Answer:
All real numbers
Step-by-step explanation:
Solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
What is equation?
" Equation is defined as when two algebraic expression which are related with the sign of equality."
According to the question,
Given,
-2(x + 3) = -2x - 6
Open the brackets of the equation we get,
-2(x) + (-2)(3) = -2x - 6
⇒ -2x - 6 = -2x - 6
Add 6 on both the sides of the equation we get,
-2x = -2x
Divide by -2 of the equation both sides
x = x _____(1)
Add (-x) both the sides we get,
0 = 0 _____(2)
From (1) and (2) we conclude ,
Solution is true for all the real values of x.
Hence, solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).
Learn more about equation here
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Find the value of x in each case:
Answer:
[tex] x = 18 [/tex]
Step-by-step explanation:
Given:
Angle ABC = 2x
Angle CDE = 8x
Required:
Value of x
SOLUTION:
Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:
Angle ABC = Angle BCD = 2x
Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.
Consecutive interior angles are supplementary, therefore:
Angle BCD + Angle CDE = 180°
[tex] 2x + 8x = 180 [/tex]
Use this equation to solve for x
[tex] 10x = 180 [/tex]
Divide both sides by 10
[tex] \frac{10x}{10} = \frac{180}{10} [/tex]
[tex] x = 18 [/tex]
Write the quadratic equation whose roots are -4 and 4 and whose leading coeffiecient is 3. Use the letter X to represent the variavble.
Answer:
3x^2 - 48 = 0
Step-by-step explanation:
The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.
The two forms we know for the quadratic equation are the factored binomials:
(ax + cy)(bx + dz) = 0
and the full equation
ax^2 + bx + c = 0
We will start with the factored form:
(x + 4) ( x - 4) = 0
Note that if we solve this, we get the roots: x + 4 = 0 ==> -4 && x - 4 = 0 ==> 4
Now we apply foil to get the unfactored form:
(x + 4) (x - 4) = 0
x * x + x * -4 + 4 * x + 4 * -4 = 0
x^2 + -4x + 4x + -16 = 0
x^2 - 16 = 0
And now we want the leading coefficient to be 3.
3x^2 - 16 = 0
This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4. So, we need to re-evaluate.
Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:
(3x + 12) (x - 4) = 0
Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.
3x + 12 = 0 x - 4 = 0
3x = -12 x = 4
x = -4
So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:
(3x + 12) (x - 4) = 0
3x * x + 3x * -4 + 12 * x + 12 * -4 = 0
3x^2 + -12x + 12x + -48 = 0
3x^2 - 48 = 0
This is our quadratic equation we wish to use.
Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.
Cheers.
Simplify: 2 + 7(1 - 3x)
2 + 14x
16x
9-27x
9 - 21x
Answer:
9 - 21x
Step-by-step explanation:
Simplify the following:
7 (1 - 3 x) + 2
Hint: | Distribute 7 over 1 - 3 x.
7 (1 - 3 x) = 7 - 21 x:
7 - 21 x + 2
Hint: | Add the numbers in -21 x + 2 + 7 together.
Add like terms. 2 + 7 = 9:
9 - 21 x
Hint: | Factor out the greatest common divisor of the coefficients of 9 - 21 x.
Factor 3 out of 9 - 21 x:
Answer: 3 (3 - 7 x)
(of the given solutions it's the only correct one, but can be further simplifued to 3 (3 - 7 x)
According to the U.S. Census Bureau, as of April 1, 2000, the total population of the United States was about 3 x 10^8 . The population of Vermont was 6 × 10^5 . The population of the U.S. was how many times the population of Vermont in April of 2000?
2 times
500 times
1,000 times
50,000 times
Divide US population by Vermont :
3x 10^8 / 6x10^5
3/6 = 1/2 = 0.5
10^8 / 10^5 = 10^3
0.5 x 10^3 = 500
The answer is 500 times
All we need to do is divide.
3*10^8/6*10^5
0.5^8-5
0.5^3
500
Therefore, the answer is 500 times.
Best of Luck!
Add 6 and 8 the add p
Answer:
Step-by-step explanation:
6 + 8 + p = 14 + p
Answer: 14+p
Step-by-step explanation: We have to add these numbers-
6 + 8 + p
14+p
(Since we don't know the value of p this is how far we can simplify )
Which of the following fractions is greater than 2/5 and less than 3/5 ?
Answer:the answer would be 2.5/5
FIRST TO ANSWER GETS BRAINLYEST!!!!!!
Answer:
m ≈ 3
Step-by-step explanation:
3.53631284916 x 10^3 ≈ 3 x 10^3
Give the Domain and Range of H={(-2,-3),(5,9),(5,-2)}
Write your answer using set notations
The domain is the set of possible x values or inputs. We list each unique x value once (ignoring any repeats)
The range is the set of possible y outputs. Convention is to sort the values from smallest to largest.
This relation is not a function because the x value x = 5 corresponds to multiple y values.
Which is the graph of y<2x-1
Answer:
the last one is the only one with a y intercept of -1
Step-by-step explanation:
*BRAINLIEST* The lines below are parallel. If the slope of the green line is 8/5, what is the slope of the red line?
