Carla earned $27,500 during the year, while William attended law school full-time for 9 months and earned no income. They would not get dependent child care credit.
Credit for dependent care:
A married couple or single person who cares for his or her own or dependent child can earn this dependent care credit.
'The dependent tax credit is non-refundable.
* General credit qualifications.
- Employment-related care cost is required for a
= dependent under the age of 13 or
A dependent or spouse who lives with the taxpayer for more than half the year and is physically or mentally incapacited.
* amount of credit.
* applicable percentage - eligible care cost
- the appropriate percentage ranging from 20% to 35% depending on AGI
If your income is less than $15,000, the rate will be 35%. Income above $15,000 will decrease by 1% for every 2000.
* To get credit, married taxpayers must file a joint return.
*the cost of eligible care has been defined.
- costs for qualified individual care within the taxpayer's homr or outsider's home.
= if outside the home, the dependent or spouse must spend at least 8 hours per day within the taxpayer's home.
= unless the relative is a child under the age of 19, child care payments to a relative are eligible for the credit.
- The amount of costs that qualify is the lower of the actual cost or 3000 for one qualified individual and 6000 for two or more qualified individuals.
* Limitation on earned income.
- The amount of eligible care costs may not exceed the lower of the taxpayer's or spouse's earned income.
- Full-time students, disabled taxpayers, and spouses are deemed to have earned income up to the monthly limits of $250 for one child and $500 for two.
William and carla submit a combined tax return.
Carla earned $27,500 last year.
William attended law school full time for 9 months without earning any money.
They paid $3,500 for carl, their 3 year old child.
William and Carla are ineligible for dependent care credit. Because they should both have employment income.
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The graphs of lines k1 and k2 are shown on the grid. Which system of equations is best represented by this graph?
F. 3x-y=2
4x+9y=36
G. 3x-y=6
4x+9y=4
H. x-3y=-18
9x+4y=9
J. x+y=10
9x+4y=13
3x-y=2 and 4x+9y=36 make up the graph equation in option F. next we receive [tex]x=\frac{2+y}{3}$$[/tex] and [tex]x=\frac{36-9 y}{4}$$[/tex] .
Which is then graph equation ?solve for [tex]$x, 3 x-y=2 \quad: \quad x=\frac{2+y}{3}$[/tex]
Steps
3 x-y=2
Turn y to the right.
3 x=2+y
Divide both sides by 3
[tex]\frac{3 x}{3}=\frac{2}{3}+\frac{y}{3}$$[/tex]
Simplify
[tex]x=\frac{2+y}{3}$$[/tex]
solve for x, 4 x+9 y=36: x=[tex]\frac{36-9 y}{4}[/tex]
Steps
4 x+9 y=36
Turn 9 y to the right.
4 x=36-9 y
By dividing both sides by 4,
[tex]\frac{4 x}{4}=\frac{36}{4}-\frac{9 y}{4}$$[/tex]
Simplify
[tex]x=\frac{36-9 y}{4}$$[/tex]
Therefore the correct answer is option F ) 3x-y=2 , 4x+9y=36 .
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A small college has 800 students, 10%, percent of which are left-handed. Suppose they take an SRS of 30 students. Let X= equals the number of left-handed students in the sample.
What is the probability that less than 7 of the 30 students are left-handed?
.
The probability that less than 7 of the 30 students are left-handed is given as follows:
0.9742 = 97.42%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 30, p = 0.1.
The probability that less than 7 of the 30 students are left-handed is given as follows:
P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
Using a binomial distribution calculator with the parameter, finding each of the probabilities and adding them, we have that:
P(X < 7) = 0.9742 = 97.42%.
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Use the distributive property to fill in the blanks below.
