For this system of equations, there will be infinitely many solutions.
Two equations are said to represent a line when they have the same slope and y-intercept. In this instance, one equation is created by adding a constant to the other equation.
Such equations will lay on each other on a graph if we plot them since they represent the same line. We can claim that these equations have an endless number of solutions because every point on that line will satisfy both of the aforementioned equations.
Here's an illustration:
Eq. 1: 2x + y = 4.
4x + 2y Equals 8 in equation 2
The second equation is created by multiplying the previous equation by two, as can be seen if you look at the two equations. The same outcome will be obtained for both if we write them in slope intercept form, as illustrated below:
Equation 1's slope intercept form is y = -2x + 4
Equation 2's slope intercept form is 2y = -4x + 8 and y = -2x + 4
The y-intercept and slope of both equations are identical. Equation 2 applies to any place that satisfies Equation 1. We can therefore draw the conclusion that there are an endless number of solutions to two linear equations with the same slope and y-intercept.
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Answer:
1
Step-by-step explanation:
If P=2500, r=6 %, and m=12, find the accumulated amount after 5 years.
hello
the question presented here related to compound interest and we can solve that using the formula
[tex]\begin{gathered} A=p(1+\frac{r}{n})^{nt}^{} \\ r=\text{rate}=6\text{ \% = 0.06} \\ n=12 \\ p=2500 \\ t=5 \\ \end{gathered}[/tex]let's proceed to substitute the values into the equation
[tex]\begin{gathered} A=2500(1+\frac{0.06}{12})^{12\times5} \\ A=2500(1+0.005)^{60} \\ A=2500(1.005)^{60} \\ A=2500\times1.005^{60}^{} \\ A=2500\times1.3488 \\ A=3375 \end{gathered}[/tex]the compounded interest compounded monthly at 6% for 5 years is 3375
The amount is 3250
The accumulated amount is calculated using the initial investment and interest earned in the given duration
The formula for simple interest is P×R×T and further, it is divided by 100
SI= 2500 × 6 × 5 =75000 ÷100 = 750
Now, for calculating the accumulated amount we will add the initial investment and the interest gained
ie, 2500+750 =3250
Here we are using the simple interest method to calculate the interest as it is assumed to be taken as simple interest when nothing is specified.
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Solve asap giving brainliest all the info you need is in the photo
Answer:
[tex]\textsf{C:}[/tex]
[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]
Step-by-step explanation:
Given information:
40 = Total number of scarves and hats sold.$700 = Total amount made from the sale.$18 = Charge for each scarf.$14 = Charge for each hat.Define the variables:
Let s = number of scarves sold.Let h = number of hats sold.Create an equation for the total number of scarves and hats sold:
⇒ s + h = 40
Create an equation that represents the total amount made from sales considering the cost per item:
⇒ 18s + 14h = 700
Therefore, the system of equations that represents the given constraints is:
[tex]\begin{cases}s + h = 40\\18s + 14h = 700 \end{cases}[/tex]
What is the complete factorization of the polynomial below? x3 - 2x2 + x - 2
A.(x + 2)(x + i)(x - i)
B.(x - 2)(x - i)(x - i)
C.(x - 2)(x + i)(x - i)
D.(x + 2)(x - i)(x - i)
The polynomial factors are (x -2)(x+ i)(x - i)
What is Factorization of PolynomialsIn mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
To find the factors of the given polynomial, we can proceed as
[tex]x^3 -2x^2 + x - 2[/tex]
Let's factor out a common term
[tex]x^3 - 2x^2 + x - 2 = x^2(x-2) + (x-2)\\x^2(x-2)+(x-2)\\(x-2)(x^2+1) = (x-2)(x+i)(x-i)[/tex]
The factors of the given polynomial is (x-2)(x+ i)(x- i)
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This double number line shows the distance a car travels over a period of time.
0
0
20
30
OB. 30
OC. 60
40
OD. 40
60 80 100
At what rate is the car traveling in maes per hour (mph)?
O A 20
Miles
60 90 120 150
Minutes
The rate at which the car is traveling is given as 1.5 miles/minute.
Given that,
This double-number line depicts the overall distance traveled by a car. It is necessary to determine the car's speed in miles per hour (mph).
