For each system of linearequations shown below, dassify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solutionSystem ASystem DSystem
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A system of linear equations is said to be consistent independent if the lines intersect each other only once, then there is only one solution, a system is said to be consistent dependent if the equations represent the same line and then they intersect each other in every point over the line and there are an infinite number of solutions. A system is said to be inconsistent if the lines are parlallel ad then they never intersect and there is no solution for the system.
According to the above definition, system A is consistent independent because the lines intersect only once and this means it has a unique solution.
System B is consistent dependent because both equations represent the same line and this means it has an infinite many solution.
System C is inconsistent because the lines never intersent each other and then this means system has no solution.
Related Questions
ndiana’s population has increased by 9.5% since 2000, when it was about 6 million people. What is Indiana’s population now? Write your answer as a standard number. Hint: the number will have 7 digits with two commas.
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Solution:
Given that the initial population was 6 million, and the population increased by 9.5% since 2000, this implies that
[tex]Percentage\text{ increase=}\frac{new\text{ population -inital population}}{initial\text{ population}}\times100[/tex]Let x represent the new population.
By substitution, we have
[tex]\begin{gathered} 9.5=\frac{x-6000000}{6000000}\times100 \\ \Rightarrow9.5=\frac{x-6000000}{60000} \\ solving\text{ for x, we have} \\ x=6570000 \end{gathered}[/tex]Hence, the new population is 6570000
Find the slope of the line that passesthrough these two points.Point 1 Point 2(3,5) (4,2)X1 У1X2 Y2m =y2-yiX2-X1m = [?]
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The coordinates are given as
[tex](3,5),(4,2)[/tex]Then find the slope of the line of the equation using
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values.
[tex]m=\frac{2-5}{4-3}=-\frac{3}{1}=-3[/tex]Hence the slope is -3.
Determine the value of y, if x is 1. y = |x – 11l
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y=l1-11l=l-10l=10 then the final answer is y=10 when x=1
a triangular prism has an equilateral triangular base. An edge of the base is 8cm. The height of the triangular base is 6.9 units. The height of the prism is 10 cm. What is the volume of the prism?
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The Volume of a Prism
Given a prism of a base area of value B and height H, the volume can be calculated as follows:
[tex]V=B\cdot H[/tex]We are given a triangular prism with an equilateral triangular base. The base has an edge of 8 cm and a height of 6.9 cm.
The area of a triangle of a base b and height h is:
[tex]B=\frac{b\mathrm{}h}{2}=\frac{8\cdot6.9}{2}=27.6\operatorname{cm}^2[/tex]Now calculate the volume:
[tex]\begin{gathered} V=27.6\cdot10 \\ V=276\operatorname{cm}^3 \end{gathered}[/tex]I have done the math but i did not get any of the answers I think I did something wrong
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ANSWER
[tex]\text{between }11.1\text{ and }12.1[/tex]EXPLANATION
We want to find the range that contains the value of the given radical:
[tex]\sqrt{5(20+9)}[/tex]To do this, simply the radicand:
[tex]\begin{gathered} \sqrt{5(29)} \\ \sqrt{145} \\ 12.04 \end{gathered}[/tex]Therefore, as we can see from the value above, the value of the radical given is contained between 11.1 and 12.1.
That is the answer.
An athlete buys Gatorade and water for hersporting event. The Gatorade costs $3 and thewater costs $1.00. She spent a total of 12dollars. Identify your variables and write anequation.
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Let x be the amount of Gatorade.
Let y be the amount of Water.
Cost of 1 Gatorade is $ 3.
Cost of water is $1.00
Total amount spend is $12.
Therefore the required equation is,
[tex]3x+y=12[/tex]Chris drinks 0.55 L of milk everyday. How much milk does he drink in 5 days? Write your answer in milliliters.
