Answer: THIRD OPTION.
Step-by-step explanation:
We need to remember that we can create a perfect square trinomial by squaring a binomial:
[tex](a\±b)^2=a^2\±2ab+b^2[/tex]
Then we need need to pick the coefficient of the x term of the given expression, divide it by 2 and square it:
[tex](\frac{3}{2})^2=\frac{9}{4}[/tex]
Therefore, the number that should be added to the given expression in order to create a perfect square trinomial is:
[tex]\frac{9}{4}[/tex]
A bank teller notices that an account was overdrawn and had a balance that can be represented by-324. The account holder then deposited 3 checks for $150 each and made 4 withdrawals of $20 each. The teller used the steps below to find the new balance for the account.
Step 1- start: -$324
Deposits: $150 each
Withdrawals: -$20 each
Step 2- -324+3(150)+4(-20)
Step 3- -324+450-80=46
Step 4- the account is overdrawn by $46
In which step did the teller make the first error?
Step 1
Step 2
Step 3
Step 4
Answer:
step 4 it not overdrawn any more it postive 46 not negtive
Step-by-step explanation:
Answer:
Step 4 : the account is overdrawn by $46
Step-by-step explanation:
Please see that when an account is in negative figure , we call it overdrawn. but when it is in positive figure we called is in credit.
Here we see from the calculation that the final balance available in the account of teller is $46, hence the account is having positive balance . hence it is not overdrawn.
So the mistake is in last step.
Which choice shows a function with a domain of {-4, -2, 2, 4}?
Answer:
Option C.
Step-by-step explanation:
Domain of any function is always represented by x - values when graphed.
Option A.
it has only one x value that is x = 2
Not correct.
Option B.
In this graph straight line doesn't intersect x - axis at x = -2 and -4.
So Not correct.
Option C.
If we see the x- values of the given set of coordinates, we find domain of the given function is { -4, -2, 2, 4}
Therefore, it's correct option.
Option D.
Given set with the coordinates shows domain set as {1, 0, 2, 6}
So it's not the answer.
Therefore, option C is correct.
Tom bought a soft drink for two dollars and five candy bars. He spent a total of $22. How much did each candy bar class?
Answer:
c = $5.00
Step-by-step explanation:
Let c = the cost of each candy bar
3 + 8c = 43
8c = 40
What is the tangent ratio for angle F?
HF (hypotenuse) = 13
FG (leg a) = 5
HG (leg b) = 12
Answer:
12/5
Step-by-step explanation:
tan(F) =opposite side to angle F over (Fraction Bar) adjacent side to angle F
[tex] \tan(F)=\frac{\text{ opposite side to angle F } }{ \text{ adjacent side to angle F} } [/tex]
The side that is opposite is the side that doesn't include F.
The side the is adjacent will include F (this is not the hypotenuse which is opposite the 90 degree angle).
So
[tex]\tan(F)=\frac{12}{5}[/tex]
Jonathan bought a new computer for $2,016, using the electronics store's finance
plan. He will pay $112 a month for 18 months. Which equation can Jonathan use to
find out how much money he still owes after each month of the plan?
Select one:
a. y = 2,016 - 112x
b. y = 2,016 + 112x
C. y = 112r
d. y = 1126 – 2,016
Answer:
a. 2016-112x
Step-by-step explanation:
because each month he need to pay $112 so it have to be multiplied to the number of month and then answer should be subtracted from 2016
The point (-2, 7) is reflected across the y-axis. What is the location of the image of the point?
