Answers
[tex] {x}^{2} - 4 = 0 \\ {x}^{2} = + 4 \\ x = \sqrt{4} = 2[/tex]
2 it's not true
[tex] {x}^{2} = - 4 [/tex]
3 it's not true
[tex]3 {x}^{2} + 12 = 0 \\ 3 {x}^{2} = - 12 \\ {x}^{2} = \frac{ - 12}{3} = - 4 \\ [/tex]
4 it's true
[tex]4 {x}^{2} = 16 \\ {x}^{2} = \frac{16}{4} = 4 \\ x = \sqrt{4} = 2[/tex]
5- it's true
[tex] {2(x - 2)}^{2} = 0 \\ {(x - 2)}^{2} = 0 \\ x - 2 = 0 \\ x = 2[/tex]
Answer:
A. [tex]x^2-4=0[/tex]
D. [tex]4x^2=16[/tex]
Step-by-step explanation:
To check which of the given equations have solution [tex]x=-2\text{ and }x=2[/tex], we will solve our given equations one by one.
A. [tex]x^2-4=0[/tex]
[tex]x^2-4+4=0+4[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option A is the correct choice.
B. [tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option B is not a correct choice.
C. [tex]3x^2+12=0[/tex]
[tex]3x^2=-12[/tex]
[tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option C is not a correct choice.
D. [tex]4x^2=16[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option D is the correct choice.
E. [tex]2(x-2)^2=0[/tex]
[tex](x-2)^2=0[/tex]
[tex]\sqrt{(x-2)^2}=\sqrt{0}[/tex]
[tex]x-2=0[/tex]
[tex]x=2[/tex]
Therefore, option E is not a correct choice.
Related Questions
Will Give 100 points and brainliest!
An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer. (5 points) Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer. (5 points)
Answers
Part B: Rectangle cross-section
The Part A cross section will be rectangle and Part B cross section will be triangle .
What is rectangular pyramid ?A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apx. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid.
According to the question
Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base.
When we cut a cross section parallel to base of the rectangular pyramid which have rectangular base
The cross section will always be a rectangle.
Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex .
When we cut a cross section perpendicular to the base, passing through the top vertex of the rectangular pyramid
The cross section will always be a Triangle.
As the lateral face of a rectangular pyramid is a triangle, so a cross section that passes through the top vertex and the base is also a triangle.
Hence , The Part A cross section will be rectangle and Part B cross section will be triangle .
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!!!!!GIVING BRAINLIEST!!!!!
Select the graph for the solution of the open sentence. Click until the correct graph appears. 3|x| > 6
Answers
Your equation has only one variable, so a graph on the number line is appropriate. It would extend outward from ±2, where the points would be indicated by open circles.
Answer:
Given equation,
3|x| > 6 -----(1)
∵ [tex]\frac{1}{3}>0[/tex]
Thus, multiplying both sides of inequality (1) by [tex]\frac{1}{3}[/tex]
We get,
[tex]|x| > 2[/tex]
⇒ 2 < x or 2 < - x
⇒ 2 < x or -2 > x (when a > b where a > 0, b > 0, If c < 0 ⇒ ac < bc),
⇒ (2, ∞ ) ∪ (-∞, -2)
By plotting the above interval in the number line we can get the graph of the given equation ( shown below )
Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26
Answers
meaning 26 is less than 54 which is true
True: If it is a function
False: If it is not a function
{(2, 3), (4, 5), (4, 3), (3, 4)}
Answers
Explanation:
The given relation does not fit the definition of function.
A function is a relationship that states unambigously the image (output) of the input (independent) variable.
In the set of ordered pairs it is true form the input-values 2, and 3, because their images are 3 and 4, respectively.
But, could you tell the image of 4?. It may be 5 or 3. That is an ambiguity. That is why the given relationship is not a function.
This means if more than one ordered pairs will have the same first component, the relation will not be a function.
In the given relation, the first component of 2nd and 3rd ordered pair is the same, so the relation {(2, 3), (4, 5), (4, 3), (3, 4)} is not a function.
So the Answer is False.
