Answer:
13/48
Step-by-step explanation:
1 7/16 - 1 1/6
Make improper fraction
23/16 - 7/6
Common Denominator
69/48 - 56/48
Subtract
13/48
Hope that helped!!! k
Answer:
13/48
Step-by-step explanation:
1 7/16=1+7/16
1 1/6=1+1/6
So: 1 7/16 - 1 1/6=
1+7/16-(1+1/6)=
1+7/16-1-1/6=
7/16-1/6= (48 common denominator)
(7×3-8)/48=
(21-8)/48=
13/48
Write the equation of the line that is parallel to the line y=−14x−3 through the point (4,4). A. y=x+5 B. y=−14x+5 C. y=5x+1 D. y=5x−14
Answer:
None of the answers seem to be correct.
Step-by-step explanation:
The given equation is of the form y = mx + b where m is the slope and b is the y-intercept.
Here, m = -14
Two parallel lines have the same slope. So, the slope of the new line will be -14.
To calculate the y-intercept substitute x=4 and y=4 in the equation.
4 = (-14)(4) + b
Solving for b, we get b = 60.
So, the new equation will be y = -14x + 60
The equation of the line parallel to the given line is y =-14x+60, none of the given options is correct.
What is the equation of a straight line ?The equation of the straight line is given by y = mx +c , Where m is the slope of the line and c is the y-intercept.
The equation of the line is y = -14x -3
The slope of the line parallel to this will be the same as the given line.
m = -14 for both the lines
The line equation parallel to the given line is
y = -14x +c
The line passes through the points (4,4)
4 = -14 * 4 + c
c = 60
y = -14x +60
Therefore, the equation of the line parallel to the given line is y =-14x+60.
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Without using a calculator, convert the fraction to a decimal
Answer:
what's the fraction though?
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 | 20
3 | 10
5 | 0
7 | -10
A. Initial value: 20, rate of change: 10
B. Initial value: 30, rate of change: 10
C. Initial value: 25, rate of change: -5
D. Initial value: 20, rate of change: -10
Answer:
C, at 0/25, 1/20, 2/15, 3/10,...
Answer:
C
Step-by-step explanation:
Derivative of sin3x using first principle
[tex]\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}[/tex]
[tex]\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)[/tex]
The derivative of sin 3x using first principles is; 3cos(3x)
We want to find the derivative of sin 3x using first principles.
Step 1;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin3(x + h)) - sin(3x)}{h}[/tex]
Step 2; Expand the bracket to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin(3x + 3h)) - sin(3x)}{h}[/tex]
Step 3: According to trigonometric identities, we know that;
sin A - sin B = [tex]2cos\frac{A + B}{2} sin\frac{A - B}{2}[/tex]
Applying that to the answer in step 2 gives;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(3x + 3h + 3x)}{2}) sin\frac{(3x + 3h - 3x)}{2})}{h}[/tex]
Step 4; Simplify the brackets to obtain;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{h}[/tex]
Step 5; Rewrite the denominator to get;
f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{\frac{3h}{2}*\frac{2}{3}}[/tex]
Step 6; Input the limit of 0 for h to get;
f'(x) = [tex]\frac{2(cos\frac{(6x)}{2}) sin\frac{(0)}{2})}{\frac{0}{2}*\frac{2}{3}}[/tex]
⇒ f'(x) = [tex]\frac{2(cos3x)}{2/3} \frac{ 0}{{0}}[/tex]
0/0 = 1. Thus;
f'(x) = 3cos(3x)
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what are two ways of determining the distance between two points
Answer:
The linear distance between the two points is the square root of the sum of the squared values of the x-axis distance and the y-axis distance. To carry on the example: the distance between (3,2) and (7,8) is sqrt (52), or approximately 7.21 units.
Step-by-step explanation:
Answer:
Step-by-step explanation:
distance formula and pythagorean formula
2 divided by 3 + 2 divedes by 3 +3 divided by 3 =?
Answer:
1/5
Step-by-step explanation:
1/5
2/3+3/3+4/3
=2/5*3/6
= 1/5
I'm not sure.
Answer:
The answer should be 0.022
prove that (3-4sin^2)(1-3tan^2)=(3-tan^2)(4cos^2-3)
Answer:
Proof in the explanation.
Step-by-step explanation:
I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)
This means we want to show the following:
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].
After this I played with only the left hand side to get it to match the right hand side.
One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]
Distribute:
[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
Combine like terms and reorder left side to organize it based on right side:
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Combined like terms while keeping the same organization as the right:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]
Combine like terms:
[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]
Reorder again to fit right side:
[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]
This does match the other side.
The proof is done.
Note: Reordering was done by commutative property.
3 sides of the triangle are consecutive odd numbers. What is the smallest possible perimeter of the triangle ?