Answer:I dontvknow
Step-by-step explanation:
«
In simplified form, V18 is _
Answer:
3V2
Step-by-step explanation:
V18
V9 times 2 equals 18
V3 to the second power because 3 times 3=9 so we get 3V2
Answer I need help this question because I don’t know what it is and I need help
Answer:
17
Step-by-step explanation:
QS and RS equal the same
5x - 8 = 3x + 2
-3x +8 -3x +8
2x = 10
x = 5 you would then plug x into QS
5(5) - 8
25 - 8
17
Answer:
17
YA
Step-by-step explanation:
Hi i need help with 15a(ii)
Answer:
x = 5/2
Step-by-step explanation:
log4(x^2+5x)-log8(x^3)=1/log3(4)
log(x^2 + 5 x) / log(4) - log(x^3) / log(8) = log(3) / log(4)
log(x (x+5))/log(4) - log(x^3) / log(8) = log(3) / log(4)
(3 log(x (x+5)) - 2 log(x^3)) / log(64) = log(3) / log(4)
3 log(x (x+5)) - 2 log(x^3) = 3 log(3)
log((3 x)/(x+5))=0
x=5/2
Answer:
5/2
Step-by-step explanation:
So first of all 1/log_3(4) can be written as log_4(3)...
So everything is base 4 except the log_8(x^3)...
We can play with this to get it so that the base is 4.
Let y=log_8(x^3) then 8^y=x^3
Rewrite 8 as 4^(3/2) so we have
4^(3/2 *y)=x^3
Now rewriting in log form gives: log_4(x^3)=3/2*y
Then solving that for y gives 2/3*log_4(x^3) or log_4(x^2)... let's put it back into the equation:
log_4(x^2+5x)-log_4(x^2)=log_4(3)
log_4((x^2+5x)/x^2)=log_4(3)
Set insides equal:
(x^2+5x)/x^2=3
Cross multiply:
x^2+5x=3x^2
Subtract 3x^2 on both sides:
-2x^2+5x=0
Factor
-x(2x-5)=0
So solutions are 0 and 5/2.
We have to verify these...
0 isn't going to work because we can't do log of 0
it makes x^2+5x 0 and x^3 0
The only solution is 5/2.
What is the difference of the complex number ms below (11-3i) - (4+5i)
Answer:
11-3i-4-5i
=11-4-3i-5i
=7-8i
Follow below steps:
The difference of the complex numbers (11-3i) and (4+5i) is computed by subtracting the real and imaginary parts separately. The real parts are 11 and 4, and their difference is 11 - 4 = 7. The imaginary parts are -3i and +5i, and their difference is -3i - 5i = -8i. Therefore, the difference of the two complex numbers is 7 - 8i.
Shining Star Preschool purchased a van for $38,000. Suppose MACRS allows vans to be depreciated fully in 6 years according to six fixed percents: 20% the first year, 32% the second year, 19.2% the third year, 11.52% the fourth and fifth years, and 5.76% the sixth year. What is the book value for the van at the end of the first year?
Answer:
The book value for the van at the end of first year will be $30400
Step-by-step explanation:
Cost of van = $38,000
Amount of depreciation after one year = 20%
Finding 20% of 38,000
=38,000 *(20/100)
= 7600
so, amount of van after 1 year = 38,000 - 7600
= 30400
So, the book value for the van at the end of first year will be $30400
The book value of the Shining Star Preschool's van at the end of the first year is $30,400, after depreciating 20% of its original cost of $38,000 using the MACRS method.
Using the Modified Accelerated Cost Recovery System (MACRS), the van is depreciated over 6 years with fixed percentages assigned to each year. The first year's depreciation is 20% of the purchase price.
To calculate the depreciation expense for the first year, we multiply the purchase price by the first year's depreciation rate:
Depreciation Expense (Year 1) = Purchase Price imes Depreciation Rate
Depreciation Expense (Year 1) = $38,000 imes 20%
Depreciation Expense (Year 1) = $7,600
Now, we subtract this depreciation expense from the purchase price to find the book value at the end of the first year:
Book Value (End of Year 1) = Purchase Price - Depreciation Expense (Year 1)
Book Value (End of Year 1) = $38,000 - $7,600
Book Value (End of Year 1) = $30,400
Therefore, the book value of the van at the end of the first year is $30,400.
