values, we have:
Raw Score = (2.00 × 15) + 100Raw Score = 30 + 100Raw Score = 130Therefore, a z score of 2.00 in this distribution corresponds to a raw score of 130.
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Give an example of a pair of series an and bn with positive terms where limn rightarrow infinity (an/bn) = 0 and bn diverges, but an converges. (Note this demostrates the contrapositive of the limit comparison test: "If one of an and bn converges and the other diverges, then limn rightarrow infinity (an/bn) = 0 or infinity or DNE. ")
Answers
Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.
Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n
Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))
To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)
As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0
Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.
Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.
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use the ratio test to determine whether the series is convergent or divergent. [infinity] n 7n n = 1 identify an.
Answers
To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.
In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:
lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|
Simplifying the expression, we get:
lim(n→∞) |7(n+1)/n|
As n approaches infinity, the limit evaluates to:
lim(n→∞) |7(n+1)/n| = 7
Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.
However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.
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Can someone please help me on this!!
Answers
Used the given information to determine the probability below round solution with 3 decimal places
Answers
The conditional probability formula is
\(P(B|A)=\frac{P(B\cap A)}{P(A)}\)which gives
\(P(B\cap A)=P(A)\times P(B|A)\)Then, for the first question, we get
\(\begin{gathered} P(A\cap B)=P(B\cap A)=P(A)\times P(B|A) \\ P(A\cap B)=0.46\times0.05 \end{gathered}\)which gives
\(P(A\cap B)=0.023\)Now, for the second question, we know that, for independent events
\(P(A\cap B)=P(A)\times P(B)\)then, we have
\(P(A\cap B)=0.46\times0.28\)which gives
\(P(A\cap B)=0.129\)Now, for question 3, we know that, when the events are dependent and mutually non-exclusive
\(\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=P(A)+P(B)-P(A)\times P(B|A) \end{gathered}\)By substituting the given values, we have
\(\begin{gathered} P(A\cup B)=0.46+0.28-(0.46\times0.05) \\ P(A\cup B)=0.74+0.023 \\ P(A\cup B)=0.763 \end{gathered}\)Finally, for the 4th question, we have
\(P(A\cup B)=P(A)+P(B)\)which gives
\(\begin{gathered} P(A\cap B)=0.46+0.28 \\ P(A\cap B)=0.74 \end{gathered}\)In summary, the solutions are:
Question 1:
\(P(A\cap B)=0.46\times0.05=0.023\)Question 2:
\(P(A\cap B)=0.46\times0.28=0.129\)Question 3:
\(P(A\cup B)=0.46+0.28-(0.46\times0.05)=0.763\)Question 4:
\(P(A\cap B)=0.46+0.28=0.74\)A 3-gallon bottle of bleach costs $14.88. What is the price per quart?
Answers
Answer:
1.24
Step-by-step explanation:
there are 4 quarts to a gallon. you have 3 gallons. so you have 12 quarts. 14.88 divided by 12 is 1.24! hope this helps! :)
I need help ASAP!!! The entire question is right here.
Answers
Answer:
R1. Given
R2. Subtraction Property of Equality
R3. Distributive Property
S4. 9x = 61
R5. Division Property of Equality
2 A marathon race is 42 195 m in length. The world record in 2016 was
2 hours, 2 minutes and 57 seconds held by Dennis Kimetto of Kenya.
a How many seconds in total did Kimetto take to complete the race?
b Calculate his average speed in m/s for the race, giving your answer to
2 decimal places.
c What average speed would the runner need to maintain to complete
the marathon in under two hours?
Answers
Answer:
A. 7377 s
B. 5.72 m/s
C. 5.86 m/s
Step-by-step explanation:
A. Determination of the time in second.
Time (t) = 2 hours, 2 minutes and 57 seconds
We'll begin by converting 2 hours to seconds. This can be obtained as follow:
1 hour = 3600 s
Therefore,
2 hour = 2 hours × 3600 s / 1 hour
2 hours = 7200 s
Next, we shall convert 2 mins to seconds. This can be obtained as follow:
1 min = 60 s
Therefore,
2 mins = 2 mins × 60 s / 1 min
2 mins = 120 s
Finally, we shall determine the total time in second. This can be obtained as follow:
2 hours, 2 minutes and 57 seconds = 7200 s + 120 s + 57 s
= 7377 s
Therefore, the total time in second is 7377 s
B. Determination of the average speed.
Total distance = 42195 m
Total time = 7377 s
Average speed =?
