Answers
Given the system of equations:
[tex]\text{ x + y = 6}[/tex][tex]\text{ y = -x + 6}[/tex]The two equations appear to be just the same, thus, we are only given one system of equations.
Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.
Related Questions
13 nickels to 43 dimes in a reduced ratio form
Answers
The reduced ratio form of 13 nickels to 43 dimes is 13/86.
What is a ratio?
a ratio let us know that how many times one number contains another number.
We are given 13 nickels and 43 dimes.
We know that 1 dime equal to 2 nickels.
Hence 43 dimes equals 86 nickels.
Now we find the ratio of the 2.
Which will be [tex]\frac{13}{86}[/tex]
Hence the reduced ratio form is 13/86.
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how do I determine the hypotenuse, opposite, and adjacent angles when I'm only given sides and no angles?
Answers
[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]
Here is a list of questions about the students and teachers at a school. Select the questions that are statistical questions.
Answers
As observed, all the questions in the list can be answered on the basis of some data collection and analysis.
So they all can be considered as statistical questions.
Thus, all the questions in the given list are statistical questions.
1.
If you have to answer the question for most popular lunch choice, you have to collect data of the lunch choices by a large portion of the called population. Then the lunch choice corresponding to highest frequency will be considered as the most popular lunch choice. Since the conclusion is data driven, this is a statistical question.
2.
In order to answer the question, you need to collect the information about the name of school each of the called population is admitted to. If all the students are found to be admitted to the same school, then the name of that school would be the answer.
Here also, the conclusion is data driven, so this is also a statistical question.
3.
To answer this question, you have to gather all the teaching staff of the school, and take individual answers to which subject they teach. The number of teachers who answered math will be the answer for this question.
Here also, the conclusion is data driven, so this is also a statistical question.
4.
To answer this question, you have to gather the individual age of each teacher in the school. The age corresponding to the maximum frequency would be the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
5.
To answer this question, you have to collect data about how much sleep each student gets in the school. Then only you can answer this question.
Since the conclusion is data driven, this is a statistical question.
6.
To answer this question, you have to collect data that how many students travel by which mode of transport to travel from home to school. The mode corresponding to highest frequency is the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
Thus, it is seen that all the six questions are statistical questions.
Find ca^2+b^2=c^2 3^2+2^2=c^29+4=13
Answers
Substituting with a = 3 and b = 2, we get:
[tex]\begin{gathered} 3^2+2^2=c^2 \\ 9+4=c^2 \\ 13=c^2 \\ \sqrt[]{13}=c \\ 3.6\approx c \end{gathered}[/tex]questionSuppose $24,000 is deposited into an account paying 7.25% interest, which is compoundedcontinuouslyHow much money will be in the account after ten years if no withdrawals or additional depositsare made?
Answers
This is a compound interest question and we have been given:
Principal (P) = $24000
Rate (r) = 7.25%
Years (t) = 10
However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.
The formula for finding the compound interest is:
[tex]\text{Amount}=P(1+\frac{r}{n})^{nt}[/tex]But because the compounding period is continuous and therefore, infinitesimal,
[tex]\begin{gathered} Amount=P(1+\frac{r}{n})^{nt} \\ But, \\ n\to\infty \\ \\ \therefore Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \end{gathered}[/tex]This is similar to the general formula for Euler's number (e) which is:
[tex]e=\lim _{n\to\infty}(1+\frac{1}{n})^n[/tex]Thus, we can re-write the Amount formula in terms of e:
[tex]\begin{gathered} \text{Amount}=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \\ \text{This can be re-written as:} \\ \\ Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{\frac{n}{r}\times r\times t}\text{ (move P out of the limit because it is a constant)} \\ \\ \text{Amount}=P\lim _{n\to\infty}((1+\frac{r}{n})^{\frac{n}{r}})^{r\times t} \\ \\ \text{Amount}=P(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{5}})^{rt} \\ \\ \text{but,} \\ e=(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{r}} \\ \\ \therefore\text{Amount}=Pe^{rt} \end{gathered}[/tex]Therefore, we can find the amount of money in the account after 10 years:
[tex]\begin{gathered} \text{Amount}=Pe^{rt} \\ P=24000 \\ r=7.25\text{ \%=}\frac{7.25}{100}=0.0725 \\ t=10\text{ years} \\ \\ \therefore\text{Amount}=24000\times e^{10\times0.0725} \\ \\ \text{Amount}=24000\times2.06473 \\ \\ \therefore\text{Amount}=49553.546\approx49553.55 \end{gathered}[/tex]Therefore the amount after compounding continuously for 10 years is:
$49553.55
What is the image point of (-12, —8) after the transformation R270 oD ?
Answers
Answer
(-12, -8) after R270°.D¼ becomes (-2, 3)
Explanation
The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.
The coordinates to start with is (-12, -8)
R270° changes A (x, y) into A' (y, -x)
So,
(-12, -8) = (-8, 12)
Then, the second operation dilates the new coordinates obtained after the first operation by ¼
D¼ changes A (x, y) into A' (¼x, ¼y)
So,
(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)
Hope this Helps!!!
