Solve the system. Is the answer (3,0) or (0, -1) or no solution or infinitely many solutions?
Answers
Given:
[tex]\begin{gathered} \frac{1}{3}x+y=1\ldots..(1) \\ 2x+6y=6\ldots\text{.}(2) \end{gathered}[/tex]Solve the system of equations.
Equation (2) can be simplified as,
[tex]\begin{gathered} 2x+6y=6 \\ \text{Divide by 6 on both sides} \\ \frac{2x}{6}+\frac{6y}{6}=\frac{6}{6} \\ \frac{1}{3}x+y=1\text{ which represents the equation (1)} \end{gathered}[/tex]Moreover, the slope and y-intercept of both the equation of lines are the same.
It shows that the lines are coincident.
The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.
Related Questions
3. Which of the following points would produce a negative slope? (A) (B) (C) (D) (-1,2) and (4,2) (-2,-2) and (0,4) (1,3) and (-1,4) (2,4) and (-2,-1)
Answers
The sequation to calculate the slope is,
[tex]m=\frac{y2-y1}{x2-x1}[/tex]The solpe of line joining (-1,2) and (4,2) is,
[tex]\begin{gathered} m=\frac{2-2}{4+1} \\ m=0 \end{gathered}[/tex]The slope of the line joining (-2,-2) and (0,4) is,
[tex]\begin{gathered} m=\frac{4+2}{0+2} \\ m=3 \end{gathered}[/tex]The slope of the line joining (1,3) and (-1,4) is,
[tex]\begin{gathered} m=\frac{4-3}{-1-1} \\ m=-\frac{1}{2} \end{gathered}[/tex]Negative slope.
The slope of the line joining (2,4) and (-2,-1) is,
[tex]\begin{gathered} m=\frac{-1-4}{-2-2} \\ m=\frac{5}{4} \end{gathered}[/tex]Positive slope.
Use the Pythagorean Theorem to find the missing side length. *A. 12B. 144C. 10D. 24
Answers
We use the Pythagorean theorem formula to find the missing side length.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the sides} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=x \\ b=16 \\ c=20 \end{gathered}[/tex][tex]\begin{gathered} a^{2}+b^{2}=c^{2} \\ x^2+16^2=20^2 \\ x^2+256=400 \\ \text{ Subtract 256 from both sides} \\ x^2+256-256=400-256 \\ x^2=144 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{x^2}=\sqrt{144} \\ x=12 \end{gathered}[/tex]AnswerThe length of the missing side is 12.
Use the x and y intercepts to sketch a graph of each equation.
Answers
The given equation is expressed as
x + 4y = 8
4y = 8 - x
y = 2 - x/4
The first step is to input values for x into the equation and determine the corresponding y values. These values are then plotted on the graph.
For x = 0, y = 2 - 0/4 = 2
For x = 1, y = 2 - 1/4 = 1.75
For x = 2, y = 2 - 2/4 = 1.5
We would plot these points on the graph
Express the answer in simplest formIf A die is rolled one time find the probability of
Answers
Solution
If A die is rolled one time find the probability of getting an even number
The total number in a die rolled once = 6
number of even number = 3
Probability = number of required outcome / number of possible outcome
[tex]\begin{gathered} Pr(evene\text{ number\rparen = number of even / total number} \\ Pr(even)\text{ = 3/6} \\ =\frac{1}{2} \end{gathered}[/tex]Therefore the probability of getting an even number = 1/2
Question 5 Multiple Choice Worth 1 points)(05.02 MC)A nurse collected data about the average birth weight of babies in the hospital that month. Her data is shown using the dot plot. Create a box plot to represent the data.Monthly Birth Weight:8.28.3 8.4 8.5 8.6Birth Weight (in pounds)82 83 8.4 85 86 87 8.882 8384 8.5 86 87 60 6.982 83 84 8.5 8.6 8.7 8.0 8.9 98283 84 85 86 87 88 8.998.1816.181$F
Answers
Given:
Here we have data about the average birth weight of babies in the hospital that month.
Required:
We need to create a box plot to represent the data.
Explanation:
Here we have monthly birth weight in pounds as
8.2 , 8.2 , 8.3 , 8.3 , 8.4 , 8.4 , 8.5 , 8.5 , 8.5 , 8.7 , 8.9
now by data we get Q2 is 8.4
now for this data
8.2 , 8.2 , 8.3 , 8.3 , 8.4
we get Q1 is 8.3
by this data
8.5 , 8.5 , 8.5 , 8.7 , 8.9
we get Q3 is 8.5
and we have maximum 8.9 and minimum 8.2
now make a box plot
Final answer:
What is the area of the circle to the nearest 10th unit?