Any two parallel lines always have the same slope (but different y intercepts)
The equation of the green line is y = (8/5)x+6
The equation of the red line is y = (8/5)x-3
Slope intercept form is y = mx+b with m as the slope and b as the y intercept.
The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.
Evaluate a + b for a = -46 and b = 34.
Answer:
-12
Step-by-step explanation:
a + b
a = -46
b = 34
-46 + 34 = -12
A pink crayon is made with 12 ml
Answer:
ok
Step-by-step explanation:
John invests $200 at 4.5% compounded annually. About how long will it take for John’s investment to double in value?
Answer:
The number of years needed is 15.75 years.
Step-by-step explanation:
The investment amount (present value) = $200
Interest rate =4.5%
Double of investment = $400
Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.
Future value = present value ×(1+interest rate)^n
400 = 200×(1+4.5%)^n
N = 15.75 years
The number of years required to double the amount is 15.75 years.
I am a real number I am a rational number I am not a natural number I am less than -13 what number am I
Answer:
Any number less than -13.
Step-by-step explanation:
If the number is real and rational and non-natural, this means that it can be any number in the negative number space.
Additionally, since the number has to be less than -13, then the number could be any number less than -13.
With all these things considered, the number is any number less than -13 that is real and rational.
Cheers.
Dhshshsjehsjsjjsjssjsjsjsjsjsjshshdhdhdhdjdjdjdjhdbd djdhdhdjjdjdjdjdjdjd
Answer:
Dhshshshhshsjehsjsjjsjssjsjsjsjsjsjjshhdhddhhdjdjddjdjjhdhdkdhjsdfggdhjjjjd
Step-by-step explanation:
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.a) 91.69 < μ < 98.31b) 92.95 < μ < 97.05c) 91.68 < μ < 98.32d) 92.03 < μ < 97.97
Answer: c) 91.68 < μ < 98.32
Step-by-step explanation:
Let μ be the mean score of all students.
Let [tex]\overline{x}[/tex] represents the sample mean score.
As per given , we have
Sample size : n= 30
Sample mean : [tex]\overline{x}=95[/tex]
Sample standard deviation: [tex]s=6.6[/tex]
Significance level [tex]\alpha=0.01[/tex]
Now, Confidence interval of mean when population standard deviation is unknown is given by :-
[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]
Degree of freedom = n-1 = 29
Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]
Confidence interval of mean will be:
[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]
i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32
So correct option is c) .
Three and a half more than a number
Answer:
x + 3.5
Step-by-step explanation:
You are adding
hopefully this helps you:)
Avni designs a game in which a player either wins or loses 4 points during each turn. Which equation
represents all numbers of points, p, a player may have after his or her first turn of the game?
O p = 4
O p = -4
O pl = 4
Op = -4
Answer:
Equation to represent all number of points = |4|
Step-by-step explanation:
We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.
Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.
Thus, it's |4|
HELP ME PLS i truly need help on this
Step-by-step explanation:
75+54
129°
the answer is 129°
Someone help me please i attached a picture...
Answer:
the perimeter is 13yd + 13yd + 5yd +5yd = 36yd
the area is 5yd + 5yd = 10yd, 10yd × 12yd ÷ 2 = 60yd
Which number is equivalent to
A 2
B 9
с
81
729
The answer would be
B. 9
a turtle crawled at a speed of 1.2 meters per minute for nine minutes how far did the turtle crawl
Answer:
10.8 meters
Step-by-step explanation:
1.2 times 9 minutes= 10.8
Answer:
10.8 meters
Step-by-step explanation:
9 * 1.2 = 10.8
How is completing the square beneficial ? Edge 2020 key words
To which graph does the point (8;-2) belong?
quadrant 4
.................
Answer:
Quadrant 4
Step-by-step explanation:
In Quadrant 4 the x-axis is positive (+) and the y-axis is negative (-). Here is the point plotted on a coordinate grid to help you understand better.
Hope this helps :)
David noticed that locker 49 was changed exactly 3 times it was opened by Student one closed by student seven and open my Student 49 what other lockers were changed exactly 3 times what is the relationship between these numbers
Answer:
The other lockers that were changed exactly 3 times are:
Locker 1 and Locker 7
Step-by-step explanation:
Question: What other lockers were changed exactly 3 times?
Answer: Lockers 1 and 7
How?
Locker 1 was opened by a student other than student 1; it was closed by a student other than student one; and it was opened by student 1.
Same happened with Locker 7.
The relationship between these numbers is an associative relationship.
Factor completely 4x^4− 20x^3 + 12x^2
Answer:
Step-by-step explanation:
4x^2(x^2 - 5x + 6)
4x^2(x - 3)(x - 2)
Paul says that in the number 6,367, one 6 is 10 times as great as the other 6. Is he correct?
Answer:
Yes
Step-by-step explanation:
6,000 is 10 times greater than 60
Help me please i dont know what to write
Answer:
Decomposers in a food web are organisms that break down dead or decaying organisms and turn them into simpler, inorganic materials, making nutrients available for primary producers. A rotten fruit is not completely wasted because it will go back into the dirt for a producer to use, and the food chain continues.
Hope this helps!
What is (-9)+9 simplified
Answer:
the answer is zero
Step-by-step explanation:
-9+9=0
Unit rate for 150 students in 3 classes.
Answer:
Step-by-step explanation:
150 students/3 classes= 50 students per class