D^2+d-30/d^2+3d-40 + d^2+14d+48/d^2-2d-48
A. D^2+14d+16/(d+8)(d-8)
B. 2d^2+14d+16/(d+8)(d-8)
C.2d^2+15d+18/2d^2+d-88
D.2d^2+15d+18/(d+8)(d-8)
Answers
2d^2 + 14d + 16
----------------------------
(d+8)(d-8)
Explanation:
The question is:
[tex] \frac{d^2+d-30}{d^2+3d-40} + \frac{d^2+14d+48}{d^2-2d-48} [/tex]
1) Start factoring all the polynomials to rewrite the fractions.
2) d^2 + d - 30 = (d + 6)(d - 6)
3) d^2 + 3d - 40 = (d + 8)(d - 5)
4) d^2 + 14d + 48 = (d + 6) (d + 8)
5) d^2 - 2d - 48 = (d - 8)(d + 6)
6) rewrite the fractions:
(d+6)(d-5) (d+8)(d+6)
----------------- + -----------------
(d+8)(d-5) (d-8)(d+6)
7) simplify the fractions cancelling the factors that are equal in the numerator and the denominator:
d+6 d+8
-------- + -------
d+8 d-8
8) take least common denominatior: (d+8)(d-8), and sum the fractions:
(d-8)(d+6) + (d+8)^2
--------------------------------
(d+8)(d-8)
9) expand the parenthesis in the numerator and combine like terms:
d^2 - 2d - 48 + d^2 + 16d + 64
------------------------------------------- =
(d+8)(d-8)
2d^2 + 14d + 16
= ----------------------------
(d+8)(d-8)
And that is the option B.
What is the correct data set for the box & whisker plot shown above??
Answers
Answer: It’s A.
Step-by-step explanation:
for a p e x
A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.
Answers
Cost for spending 5 min is $4, any additional minutes will be $0.75 per minutes.
amount of cash Nick will remain with after spending $4 will be:
10-4=$6
the total extra minutes he will spend will be:
6=0.75*m
0.75m=6
thus
m=6/0.75
m=8 min
the total number of minutes that Nick will spend with $10 will be:
8+5=13 min
Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.
Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:
Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)
First, subtract the initial charge from the total amount Nick has:
$10 - $4 = $6
This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:
$6 / $0.75 per minute = 8 minutes
Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.
What are two items that weigh less than 1 oz
Answers
An ounce is about the weight of 11 pennies. So anything that weighs less than about 11 pennies would weigh less than 1 oz.
You could have a piece of paper, blade of grass, a pill, a quarter, etc.
I hope this helps!
MrEquation
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Answers
Choice A
Answer:
its a ik it
Step-by-step explanation:
what is the variable in this algebraic expression 8+6, 4d-2, 7r-15=6, 11+14=25
Answers
For this case we have that by definition, a variable is a symbol that can be replaced or that takes a numerical value in an equation or expression, mathematical in general.
Then we have the following options:
A) [tex]8 + 6[/tex]
It is a sum of two real numbers. There are no variables.
B)[tex]4d-2[/tex]
In this case the variable is "d"
C) [tex]7r-15 = 6[/tex]
In this equation, the variable is represented by "r"
D) [tex]11 + 14 = 25[/tex]
It is a sum of two real numbers. There are no variables.
Answer:
A) There are no variables
B) "d"
C) "r"
D) There are no variables
A rectangular window is 1 meter high and 2 meters wide. What is the perimeter of the window in meters? What is it in centimeters?
Answers
It is 1 meter + 1 meter + 2 meter + 2 meter = 6 meters
1 meter = 100 centimeter
6(100) = 600 centimeter
Hope this helps! :)
What is the circumference of a circle with a radius of 5.4 inches? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. in.
Answers
Answer:
33.9
Step-by-step explanation
I got 100% on my test and just wanted everyone to know that it is correct.
check all that apply
Answers
Answer:
A, D, E
Step-by-step explanation:
Squaring both sides of the inequality, we get
x < 25 . . . . . with the restriction x ≥ 0
The listed numbers that are in the range [0, 25) are 1, 18, 24.
library library currently has 125 audiobook the library plan purchase the same number of books each month after 4 months the library has 20 more audiobook which equation can be used to determine t and a total number of audio books the library will have after and months
Answers
what's a Fibonacci sequence?
Answers
A Fibonacci Sequence is a series of number . It is the sum of two preceding numbers.