Answers
First, lets find the radius of the circle.
For a circle inscribed in a square, the diameter of this circle is equal to the side lenght.
D = 4.4
Since the radius (r) is D/2
r = 4.4/2 = 2.2
Now, we can calcule the area of the circle (A), using the following equation:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot2.2^2 \\ A=4.8\pi units^2 \\ Or,\text{ since }\pi=3.14 \\ A=4.8\cdot3.14 \\ A=15.2\text{ }units^2 \end{gathered}[/tex]Find the distance between the pair of parallel lines with the given equations.y = -5xy = -5x + 26O A) 5 unitsO B) 14.14 unitsC) C) 5.10 unitsO D) 6 units
Answers
Solution:
Consider two lines with the following equations:
[tex]y_1=mx+c[/tex]and
[tex]y_2=mx+c_2[/tex]the distance d between these two parallel lines is given by the following equation:
First, we need to take one of the lines and convert it to standard form. For example, take the line:
y = -5x + 26
then, we obtain:
-5x-y+26=0
in this case, we get that
A = -5
B= -1
C = 26
Now we can substitute A, B, and C into our distance equation along with a point, (x1,y1) from the other line. We can pick any point on the line y2. Just plug in a number for x, and solve for y. I will use x = 2, to obtain:
y = -5(2) = -10
then
(x1,y1) = (2,-10)
Replacing these values into the distance equation, we obtain:
[tex]d\text{ = }\frac{|-5(2)+(-1)(-10)+26|}{\sqrt[]{(-5)^2+(-1)^2}}[/tex]that is:
[tex]d\text{ = }\frac{|-10+10+26|}{\sqrt[]{(-5)^2+(-1)^2}}=\frac{26}{\sqrt[]{26}}=5.09\approx5.10[/tex]so that, the correct answer is:
[tex]5.10\text{ units}[/tex]An extrasolar planet is observed at a distance of
4.2 × 10⁹ kilometers away. A group of scientists
has designed a spaceship that can travel at the
speed of 7 × 108 kilometers per year. How many
years will the spaceship take to reach the extrasolar
planet? Enter the answer in the box.
Answers
After conducting some mathematical operations, we can conclude that it would take the spaceship 5555556 years to reach the extrasolar planet.
What do we mean by mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The four mathematical operations are functions that change one number into another by taking input values, or numbers, as inputs.They are addition, subtraction, multiplication, and division.So, years were taken by the ship to reach the extrasolar planet:
Distance of the planet: 4.2 × 10⁹ kmSpeed of the spaceship: 7 × 108 per/yearNow, calculate the number of years as follows:
= (4.2 × 10⁹)/(7 × 108)= (4.2 × 1000000000)/756= 4,20,00,00,000/756= 5555555.56Rounding off: 5555556 years
Therefore, after conducting some mathematical operations, we can conclude that it would take the spaceship 5555556 years to reach the extrasolar planet.
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log (2x+ 9) = 1+ log(x- 8)
Answers
x = 11.125
STEP - BY - STEP EXPLANATION
What to do?
Solve the given equation.
Given:
log (2x+ 9) = 1+ log(x- 8)
To solve, we will follow the steps below:
Step 1
Re-arrange by subtracting log(x-8) from both-side of the equation.
[tex]log(2x+9)-log(x-8)=1[/tex]Step 2
Apply the law of logarithm that is applicable to the given problem.
[tex]log\frac{(2x+9)}{(x-8)}=1[/tex]Step 3
Replace 1 by log10
Step 4
[tex]log\frac{(2x+9)}{(x-8)}=log10[/tex]Step 5
Cancel-out the log from both-side of the equation.
[tex]\frac{2x+9}{x-8}=10[/tex]Step 6
Cross - multiply
[tex]2x+9=10(x-8)[/tex]Step 7
Open the parenthesis.
[tex]2x+9=10x-80[/tex]Step 8
Collect like term.
