A linear equation can have solutions in three forms: one solution, no solution, and infinite solutions.
ONE SOLUTION EQUATION:
These are equations that will give only one solution when solved, such that the variable is equal to a single answer.
If the graph is drawn, the linear equations all cross or intersect at one point in space.
An example of a one-solution equation is shown below:
[tex]3x+5=2x-7[/tex]Solving this equation, we have:
[tex]\begin{gathered} 3x-2x=-7-5 \\ x=-12 \end{gathered}[/tex]We can therefore see that it has only one solution, one value for x which is -12.
NO SOLUTION EQUATION:
In this case, the coefficients of the variables on both sides of the equation are the same. Simplifying the equation will give an expression that is not true.
Graphically, the system is inconsistent and the linear equations do not all cross or intersect.
Consider the equation below:
[tex]2x+5=2x-7[/tex]If we attempt to solve the equation by subtracting 2x from both sides, we have the solution below:
[tex]\begin{gathered} 2x+5-2x=2x-7-2x \\ 5=-7 \end{gathered}[/tex]We can see that what we have left is not a valid statement, since 5 is not equal to -7:
[tex]5\neq-7[/tex]Thus, we can say that the equation has no solutions.
INFINITE SOLUTION EQUATION:
This follows the same format as the no solution equations. However, the final statement gotten from the simplification of the equation will give us a true statement instead.
Graphically, the linear equations are the same line in space and some variables are unconstrained.
Consider the equation below:
[tex]2x+5=2x+5[/tex]If we subtract 2x from both sides, we have:
[tex]\begin{gathered} 2x+5-2x=2x+5-2x \\ 5=5 \end{gathered}[/tex]Since the statement left is true, as 5 is equal to 5, then the equation has an infinite number of solutions.
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y = (5/7)x - 13
The slope of this line is (5/7)
I a line has a slope m, then a line perpendicular would have a slope -1/m
In this case m= 5/7
So the perpendicular would be: -1/m = -7/5
Answer: -7/5
In decimal numbers: -1.4
Answer:
Is there a real question?
I can't seem to find it...
Step-by-step explanation:
A car wheel has a radius of 35 cm.(a) What is the circumference of the wheel? Give your answer correct to 2 decimal places.(b) If the wheel rotates 100 000 times, how far does the car travel?
Explanation
(a) The formula for the circumference of a circle is as follows:
[tex]C=2\pi r[/tex]Where r is the radius of the circle. So, we have:
[tex]X=2\pi r=2\cdot3.1415\ldots\cdot35=219.9114\ldots\approx219.91[/tex]So, the circumference is approximately 219.91 cm.
(b) Assuming the wheel is always in contact and every rotation make sthe exact same length of travel, every rotation will make the car travel approximately 219.91 cm.
If the wheel rotates 100,000 times, the car will travel 100,000 times as many, so it will travel:
[tex]100,000\cdot219.91=21,991,000[/tex]So, the car will travel approximately 21,991,000 cm which is equivalente to 219.91 km.
Answer
(a) the circumference is approximately 219.91 cm
(b) the car will travel approximately 21,991,000 cm or 219,91 km.
The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?Give the exact answer in simplest form. ____ square kilometers.
It is given that the radius is 6 kilometers and the arc is 126 degrees.
The area of sector is given by:
[tex]\frac{126}{360}\times\pi\times6^2=39.5840\operatorname{km}^2[/tex]Therefore the area is 39.5840 square kilometers.
Which number line shows the correct solution to 4y - 82-20 ? H 4 -3 -2 -1 0 1 2 3 4 5 HHH O > & -3 -2 -1 0 1 2 3 4 5 HH H -4 -3 -2 -1 0 1 1 2 3 4 5 H → -3 -2 -1 0 1 2 3 4 5
To find which of the lines represent the solution we first need to solve the inequality:
[tex]\begin{gathered} -4y-8\ge-20 \\ -8+20\ge4y \\ 12\ge4y \\ \frac{12}{4}\ge y \\ 3\ge y \end{gathered}[/tex]the last line is equivalent as:
[tex]y\leq3[/tex]Now that we have the solution we can look at the line that represents it. The solution tells us that y is less or equal to 3, this means that the solutions are to the left of the number 3. Now, since the inequality is not an exact one that means that the 3 is also a solution, which also means that the circle over the 3 has to be a solid one.
With this in mind we conclude that the line representing the solution is the third option.