Answer:
8
Step-by-step explanation:
The there smallest consecutive odd numbers are 1,3 and 5
Therefore the smallest possible perimeter of such triangle = 8
i think the answer. . .is the second one please correct me if i'm wrong
Answer: You are correct, it is the second option.
Step-by-step explanation:
Volume of a cylinder formula is: pi*r^2*h. The diameter is 6 and the radius is half the diameter so we get r=3. The height is 10 inches, so h=10. pi(3)^2(10) is the volume of the vase.
Volume of a sphere (marbles) formula is: 4/3*pi*r^3
The marbles have a diameter of 3 so 3/2=1.5. r=1.5.
The volume of the marbles is 8(4/3*pi*1.5^3).
Then you subtract the volume of the marbles from the volume of the vase to find the volume of the water in the vase.
pi(3)^2(10) - 8(4/3pi(1.5)^3)
Hope this helps. :)
Answer:
You are absolutely correct, second option is the correct answer.
Step-by-step explanation:
Diameter of vase = 6 inches
Therefore, radius r = 3 inches
Diameter of marbles = 3 inches
Radius of marbles = 1. 5 inches
Height of water h = 10 inches
Volume of water in the vase = Volume of vase - 8 times the volume of one marble
[tex] = \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\
= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\[/tex]
A line passes through the point (4,8) and has a slope of -3/2
Write an equation in Ax+By=C
Answer:
The answer is
3x + 2y = 28Step-by-step explanation:
To find an equation of the line using a point and the slope we use the formula
y - y1 = m(x - x1)
where
m is the slope
(x1 , y1) is the point
From the question
slope = -3/2
Point = (4,8)
So the equation of the line is
[tex]y - 8 = - \frac{3}{2} (x - 4)[/tex]
Multiply through by 2
2y - 16 = -3( x - 4)
2y - 16 = - 3x + 12
3x + 2y = 16 + 12
We have the final answer as
3x + 2y = 28Hope this helps you
the sum of n and the sum of 8 and 6"
Answer:
Its 14
Step-by-step explanation:
8+6=14
Answer:
The answer is 16
08
+ 06
----------
16
Hope it helps ;)
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En una fábrica de automóviles que trabaja las 24 horas se arman diariamente 24
automóviles tipo Sedan, 16 camionetas tipo SUV, 12 camionetas tipo VAN, 8
Camionetas tipo Pick-up y 2 automóviles deportivos.
Cl costo de producción y el precio de venta de cada vehículo es el siguiente:
Costo de
Vehículo
Precio de
Producción Venta
SEDAN
SEDAN
DEPORTIVO
$140,000 $185.000
SUV
$250,000
$320,000
VAN
$310,000
$400,000
PICK-UP
PICK-UP
$210,000
$285,000
VAN
DEPORTIVO
$400,000
$550,000
SUV
Cada año transcurrido, posterior a su fabricación, el precio de venta de los
vehículos disminuye una octava parte de su valor.
a suponiendo que en un día se vendan los vehículos en igual cantidad de los
que se fabricaron, como podrías calcular la ganancia?
b
Si la fábrica trabajara solo 12 horas, existe una forma de calcular cuántos
vehiculos se fabrican, ¿cuantos se fabricaron en este lapso? Sustenta tu
respuesta
Answer:
a. La ganancia es de $ 4,060,000.00
b. 31 vehículos
Step-by-step explanation:
(a) Los parámetros dados son;
El número de automóviles tipo sedán fabricados = 24
El número de camiones tipo SUV fabricados = 16
El número de camiones tipo VAN fabricados = 12
El número de camionetas pick-up fabricadas = 8
El número de autos deportivos fabricados = 2
La ganancia por la venta de autos tipo sedán = $ 185,000 - $ 140,000 = $ 40,000
La ganancia por la venta de camionetas tipo SUV = $ 320,000 - $ 250,000 = $ 70,000
La ganancia por la venta de camiones tipo VAN = $ 400,000 - $ 310,000 = $ 90,000
La ganancia por la venta de las camionetas pick-up = $ 285,000 - $ 210,000 = $ 75,000
La ganancia por la venta de los autos deportivos = $ 550,000 - $ 400,000 = $ 150,000
La ganancia = 24 * $ 40 000 + 16 * $ 70 000 + 12 * $ 90 000 + 8 * $ 75 000 + 2 * $ 150 000 = $ 4060 000
(b) Por lo que hay una tasa de producción constante, solo la mitad de los automóviles se producirán dentro del período de 12 horas
Por lo tanto, tu fabricado
12 autos sedán, 8 camionetas tipo SUV, 6 camionetas tipo VAN, 4 camionetas pick-up y 1 auto deportivo para hacer un total de 31 vehículos.