[tex]10x-2x=80+9[/tex][tex]8x=89[/tex]Step 9
Divide both-side of the equation by 8
[tex]\frac{8x}{8}=\frac{89}{8}[/tex][tex]x=11.125[/tex]Therefore, the value of x is 11.125
I need help in math can you please help me
Answers
We have the following:
[tex]\begin{gathered} \sin \theta=-\frac{8}{17} \\ \theta=\sin ^{-1}(-\frac{8}{17}) \\ \theta=-28.07 \end{gathered}[/tex]now, in Quadrant III (180° to 270°):
[tex]\theta=180+28.07=208.7[/tex]now, for cosine:
[tex]\cos 2\theta=\cos (2\cdot208.7)=0.538=\frac{539}{1000}[/tex]The answer is 539/1000
The triangles below are congruent by SSS, so we can say that < E is congruent to ______ by CPCTC.
Answers
The triangles are given to be congruent by the side-side-side (SSS) congruence property.
Hence, the congruent statement is:
[tex]\triangle DEF\cong\triangle HIJ[/tex]It is required to complete the given statement.
Recall that CPCTC means Corresponding Parts of Congruent Triangles are Congruent.
The corresponding part to ∠ E is ∠I. Hence, by CPCTC, the angle congruent to ∠E is ∠I.
The answer is option b.
The adult skeleton consist of 206 Bones in the school and 30 bones in the arm and legs. Out of the 28th skull bones, 14 are facial bones. Six or ear bones and eight are cardinal bones. How many more bones are there in the arm and legs than in the faceA) 2B) 6C) 14D) 16
Answers
We need to compare the number of bones in the arms and legs with the number of bones in the face.
The question says that there are 30 bones in the arms and legs.
The question also says that there are 14 bones on the face.
So, the difference between these will be how many more bones there are in the arms and legs than in the face:
[tex]30-14=16[/tex]A triangular banner has an area 2000 square yards. Find the measures of the base and height of the triangle if the base is five-eighths of the height. What are the units of measurement.
Answers
ANSWER:
Height = 80 yds
Base = 50 yds
STEP-BY-STEP EXPLANATION:
Given:
Area = 2000 square yards
Height = h
Base = 5/8h
We can calculate the value of the height using the triangle area formula, just like this:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ We replacing} \\ 2000=\frac{h\cdot \frac{5}{8}h}{2} \\ h^2=\frac{2000\cdot2\cdot8}{5} \\ h=\sqrt{6400} \\ h=80\text{ yd} \\ \text{ therefore, the base is:} \\ b=\frac{5}{8}\cdot80 \\ b=50\text{ yd} \end{gathered}[/tex]Height = 80 yds
Base = 50 yds
Which of the following values have 3 significant figures? Check all that apply.A. 10.1B. 100.05C. 120D. 129
Answers
The number of significant figures in 10.1 is 3 as there are two digits before the decimal and one digit after the decimal.
The number of significant digit in 100.05 is 5 as there are 3 digits before the decimal and two digits after the decimal.
The number of significant digits in 120 is 2.
The number of significant digits in 129 is 3.
Hence, the correct answers are (A) and (D)digit
The Jones family took a 12-mile canoe ride down the Indian River in 2 hours. After lunch, the return trip back up the river took 3 hours. Find the rate of the canoe in still water and the rate of the current.
Answers
Answer:
Step-by-step explanation:
As per the distance formula, the rate of the canoe in still water is 5 mph; the rate of the current is 1 mph.
Distance formula:
Distance is defined as the total movement of an object without any regard to direction. So, it is defined as the distance that covers how much ground an object despite its starting or ending point.
Distance = Speed x time
Given,
The Jones family took a 12-mile canoe ride down the Indian River in 2 hours. After lunch, the return trip back up the river took 3 hours.
Here we need to find the rate of the canoe in still water and the rate of the current.
According to the given question we know that,
Speed downriver = (12 mi)/(2 h) = 6 mph.
Speed upriver = (12 mi)/(3 h) = 4 mph.
Now, we need to find the canoe's rate in still water is the average of these speeds:
=> (6+4)/2 = 5 miles per hour.
Then the current's rate is calculated as the difference between the actual rate and the canoe's rate:
=> 6 - 5 = 1 miles per hour.
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A leaking pond loses 16 gallons of water in 47 hours. How many gallons of water will it lose in 33 hours?
Answers
A leaking pond loses 16 gallons of water in 47 hours.
How many gallons of water will it lose in 33 hours?
To solve this question we can use a rule of three:
16 gallons is to 47 hours as x gallons is to 33 hours:
[tex]\frac{16}{47}=\frac{x}{33}\Longrightarrow x=\frac{33\cdot16}{47}=\frac{528}{47}=\text{ 11.23}[/tex]Answer:
11.23 gallons
How many solutions does this equation have?-4k + 4k = 0
Answers
Let's try so solve this equation:
[tex]\begin{gathered} -4k+4k=0 \\ 0=0 \end{gathered}[/tex]When you have a result of 0 = 0, that means the equation has infinite solutions, that is, any value of k we use would satisfy the equation.