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Chris drinks 0.55 L of milk everyday
1 day= 0.55L
5days = 0.55 L *5
5days= 2.75 L
1 L = 1000 ml
then
2.75L = 2.75 * 1000 ml
2.75L= 2750 milliliters
Chris drinks 2750 mililiters in 5 days
Question 55 ptsIris likes to go for boat rides along the river with her family. In still water, the boat travels 6kilometers per hour. In the river, it takes them the same amount of time to go upstream 5 kilometersas it does to go downstream 10 kilometers. Write and solve an equation to calculate the speed ofthe river, r. Explain or show your reasoning
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Let's define
r: speed of the river
By definition:
speed = distance/time
The speed of the boat depends on the boat's own speed and the speed of the river. Then upstream:
6 - r= 5/t
or
t = 5/(6 - r)
and downstream:
6 + r= 10/t
or
t = 10/(6 + r)
It takes them the same amount of time to go upstream as it does to go downstream, then:
[tex]\begin{gathered} \frac{5}{6-r}=\frac{10}{6+r} \\ 5\cdot(6+r)=10\cdot(6-r) \\ 30+5r=60-10r \\ 5r+10r=60-30 \\ 15r=30 \\ r=\frac{30}{15} \\ r=2 \end{gathered}[/tex]The speed of the river is 2 kilometers per hour
Please help me understand this!Problem:The net of a rectangular prism and it's dimensions are shown in the diagram.Question:What is the total surface area of the rectangular prism in square inches?A. 143.25 in.^2B. 241.5 in.^2C. 258.75 in.^2D. 286.5 in.^2
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Surface Area
The image shows the shape of a rectangular prism
The surface area of the shape is the sum of all the individual rectangles
There are 6 small rectangles. We'll find their area and add them up to find the total surface area.
The area of a rectangle of dimension L and W is:
A=L.W
First rectangle: 3 in x 7.5 in
A1 = 3 * 7.5 = 22.5 square inch
Second rectangle: 11.5 in x 3 in
A2 = 3 * 11.5 = 34.5 square inch
Note this rectangle is repeated twice
The third rectangle has the same area of the first rectangle:
A3 = 3 * 7.5 = 22.5 square inch
The fourth rectangle has dimensions of 7.5 x 11.5
A4 = 7.5 * 11.5 = 86.25 square inch
This rectangle is also repeated twice
The total area is :
A = A1 + A2 + A2 + A3 + A4 + A4
A = 22.5 + 34.5 + 34.5 + 22.5 + 86.25 + 86.25
A = 286.5 square inch
Answer: D.
Which expression represents the phrase "three times the sum of a number and 4"? 3x−43(x+4)3x + 43(3x+4)
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Hence, the correct option is B
9. Find the x coordinates where the line y = 3x-2 intersects the circle x + y = 116. Only an algebraicsolution is acceptable.
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As given by the question
There are given that the y intersect and equation of circle is:
[tex]\begin{gathered} y-\text{intersect: y=3x-2} \\ Circle\colon x+y=116 \end{gathered}[/tex]Now,
From the equation of the circle
[tex]x+y=116[/tex]Then,
Substitute the value of y which is given in the question, into the given equation of a circle:
So,
[tex]undefined[/tex]basketball court is being painted the intersection below will be painted blue determine how many square feet of paint will be used
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
w = 8 ft
l = 15 ft
total area (paint) = ?
Step 02:
rectangle area
A = l * w
A1 = 15 ft * 8 ft = 120 ft²
circle area
A = π r²
half circle area
A = (π r²) / 2
A2 = (π * (4ft)²) / 2
A2 = 25.13 ft²
total area = A1 + A2 = 120 ft² + 25.13 ft² = 145.13 ft²
The answer is:
They will used 145.13ft² of paint.
Could I please get help on this word problem answer 13
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Let y = the larger number; and x = the smaler number.
Step 1.
Set up a system of equations:
y - x = 1 eq. 1
3y - 2x = 9 eq 2.
Step 2.
Solve the system by elimination:
1. Multiply eq. 1. by -3:
-3y + 3x = - 3 eq 3.
2. Subtract eq. 2. from eq. 3.:
-3y + 3x = - 3
3y - 2x = 9
_____________
x = 6
3. Substituting x = 6 on eq. 1:
y - x = 1
y - 6 = 1
y = 7
Answer: The larger number is 7.