Suppose U={1,2} is the universal set and T={2}. Then what is the complement of T
Answer:
T'={1}
Step-by-step explanation:
Definition:
Given a set T, the complement of T is the set of all elements in the universal set U, but not in T.
We can write T^c
You can also say complement of T in U
Complement of T( T')= U-T
where U={1,2} and T={2}
Now put the sets of U and T in the formula:
T'=U-T
T'={1,2}-{2}
T'{1}
Thus the Complement of T(T')={1}....
The complement of a set T in a universal set U is all the elements in U that are not in T. If U={1,2} and T={2}, the all the elements in U that are not in T corresponds to {1}. So, the complement of T is {1}.
Explanation:In the field of Mathematics, specifically in set theory, the complement of a set T in a universal set U is the set of all elements in U that are not in T. When we say complement of T, we are referring to the set of all outcomes in the universal set U that are NOT in T.
In this case, the universal set U={1,2}, and the event T={2}. Therefore, the complement of the set T in relation to U would be the set of all elements in U that are not in T. Hence, since 2 is in T, the only number left in U that is not in T is 1. So, the complement of T is {1}.
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If sin(x) = 0 and cos(x) = 1, what is tan(x)?
Answer:
tan(x) = 0
Step-by-step explanation:
We know that tan = sin /cos
tan (x) = sin(x)/ cos (x)
Substituting what we know, sin (x) =0 and cos(x) =1
= 0/1
=0
Answer:
Its tan(x) = 0 on Edge 2020.
Step-by-step explanation:
On jah.
What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]?
x f(x)
-6 2.5
-
22.5
02
20
A. 5
B. 25
c. 1
D.
0.5
Write an explicit formula for the sequence . Use this to find the 80th term of the sequence that begins -3 , 1 , 5 , 9
[tex]\bf -3~~,~~\stackrel{-3+4}{1}~~,~~\stackrel{1+4}{5}~~,~~\stackrel{5+4}{9}...\qquad \stackrel{\textit{common difference}}{d=4} \\\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common}\\ \qquad \textit{difference}\\ \cline{1-1} d=4\\ a_1=-3 \end{cases}\implies a_n=-3+(n-1)4 \\\\\\ a_n=-3+4n-4\implies a_n=4n-7[/tex]
Answer:
A n = 4n - 7
Step-by-step explanation:
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
For this case we must find the value of the variable "x" of the following expression:
[tex]2 (3x-1) \geq4x-6[/tex]
We apply distributive property to the terms within parentheses: [tex]6x-2 \geq4x-6[/tex]
We subtract 4x on both sides:
[tex]6x-4x-2 \geq-6\\2x-2 \geq-6[/tex]
We add 2 to both sides:
[tex]2x \geq-6 + 2\\2x \geq-4[/tex]
We divide between 2 on both sides:
[tex]x \geq \frac {-4} {2}\\x \geq-2[/tex]
Answer:
[tex]x \geq-2[/tex]
Answer: [tex]x\geq -2[/tex]
Step-by-step explanation:
Given the inequality [tex]2(3x - 1) \geq 4x -6[/tex] you need to solve for "x".