So the equation has infinitely many solutions.
The cost of 15 toys is $225. Identify the equation that represents this situation.
Answers
Question:
Solution:
Let us denote by c the cost of each toy. Then, according to the problem, the cost of 15 toys would be:
[tex]15c\text{ = 225}[/tex]So, we can conclude that the correct answer is:
[tex]15c\text{ = 225}[/tex]For the simple harmonic motion equation d=5sin (pi/4^+), what is the period?
Answers
the period is 8
Explanation
the function sin has the form
[tex]\begin{gathered} y=Asin(B(x+c))+D \\ where \\ Period=\frac{2\pi}{B} \end{gathered}[/tex]so
Step 1
a) identify B in the given function
given
[tex]d=5\text{ sin\lparen}\frac{\pi}{4}t)[/tex]hence
[tex]\begin{gathered} \frac{\pi}{4}t\Rightarrow B(t+c) \\ so \\ c=0 \\ \frac{\pi}{4}t=Bt \\ therefore \\ B=\frac{\pi}{4} \end{gathered}[/tex]b) now, replace in the formula to find teh period
[tex]\begin{gathered} Per\imaginaryI od=\frac{2\pi}{B} \\ Period=\frac{2\pi}{\frac{\pi}{4}}=\frac{2\pi *4}{1*\pi}=\frac{8\pi}{\pi}=8 \\ so \\ Period=8 \end{gathered}[/tex]therefore, the period is 8
I hope this helps you
Answer:
8
Step-by-step explanation:
A
P
E
X
Given rectangle BCDE below. If BF = 22, find EF.
Answers
Okay, here we have this:
Considering the provided graph, we are going to find the requested measure, so we obtain the following:
Let us remember that a rectangle besides having the properties of a parallelogram also stands out because it has congruent diagonals. So considering this we have:
BD=EC
EF=BF
EF=22
Finally we obtain that EF is equal to 22 units.
Please help me and tell me the process I have a test in an hour.Value of x.
Answers
Vertical angles are congruent.
From the figure, angle 3 and angle (7x + 3) are vertical angles, therefore angle 3 is (7x + 3)
Angle 1 and 127 degrees are supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle1+127=180 \\ \angle1=180-127 \\ \angle1=53 \end{gathered}[/tex]Angle 2 and 133 degrees are also supplementary angles and have a sum of 180 degrees.
That will be :
[tex]\begin{gathered} \angle2+133=180 \\ \angle2=180-133 \\ \angle2=47 \end{gathered}[/tex]Now we have angles 1, 2 and 3 which are angles in a triangle, and the sum of interior angles in a triangle is 180 degrees.
[tex]\begin{gathered} \angle1+\angle2+\angle3=180 \\ 53+47+(7x+3)=180 \\ \text{Solve for x :} \\ 100+7x+3=180 \\ 7x+103=180 \\ 7x=180-103 \\ 7x=77 \\ x=\frac{77}{7} \\ x=11 \end{gathered}[/tex]ANSWER :
x = 11
the top ten medal- winning nations in a tournament in a particular year are shown in the table. use the given information and calculate the mean number of gold medals for all nations
Answers
The number line below shows the values of x that make the inequality x > 1 true. Select all the values of x from this list that make the inequality x> 1 true. a. 3 b. -3c. 1 d. 700 e. 1.052. Name two more values of x that are solutions to the inequality.
Answers
Answer:
(a)3, 1, 700 and 1.05
(b)6 and 9
Explanation:
(a)The values of x from the list that make the inequality x> 1 true are:
3, 1, 700 and 1.05
(b)Two more values of x that are solutions to the inequality x>1 are:
6 and 9.
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answers
Answer:
True.
area of green square + area of purple square = area of red square
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
6.724x
Melinda went for a run. She was doing a great job until she got to a hill. She was so tired
running up the hill that she tripped over a rock at the top of the hill. She rolled all the way
down the hill. It took her 90 seconds to reach the bottom of the hill. She rolled for 225
feet. What is Melinda's rate of decent?
Answers
The Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
What is termed as the rate of decent/speed?Speed is defined as the proportion of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity. When an object travels the same distance in equal time intervals, it is said to be moving at a uniform speed.For the given question;
The distance covered by the Melinda after she tripped over a rock at the top of the hill is 225 feet.