10. A car dealership offers a loan with 3.9% interest for 36 months, and you plan to purchase a car for $19,500. You can afford a down payment of $2,500.(a) What will your monthly payment be? $(b) How much will you pay in total for the car? $(c) How much will you pay in interest over the life of the loan? $
The monthly payment formula is :
[tex]M=P\times\frac{r(1+r)^n}{(1+r)^n-1}[/tex]where M is the monthly payment
P is the Financed amount
r is the rate of interest monthly, annual rate divided by 12
n is the number of payments
From the problem,
The financed amount is the difference between the car's cost and the down payment.
P = $19,500 - $2,500
P = $17000
The monthly interest rate is :
r = 3.9%/12 or 0.039/12 = 0.00325
n = 36 months
The monthly payment will be :
[tex]\begin{gathered} M=17000\times\frac{0.00325(1+0.00325)^{36}}{(1+0.00325)^{36}-1} \\ M=501.15 \end{gathered}[/tex]a. M = $501.15
b. The total payment for the car is monthly payment multiplied by the number of payment made together with the downpayment.
501.15 x 36 + 2500 = $20,541.4
c. The interest is the difference between the total payment made and the financed amount.
I = 501.15 x 36 - 17,000 = $1,041.4
Identify the coffecient of x in the expression below.-5x-4y^2
A coeffecient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression,
So in the given expression, the value "-5" is placed before x and hence is the coffecient of x .
Answer:
Step-by-step explanation:
3
See attached pic for problem. Only need help with #2
SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
[tex]x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }[/tex]Hence
The data plot will be
The linear is given by the form
[tex]\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}[/tex]THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
[tex]\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}[/tex]Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
[tex]\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}[/tex]Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning
Part 1
The labelled disgram is shown below.
We would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
Considering triangle ABE
Sin 60 = 10/BE
BE = 10/Sin60 = 11.55
tan60 =10/AE
AE = 10/tan60 = 5.77
Part 1
Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)
angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30
The sum of the angles in a triangle is 180 degrees. Thus,
angle DBC + angle DCB + angle BDC = 180
30 + 90 + angle BDC = 180
angle BDC = 180 = 180 - (30 + 90 = 180 - 120
angle BDC = 60
Sin 30 = CD/BD = 10/BD
BD = 10/Sin30
BD = 20
tan 30 = DC/BC = 10/BC
BC = 10/tan30
BC = 17.32
Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC
= BD + DC + BC
= 20 + 10 + 17.32
Perimeter = 47.32 feet
sum 0f 5 times a and 6
Answer:
30a
Step-by-step explanation:
it says how many one eights are in the product of 9x7/8
Answer
63
Explanation
Given the product 9 * 7/8
We are to find the number of one eighths that are in the product
Finding the product;
= 9 * 7/8
= (9*7)/8
= 63/8
= 63 * 1/8
= 63 * one-eighth
This shows that there are 63 one eighth in the product
A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.
A line can be written as an equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know the slope:
[tex]m=3[/tex]The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.
We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:
[tex]b=3[/tex]Thus, we have the equation:
[tex]y=3x+3[/tex]To calculate the other points, we just need to substitute their x values and get their y values:
x = 1:
[tex]y=3\cdot1+3=3+3=6[/tex]So, when x = 1, y = 6
x = 2:
[tex]y=3\cdot2+3=6+3=9[/tex]So, when x = 2, y = 9.
x = 3:
[tex]y=3\cdot3+3=9+3=12[/tex]So, when x = 3, y = 12;
So, the complete table is:
x | 0 | 1 | 2 | 3
y | 3 | 6 | 9 | 12
Rewrite the polynomial in standard form: 2x + 7x^2 - 3+ x^3
The given polynomial is
[tex]2x+7x^2-3+x^3[/tex]The standard form refers to organizing the terms where the exponents are placed in decreasing order.
[tex]x^3+7x^2+2x-3[/tex]At a point 125 feet from the base of a building, the angle of elevation to the third floor is 22°. What is the height of the third floor?A 53.9 feetB 14,124 feetC. 50.5 feetD. 333.3 feet
From the problem statement, we can draw the triangle shows below:
H is the height of the building we will solve for.
Shown below >>>
[tex]\begin{gathered} \tan 22=\frac{H}{125} \\ H=125\tan 22 \\ H=50.5\text{ f}eet \end{gathered}[/tex]AnswerCWhich of the following could be the product of two consecutive prime numbers? A. 2 B. 10 C. 14 D. 15
15 because it is the product of 3 and 5 which are consecutive prime numbers.
14. A waterway contains 10.3 milligrams of an impurity per gallon of water. How many micrograms of impurity arepresent per liter of water?