Average speed = Total distance / total time
Average speed = 42195 / 7377
Average speed = 5.72 m/s
Therefore, the average speed is 5.72 m/s
C. Determination of the average speed.
We'll begin by converting 2 hours to seconds. This can be obtained as follow:
1 hour = 3600 s
Therefore,
2 hour = 2 hours × 3600 s / 1 hour
2 hours = 7200 s
Finally, we shall determine the average speed. This can be obtained as follow:
Total distance = 42195 m
Total time = 7200 s
Average speed =?
Average speed = Total distance / total time
Average speed = 42195 / 7200
Average speed = 5.86 m/s
Therefore, the average speed is 5.86 m/s.
A multiple choice test has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?
a-0.2816
b-0.0021
c-0.5006
d-0.0156
e-0.2503
Answers
option a-0.2816. To find the probability that Judy will answer exactly 3 questions correctly, we can use the binomial probability formula. In this case, the number of trials is 10 (since there are 10 questions), the probability of success is 1/4 (since there is only one correct answer out of 4 possible choices), and we want to find the probability of getting exactly 3 successes.
The binomial probability formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- (n choose k) represents the number of ways to choose k items out of n items
- p is the probability of success on a single trial
- k is the number of successes
- n is the number of trials
Using this formula, we can calculate the probability as follows:
P(X=3) = (10 choose 3) * (1/4)^3 * (3/4)^(10-3)
(10 choose 3) = 10! / (3! * (10-3)!)
= 10! / (3! * 7!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120
Now we can substitute the values into the formula:
P(X=3) = 120 * (1/4)^3 * (3/4)^(10-3)
= 120 * (1/64) * (3/4)^7
= 120 * (1/64) * (2187/16384)
= 0.2816
Therefore, the probability that Judy will answer exactly 3 questions correctly is 0.2816.
The correct answer is option a-0.2816.
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f(x)=5sinx+cosx then f ′
(x)=−5cosx−sinx Select one: True False
Answers
False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.
To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).
Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.
Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:
f'(x) = 5cos(x) - sin(x).
This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).
In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).
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Evaluate using the integration by Parts formula
∫(2x+9)e^x
dx; u=2x+9, dv=e^x dx
Answers
the integration by Parts formula ∫(2x+9)\(e^x\) dx; u=2x+9, dv=\(e^x\) dx is (2x + 9) \(e^x\) - 2 \(e^x\) + C.
Let us evaluate the given integral using integration by parts formula below;
∫udv = uv - ∫vdu Where u = 2x + 9 and dv = \(e^xdx\).
Hence, we have ;du/dx = 2 , then u' = 2dv/dx = \(e^x\) , then v =\(e^x\)Therefore,∫(2x + 9)\(e^x\)dx = (2x + 9) ∫ \(e^x\) dx - ∫ [d/dx (2x + 9)]\(e^x\)dx .....Using the Integration by Parts formula
(2x + 9) \(e^x\) - ∫ (2)\(e^x\) dx= (2x + 9) \(e^x\) - 2 \(e^x\) + C, where C is the constant of integration.
Therefore, the answer is (2x + 9) \(e^x\) - 2 \(e^x\) + C.
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help me plss ty in advance:))
Answers
Answer:
AACBC7Step-by-step explanation:
Q1
A graph which uses horizontal or vertical bars with no gaps to represent data is called bar graph.
Q2
Data plotted against the frequency in a histogram is class interval.
Q3
The data plotted against the frequency in an ogive is cumulative frequency.
Q4
A score of 50 under the column > c.f. with the boundaries 23.5 - 28.5 means 50 students got a score greater than 23.5.
Q5
Mean = 2(2) + 3 + 4 + 7(3) + 10 + 11 + 2(12) / 11
Mean = 4 + 7 + 21 + 21 + 24 / 11
Mean = 77/11
The mean is 7
Q6
The median is the middle term.
The median of the distribution is 7
Please help me with this math!!
Answers
Answer:
Step-by-step explanation:
Distance formula looks a little like pythagorean because that where it comes from
d = \(\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }\)
=\(\sqrt{(-1-(-2))^{2}+(3-1)^{2} }\)
=\(\sqrt{1^{2}+2^{2} }\)
=√5 or 2.24