What is Distance?Distance is referred to as an object moving between two points in time at a specific speed.
here,
The distance traveled = 150 miles
Time taken = 100 minutes
Rate = distance/time
Rate = 150 / 100
Rate = 1.5 miles per minute
Thus, The rate at which the car is traveling is given as 1.5 miles/minute.
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a brokerage survey reports that 30 percent of individual investors have used a discount broker; that is, one which does not charge the full commissions. in a random sample of 9 individuals, what is the probability that exactly two of the sampled individuals have used a discount broker
The probability that precisely two of the sampled people utilized a discount broker is 0.2668.
A discount broker was employed by 30% of individual investors.
p = 30 ÷ 100 = 0.3
q = 1 - p
q = 1 - 0.3
q = 0.7
n = 9
P(x) = [tex]{}^{n}C_{x}p^{x}q^{n - x}[/tex]
Only two of the people polled had utilized a broker.
x = 2
P(2) = [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex]= 0.2668
Only three persons have used a deal broker.
= P(3) + P(2) + P(1) + P(0)
= [tex]{}^{9}C_{3}[/tex](0.3)³[tex](0.7)^{6}[/tex] + [tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] + [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] + [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex]
= (84 × 0.027 × 0.1176) + (36 × 0.09 × 0.0823) + (9 × 0.3 × 0.0576) + (1 × 1 × 0.0403)
= 0.7291
Probability of a broker has been employed by at least three of them.
= P(2) - P(1) - P(0) - 1
= -([tex]{}^{9}C_{2}[/tex](0.3)²[tex](0.7)^{7}[/tex] - [tex]{}^{9}C_{1}[/tex](0.3)¹[tex](0.7)^{8}[/tex] - [tex]{}^{9}C_{0}[/tex](0.3)⁰[tex](0.7)^9[/tex] - 1)
= -((36 × 0.09 × 0.0823) - (9 × 0.3 × 0.0576) - (1 × 1 × 0.0403) - 1)
= 0.9291
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A shot-putter throws a shot and its height is noted every 20 feet, the data is in the table below:
Feet Traveled Feet Above Ground
20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64
Please find the quadratic function of best fit for these data and, to the hundredths place, say what height, in feet, the shot started its flight.
The quadratic function of best fit for the data is given as follows:
h(t) = -0.004t² +1.032t + 5.667.
Using this function, the initial height of the shot is of 5.67 feet.
Why a quadratic function of best fit is used, and how to find it?The input and the output of the data are given as follows:
Input: feet traveled.Output: feet above the ground.As the input increases, the output increases and then it decreases. Since this behavior of increase/decrease is not uniform over the entire domain of the relation, a quadratic function best models this data.
To find the quadratic function of best fit, we insert the points (input,output) into a calculator, from point (20, 25) to point (200,64).
Inserting the points into the calculator, the function is defined as follows:
h(t) = -0.004t² +1.032t + 5.667
The height in which the shot started its flight is given by the height when t = 0, hence:
h(0) = -0.004(0)² + 1.032(0) + 5.667 = 5.667 feet = 5.67 feet (rounded to the hundredths place).
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Find g(x), where g(x) is the translation 6 units down of f(x)=6x+2.
Write your answer in the form mx+b, where m and b are integers.
Help please!
The image of the function after the translation is g(x) = 6x - 4
What is translation?Translation involves shifting a function across the coordinate plane
How to determine the equation of g(x)?The given parameters are:
f(x) = 6x + 2
The transformation is given as
Translation 6 units down
Mathematically, this transformation can be represented as
(x, y) = (x, y - 6)
When represented as a function, we have
g(x) = f(x) - 6
Substitute the equation f(x) = 6x + 2 in the equation g(x) = f(x) - 6
So, we have the following equation
g(x) = 6x + 2 - 6
Evaluate the like terms
g(x) = 6x - 4
Hence, the equation of g(x) is g(x) = 6x - 4
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Support staff is paid $x each shift and each doctor is paid $150 more than each support. during a shift with 22 doctors and 71 support staff, the total salary is $26,565. solve for x.
Answer:
X = $250.16
Step-by-step explanation:
22( +150) + 71 = 26,565
22 + 3300 + 71 = 26,565
93 = 23,565
= 250.16
Each support staff is paid $250.16 per shift.
find the value of the arc shown in red leave ir answer in terms pi
The arc marked in red is a quarter of the circle's circumference.
