Answer:
x = 5 (If solved algebraically)
No Solution (If the parentheses are absolute value lines)
Step-by-step explanation:
Result when solving this way: 3|-3x + 9| = -18
1) Divide both sides by 3
|-3x + 9| = -18/3
2) Simplify 18/3 to 6
|-3x + 9| = -6
3) Break down the problem into these 2 equations.
-3x + 9 = -6
- (-3x + 9) = -6
4) Solve the 1st equation: -3x + 9 = -6
- Subtract 1 from both sides.
-3x = -6 - 9
-Simplify -6 - 9 to -15.
-3x = -15
-Divide both sides by -3.
x = -15/-3
- Two negatives make a positive.
x = 15/3
- Simplify 15/3 to 5.
x = 5
6) Solve the 2nd equation: - (-3x+ 9) = -6
1 - Remove parentheses
3x - 9 = -6
2 - Add 9 to both sides
3x = -6 + 9
3 - Simplify -6 + 9 to 3.
3x = 3
- Divide both sides by 3.
x = 1
6) Collect all solutions.
x = 1,5
7) Check solution.
When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.
We will drop x = 1 from the solution set.
8) Check solution.
When x = 5, the original equation 3|-3x + 9| = -18 does not hold true.
We will drop x = 5 from the solution set.
9) Therefore,
No solution exists.
Result when solving algebraically:
Simplifying
3(-3x + 9) = -18
Reorder the terms:
3(9 + -3x) = -18
(9 * 3 + -3x * 3) = -18
(27 + -9x) = -18
Solving
27 + -9x = -18
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-27' to each side of the equation.
27 + -27 + -9x = -18 + -27
Combine like terms: 27 + -27 = 0
0 + -9x = -18 + -27
-9x = -18 + -27
Combine like terms: -18 + -27 = -45
-9x = -45
Divide each side by '-9'.
x = 5
Simplifying
x = 5
Solve each inequality and graph the solution set and a number lined, express the Solution set in interval notation. 6 < x + 3 < 8 Solve each inequality and graph the solution set and a number lined , express the Solution set in interval notation . 6 < x + 3 < 8
The solution set for the given inequality is 3<x<5.
The given inequality is 6<x+3<8.
What is the solution set?In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
Now, solve the given inequality:
6<x+3<8⇒6<x+3 and x+3<8
6-3<x ⇒3<x
x+3<8⇒x<5
Thus, 3<x<5.
Therefore, the solution set is 3<x<5.
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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5
6<x+3<8
[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]
What is the rule of inequality?[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]
[tex]3 < x < 5[/tex]
Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.
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The y-intercept of the line whose equation is 2x - 3y = 6 is
-2
3
6
Answer:
y = -2
(first option listed)
Step-by-step explanation:
a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.
So, the y-intercept is actually pretty each to find.
this is the easier way to find it: {plug directly into equation given}
2x - 3y = 6
(set x equal to 0)
[0] - 3y = 6
(divide both sides by -3)
y = -2
but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}
[this method is helpful to know/practice for when equations for functions get more complex]
2x - 3y = 6
+ 3y + 3y {add 3y to both sides}
2x = 3y + 6
-6 -6 {subtract 6 from both sides}
2x - 6 = 3y
÷3 ÷3 {divide both sides by 3 to isolate y}
[tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex] [flip sides of the equation]
[tex]y=\frac{2}{3}x-2[/tex]
set x equal to 0 (x = 0)
y = [tex]\frac{2}{3} (0)[/tex] - 2
y = 0 - 2
y = -2
So, the y-intercept is -2.
The following table shows the probability distribution for a discrete random
variable.
13
16
17
21
23
25
26
31
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08
What is the mean of this discrete random variable? (That is, what is E(X), the
expected value of X?)
A. 21.5
B. 22
) C. 21
D. 20.42
Which graph shows the solution to the system of linear inequalities?
y≥ 2x + 1
y≤2x-2
Answer:
g
Step-by-step explanation:
jjnnkvigific and it's a boy f a horse y
is y=6x-3 a function
Yes it is
Step-by-step explanation:
it is a linear function as it is written in the standard form Y=MX+C
Prove that the function
Answer:
See proof below
Step-by-step explanation:
Important points
understanding what it means to be "onto"the nature of a quadratic functionfinding a value that isn't in the rangeOnto
For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.
However, the co-domain here is suggested to be [tex]\mathbb R[/tex], whereas the range of f is not [tex]\mathbb R[/tex] (proof below).
Proof (contradiction)
Suppose that f is onto [tex]\mathbb R[/tex].
Consider the output 7 (a specific element of [tex]\mathbb R[/tex]).
Since f is onto [tex]\mathbb R[/tex], there must exist some input from the domain [tex]\mathbb R[/tex], "p", such that f(p) = 7.
Substitute and solve to find values for "p".
[tex]f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2[/tex]
Next, apply the square root property:
[tex]\pm \sqrt{-1} =\sqrt{p^2}[/tex]
By definition, [tex]\sqrt{-1} =i[/tex], so
[tex]i=p \text{ or } -i =p[/tex]
By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots. Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.
