Answer:
0
Step-by-step explanation:
We find the determinant of a matrix by the method below. If we have a matrix:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
The determinant is [tex]ad-bc[/tex]
Now, using cramer's rule, we find x-value by the formula:
[tex]x=\frac{D_x}{D}[/tex]
Where D is the determinant of the original problem and [tex]D_x[/tex] is the determinant of the x-value matrix. How do we get those?
To get original matrix and thus D, we set up the matrix as the coefficients of x and y (s) of both the equations and to get matrix of x-value and thus [tex]D_x[/tex], we replace the x values of the matrix with the numbers in the right hand side of the 2 equations. We show this below:
To get D:
[tex]\left[\begin{array}{cc}3&4\\1&-6\end{array}\right] \\D=(3)(-6)-(1)(4)=-18-4=-22[/tex]
To get [tex]D_x[/tex]:
[tex]\left[\begin{array}{cc}12&4\\-18&-6\end{array}\right] \\D_x=(12)(-6)-(-18)(4)=0[/tex]
Putting into the formula, we get:
[tex]x=\frac{D_x}{D}=\frac{0}{-22}=0[/tex]
Thus, the value of x is 0
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.
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.
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]
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 )
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]
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
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
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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What is the range of the function f(x) = -(x + 3)2 + 7?
all real numbers less than or equal to 7
all real numbers greater than or equal to 7
all real numbers less than or equal to -3
all real numbers greater than or equal to -3
Answer:
It's A-all real numbers less than or equal to 7
Step-by-step explanation:
I just took the unit test and got a 100 on it!
The range of the function f(x) = -(x + 3)² + 7 is {y: y ∈ R, y ≤ 7}. So, option A is correct.
How to find the range of a function?Consider the given function as y = f(x)Solve for x ( isolate x from the equation)The domain of the obtained function is the range of the function f(x).Finding the range:Given that,
f(x) = -(x + 3)² + 7
⇒ y = -(x + 3)² + 7
⇒ (x + 3)² = 7 - y
⇒ (x + 3) = √(7 - y)
⇒ x = (√(7-y)) - 3
Thus, all the real values less than or equal to 7 for y define the function. So, the domain for the obtained function is {y: y ∈ R, y ≤ 7}.
Therefore, the range of the given function is {y: y ∈ R, y ≤ 7}.
Learn more about the range of a function here:
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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]
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:
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]
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]
A circle has a circumference of 28.36 units what is the diameter of the circle
Answer:
The diameter of circle d is 9.03
Step-by-step explanation:
Circumference of Circle = 28.36
We need to find the diameter of circle.
The formula used to find the circumference of circle is:
C = 2πr
we know that radius is half of diameter
so r = d/2
Putting value of r in above equation
C = 2π(d/2)
C = πd
The value of π is 3.14. finding value of d
28.36 = 3.14 * d
=> d = 28.36 / 3.14
d = 9.03
So, the diameter of circle d is 9.03
Answer:
The diameter is approximately 9 units
Step-by-step explanation:
Circumference is given by
C = pi *d
28.36 = pi *d
Let use 3.14 for pi
28.36 = 3.14 *d
Divide each side by 3.14
28.36 /3.14 = 3.14 d/3.14
9.031847134 = d
The diameter is approximately 9 units
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
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
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
The ratio (m-2c) : (m+c) is equivalent to 1 : k show that m= c(2k+1)/k-1
[tex]\bf m-2c~:~m+c~~=~~1:k\qquad \implies \cfrac{m-2c}{m+c}=\cfrac{1}{k}\implies k(m-2c)=m+c \\\\\\ mk-2kc=m+c\implies mk-m-2kc=c\implies mk-m=2kc+c \\\\\\ \stackrel{\textit{common factor}}{m(k-1)=c(2k+1)}\implies m=\cfrac{c(2k+1)}{k-1}[/tex]
kurt is buying a new cell phone. he knows that the more features the cell phone has, the more expensive it will be
Answer:the cost of the cell phone is a function of the number of features
Step-by-step explanation:
Because the cost depends on the features
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
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)
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.
If my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this? I need an equation...
Your question asks to make an equation with the information that was given.
Answer: y = -5x + 30In order to make an equation for your question. We would be making an equation with the formula: y = mx + b.
Formula: y = mx + b
m = change
x = amount of ice cream
b = starting value
We would need to gather the key information from the question.
Key information:
You have $30
Each ice cream cost $5
With the information above, we can make an equation for the question.
What we know is that you started with $30, so that means that 30 would be your b value (starting value).
Your equation should look like this:
y = mx + 30
Now, we know that each ice cream cost $5, but since we're paying for the ice cream, we would subtract that from our starting value. This means that our change would be -5, since we are taking away $5 each time we buy ice cream.
Your equation should look like this:
y = -5x + 30
The equation above would be the equation for your question.
We would do nothing to x but just leave it as is, since we don't know how many ice creams you're going to buy.
y = -5x + 30 should be your FINAL answer.
I hope this helps!Best regards, MasterInvestorAngles whose terminal sides lie on the x-or y-axis are _____.
a)reference angles
b)quadratic angles
c)quadrantal angles
d) terminal angles
Angles whose terminal sides lie on the x and y axis are Quadrantal angels.
Hope it helps.
Answer:
The correct answer option is c) quadrantal angles.
Step-by-step explanation:
When the terminal sides lie on the x axis or the y axis in the standard position, the angles are called as quadrantal angles.
For example when one of the sides lie on the x axis and one lies on the y axis, it makes an angle of 90 degrees which is a quadrantal angle (as shown in the picture attached).
I need help on this question
Answer:
6e^2f (3f^2-2e)
Step-by-step explanation:
18 e^2 f^3 - 12 e^3 f
18 e^2 f^3 = 2*3*3 ee fff
12 e^3 f = 2*2*3 eee f
The common terms are 2 *3*eef
Factor that out
2*3*eef (3ff - 2e)
Combine like terms
6e^2f (3f^2-2e)
1/6 + 2/3 tell me wat it is pls
Answer: 5/6
Step-by-step explanation:
2/3=4/6
1/6 + 4/6 = 5/6
Answer:
5/6
Step-by-step explanation:
you can rewrite 2/3 plus 1/6 as:
2/3+1/6
To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator. To convert 2/3 we need to multiply it by the appropriate form of 1. We can multiply by 1 because 1 times anything does not change the value:
(2/2⋅2/3)+1/6⇒2/2⋅2/3+1/6⇒4/6+1/6⇒5/6
«
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
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
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