Hence the arc marked red subtends an angle of 90degrees.
[tex]\begin{gathered} \text{Given an arc that subtends }\theta\text{ at the center of with radius r} \\ \end{gathered}[/tex][tex]\text{arc length, l = }\frac{\theta}{360}\times2\pi r[/tex]In our case
[tex]\theta=90^o,\text{ r = 6m}[/tex][tex]l=\frac{90}{360}\times2\pi(6)=\frac{1}{4}\times2\pi(6)=3\pi m[/tex]$7.50x10 ANSWER PLEASE I FORGOT ABOUT THIS NOW IM LEARNING IT AGAIN
Answer:
$75
Step-by-step explanation:
basically 7.50 x 10
what is a set of relations
The relation is the relationship between two or more sets of values. Suppose, x and y are two sets of ordered pairs. If set x has a relation with set y, then the values of set x are called domain whereas the values of set y are called range. A relation from a set A to a set B is a subset of A×B. Hence, a relation R consists of ordered pairs (a,b), where a∈A and b∈B. If (a,b)∈R, we say that is related to, and we also write aRb. A connection between the elements of two or more sets is a relation. The sets must be non-empty. A subset of the Cartesian product also forms a relation R. A relation may be represented either by the Roster method or by the Set-builder method.
Which balloon is was farther from the town at the beginning, and which traveled more quickly?
The balloon that was farther from the town at the beginning, and which traveled more quickly is Henry's balloon.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Henry's balloon is 48 miles after 2 hours.
Tasha's balloon after 2 hours will be:
= 8x + 20
= 8(2) + 20
= 32 miles
In this case, Henry's balloon is farther.
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In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class how many boys are there
which transformation would result in the area of a polygon being different from the area of its pre image
Answer:
Dilation
Step-by-step explanation:
A dilation is a transformation that will shrink or expand a figure, so the area will change.
–3(33b+65)=–95b–6b–87
Answer:
b = 54Step-by-step explanation:
[tex]\sf -3\left(33b+65\right)=-95b-6b-87[/tex]
Combine like terms:
[tex]\sf -3\left(33b+65\right)=-101b-87[/tex]
Expand:-
[tex]\sf -99b-195=-101b-87[/tex]
Add 195 to both sides:-
[tex]\sf -99b-195+195=-101b-87+195[/tex]
Simplify:-
[tex]\sf -99b=-101b+108[/tex]
Add 101b to both sides:-
[tex]\sf -99b+101b=-101b+108+101b[/tex]
Simplify:-
[tex]\sf 2b=108[/tex]
Divide both sides by 2:-
[tex]\sf \cfrac{2b}{2}=\cfrac{108}{2}[/tex]
Simplify:-
[tex]\sf b=54[/tex]
Therefore, your answer is b = 54!!
___________________________
Hope this helps you!
Have a great day! :)
To write 1 trillion in scientific notation, you would use the
exponent
Writing 1 trillion in scientific notation is 1 × 10^12.
What is a scientific notation?A scientific notation simply means the way of expressing numbers that are either too large of too small. Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.
In this case, I trillion is written as 1,000,000,000,000.
Therefore, it has 12 zeros.
The scientific notation is 1 × 10^12.
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Ray Horton is a laborer. He earns $16.25 per hour. How many hours per week must he work if
he wants to earn approximately $585.00 per week?
Circle A is given by the equation (x-4) +(3-3)* = 25. Circle A is shifted up five units and left by six units. Then, its radius is doubled. What is the new equation for circle A? A. (x+2)+(y-2)* = 50 B. (x+2)+(y –8)* = 100 C. (x-2)* +(y+2) = 100 D. (x-2)+(+8)* = 50
The correct answer is B
A straight line, L2, is parallel to the straight line L1 and passes through the point (0,-5).
Find an equation of the straight line L2.
Based on the straight line being parallel to the line, L1, and the gradient, the equation of the straight line L2 is y = 2x - 5
How to find the equation of the line?The equation of a straight line takes the form:
y = mx + b
Where:
m = slope
b = y - intercept
The slope is the same as the gradient and parallel lines have the same gradient. The gradient of L2 is therefore 2 as well.