Your wheat drill has a 7 1/2 inch row spacing. What is the row spacing in centimeters?
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Answer:
19.05 cm
Explanation:
First, we need to write 7 1/2 inches in decimal form, so we get:
[tex]7\frac{1}{2}=7+\frac{1}{2}=7+0.5=7.5\text{ inches}[/tex]Then, 1 inch has 2.54 centimeters, so 7.5 inches are equal to:
[tex]7.5\text{ in}\times\frac{2.54\text{ cm}}{1\text{ in}}=19.05\text{ cm}[/tex]Therefore, the row spacing is 19.05 cm
Hi I need help with this practice question from my calculus prep guide
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Explanation:
Limit of the function:
Limit is the approximate value of the function at a defined value of x.
[tex]\begin{gathered} \lim _{x\to a}f(x)=L \\ As\text{ }x\rightarrow a\text{ then, f(x)}\rightarrow L \end{gathered}[/tex]a)
[tex]\lim _{x\to-\infty}(2x^3-2x)=-\infty[/tex]This limit is true. As x approaches negative infinity the function is also approached to negative infinity.
b)
[tex]\lim _{x\to\infty}(-2x^4+6x^3-2x)=-\infty[/tex]As x tends to infinity. The functions tend to have negative infinity.
This statement is true.
c)
[tex]\lim _{x\to\infty}(9x^5-6x^3-x)=-\infty[/tex]When x tends to infinity, the function will also go to infinity.
So, This statement is false.
I was working with tutor Valerie Millan on a geometry problem and I somehow got disconnected when I tried to take a picture of the diagram to send to her. I also contacted another tutor but the system keeps kicking me out! I have a geometry question where I’m asked that
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From triangle ABC;
[tex]\angle A+\angle B=\angle ACD\ldots\ldots.\ldots\ldots\text{.}\mathrm{}\text{equation 1}[/tex]Also, from triangle BPC;
[tex]\begin{gathered} \angle PBC+\angle BPC=\angle PCD \\ \frac{\angle B}{2}+\angle BPC=\frac{\angle ACD}{2}\ldots\ldots...\ldots\ldots\ldots\ldots\text{.equation 2} \end{gathered}[/tex]Then, we multiply equation 2 by 2, we have;
[tex]\angle B+2(\angle BPC)=\angle ACD\ldots\ldots.\ldots\ldots.\ldots..equation\text{ 3}[/tex]Then, we find the difference of equation 1 and equation 3, we have;
[tex]\begin{gathered} \angle A+\angle B-\angle B-2(\angle BPC)=\angle ACD-\angle ACD \\ \angle A-2(\angle BPC)=0 \\ \angle A=2(\angle BPC) \end{gathered}[/tex]North High School has 5000 students. South Highschool has 1/10 as many students as North Highschool. Hom many students are there are South Highschool?
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SOLUTION
North High School has 5000 students
South Highschool has
[tex]\frac{1}{10}\text{ of the students in North Highschool}[/tex]The number of students in South Highschool will be
[tex]\begin{gathered} \frac{1}{10}\times5000 \\ =500\text{ students } \end{gathered}[/tex]Hence, the answer is 500 students
At the school bookstore, Dakota purchased a notebook for53.75, 6 pencils for $0.20 each, and 2 pens for 51.19 each.By what amount (a ) was cost of the pens greater than thecost of the pencils?
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COST OF ONE PRNCIL = 0.20
COST OF 6 PENCILS =6X0.20=$1.2
COST OF ONE PEN =51.19
COST OF 2 PENS =51.19X2=102.38$
SO 102.38-1.2=101.18
tHUS THE REQUIRED ANSWER IS 101.18
Solve 3x2 + 4x = 2. (2 points)O 2+ V106-2+2V1030 -2+ V103O 41103
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Solve :
[tex]3x^2+4x=2[/tex]so, 3x^2 + 4x - 2 = 0
using the formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]so, a = 3 , b = 4 and c = -2
so,
[tex]x=\frac{-4\pm\sqrt{4^2-4\cdot3\cdot(-2)}}{2\cdot3}=\frac{-4\pm\sqrt{16+24}}{6}=\frac{-4\pm\sqrt{40}}{6}[/tex][tex]x_1=\frac{-4+\sqrt{40}}{6}=0.387[/tex]And
[tex]x_2=\frac{-4-\sqrt{40}}{6}=-1.721[/tex]so, x = 0.387 or -1.721
The answer is rounded to 3 decimals.