However, neither [tex]i[/tex] nor [tex]-i[/tex] are in [tex]\mathbb R[/tex], so there are zero values of p in [tex]\mathbb R[/tex] for which f(p)= 7, which is a contradiction.
Therefore, the contradiction supposition must be false, proving that f is not onto [tex]\mathbb R[/tex]
Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.
Which is the equation for y?
Answer:
y = -t
Step-by-step explanation:
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t (answer)
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....................
..................................
Find and prove an inequality relating 100n and n^{3} .
An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.
Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
Induction hypothesis:
Suppose 100n ≤ k³ for some positive integer k ≥ 10.
We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.
Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100
≤ k³ + 3k² (∵ k ≥ 10 )
≤ k³ + 3k² + 3k
≤ k³ + 3k²+3k + 1
So 100( k + 1 ) ≤ ( k + 1 )³, which is true.
Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.
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A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766. Find the percent increase in the property's value. Round your answer to the nearest hundredth, if necessary.
Answer:
7%
Step-by-step explanation:
[tex] \frac{14766 - 13800}{13800} \times 100 = 7 [/tex]
The percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766
Percentage increase:
[tex]= \rm \dfrac{14766-13800}{13800}\times 100[/tex]
= 7%
Thus, the percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
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log(2t+4)=log(14-3t)
Answer:
t = 2
Step-by-step explanation:
[tex]2t + 4 = 14 - 3t[/tex]
[tex]5t = 10[/tex]
[tex]t = 2[/tex]
Checking:
[tex] log(2(2) + 4) = log(8) [/tex]
[tex] log(14 - 3(2)) = log(8) [/tex]
y - wy = m (solve for w)
I need an answer ASAP.
answer:
w = (-m+y)/y
Step-by-step explanation:
y-wy = m
-wy = m-y
y = -(m-y)/w
wy= -m + y
w = (-m+y)/y
.
Express the radical using the imaginary unit, i sqrt{-27}
Answer:
27i
Step-by-step explanation:
Since we define i as [tex]\sqrt{-1}[/tex], [tex]\sqrt{-27} = 27i[/tex]
Answer:
Step-by-step explanation:
i [tex]i \sqrt{-27} =i\sqrt{-1 \times 27} =i\sqrt{27i^2} =i \times i\sqrt{27} =i^2\sqrt{9 \times 3} \\=-1\times 3\sqrt{3} \\=-3\sqrt{3}[/tex]
How can the next term in the infinite sequence 1, 5, 12, 22, 35, be generated? O Square the term number, subtract the term number from the result, multiply by 3, and divide the result by 2. O Square the term number, multiply the result by 3, divide by 2, and subtract the term number from the result. O Square the term number, divide the result by 2, subtract the term number, and multiply the result by 3. O Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Check the forward differences of the sequence.
• first-order differences
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
• second-order differences (i.e. differences of the first differences)
7 - 4 = 3
10 - 7 = 3
13 - 10 = 3
The second differences are all 3 (as far as we know), so the sequence of first differences is arithmetic/linear, which means the original sequence is quadratic. Let the [tex]n[/tex]-th term be
[tex]x_n = an^2 + bn + c[/tex]
Given that [tex]x_1=1[/tex], [tex]x_2=5[/tex], and [tex]x_3=12[/tex], we have
[tex]\begin{cases} a + b + c = 1 \\ 4a + 2b + c = 5 \\ 9a + 3b + c = 12 \end{cases} \implies a=\dfrac32, b=-\dfrac12, c=0[/tex]
and so the [tex]n[/tex]-th term of the sequence is generated by the rule
[tex]x_n = \dfrac{3n^2 - n}2[/tex]
which most closely resembles the last option,
Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
An equivalent ratio to the tape diagram shown is
to pls i need a answer
An equivalent ratio to the tape diagram shown is 1 to 2
How to determine the equivalent ratio?From the tape diagram, we have:
Red = 2
Blue = 4
Express as a ratio
Red : Blue = 2 : 4
Divide by 2
Red : Blue = 1 : 2
Hence, an equivalent ratio to the tape diagram shown is 1 to 2
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Which of the following is a requirement for multiple regression?
3.
Categorical variables only
O b. A small sample size
O c. Obiective measures only
O d. Absence of multicollineerity between variables
0 e.
Subjective measures onlv
Answer:
insectistics a category variable also called various validity variable is a variable that can take on a limited as usually fixed number two possible values assigning each into visual or other unit of the vision 2 a particular group aur nominacle category of the basis some qualitative
if x=-2 solve 4x^3-6x^2+x-1
Answer:
-59
Step-by-step explanation:
x = -2
4(-2)³ - 6(-2)² + (-2) - 1
= -32 - 24 - 2 - 1
= - 59
The ages of Sonu and Monu are in the ratio 5:7.If Sonu were 9 years older and Monu 9 years younger, the age of Sonu would have been twice the age of Monu .Find their p present age 2 ) The ages of Sonu and Monu are in the ratio 5 : 7.If Sonu were 9 years older and Monu 9 years younger , the age of Sonu would have been twice the age of Monu .Find their present age.