Apply Distributive property on the left side of the equation:
[tex]6x - 2 \geq 4x -6[/tex]
Now add 2 to both sides:
[tex]6x - 2+(2) \geq 4x -6+(2)[/tex]
[tex]6x \geq 4x -4[/tex]
The next step is to subtrac [tex]4x[/tex] from both sides:
[tex]6x-(4x) \geq 4x -4-(4x)[/tex]
[tex]2x \geq -4[/tex]
And finally, divide both sides by 2:
[tex]\frac{2x}{2}\geq \frac{-4}{2}\\\\x\geq -2[/tex]
Rationalize the denominator and simplify 15sqaure root 6 over 3sqaure root 5
[tex]\bf \cfrac{15\sqrt{6}}{3\sqrt{5}}\implies \cfrac{15\sqrt{6}}{3\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{15\sqrt{6}\cdot \sqrt{5}}{3(\sqrt{5})^2}\implies \cfrac{15\sqrt{6\cdot 5}}{3(5)} \\\\\\ \cfrac{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{30}}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \sqrt{30}[/tex]
Which is equivalent
Answer:
D
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
• [tex]a^{\frac{1}{2} }[/tex] ⇔ [tex]\sqrt{a}[/tex]
Hence
[tex]36^{-\frac{1}{2} }[/tex] = [tex]\frac{1}{36^{\frac{1}{2} } }[/tex] = [tex]\frac{1}{\sqrt{36} }[/tex] = [tex]\frac{1}{6}[/tex]
For this case we must find an expression equivalent to:
[tex]36 ^ {- \frac {1} {2}}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, rewriting the expression we have:
[tex]\frac {1} {36 ^ {\frac {1} {2}}}=[/tex]
By definition of power properties we have to:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]\frac {1} {\sqrt {36}} =\\\frac {1} {\sqrt {6 ^ 2}} =\\\frac {1} {6}[/tex]
Answer:
Option D
How many solutions does this system have?
Answer:
One Solution
(2, 1)
Step-by-step explanation:
We have the following system of equations
[tex]x+4y = 6\\y=2x-3[/tex]
To solve the system, substitute the second equation in the first equation and solve for the variable x
[tex]x+4(2x-3) = 6[/tex]
[tex]x+8x-12 = 6[/tex]
[tex]9x = 6+12[/tex]
[tex]9x = 18[/tex]
[tex]x = \frac{18}{9}[/tex]
[tex]x = 2[/tex]
Now substitute the value of x into any of the two equations and solve for the variable y.
[tex]y=2(2)-3[/tex]
[tex]y=4-3[/tex]
[tex]y=1[/tex]
Finally the system of equations has one solution
(2, 1)
Describe the relationship between the two quantities. Distance traveled by car; Amount of gas in the car.
The distance traveled by a car and the amount of gas used are directly proportional. The more distance covered, the more gas is consumed. This relationship can be quantified to make estimates for a specific car's fuel needs over given distances.
Explanation:The relationship between the distance traveled by a car and the amount of gas in the car is directly proportional, that is, the more distance the car travels, the more gas it consumes. This correlation can be quantified for a specific car and then used to estimate gas consumption for given distances based on the car's average speed.
For example, let's say that a 2014 Lamborghini Aventador Roadster travels from Philadelphia to Atlanta, covering a distance of about 1250 km, and uses 213 L of gasoline. This gives us a standard ratio of gas consumption against the distance. We could say that for every 1250 km traveled, the car would need about 213 L of gas. This is a simplified model as there are other variables at play such as traffic conditions, velocity, etc.
Gasoline powers the engine which provides the force needed to move and maintain the car's speed. As the path traced (distance) increases, more fuel is consumed. This relationship of distance traveled and fuel consumed can be defined as a directly proportional relationship.
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Which of the following is used to determine the sample space of a compound event?
counting principle
tree diagram
fair game
compound event
answer is #2
Answer:
tree diagram
Step-by-step explanation:
A tree diagram is an organizing tool used to determine the sample space of a compound event.
A compound event is an event that has more than one possible outcomes
5. What is the length of an arc that subtends a central angle of 75° in a circle whose radius is 5 inches?
Round off your answer to the nearest whole number.
A. 7
B. 4
C. 16
D. 21
Answer:
[tex]\boxed{\text{A. 7 in}}[/tex]
Step-by-step explanation:
The formula for the arc (s) of a circle is
[tex]s = r\theta \times \dfrac{\pi}{180^{^{\circ}}}[/tex]
where θ is measured in degrees.