Two functions, function A and function B, are shown below:Function Axy714816918Which statement best compares the rate of change of the two functions?The rate of change of both functions is 2.The rate of change of both functions is 3.The rate of change of function A is greater than the rate of change of function B.The rate of change of function B is greater than the rate of change of function A.
Answers
Answer
The rate of change of both functions is 2.
Explanation
To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.
Rate of change of function A
Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16
Rate of change = Δy/Δx
Δy = (y₂ - y₁) = 16 - 14 = 2
Δx = (x₂ - x₁) = 8 - 7 = 1
⇒ Rate of change = 2/1 = 2
Rate of change of function B
From the graph
Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6
Rate of change = Δy/Δx
Δy = (y₂ - y₁) = 6 - 4 = 2
Δx = (x₂ - x₁) = 3 - 2 = 1
⇒ Rate of change = 2/1 = 2
Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"
Use mental math to find all of the quotients equal to 50. Drag the correct division problems into the box.
4
,
500
÷
900
450
÷
90
45
,
000
÷
900
4
,
500
÷
90
450
÷
9
Quotients equal to 50
Answers
Answer: 45,000 ÷ 900=50
Step-by-step explanation:
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17. 8(x + 1) = 24. 5(x - 2) = 20. 34 - 7x = 20. 31 - x = 29. 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
Answers
We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]open up or down, vertex:(0,-4), passes through: (-3,5)
Answers
open up or down, vertex:(0,-4), passes through: (-3,5)
In this problem we have a vertical parabola open upward
the equation in vertex form is equal to
y=a(x-h)^2+k
where (h,k) is the vertex
we have
(h,k)=(0,-4)
substitute
y=a(x)^2-4
Find the value of a
with the point (-3,5)
substitute in the equation
5=a(-3)^2-4
5=9a-4
9a=5+4
9a=9
a=1
therefore
the equation is
y=x^2-4
answer is
f(x)=x^2-4Evaluate the rational expression for the given x value. Express the answer as a fraction in simplest form.
Answers
Given the expression:
[tex]\frac{x-3}{2x+3}[/tex]We need to find the value of the expression when x = 7
So, we will substitute with x = 7 into the expression as follows:
[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]so, the answer will be 4/17
RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
Answers
It takes chuck 24 minutes to type and spell check 14 pages. Find how many pages he can type and spell check in 1.5 hours. Remember to convert 1.5 hours to minutes
Answers
In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:
[tex]\begin{gathered} 1\text{ hour}\to60\text{ minutes} \\ 1.5\text{ hour}\to x\text{ minutes} \\ \\ \frac{1}{1.5}=\frac{60}{x} \\ x=60\cdot1.5 \\ x=90 \end{gathered}[/tex]Then, to find the number of pages, let's do the following rule of three:
[tex]\begin{gathered} 14\text{ pages}\to24\text{ minutes} \\ x\text{ pages}\to90\text{ minutes} \\ \\ \frac{14}{x}=\frac{24}{90} \\ 24x=14\cdot90 \\ x=\frac{14\cdot90}{24}=52.5 \end{gathered}[/tex]Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.
2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
Answers
We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q17
Answers
The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.
The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.
Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:
[tex]f^{-1}(-5)=2[/tex][tex]\text{Thus, the point on the graph of f}^{-1}\text{ is }(-5,2\text{ )}[/tex]Hence, the correct option is option B
Janelle says that lines l and m are skew lines. Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal. Is Janelle correct? Yes, because the lines are not parallel. Yes, because the lines will intersect. No, because the lines are in the same plane. No, because the lines are perpendicular.
Answers
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
What is a line that is perpendicular?
Perpendicular lines are those that cross at a perfect right angle. Parallel lines are those that are always the same distance apart from one another.
The question is incomplete.
Please see the accompanying image for a comprehensive explanation of the question.
Line l and line m are the two lines that are depicted in the image.
The skew lines are in different planes and do not overlap, as far as we are aware.
Therefore,
Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.
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The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)
Answers
To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:
[tex]\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}[/tex]Let us subtract the second equation to the first one:
This implies that
[tex]\beta_1=\frac{-1}{-21}=\frac{1}{21}[/tex]Now, let us replace this value we just got into the second equation to find beta_0:
[tex]\begin{gathered} 4=\beta_0+\frac{1}{21}\cdot11, \\ 4=\beta_0+\frac{11}{21}, \\ \beta_0=4-\frac{11}{21}=\frac{4\cdot21}{21}-\frac{11}{21}=\frac{84-11}{21}=\frac{73}{21} \end{gathered}[/tex]At last,
[tex]\beta_1=\frac{1}{21},\beta_0=\frac{73}{21}[/tex]Then, the equation of the line is just
[tex]y=\frac{73}{21}+\frac{1}{21}x[/tex]Which of the following polygons has reflective symmetry but not rotational symmetry?
a) square
b) regular decagon
c) kite
d) equilateral triangle
Answers
A kite has reflective symmetry but not rotational symmetry.
Define symmetry.In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.
Given,
A kite has reflective symmetry but not rotational symmetry.
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Sketch the graph of a function that has a local maximum value at x = a where f'(a) is undefined.