Use this gradient and the point (0, -5) to find the y - intercept:
-5 = 2(0) + y - intercept
y - intercept = -5
The equation of the line is:
y = 2x - 5
Full question is:
A straight line, L2, is parallel to the straight line L1 and passes through the point (0,-5). L1 has a gradient, 2.
Find an equation of the straight line L2.
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Quadrilateral MATH is congruent to quadrilateral WXYZ. Which
statement is always true?
(1) MA - XY
(2) m/H=mZW
(3) Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a
sequence of rigid motions.
(4) Quadrilateral MATH and quadrilateral WXYZ are the same shape, but
not necessarily the same size.
Answer:
2
Step-by-step explanation:
The true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.
What is Congruency?The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Given:
MATH is congruent to quadrilateral WXYZ.
Then congruent sides are
MA= WX
AT = XY
TH = YZ
and, congruent angles are
<M = <W
<A = <X
<T= <Y
<H = <Z
So, if the quadrilateral is congruent then they equal in measure.
Hence, the true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.
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The chart below shows the approxinate distance from the Sun ti Earth, Mars, and Jupiter.
The speed of light is approximately 1.86 x 10^5 miles per second.
• The time it takes for a beam of light to travel from the Sun to the Earth is found by dividing the distance between the Sun and Earth by the speed of light. Find the amount of time it takes gir a beam if light fron the Sun to reach Earth. Show all work and express your answer in minutes.
• Explain or show how to use the numbers in scientific notation to calculate the difference in the distance from Jupiter to the Sun and the distance from Mars to the Sun. Then find the differences and express your answers in scientific notation.
• Explain ir show how to find the number if miles light will travel in 1/2 minute.
The amount of time it takes to reach the beam of sum from sun to earth is 200 seconds approximately
What is division?
Division is one of the basic arithmetic operation in which we find a number such the product of the number with the denominator is equal to the numerator.
We are given that the distant of earth from sun is 9.3 ×10^7
And the speed of light is 1.86×10^5
We divide the distance by the speed to get the value of time
[tex]\frac{9.3}{1.86}[/tex]×[tex]\frac{10^7}{10^5}[/tex]
On simplifying we get
200 seconds
Hence, The approximate time require to reach the beam of sun from sun to earth is 200 seconds
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A jet travels 1983 miles against a jetstream in 3 hours and 2373 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?Solve using a system of linear equations
Let:
x = Speed of the jet
y = Speed of jetstream
so:
[tex]1983=3x-3y_{\text{ }}(1)[/tex]and
[tex]2373=3x+3y_{\text{ }}(2)[/tex]Solve the system using elimination method:
[tex]\begin{gathered} (1)+(2) \\ 1983+2373=3x+3x-3y+3y \\ 4356=6x \\ x=\frac{4356}{6} \\ x=726mph \end{gathered}[/tex]Replace x into (1)
[tex]\begin{gathered} 1983=3(726)-3y \\ 1983=2178-3y \\ 195=3y \\ y=\frac{195}{3} \\ y=65mph \end{gathered}[/tex]Answer:
Rate of the jet in still air: 726 mph
Rate of the jetstream: 65mph
el 4.0
1. Jenny is going to the store for some snacks. Jenny only wants to buy a Pepsi and two candy
bars. The Pepsi costs $2.19 and each candy bar costs $1.99. How much money will Jenny
need to take to the store to make sure she has enough?
Step-by-step explanation:
can we become friends???
Answer:
6.17
Step-by-step explanation:
add the pepsi wich is 2.19 then do 1.99 x 2 wich would be 3.98 then add them all together
Roaring Zoo has 68 different species of birds. Because of cold weather, only 24 species stayed at the zoo, while the others were transported to the barn until warmer weather returned.