(3 x 5) + (3 x 2) = 3 × (_ + _)
Answer:
3 x (5 + 2)
Step-by-step explanation:
Just use the distributive property, it's very simple.
equation of the line that is parallel to x-3y=9 and passes through the point (-10,9)
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}[/tex]
i need help please and thanks
An isosceles triangle has two sides of equal
length. The third side is 5 less than twice the
length of one of the other sides. If the
perimeter of
the triangle is 23 cm, what is the length of the third
side?
Explain how you would define a variable for this
problem.
The required length of of the third side of isosceles triangle is 9 units.
Explain about isosceles triangle.An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.
According to question:Let the length of Equal two sides is x.
Third side = 2x - 5
Then, perimeter is 23 cm
x + x + 2x - 5 = 23
4x - 5 = 23
4x = 28
x = 7
Then, third side is 2x - 5
= 2(7) - 5
= 14 - 5
= 9 units
Thus, required length of third side is 9 units.
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a person weighing 180 pounds stands on snowshoes if the total area of the 2 snowshoes is 900 square inches, what is the total pressure on the snow
The pressure on the snow on the boy is P=1379.83 N.
A person weighing 180 pounds stands on snowshoes.
If the total area of the 2 snowshoes is 900 square inches
The mass of person on the snowshoes is given by,
m=180 pounds=180×0.454=81.6455≅81.65 kg
Force acting on a body due to gravity is given by, f = mg
Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body.The weight force of the person is given by,
W=F=mg=81.65×9.81=800.99N.The area of the snowshoes is given by,
⇒A=900 square inches
⇒1inch=0.025 m
Thus, Area in [tex]m^{2}[/tex] given by A=900×[tex]0.0254^{2}[/tex]
=900×0.000645
=0.5805[tex]m^{2}[/tex]
The expression of the pressure in the fluid containing tube is given by FA
; where F is the force exerted by the liquid and A is the area of the tube.
From the expression of pressure, the resulting pressure value is given by FA.
=800.900.5805
=19.82≈19.8pa
The pressure on the snow on the boy is =1379.83 N.
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25 POINTS!! ... Guessers shall be reported!
Q: Write a set of all natural numbers which divide 24 in tabular and set-builder form.
Set of all natural numbers which divide 24 in tabular form {1,2,3,4,6,8,12,24} and set-builder form is {x ∈ ℕ | x ∣ 24} ℕ denotes the set of natural numbers and x ∣ 24 means x divides 24.
What do math natural numbers mean?Normative Data We utilize the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 to count or arrange objects in a particular order. Complete numbers are those that fall between the zero and artificial number range. not a decimal or fraction.
Integers make up all natural numbers, right?Decimal numbers and fractions are not integers. Although all natural whole and numbers are integers (as well as all whole numbers), not all integer are whole or natural numbers. 5 is an integer even though it is not a whole number or a natural number.
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Reflected over the x-axis, then translated 6
units left
Write an equation to represent the function
Required equation to represent the translation 6 units left and reflected over x-axis is y = - (x + 6 ).
Let us consider the original equation be y = x.
Translation to the left by k unit is f(x) = f ( x + k )
Now the equation gets translated 6 units to the left represents as
y = ( x + 6 )
Now the reflected over the x-axis is represented by :
Here y -coordinates change the sign.
If ( x, y ) after reflection over x -axis it is ( x , -y ).
y = - ( x + 6 )
Equation to represents the reflected over x-axis and translated 6 units left of the original function y = x is written as y = - ( x + 6 ).
Therefore, the equation to represent the required translation and reflection is given by y = - ( x + 6 ).
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The sum of 500 consecutive integers is 250.
what is the product of the same 500 numbers?
The required product of the same 500 consecutive integers whose sum is equal to 250 is zero.
Let us consider consecutive integers represented by x, x+ 1, x+ 2 , ..... so on.