If ABC is reflected across the y-axis, what are the coordinates of A? A> (4,-2)
Answer:
(4,2) is the answer on AP EX
The coordinate of the image of point A is (-4,-2)
What is Transformation?Transformation is the process of changing the graph to a new graph by Rotation, Reflection, Translation, and Dilation.
The coordinate of A is (4,-2)
When it is reflected across y axis, the coordinate (x,y) changes to ----> (-x,y)
So, the coordinates of A (4,-2) changes to (-4,-2)
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John needs $8,000 to buy a car. So far, he has saved $5,600. What percent of the price of the car has he saved
Answer:
70%
Step-by-step explanation:
So 5600/8000 is the fraction and 80 = 1% so 5600/80 will be your answer
Which expression gives the length of the transverse axis of the hyperbola
shown below?
X
У
Focus
Focus
O AY
O B. X-y
O c. xt
O D. X+ y
Answer:
Option (B)
Step-by-step explanation:
From the picture attached,
F1 and F2 are the focii of the hyperbola.
Point P(x, y) is x units distant from F1 and y units distant from the other focus F2.
By the definition of a hyperbola,
"Difference between the distances of a point from the focii is always constant and equals to the measure of transverse axis."
Difference in the distances of point P from focii F1 and F2 = (x - y) units
This distance is equal to the length of the transverse axis = (x - y) units
Therefore, Option (B) will be the answer.
Answer:
x-y
Step-by-step explanation:
Which point on the number line best represents√57?
Answer:
8.
Step-by-step explanation:
[tex]\sqrt{57} =\sqrt{3 * 19}[/tex]
Since this cannot be further simplified, we will calculate the square root of 57 with our calculators.
We find that the square root of 57 is 7.549834435, and since the tenths place is a 5, we will round up to the next whole number. So, the point on the number line that best represents the square root of 57 is 8.
Hope this helps!
how many are 1 raised to 5 ???
Answer: 1.
Step-by-step explanation: 1^5 is really just 1, 5 times.
1*1*1*1*=1
Which property justifies the following equation? 7[6+5+(-6)] = [6+(-6)+5] A.distributive B.commutative C.associative D.identity
4 > - 4404 true or false
Answer:
True
Step-by-step explanation:
-4404 is always smaller than 4Answer:
true as positive are bigger than negetive
Step-by-step explanation:
If x = -12, y = -3; find xy² ?
Find the value of xy².
Solution:-xy²
★ Substituting the values of x and y ,we get :
⇒ -12 × ( -3 )²
⇒ -12 × 9
⇒ -108
Given the equation −2x − 13 = 8x + 7, which order of operations completely solves for x? (1 point) Add 2x, then subtract 8x, lastly subtract 7 Add 2x, then add 13, lastly divide by 10 Subtract 8x, then add 13, lastly divide by −10 Subtract 8x, then add 2, lastly add 13
Step-by-step explanation:
We have given an equation −2x − 13 = 8x + 7
We need to find the operations that is used to find the value of x. It can be done by the following ways.
Subtract 8x on both the sides of the equation
−2x − 13 -8x= 8x + 7 -8x
-10x-13 = 7
Add 13 on both the sides of the equation,
-10x-13+13 = 7+13
-10x=21
Divide by -10 on both sides
[tex]x=\dfrac{-20}{10}\\\\x=-2[/tex]
Hence, the correct option is "Subtract 8x, then add 13, lastly divide by −10"
A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of the athletes are football players, 25% are basketball players, and 24% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer: 0.29 or 29%
Step-by-step explanation:
Given :
Probability that the athletes are football players : P(football ) = 0.28
Probability that the athletes are basketball players : P(basketball) = 0.25
Probability that the athletes play both football and basketball: P( both football and basketball ) = 0.24
Now, using formula
P(either football or basketball)= P(football )+ P(basketball+ P( both football and basketball )
⇒P(either football or basketball)= 0.28+0.25-0.24 = 0.29
Hence, the probability that they are either a football player or a basketball player = 0.29 .
What is the value of $a$ if the lines $2y - 2a = 6x$ and $y + 1 = (a + 6)x$ are parallel?
Answer:
a=-3
Step-by-step explanation:
Which property is shown in the matrix addition below?
5
-1
0
5
-7
0.4
0
-7
0
0.4
+
+
+
6.2
-8.5
-9.9
6.2
-9.9
-8.5
12
0
2
12
0
2
inverse property
identity property
commutative property
associative property
Help please!
Answer:
associative property
The solution is, property is shown in the matrix addition below is
associative property.
Here, we have,
The property shown in the given matrix addition is associative property.
Let's define associative property first,
The Associative Property of Addition for Matrices states :
Let A , B and C be m×n matrices .
Then, (A+B)+C=A+(B+C) .