Hope this helps <33
simplest sequence is 1,1,2,3,5,8 and so on
Martin put 8 pounds of grapes into a bowl. Four friends each took 2/3 pounds from the bowl. What fraction represents the total amount of grapes removed from the bowl ?
Answers
[tex]\sf 4\times\dfrac{2}{3}=\dfrac{8}{3}[/tex]
We can convert this improper fraction to a mixed number. Three goes into eight two times. 3 * 2 = 6. 8 - 6 = 2. So we have 2 and two thirds leftover, or:
[tex]\sf 2\dfrac{2}{3}[/tex]
So the total amount of grapes that was removed from the bowl is [tex]\sf\dfrac{8}{3}[/tex] or [tex]\sf 2\dfrac{2}{3}[/tex] pounds.
Answer:
-8/3
Step-by-step explanation:
i took the test on edg
You want to have $31,664 in cash to buy a car in 4 years. you expect to earn 11.5% per year on your savings. how much do you need to deposit today if this is the only money you save for this purpose?
Answers
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
We have,
To determine how much you need to deposit today, we can use the concept of present value (PV).
The present value represents the current value of a future cash flow, accounting for the time value of money and the expected interest rate.
In this case, you want to have $31,664 in cash in 4 years, and you expect to earn an annual interest rate of 11.5%.
Let's calculate the present value using the following formula:
[tex]PV = FV / (1 + r)^n[/tex]
where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
Plugging in the values, we have:
[tex]PV = $31,664 / (1 + 0.115)^4[/tex]
Calculating this equation, we find:
[tex]PV = $31,664 / (1.115)^4[/tex]
= $31,664 / 1.530749
PV ≈ $20,701.27
Therefore,
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
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The sum of 5 consecutive even numbers is 200 what is the fifth term in the sequence
Answers
if to write the given sequence as n;n+2;n+4;n+6;n+8, then it is possible to write its sum:
n+n+2+n+4+n+6+n+8=200.
5n=180; n=36.
n=36 it means that the 1st number is 36. The 5th number is n+8=36+8=44.
all the even numbers are: 36;38;40;42;44.
answer: 44.
each picnic table seats 6 people how many picnic tables are needed to seat 24 people?
Answers
Final answer:
To seat 24 people at picnic tables that each seat 6, you divide 24 by 6, which equals 4 tables needed.
Explanation:
The question is asking how many picnic tables are needed to seat 24 people, if each table seats 6 people. This is a division problem where we need to divide the total number of people by the number of seats at a single table. You divide 24 (the total number of people) by 6 (the number of seats at one table) to find out the number of tables needed.
Here is the calculation: 24 \/ 6 = 4. Therefore, you would need 4 picnic tables to seat 24 people, assuming each person takes one seat and that there are no empty seats.
Eliminate the parameter. x = one divided by two t, y = 3t^3 - 1
Answers
Answer:
y = 24x3 - 1
Step-by-step explanation:
None needed YW
I need this equation solved with the work shown please
Answers
SO THE ANSWER IS 2 1/2
Which are the solutions of x2 = –5x + 8?
Answers
hope this helps
Answer:
The solutions are 1.275 and -6.275
Step-by-step explanation:
Given
x^2 = –5x + 8
First, put all terms in the left side of the equal sign, as follows:
x^2 + 5x - 8 = 0
Then, use the quadratic formula with a = 1 (the coefficient of the quadratic term), b = 5 (the coefficient of the linear term) and c = -8 (the independent term).
[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-8)}}{2(1)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + 7.55}{2}[/tex]
[tex]x_1 = 1.275[/tex]
[tex]x_2 = \frac{-5 - \sqrt{57}}{2}[/tex]
[tex]x_2 = \frac{-5 - 7.55}{2}[/tex]
[tex]x_2 = -6.275 [/tex]
Find the coefficient of x 4 in the taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x 2 ).
Answers
Note, that it is the full solution, it is possible to make it shorter.
The coefficient of x4 in the Taylor series expansion of the given function is 0.
Explanation:To find the coefficient of x4 in the Taylor series expansion of the function f(x) = 8 ln(9 + 3x2), we need to compute the fourth derivative of f(x) and evaluate it at x = 0.