Data:
r = 5 in
θ = 75°
Calculation:
[tex]s = \text{5 in} \times 75^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{7 in}\\\\\text{The length of the arc is }\boxed{\textbf{7 in}}[/tex]
Li believes that the graph shows a direct variation. Why is Li incorrect in saying that the graph shows a direct variation?
1) The graph does not have a constant rate of change.
2) When the x-value is 0, the y-value is 1.
3) The slope is negative.
4) The relationship is proportional.
Answer:
Option 2) When the x-value is 0, the y-value is 1.
Step-by-step explanation:
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Remember that in a direct variation
For x=0, the value of y is equal to zero too
therefore
The graph is not a direct variation , because
When the x-value is 0, the y-value is 1.
the graph of an equation with a negative discriminant always has what characteristic
Answer:
See below.
Step-by-step explanation:
The zeroes of the equation will not be real so the graph will not pass through the x-axis.
What is the complex number V-36 + 10?
Answer:
Step-by-step explanation:
Answer:
= 5.099 i
Step-by-step explanation:
The problem tells us to find the square root of -36 +10
√(-36 + 10)
= √(-26)
Which is an imaginary number
Lets remember that, √(-1) = i
= i*√(26)
= 5.099 i
Please see attached images for more information
Helppp please I’ll give 28 points
Answer:
54 cm^2
Step-by-step explanation:
The area of a right triangle is the easiest triangle for which you can find the area.
The area of any triangle is Base * height / 2
The base and height of a right triangle are always the two sides that are not the hypotenuse. In this case
base = 9
height = 12
Area = 9 * 12/2
Area = 54 square cm.
Answer: A
The center of a circle is at (−5, 2) and its radius is 7. What is the equation of the circle? (x−5)2+(y+2)2=14 (x+5)2+(y−2)2=49 (x+5)2+(y−2)2=14 (x−5)2+(y+2)2=49
The standard equation of a circle is in the form:
(x-a)^2 + (y-b)^2 = r^2
where; a is the x coordinate of the center, b is the y coordinate of the center, and r is the radius of the center.
In this case, a is -5, b is 2, and r is 7.
Therefore, the equation of this circle would be
(x+5)^2 + (y-2)^2 = 49
Answer:
Second option: [tex](x +5)^2 + (y -2)^2 =49[/tex]
Step-by-step explanation:
The center-radius form of the circle equation is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where "r" is the radius and the center is at the point [tex](h,k)[/tex]
Since the center of this circle is at the point [tex](-5, 2)[/tex], we can identify that:
[tex]h=-5\\k=2[/tex]
We know that the radius is 7, then:
[tex]r=7[/tex]
Now we must substitute these values into the equation [tex](x - h)^2 + (y - k)^2 = r^2[/tex] to find the equation of this circle.
This is:
[tex](x - (-5))^2 + (y - 2)^2 = (7)^2[/tex]
[tex](x +5)^2 + (y -2)^2 =49[/tex]
Fernando has $10 to buy snacks for his friends at the baseball game. A
package of peanuts costs $0.99 and a box of Cracker Jacks costs $1.79. This
relationship can be represented by the inequality 99p+179€ 10. Two of
Fernando's friends want Cracker Jacks. Which inequality represents how
many packages of peanuts he can buy?
Answer:
6
Step-by-step explanation:
I added 2 cracker jacks to get how much money he had left the kept subtracting. 99 from the money he had left
The coordinates of s are (5,4). What are the coordinates of s after the figure is rotated 90 about the origin
A point is written as ( h, k) when a point is rotated 90 degrees about the origin the new point becomes (-k,h)
s is located at (5,4) where h = 5 and k = 4
The rotated point would be located at (-4,5 )
If 80% of M is equal to 50% of N and N≠0, what is N M equal to?
Answer:
0.625N
Step-by-step explanation:
0.50N
0.80M = 0.50N, so M = ------------
0.80
and so:
0.50N
N*M = N*------------ = (5/8)N, or 0.625N
0.80