Sum of 500 integers = 250
x + x + 1 + x+ 2 + ....+ x + 499 = 250
⇒ 500x + 1 + 2 + ...+499 = 250
⇒ 500x + ( 500 × 499 )/2 = 250
⇒ 500x + 250 × 499 = 250
⇒ 250 ( 2x + 499 ) = 250
⇒ 2x + 499 = 1
⇒x = -249
Required 500 numbers are :
-249 , -248 , -247 , ......, 0, 1, ....... 250
Here zero is also a part of 500 integers.
Product of 499 number with zero is zero.
⇒( -249 ×-248 ×.....× 250 ) × 0 = 0
Therefore, the product of 500 consecutive integers with sum 250 is equal to zero.
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How do I evaluate the integral by interpreting it in terms of areas?
The process of evaluate the integral by interpreting it in terms of areas is by apply the summation rule on it.
The term called integral is defined as a mathematical object that can be interpreted as an area or a generalization of area.
Here we need to find the way to evaluate the integral by interpreting it in terms of areas.
As we all know that the integration symbol ∫ is an elongated S, suggesting sigma or summation.
Here on a definite integral, we have to use the above and below the summation symbol are the boundaries of the interval, [a, b].
Where the numbers a and b are x-values and are called the limits of integration and it specifically a is the lower limit and b is the upper limit.
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8th grade is hard and I do online school it’s hard for me to learn
A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.
B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and 3y+19 as they are vertically opposite angles.
C. Solving for y, we have: y = -5
What is intersection?Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.
Vertically opposite angles are actually known to be equal. It then means that:
∠7 = ∠8 (Vertically opposite angles)
Also, 5y-29 = 3y+19 (Vertically opposite angles)
Thus, solving for y, we have:
5y-29 = 3y+19
5y - 29 -29 = 3y + 19 - 29
5y -3y = - 10
2y = -10
y = -10/2 = -5
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Find the surface area of a square pyramid with side length 2 m and slant height 3 m.
Answer: The surface area of a square pyramid with a side length of 2m and slant height of 3m is 12 square meters.
Step-by-step explanation:
The surface area of a square pyramid can be calculated using the formula:
Surface area = Base area + 4 * (Area of one of the lateral faces)
The base area of the pyramid is the area of the square base, which is the side length squared: 2m * 2m = 4m^2
To find the area of one of the lateral faces, we can use the Pythagorean theorem to find the length of the face, which is the hypotenuse of a right triangle with the slant height and half of the side length as the other two sides.
so, (1/2 * 2m)^2 + 3^2 = x^2
x= (1/2 * 2m)^2 + 3^2
x = 2
Therefore, the surface area of the pyramid is:
Surface area = 4m^2 + 4 * 2m^2 = 4m^2 + 8m^2 = 12m^2
So, the surface area of a square pyramid with a side length of 2m and a slant height of 3m is 12 square meters.
The total cost of producing a type of car is given by C(x)=21000−90x+0.1x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost? Please explain how you got the answer, THANKS!
Answer: To find the number of cars that should be produced to incur minimum cost, we need to find the minimum value of the cost function C(x). Since C(x) is a quadratic function, it will have a minimum value, which is either a relative minimum or an absolute minimum. To find the number of cars that should be produced to incur the minimum cost, we will find the derivative of C(x) and set it equal to zero.
To find the derivative of C(x), we can use the power rule, which states that the derivative of x^n is n*x^(n-1).
The derivative of C(x) = 21000 - 90x + 0.1x^2 is
C'(x) = -90 + 0.2x
To find the minimum cost, we set C'(x) equal to zero and solve for x:
-90 + 0.2x = 0
0.2x = 90
x = 450
So, producing 450 cars will incur the minimum cost.
To verify that this is indeed a minimum, we can find the second derivative of C(x) which is 0.2, since the second derivative is positive, we can confirm that x = 450 is a relative minimum.
Alternatively, we can substitute x = 450 into the cost function and find the minimum value, which is C(450) = 21000 - 90(450) + 0.1(450)^2, which is less than any other value of C(x) for x≠450.
Therefore, to incur the minimum cost, 450 cars should be produced.