The Taylor series expansion for a function centered at the origin is given by:
f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + f''''(0)x4/4! + ...
In this case, we have:
f'''(x) = 48x/(9 + 3x2)
Evaluating f'''(x) at x = 0 gives:
f'''(0) = 0/9 = 0
Therefore, the coefficient of x4 in the Taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x2) is 0.
thank youuuuuuuuuuuuuu
Answers
14)
[tex]\bf (x+3)+(2x+4)+(y)=\stackrel{perimeter}{6x}\implies 3x+7+y=6x \\\\\\ 7+y=3x\implies y=3x-1[/tex]
15)
a rectangle has twin widths and twin lengths, therefore
[tex]\bf \stackrel{width}{(3x-3)}+\stackrel{width}{(3x-3)}+\stackrel{length}{(y)}+\stackrel{length}{(y)}=\stackrel{perimeter}{10x+6} \\\\\\ 6x-6+2y=10x+6\implies -6+2y=4x+6\implies 2y=4x+12 \\\\\\ y=\cfrac{4x+12}{2}\implies y=\cfrac{4x}{2}+\cfrac{12}{2}\implies y=2x+6[/tex]
A segment has endpoints at (3,−4) and (3,−17) How many units long is the segment?
Answers
Answer:
what the other person said
Step-by-step explanation:
how do you reduce 4/8?
Answers
so you get 2/4 which is equal to 1/2 which is your answer!!
Hope this helps!!
Which expression is equivalent to (2mn)^4/6m^-4n^-2? Assume m=/0 n=/0.
Answers
EXPLANATION
(2mn)^4/6m^-4n^-2
⇒(2mn)⁴/6m⁻⁴n⁻²
= 2⁴ · m⁴ · n⁴ / 6 · m⁻⁴ · n⁻²
= [tex] \frac{2 ^{4} }{6} [/tex] · m⁴⁻⁽⁻⁴⁾ · n⁴⁻⁽⁻²⁾
= [tex] \frac{16}{6} [/tex] · m⁴⁺⁴ · n⁴⁺²
= [tex] \frac{8}{3} [/tex] · m⁸ · n⁶
= 8m⁸ n⁶/3
Same as (8m^8n^6)/3
In a normal distribution, most numbers in the data set fall within one standard deviation of the mean. True or False
Answers
Answer:
True
Step-by-step explanation:
The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.
Answers
Let
P1-------------> Perimeter of parallelogram ABCD
P2-------------> Perimeter of △ABD
we know that
P1=10 cm
P1=2*(AD)+2*(AB)=10------------> AB+AD=5-----------> equation 1
and
P2=AD+AB+DB
P2=8 cm------------>AD+AB+DB=8-------- AB+AD=8-DB-----> equation 2
I substitute 1 in 2
(5)=8-DB----------> DB=8-5-----------> DB=3 cm
the answer is DB=3 cm
The length of the diagonal BD is 3 centimeters.
Procedure - Length determination in a parallelogram sideA parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).
Expressions for the parallelogramPerimeter equations for the parallelogram are the following:
[tex]AB + BD + AD = 8\,cm[/tex] (1)
[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)
Where:
[tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters. [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.Resolution of the systemBy (2) we have the following conclusion:
[tex]AB + AD = 5\,cm[/tex]
And we find the length of the diagonal BD by (1):
[tex]5\,cm + BD = 8\,cm[/tex]
[tex]BD = 3\,cm[/tex]
The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]
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How many positive integers between 100 and 999 inclusive are divisible by three or four?
Answers
There are 900 numbers between 100 and 999 (inclusive)
We group the numbers into groups of 3s. So we find one number divisible by 3 in every group.
Number of numbers that can be divided by 3 = 900 ÷ 3 = 300
Number of numbers that can be divided by 3 = 300
We group the numbers into groups of 4s. So we find one number divisible by 4 in every group.
Number of numbers that can divided by 4 = 900 ÷ 4 = 225
Number of numbers that can divided by 4 = 225
Among the group of 4s, there is 1/3 that are already inclusive in divisible by 3.
225 ÷ 3 = 75
Number of numbers that can divided by 4 = 225 - 75 = 150
Total numbers of positive integers divisible by three and fours = 300 + 150 = 450
The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.
Explanation:The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]
In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]
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