Associative Law of Addition of Matrix:
Matrix addition is associative. This says that, if A, B and C are Three matrices of the same order such that the matrices B + C, A + (B + C), A + B, (A + B) + C are defined then A + (B + C) = (A + B) + C.
Since P and Q are of the same order and pij = qij then, P = Q.
Here, from the given information,
we get, A , B and C be 4×1 matrices,
and, (A+B)+C=A+(B+C)
So, The solution is, property is shown in the matrix addition below is
associative property.
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What is equivalent to 9 3/4?
The answer is supposedly is 3 square root 3, but how is that the answer? can someone tell me the steps?
9 3/4 is a mixed fraction.
3√3 is not equivalent to 9³/₄
3√3 is equivalent to [tex]9^\frac34[/tex]
step-by-step:
[tex]9^\frac34=(3^2)^\frac34=3^{2\cdot\frac34}=3^{\frac32}=3^{1+\frac12}=3^1\cdot3^\frac12=3\cdot\sqrt3=3\sqrt3[/tex]
The simplest form of the number [tex]9^\frac{3}{4}[/tex] is [tex]3 \ \sqrt[]{3}[/tex].
It is given that the [tex]9^\frac{3}{4}[/tex]
It is required to find the simplest value of [tex]9^\frac{3}{4}[/tex]
What is the square root of a number?It is defined as the number if we multiply the number by itself we get the original number it is a non-negative number.
We have:
= [tex]9^\frac{3}{4}[/tex]
We can write the above number as below:
[tex]= (3^2)^\frac{3}{4}[/tex]
By the property of powers:
[tex]\rm (x^a)^b= x^a^\times ^b[/tex] , we get:
[tex]3^2^\times^\frac{3}{4} \\\\\\3^\frac{3}{2} \\\\\sqrt{3^3} \\\\\sqrt{3}\times \sqrt{3}\times\sqrt{3}\\\\3\sqrt{3}[/tex]
Thus, the simplest form of the number [tex]9^\frac{3}{4}[/tex] is [tex]3 \ \sqrt[]{3}[/tex].
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Please answer this IQ maths question and tell method please
1) if 32 and 43 makes 35 , then 76 and 15 makes ______?
a)69 (b) 92 (c) 94 (d) 78
2)(3,6,11) and (13, 10,7) then (15,?,3) find the missing one
Answer:
3
3+3=6
3+3+5=11
13
13-3=10
10-3=7
15
15-7=8
8-5=3
32+43=75
75-40(highest ten)=35
76+15=91
91-70=21
What is a21 of the arithmetic sequence for which a7=−19 and a10=−28? A. -35 B. 35 C. -58 D. -61
Answer:
a21 = -61
Step-by-step explanation:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
[tex]-19=a_{1}+(7-1)d[/tex]
[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)
9 = -3d
d = -3
-19 = a₁ + (6)(-3)
-1 = a
a21 = -1 + (21 - 1)(-3)
= -61
Answer:
-61 (Answer D)
Step-by-step explanation:
The general formula for an arithmetic sequence with common difference d and first term a(1) is
a(n) = a(1) + d(n - 1)
Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19
and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28
Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d. We substitute this result for a(1) in the second equation:
-19 - 6d + 9d = -28. Grouping like terms together, we get:
3d = -9, and so d = -3.
Going back to an earlier result: a(1) = -19 - 6d.
Here, a(1) = -19 - 6(-3), or a(1) = -1.
Then the formula specifically for this case is a(n) = -1 - 3(n - 1)
and so a(21) = -1 - 3(20) = -61 (Answer D)
The number 7 is a factor of
Answer:
itself and numbers divisible by 7
Select the correct answer.
Which phrase best describes taxable income?
A.
all income and wages received from working
B.
all income received
C.
adjusted gross income minus any allowable tax credits
D.
adjusted gross income minus any allowable tax deductions
E.
income from sources other than wages, such as interest and dividends
Answer:A
Step-by-step explanation:
The phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.
What is adjusted gross income ?"Adjusted gross income, or AGI, is your gross income minus certain adjustments. The IRS uses this number as a basis for calculating your taxable income. AGI can also determine which deductions and credits you may qualify for."
Since, Taxable income is the portion of your gross income used to calculate how much tax you owe in a given tax year.
It can be described broadly as adjusted gross income (AGI) minus allowable itemized or standard deductions.
Taxable income includes wages, salaries, bonuses, and tips, as well as investment income and various types of unearned income.
Hence, the phrase can be described broadly as adjusted gross income (AGI) minus allowable tax deductions.
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How many three-digit positive integers [tex]x[/tex] satisfy [tex]3874x+481\equiv 1205 \pmod{23}[/tex]
Answer:
40
Step-by-step explanation:
Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.
As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.
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The equation reduces, mod 23, to ...
10x = 11
Its solutions are x = 23n +8.