Answer:
Sonu is 15years and Monu is 21 years
Find the 10th term of the geometric sequence whose common ratio is 3/2 and whose first term is 8
Answer: 19683/64
Step-by-step explanation:
[tex]a_{n}=8\left(\frac{3}{2} \right)^{n-1}\\\\\implies a_{10}=8 \left(\frac{3}{2} \right)^{10-1}=\boxed{\frac{19683}{64}}[/tex]
x(x - 5) = -4
Solve the equation, using the quadratic formula.
Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height. [Assume π = 22/7]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Curved surface area of right circular cylinder is 4.4 m².
★ Radius of base of the cylinder is 0.7 m.
★ [tex]\tt \pi = \dfrac{22}{7}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The height of cylinder.
[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]
[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
❍ The height of circular cylinder be [tex]h[/tex]
❍ Radius [r] of base of cylinder be 0.7 m
We know,
[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]
Putting,
☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]
☆ r as 0.7
[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]
[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]
[tex] \longrightarrow \tt 44 m = 44h[/tex]
[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]
[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]
Therefore, the height of cylinder = 1 m.
[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]
quest
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
D)
10
Days People
1
26
2
30
3
34
4
38
5
42
6 46
og php?totalQuestions-10&testid-5
strand-5716&element-18789&condition-random #
Answer:
Day 5 ................
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. what is the value of this function
The range of y will be all real numbers such that 0≤y≤40
The complete question is:
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute.
The amount of water remaining in the bathtub = y
The function of time in minutes, that it has been draining = x
At 0 minutes the amount of water is 40 gallons.
The highest volume of water is 40 which is decreasing at the rate of 1.5 gallons per minute.
The given function is a linear function
y = 0
However, the volume of water can be 0 but cannot ever be negative.
Therefore the range of y will be all real numbers such that 0≤y≤40
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Rob bought a pair of jeans at 30% off the original price. If the original price was $55, how much did he pay for the jeans?
Answer:
$38.50
Step-by-step explanation:
(100-30)% of $55
= 70% of $55
= $38.50
Hope this helps :)
What is the approximate area of the shaded sector in the circle shown below
A.29.04 in^2
B.13.51 in^2
C.7.26 in^2
D.6.75^2
Answer:
please provide the diagram
Step-by-step explanation:
for the solution figure is necessary so provides us to solve this problem
0.0000000019 written in scientific notation is
Answer:
1.9x10^8
hope I helped
Answer:
0.0000000019= 1.9*10^ -9
A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles 3:4; but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday
The weight of each pile yesterday will be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is Given that Yesterday the ratio of seeds in these piles was 3:4.
Let 3x and 4x represent the seeds.
If the 2 pounds of seeds are added in the bigger pile, then
4x + 2
He also ate 1/4 pound from the smaller pile,
3x - 1/4
The quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of each pie will be
3x = 6 pound
4x = 8 pound
Hence, The weight of each pile yesterday would be 6 and 8 pounds.
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College students (ages 18-26) tend to make decisions which are
tentative (more short-range) and support a desire for autonomy.
a result of a greater sense of commitment and stability.
more permanent choices.
College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.
How to illustrate the information?
It should be noted that values are a compass that helps us make decisions and choices.
Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.
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For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.21 probability of failure. Complete parts (a) through (c) below.
Would it be unusual to observe one component fail? Two components?
It
▼
would not
would
be unusual to observe one component fail, since the probability that one component fails,
enter your response here, is
▼
less
greater
than 0.05. It
▼
would not
would
be unusual to observe two components fail, since the probability that two components fail,
enter your response here, is
▼
greater
less
than 0.05.
Using the probability concept, we have that:
a) It would not be unusual to observe one component fail, since the probability that one component fails is greater than 0.05.
b) It would be unusual to observe two components fail, since the probability that two components fail is less than 0.05.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. If a probability is less than 0.05, the event is considered unusual.
In this problem, the probabilities are given as follows:
0.21 probability that one component fails, hence not unusual.(0.21)² = 0.0441 probability that two components fail, hence unusual.More can be learned about probabilities at https://brainly.com/question/14398287
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simplify completely 12x^2 -4x^2+8x over -2x
Answer:
-4*(x+1)
Step-by-step explanation:
Simplify
⇒ 8x2 + 8x/-2x
2: Pulling out like terms
4.1 Pull out like factors :
8x2 + 8x = 8x • (x + 1)
Canceling Out :
4.2 Canceling out x as it appears on both sides of the fraction line
Final result :
-4 • (x + 1)
Answer:
-4(x+1)
Step-by-step explanation:
factor out -2x
-2x(-6x + 2x - 4) / -2x
the -2x in numerator and denominator cancel out
-6x + 2x - 4
-4x - 1
-4(x+1)