The time taken by Melinda to reach the bottom of the hill is 90 seconds.
Then, the rate of decent will be the speed at which she will fall.
Speed = distance/ time
Speed = 225/60
Speed = 3.75
Thus, the Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
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Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. What is the actual measurement of that side of the courtyard? Show your work.
Answers
Okay, here we have this:
Considering that the scale is of 1 to 60, we obtain the following:
2.75 inches * 60 =165.
A construction worker dropped a hammer while building the Grand Canyon skywalk, 8100 feetabove the Colorado River. Use the formula t=(square root of h)/4 to find how many seconds it took for thehammer to reach the river.
Answers
Given:
[tex]t=\frac{\sqrt[]{h}}{4}[/tex]To find the time when the height h=8100 feet:
Substitute h=8100 in the given function.
[tex]\begin{gathered} t=\frac{\sqrt[]{8100}}{4} \\ t=\frac{90}{4} \\ t=22.5\text{ seconds} \end{gathered}[/tex]Thus, the time required for the hammer to reach the river is 22.5 seconds.
Suppose you have 40 shirts and 15 pairs of pants to choose from in your wardrobe. Using the fundamental counting principle, how many outfit combinations are possible?
Type the correct answer in the box. Use numerals instead of words.
Answers
By taking the product between the number of shirts and pants, we coclude that there are 600 different outfit combinations.
How many outfit combinations are possible?
The total number of outfit combinations is given by the product between the numbers of each type of clothes that you have.
you have 40 shirts.
Yo have 15 pairs of pants.
Then the number of different combinations is 40*15 = 600
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A painting is worth $9000 in 2007. The value of the painting increases by 12% eachyear.Estimate the length of time it takes for the value of the painting to double.
Answers
Step 1
State the formula for exponential growth
[tex]P(0)=P(1+r)^t[/tex]where;
[tex]\begin{gathered} P=\text{ worth in 2007=\$9000} \\ r=rate=\frac{12}{100}=0.12 \\ t=\text{ time for growth in years} \\ P(0)=\text{ Required value of growth in t years} \end{gathered}[/tex]Step 2
Find double the value of the painting.
[tex]2P=9000\times2=\text{ \$18000}[/tex]Step 3
Estimate the length of time it takes for the value of the paint to double
[tex]\begin{gathered} 18000=9000(1+0.12)^t \\ \frac{18000}{9000}==\frac{9000(1+0.12)^t}{9000} \\ 2=(1+0.12)^t \end{gathered}[/tex][tex]\begin{gathered} \ln 2=\ln (1.12)^t \\ \ln 2=t\ln (1.12) \\ \frac{t(\ln1.12)}{\ln1.12}=\frac{\ln2}{\ln1.12} \\ t=6.116255374\text{ years} \\ t\approx6.1163years\text{ approxi}mately\text{ to 4 decimal places} \end{gathered}[/tex]Hence, it will take approximately 6.1163 years for the value of the paint to double.
O GRAPHS AND FUNCTIONSGraphically solving a system of linear equations
Answers
(-3,4)
Explanationhere we have a system of 2 linear functions, To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
so
Step 1
graph the function (1)
a)
[tex]y=-\frac{1}{3}x+3[/tex]to graph the line we need 2 poins, so
i) P1, when x=0
[tex]\begin{gathered} y=-\frac{1}{3}x+3 \\ y=-\frac{1}{3}(0)+3=3 \\ so \\ P1=(0,3) \end{gathered}[/tex]ii) P2; when x= 3
[tex]\begin{gathered} y=-\frac{1}{3}(3)+3=-1+3=2 \\ so \\ P2;\text{ \lparen3,2\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P1 and P2
Step 2
now, graph line 2 ( function 2)
i) P3, when x= 0
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(0)+y=-5 \\ y=5 \\ so,P3=(0,-5) \end{gathered}[/tex]ii) P5, when x= 2
[tex]\begin{gathered} 3x+y=-5 \\ replace\text{ and solve for y} \\ 3(2)+y=-5 \\ 6+y=-5 \\ subtract\text{ 6 in both sides} \\ y=-6-5=-11 \\ y=-11 \\ so,\text{ P4=\lparen2,-11\rparen} \end{gathered}[/tex]iii) now, draw a line that passes trought P3 and P4
Step 3
finally, the solution is the orderede pair where the lines intersect each other
therefore, the solution is
(-3,4)
I hope this helps you