Step-by-step explanation:
a blind man is alone on a deserted island. he has two blue pills and two red pills. he must take exactly one red pill and one blue pill or he will die. how does he do it?
Some of the other types of the separation process are used in every house and company. The process of segregating undesirable particles from necessary components is the essence of the separation method. We will study in-depth information about several physical separation techniques in this particular article. The discussion's conclusion would allow students to recognize various techniques and their importance.
The blind man could use one hand to separate the pills by color, for example by holding one group of pills in one hand and the other group of pills in the other hand. Then, he could reach into one hand and take one pill, and reach into the other hand and take one pill, ensuring that he has taken one red pill and one blue pill. Another way could be to put each color pill in a different pocket, so he can feel the different pockets and take one pill of each color.
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may I have help with this please?
Does the table below represent a linear function? Why or why not.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three (3) true statements about the quadratic function, f(x) = x^2 – 5x + 12 and its graph include the following:
A. The value of f(–10) = 82
B. The graph of the function is a parabola.
D. The graph contains the point (20, –8).
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the other true statements about the graph of this quadratic function:
At data point (-10, 82), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(-10) = -10²/5 – 5(-10) + 12
Quadratic function, f(-10) = 82
At data point (20, -8), we have the following:
Quadratic function, f(x) = 1/5 x² – 5x + 12
Quadratic function, f(x) = x²/5 – 5x + 12
Quadratic function, f(20) = 20²/5 – 5(20) + 12
Quadratic function, f(20) = -8
In conclusion, the graph of this quadratic function, f(x) = x^2 – 5x + 12 does not contain the data point (0, 0) as shown in the image attached below.
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an alloy consists of steel gold and brass in the ratio 5:3:7 determine the amount of each metal in 150g of the alloy
Answer: 50g steel, 30g gold and 70g brass
Step-by-step explanation:
This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.
5 + 3 + 7 = 15
Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.
150g / 15g = 10g
Next, we will multiply each amount of metal in one ratio by 10.
5g * 10 = 50g steel
3g * 10 = 30g gold
7g * 10 = 70g brass
Answer:
Step-by-step explanation
150g of the alloy contains a certain amount of steel,gold and brass. We thus find the total ratio of steel,gold and brass which will be equal to 15 {5 + 3 + 7}If 15 which is the total ratio is equal to 150, what about 5 which is the ratio of steel?15=150g 5 * 150g/15[we cross multiply 5=? get 5 times 150 multiply by 15to get 50g of steel.
15=150g 3*150g/15 to get 30g of gold.3=?15=150g 7*150g/15 to get 70g of bras.7=?To confirm the answer, we take 50g of steel + 30g of gold + 70g of brass to get 150g of alloy.\
The head of a hammer is located 9 cm to the left of its
center of mass, while the bottom of the handle of the
hammer is 29 cm to the right of the center of mass. Determine the length of the hammer. Justify your
answer using an appropriate geometry principle (definition, theorem, etc.)
The length of the hammer is given as follows:
30.36 cm.
How to obtain the length of the hammer?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The sides in this problem are given as follows:
9 cm and 29 cm.
The length of the hammer is the hypotenuse, hence it is obtained as follows:
l² = 9² + 29²
[tex]l = \sqrt{9^2 + 29^2}[/tex]
l = 30.36 cm.
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need answer asap ! thank you to anyone who helps <3 !
AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex].
Is AB BA correct for all matrices?AB = BA in general, even if A and B are both square. We say that A and B commute if AB = BA. We cannot argue that AB = AC provides B = C for a generic matrix A. (However, since A is invertible, we may multiply both sides of the equation AB = AC to the left by A1 to yield B = C.)
For matrices, A and B, the product AB is not necessarily equal to BA. In fact, matrix multiplication is not commutative in general. Therefore, we need to check each pair of matrices to see if their products are equal in order to determine which pair satisfies [tex]$AB \neq BA$[/tex].