1) Gathering the data
10.3 mg of impurity per gallon of water
? μg of impurity per liter?
2) Since this is a matter of units conversion, then let's work remembering
the Metrical and Customary equivalences:
1 μg = 0.001 mg
1 gallon = 3.78 liters
3) As we have a ratio, let's write it as a ratio:
[tex]undefined[/tex]y-intercept of y=3/2|x-2|
Answer:
Combine [tex]\frac{3}{2 }[/tex] and | x - 2 |
[tex]y\frac{3|x-2|}{2}[/tex]
if a certain number is added to the numerator and denominator of 9/13 the result is 9/11. find the number
We have the following:
When they tell us a certain number, we will assume a value x.
This number is added to the numerator and denominator of the fractional number 9/13 and gives us the result 9/11.
it is as follows
[tex]\frac{x+9}{x+13}=\frac{9}{11}[/tex]solving for x:
[tex]\begin{gathered} \frac{x+9}{x+13}=\frac{9}{11} \\ 11\cdot(x+9)=9\cdot(x+13) \\ 11x+99=9x+117 \\ 11x-9x=117-99 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]Therefore, the certain number is 9
HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.
We have a rectangular garden.
The length L is 8 feet more than 3 times its width.
3 times the width is 3w, so we will add 8 to it and equal it to the length L:
[tex]L=8+3w[/tex]The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:
[tex]\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}[/tex]The perimeter has a value of P=16+8w.
We can draw the diagram as:
Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?
We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.
[tex]\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=\frac{72}{8} \\ w=9.75 \end{gathered}[/tex]The width is 9.75 feet.
If d - 243 = 542, what does d-245 equal? CARA GOIECT CH 1UJAINRIகபட்ட RE Lien Answer: Your answer
Given the following expression:
[tex]d-243=542[/tex]if we add 243 on both sides of the equation we get the following:
[tex]\begin{gathered} d-243+243=542+243=785 \\ \Rightarrow d=785 \end{gathered}[/tex]thus, d = 785
Which of the following distribution belongs to discrete distribution?Even distributionOdd distributionInteger distributionReal numbers distribution
Explanation:
Discrete probability distribution:
It counts the occurrences that have countable or finite outcomes.
As the even numbers, odd numbers are countably infinite .
The real numbers are not countable.
So, the discrete distributions are Integer distribution.
Triangle
A
B
C
was dilated with the origin as the center of dilation to create triangle ′′′
A
′
B
′
C
′
. The triangle was dilated using a scale factor of 14
1
4
.
The lengths of the sides of triangle
A
B
C
are given.
Enter the lengths of the sides of triangle ′′′
A
′
B
′
C
′
below.
(Decimal values may be used.)
The lengths of the sides of the Triangle A'B'C' is A'B'=2.25 units , B'C' = 2.75 units , C'A' = 1.25 units .
in the question ;
it is given that
the lengths of the sides of the Triangle ABC is
AB = 9 units
BC = 11 units
CA = 5 units
dilation scale = 1/4
the lengths of the dilated triangle can be found using the formula
(Side length)×(Dilation scale)=Dilated length
So,
A'B' = AB*(1/4)
= 9/4 = 2.25 units
B'C' = BC*(1/4)
= 11/4
= 2.75 units
C'A' = CA*(1/4)
= 5/4
= 1.25 units .
Therefore , the lengths of the sides of the Triangle A'B'C' is A'B'=2.25 units , B'C' = 2.75 units , C'A' = 1.25 units .
The given question is incomplete , the complete question is
Triangle ABC was dilated with the origin as the center of dilation to create triangle A′B′C′. The triangle was dilated using a scale factor of 1/4. The lengths of the sides of triangle ABC are given. Enter the lengths of the sides of triangle A′B'C′ . (Decimal values may be used.)
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Sophia is in the business of manufacturing phones. She must pay a daily fixed cost of $200 to rent the building and equipment, and also pays a cost of $100 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answer:
C = 100p + 200
Step-by-step explanation:
Because C is the total cost per day, 200 is the y-intercept because it's paid daily. The 100 is the slope since "he pays a cost of $100 per phone produced
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Solve the inequality and describe the solution set.y-6 > 1232, Math symbolsRelations► Geometry► Groups► Trgonometry3 of 3 AnsweredType here to searcho66F Mosty clou
The problem gives the inequality:
[tex]y-6\ge12[/tex]solving for y we get:
[tex]\begin{gathered} y\ge12+6 \\ y\ge18 \end{gathered}[/tex]The solution set is all real numbers equal or greater than 18, i.e.,
[tex]\lbrack18,+\infty)[/tex]3. Jeremy asked a sample of 40 8th grade students whether or not they had a curfew. He then asked if they had a set bedtime for school nights. He recorded his data in this two-way frequency table. Bedtime 21 Curfew No Curfew Total No Bedtime Total 4 25 12 16 40 3 15 24 a. What percentage of students surveyed have a bed time but no curfew?