Which equation shows how many species of birds were transported?
b + 68 = 24
b − 68 = 24
b + 24 = 68
b − 24 = 68
Answer: b + 24 = 68
Step-by-step explanation:
we are told the zoo has 68 different species of birds so the equation will be = 28. The answers showing = 24 are already wrong.
transported means they are taken away, so we have to subtract 24 (animals that stayed in the zoo) to find b which are the remaining species moved to the barn.
b + 24 = 68
- 24 -24
b = 44 (transported to the barn)
24 ( stayed in the zoo)
68 ( total number of species of birds)
The correct expression to show the species of transported birds will be;
⇒ b + 24 = 68
Where, b is the number of transported birds.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Total number of birds in Roaring Zoo = 68
Number of stayed birds in Zoo = 24
Let number of transported birds = b
Then, We can formulate;
Total number of birds = Stayed birds + Transported birds
Substitute all the values, we get;
⇒ 68 = 24 + b
Therefore,
The correct expression to show the species of transported birds will be;
⇒ b + 24 = 68
Where, b is the number of transported birds.
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The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 inches, find its length and width.
Answer: length 20
width 10
Step-by-step explanation:
L = 2W
W+W+L+L=60
2W+2W+2W=60
6W=60
•1/6 to both sides
W=10
L=20
Answer:
Length = 20 in
Width = 10 in
Step-by-step explanation:
Given information:
The length of a rectangle is twice its width. The perimeter of the rectangle is 60 inches.Define the variables:
x = width2x = lengthPerimeter of a rectangle
[tex]P = 2(w + l)[/tex]
where:
w = widthl = lengthSubstitute the given values into the formula and solve for x:
[tex]\begin{aligned}\textsf{Perimeter of rectangle}&=\sf 2(width + length)\\\implies 60&=2(x+2x)\\60&=2(3x)\\60&=6x\\x&=10\end{aligned}[/tex]
Substitute the found value of x into the expressions for width and length.
Solution
Length = 20 inWidth = 10 in
help i dont understand this
Answer:
X= 15 is Undefined
Y= -3 is Zero
Y= 1/2x - 4 is a positive slope
The quotient x divided by 5 is a negative integer. Name two integers that x could represent and find the quotients.
If the values of x are -15, -20 and -25, then the solutions are -3, -4 and -5
How to solve for x and the quotients?The statement is given as
The quotient x divided by 5 is a negative integer
This means that:
x is a negative integer and it is a multiple of 5
Represent the statement as an expression
So, we have
x/5
Take for instance:
x = -15, -20 and -25
So, we have
-15/5 = -3
-20/5 = -4
-25/5 = -5
Hence, the possible values of x are -15, -20 and -25
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The diagram shows the construction of line PX perpendicular to line l.
Which statement is not always true about this construction?
-1) PA = PB
2) AX = BX
3) PX = CX
4) AC=BC
We can conclude that after the construction of line PX perpendicular to line l, which creates a square, the correct statement about the construction will be (E) none of these.
What is a square?A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle. A square is a unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).So, after drawing line PX⊥L (AB), and extending PX to the other side to point C.
We can observe that a square is created.(A) PA = PB
It will always be true as all sides of a square are equal.(B) AX = BX
It will always be true as PX⊥L (AB) bisects diagonal Ab in two equal parts.(C) PX = CX
It will always be true as PC is a diagonal of a square with X as the midpoint where both diagonals PC and AB intersect.(D) AC = BC
It will always be true as all sides of a square are equal.Therefore, we can conclude that after the construction of line PX perpendicular to line l, which creates a square, the correct statement about the construction will be (E) none of these.
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The complete question is given below:
The diagram shows the construction of line PX perpendicular to line l.
Which statement is not always true about this construction?
A) PA = PB
B) AX = BX
C) PX = CX
D) AC = BC
E) Non of these
A grocery store sells a bag of 7 oranges for $4.83. How much
would it cost for 12 oranges?
Answer:
Step-by-step explanation:
The total for 12 oranges would be $8.28
For integer values of x, if 1.75x is an integer, which of the following must be an integer?
Using integer numbers, it is found that the expressions that will also be integers are given as follows:
1.75kx, in which k is an integer.
What are integer numbers?Integer numbers are numbers that have a decimal part of zero, that is, they are whole numbers, either positive or negative.
In the context of this problem, the relevant property is that the multiplication of two integer numbers will always result in an integer number.
We have that the term 1.75x represents an integer number, hence any integer number multiplying 1.75x will result in an integer number.
Symbolically, any integer number can be represented by the variable k, hence the expressions that will also be integers are given as follows:
1.75kx, in which k is an integer.
What is the missing information?This problem could not be found on any search engine, hence the expression is given in general terms.
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