[tex]$$\begin{align*}AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 7 + 0 \cdot 3 & 1 \cdot 0 + 0 \cdot 4 \ 3 \cdot 7 - 2 \cdot 3 & 3 \cdot 0 - 2 \cdot 4\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]
[tex]$$\begin{align*}BA &= \left[\begin{array}{cc}7 & 0 \ 3 & 4\end{array}\right] \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \\\&= \left[\begin{array}{cc}7 \cdot 1 + 0 \cdot 3 & 7 \cdot 0 + 0 \cdot (-2) \ 3 \cdot 1 + 4 \cdot 3 & 3 \cdot 0 + 4 \cdot (-2)\end{array}\right] \\\&= \left[\begin{array}{cc}7 & 0 \ 15 & -8\end{array}\right]\end{align*}[/tex]
Since AB = BA, the first pair of matrices does not satisfy [tex]AB \neq BA[/tex]. We can proceed in the same manner to check the other pairs of matrices:
[tex]$$\begin{align*}\\AB &= \left[\begin{array}{cc}1 & 0 \ 3 & -2\end{array}\right] \left[\begin{array}{cc}8 & 0 \ 11 & -3\end{array}\right] \\\&= \left[\begin{array}{cc}1 \cdot 8 + 0 \cdot 11 & 1 \cdot 0 + 0 \cdot (-3) \ 3 \cdot 8 - 2 \cdot 11 & 3 \cdot 0 - 2 \cdot (-3)\end{array}\right] \\\&= \left[\begin{array}{cc}8 & 0 \ 2 & 6\end{array}\right]\end{align*}[/tex]
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a license plate begins with two letters. if the possible letters are A, B, C, D, and E, how many different ways of these letters can be made of if no letter is used more than once?
Answer:
20
Step-by-step explanation:
A, B, C, D, E is a set of 5 letters.
A letter can only be used once.
You have 5 choices for the first letter.
5
Since the letter that was selected to go first cannot be used again, now you have 4 choices for the second letter.
5 × 4
5 × 4 = 20
Answer: 20
write the equations described below. a subtraction equation with one variable that has a solution of 2/3.
Answer: SOME1 ANSWER QUICK
Step-by-step explanation:
A 3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.
Circle one: KE / GPE / both
Show your work for finding the values of each type of energy the object has:
KE GPE=mgh
Mass = Mass =
Velocity = Gravity (g) = 9.8 m/s2
Velocity2=Height =
KE = ½ (M) (V)2GPE=mgh
The ball has both kinetic energy and potential energy.
The values of each type of energy the object has are KE = 37.5 J and GPE = 2205 J
How to find the energy of the object?Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.
If a 3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.
Then ball has kinetic energy due to his motion and also has potential energy due to his height.
Thus, M = 3-kg, h = 75 m and V = 5 m/s
KE = 1/2(M)(V)² = 1/2 × 3 × 5² = 37.5 J
GPE = mgh = 3 × 9.8 × 75 = 2205 J
KE + PE = 37.5 + 2205 = 2242.5 J
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Write 7Y equals 3/8x -1
in standard form
Answer:[tex]-\frac{3}{8} x +7y=-1[/tex]
Step-by-step explanation:
Standard form is ax+by=c, where a,b,c are coefficients.
We are given [tex]7y=\frac{3}{8} x-1[/tex]. All we have to do is move some terms around so that the X is on the left side.
[tex]7y=\frac{3}{8} x-1[/tex] [subtract both sides by 3/8x]
[tex]-\frac{3}{8} x +7y=-1[/tex]
This gives out final answer of [tex]-\frac{3}{8} x +7y=-1[/tex].
a basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.T/F
True - the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).
A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.
In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.
Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.
A linear system is one in which both the superposition and homogeneity principles hold true.
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Can someone please find x for me? Thank you!