Answers
Derivative and Maximum Value of a Function
The critical points of a function are those where the first derivative is zero or does not exist.
Out of those points, we may find local maxima or minima or none of them.
One example of a function with a derivative that does not exist is:
[tex]y=-x^{\frac{2}{3}}[/tex]This function has a local maximum at x=0 where the derivative does not exist.
The graph of this function is shown below:
kindly asking for help to clarify this question and mathematical problem .
Answers
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
How are the strategies the same and how are they different
Answers
Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
Rewrite the equation by completing the square. x^{2}-6x-16 = 0
Answers
Answer:
Step-by-step explanation:
x^2 - 6x - 16 = x^2 - 6x + 9 - 9 - 16 = (x - 3)^2 - 25
Which of the following sets does the number - 12.12532 ... belong to?Select all correct answers.Select all that apply:Whole NumbersIntegersURational NumbersIrrational NumbersReal NumbersUNone of the Above
Answers
Answer:
Explanation:
Let's define each of the given types of numbers;
*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,
*Integers
If Tanisha wants the top of the ladder to reach exactly 8 feet up the building, what is X, the distance between the building and the base of the ladder in feet?
Answers
Solution:
Given:
The right triangle can be sketched as shown below;
To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ \\ \text{where;} \\ \text{hypotenuse}=10 \\ \text{adjacent}=x \\ \text{opposite}=8 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{adjacent}^2+\text{opposite}^2 \\ 10^2=x^2+8^2 \\ 100=x^2+64 \\ 100-64=x^2 \\ 36=x^2 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}[/tex]Therefore, the distance between the building and the base of the ladder in feet is 6 feet.
Property valued at $56,000 is assessed at of itsvalue. If the yearly tax is calculated as $3 per $100 ofassessed value, what is the yearly tax on this property?A. $ 420B. $1.120C. $1,260D. $1,680E $2,240
Answers
Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.
Hallum hardware created flyers to advertise a carpet sale . A portion of the flyer is shown below. Based on the chart, which statement describes the relationship between area and the cost of carpet?
Answers
The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.
Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.
Ratio = cost / area
750 / 500 = 1.50
1500 / 1000 = 1.50
2,250 / 1500 = 1.50
3000 / 2000 = 1.50
Since the ratios are constant, the relationship is proportional.
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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.
#8 help with algebra 2 question. That’s the only picture I have. I tried writing it out.
Answers
Solution:
Given a cosine function graph;
The general cosine function is
[tex]y=A\cos(Bx-C)+D[/tex]Where
[tex]\begin{gathered} A\text{ is the amplitude} \\ Period=\frac{2\pi}{B} \\ C\text{ is the phase shift} \\ D\text{ is the vertical shift} \end{gathered}[/tex]From the graph,
The midline is y = 1
The amplitude, A, is
[tex]\begin{gathered} A=4-1=3 \\ A=3 \end{gathered}[/tex]The amplitude, A is 3
Where,
[tex]\begin{gathered} Period=12 \\ Period=\frac{2\pi}{B} \\ 12=\frac{2\pi}{B} \\ Crossmultiply \\ 12B=2\pi \\ Duvide\text{ both sides by 12} \\ \frac{12B}{12}=\frac{2\pi}{12} \\ B=\frac{\pi}{6} \end{gathered}[/tex]The phase shift, C = 0, and the vertical, D, is 1
Thus, the equation of the graph is
[tex]\begin{gathered} y=A\cos(Bx-C)+D \\ Where \\ A=3 \\ B=\frac{\pi}{6} \\ C=0 \\ D=1 \\ y=3\cos(\frac{\pi}{6}x)+1 \end{gathered}[/tex]The graph is shown below
Hence, the equation is
[tex]y=3\cos(\frac{\pi}{6}x)+1[/tex]For each expression build a rectangle using all of tiles,....
Answers
a.
[tex]\begin{gathered} y^2+xy+2x+2y \\ Factor_{\text{ }}as\colon \\ (y+2)(x+y) \end{gathered}[/tex]i) Sketch each rectangle:
ii) Find its dimensions
iii)
[tex]\begin{gathered} y^2+xy+2y+2x \\ \text{grouping terms:} \\ (y^2+xy)+(2y+2x)=y(y+x)+2(y+x)=(y+x)(2+y) \end{gathered}[/tex]Simplify the expression (6^2)^46^?
Answers
The given expression is
[tex](6^2)^4[/tex]We would apply the rule of indices or exponent which is expressed as
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ \text{Therefore, the expression would be } \\ 6^{2\times4} \\ =6^8 \end{gathered}[/tex]School: Practice & Problem Solving 7.1.PS-18 Question Help A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer The areas equal. A rectangle has dimensions 5 m by 7 m, so its area is m² A parallelogram with a base of 5 m and a height of 7 m has an area of (Type whole numbers.)
Answers
The image shown below shows the relationship between areas of rectangle and parallelogram
It can be seen that the areas are equal when they have the same sides or dimension
A rectangle has dimensions 5 m by 7 m, so its area is 5m x 7m = 35m²
A parallelogram with a base of 5 m and a height of 7 m has an area of 5m x 7m = 35m²