40 students (the total) represents 100%
To find what percentage represents 3 students (number of students with bedtime but no curfew), we can use the next proportion:
[tex]\frac{40\text{ students}}{3\text{ students}}=\frac{100\text{ \%}}{x\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 40\cdot x=100\cdot3 \\ x=\frac{300}{40} \\ x=7.5\text{ \%} \end{gathered}[/tex]А.Translate the triangle.Then enter the new coordinates.A'([?], []).(4,-1) B'([ ], [])C'([],[ ](1,-3)(5,-4)<-2,3)B.
Given the triangle shown in the picture, you know its vertices:
[tex]A\mleft(4,-1\mright);B\mleft(5,-4\mright);C\mleft(1,-3\mright)[/tex]You have the following translation vector:
[tex]\langle-2,3\rangle[/tex]Therefore, you can identify that to find the Image (the figure translated) of the Pre-Image (the original figure) ABC, you have to translate each vertex 2 units left and 3 units up. Then, you get:
[tex]\begin{gathered} A^{\prime}(4-2,-1+3)=A^{\prime}(2,2) \\ \\ B^{\prime}(5-2,-4+3)=B^{\prime}(3,-1) \\ \\ C^{\prime}(1-2,-3+3)=C^{\prime}(-1,0) \end{gathered}[/tex]Then, the answer is:
[tex]undefined[/tex]Good evening, I need help on this questions. Thanks :)
Answer:
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
Explanation:
A function is increasing if we go from left to right and the graph goes up, it is constant when it is a horizontal line and it is decreasing if when we go from left to right the graph goes down.
Therefore, for each part of the function, we get
A and B ---> decreasing
B and C ---> constant
C and D ---> decreasing
D and E ---> increasing
Use Part Il of the Fundamental Theorem of Calculus to evaluate the definite integral
Answer:
[tex]4\ln (2)+\frac{49}{3}\approx19.1059[/tex]Given:
[tex]\int ^{-1}_{-2}\frac{7x^5-4x^2}{x^3}dx[/tex]Simplify:
[tex]\int \frac{7x^3-4}{x}dx[/tex]Expand:
[tex]\int (7x^2-\frac{4}{x})dx[/tex]Apply linearity:
[tex]7\int x^2dx-4\int \frac{1}{x}dx[/tex]Apply power rule and the standard integral ln(x)
[tex]7(\frac{x^3}{3})-4\ln (x)[/tex]Now, applying the Fundamental Theorem of Calculus Part 2
[tex]\int ^{-1}_{-2}\frac{7x^5-4x^2}{x^3}dx=(7(\frac{(-1)^3}{3})-4\ln (-1))-(7(\frac{(-2)^3}{3})-4\ln (-2))[/tex][tex]=4\ln (2)+\frac{49}{3}[/tex]Or approximately
[tex]\approx19.1059[/tex]will give brainlist
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 320 640 960
Create a description in words for the table.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The description for the table in word will be A. The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
What is a proportional relationship?Proportional connections are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
In this case, the table shows a proportional relationship between workout and calories burned. In 1 hour, 320 calories are burned.
In conclusion, the correct option is A.
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Use compatible numbers to determine if 455+ 229 is more than 650
Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
For 5 years, Gavin has had a checking account at Truth Bank. He uses a bank ATM 2 times per month and a nonbank ATM once a month. He checks his account statement online. How much money would Gavin save per month if he switched to Old River Bank?
EXPLANATION
Let's see the facts:
Number of years: 5
Account period = 2 times/month
Nonbank ATM -------> once/ month
If he switch the account to Old River Bank he would save:
$6 - $4.95 = $1.05
Transaction cost_Trust Bank = $1/transaction * 2 = $2
Nonbank_Trust Bank = $2/transaction = $2
Trust Bank Cost = 2 + 2 + 6 = $10
The account in the Old River Bank would be:
Account Services = $4.95
Bank ATM Cost = $0.00
Nonbank ATM Cost = $2.5/transactions * 1 = $2.5
----------------------
$7.45
The total cost at Old River would be = $7.45
The difference between Truth Bank and Old River would be $10-$7.45 = $2.55
Gavin would save $2.55 per month.