The value of the missing angle x of the triangle is; x = 18.67°
How to find the missing angles?The sum of angles on a straight line is 180 degrees. Thus, the supplementary angle to 130 degrees is;
180 - 130 = 50°
Now, the alternate angle to 80 degrees which will be located inside the triangle is 80°.
The sum of angles in a triangle is 180 degrees. Thus;
3x - 6 + 80 + 50 = 180
3x + 124 = 180
3x = 180 - 124
3x = 56
x = 56/3
x = 18.67°
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Which of the following is the equation of a line parallel to 3y = 6x + 5 that passes through (3, 3)? A. y = 2x - 1 B. y = 2x - 3 C. y + 2x = 1 D. y + 3 = 6x
First, we should find the slope of the line we're starting with.
3y = 6x + 5 can be put into slope-intercept form by dividing both sides by 3.
y = 2x + 5/3
The slope of this line is 2.
A parallel line has to have a slope of 2 as well, so we know we're looking for a line with a slope of 2.
Options A and B have that. Options C and D do not.
Now if (3,3) is a point on the line, then (3,3) must also be a solution for the equation.
Checking Option A:
3 = 2(3) - 1 is not true. 3 ≠ 6 - 1
Checking Option B:
3 = 2(3) - 3 is true. 3 = 6 - 3
Option B is the answer, since it has the right slope and works for the point (3,3).
Answer:
B) y = 2x - 3
Step-by-step explanation:
3y = 6x + 5 To put in the slope intercept form. Divide all the way through by 3
y = 2x + 5/3
When lines are parallel, they have the same slope.
So the slope will be 2. We will use the point to find the y intercept
m = 2
x = 3 This is from the point (3,3)
y = 3 this is from the point (3,3)
y = mx + b
3 = 2(3) + b
3 = 6 + b Subtract 6 from both sides
3-6 = 6- 6 + b
-3 = b
Now that we have the slope (2) and the y intercept (-3) we can write the equation.
y = mx + b
y = 2x -3
A school district signs a contract to purchase 50 of the electric typewriters (normally selling for $129. 95) from ABC at a quantity discount of 18%. What price does the school district pay for each typewriter?
The price paid by school district for each typewriter after applying 18% quantify discount is equal to $106.56.
Regular selling price of each typewriter = $129.95
Number of typewriter required by school district = 50
Total cost of 50 type writers = $129.95 × 50
= $6497.5
Discount percent on whole quantity = 18%
18% of $6497.5
= ( 18 / 100 ) × $6497.5
= $1169.55
Total price paid by school district for 50 typewriters
= $6497.5 - $1169.55
= $5327.95
Price paid by school district for 1 typewriters
= $5327.95 / 50
= $106.559
= $106.56
Therefore, the price paid school district for each typewriter is equal to
$106.56.
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Charlie tested three cameras last weekend. The table below shows the number of pictures taken and how much time it took.
Answer: First camera: 5 Pictures per second, Second camera: 6 Pictures per second. Third camera: 7 Pictures per second. The Third camera is the fastest.
Step-by-step explanation: 40/8 = 5, 30/5 = 6, 28/4 = 7
Complete each statement about angles by choosing from the drop-down menus:
The terminal side of a 130° angle in standard position lies in the ... quadrant
Two angles that are coterminal to 130° are ... and ...
The terminal side of a 130° angle in standard position lies in the second quadrant. Two angles that are co-terminal to 130° are 490° and -230°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given angle is 130°.
The first quadrant, second quadrant, third quadrant, and fourth quadrant make up the whole graph plane.
Angles in the first quadrant vary from 0° to 90°.
Angles in the second quadrant vary from 90° to 180°.
The angles in the third quadrant can be found between 180° and 270°.
Angles in the fourth quadrant can be found between 270° and 360°.
Therefore, the plot's beginning side is at zero degrees and its terminal side is at 130° in the second quadrant, since the specified angle is 130°.
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Answer: 2nd, -230, 490
Step-by-step explanation:
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