make it without simplifications
[tex]\sqrt{40}=\sqrt{4\cdot10}=2\sqrt{10}[/tex][tex]x\text{ = }\frac{-4\pm2\sqrt{10}}{6}=\frac{2\text{ (-2}\pm\sqrt{10})}{2\cdot3}=\frac{-2\pm\sqrt{10}}{3}[/tex][tex]x\text{ = }\frac{-2+\sqrt{10}}{3}\text{ OR }x\text{ =}\frac{-2-\sqrt{10}}{3}[/tex]
Use the fact that the sum of the 3 angles in a triangle is 180° to answer this question.One angle in a triangle has a measure that is three times as large as the smallest angle. Themeasure of the third angle is 20° more than that of the smallest angle. Find the measure of the eachof the angles.nsOThe SMALLEST angle has a measure of
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Let us call the angles x, y , and z. We know that these three angles must add up to 180; therefore,
[tex]x+y+z=180[/tex]If x is the smallest angle, we know that one of the angles (call it y) is 3 times this angle; therefore,
[tex]y=3x[/tex]And the other angle z is 20 more than the smallest angle x; therefore, we have
[tex]z=20+x[/tex]Putting the last two equations into the very first equation gives us
[tex]x+3x+20+x=180[/tex][tex]5x+20=180[/tex][tex]\textcolor{#FF7968}{\therefore x=32}[/tex]which is the measure of the smallest angle.
The other two angles are
[tex]y=3x=3(32)[/tex][tex]\textcolor{#FF7968}{y=96}[/tex]and
[tex]z=20+x=20+32[/tex][tex]\textcolor{#FF7968}{z=52.}[/tex]Hence, the measure of the smallest angle is 32,
The measure of the middle angle is 52
And the measure of the largest angle is 96.
what is the domain of y=-16x^2+335x+7
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Let's begin by identifying key information given to us:
[tex]\begin{gathered} y=-16x^2+335x+7 \\ x=-10 \\ y=-16(-10)^2+335(-10)+7=-4943 \\ y=-4943 \\ \\ x=0 \\ y=-16(0)+335(0)+7=7 \\ y=7 \\ \\ x=10 \\ y=-16(10)^2+335(10)+7=1757 \\ y=1757 \end{gathered}[/tex]The domain of an expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Therefore the interval notation for this function is:
[tex](-\infty,\infty)[/tex]Given the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)n = 15, p = 0.4, find P(4 successes) n = 12, p = 0.2, find P(2 success ) n = 20, p = 0.05, find P(at most 3 successes) (hint for c. P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)
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Solving the first problem: n=15 and p=0.4.
Explanation:
Step 1. We are given the number of trials n
[tex]n=15[/tex]And the probability of success:
[tex]p=0.4[/tex]We need to find the probability of 4 successes P(4).
Step 2. Since it s a problem where the outcome is either success or failure, we use the binomial distribution formula:
[tex]p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}[/tex]Where p(x) is the probability of x successes. x is the number of successes, and q is the probability of a failure.
Step 3. In this case, x is 4:
[tex]x=4[/tex]The probability of failure is defined as follows:
[tex]\begin{gathered} q=1-p \\ \downarrow \\ q=1-0.4 \\ \downarrow \\ q=0.6 \end{gathered}[/tex]Step 4. Substituting the known values into the binomial distribution formula:
[tex]\begin{gathered} p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x} \\ \downarrow \\ p(4)=\frac{15!}{(15-4)!(4!)}(0.4)^4(0.6)^{15-4} \end{gathered}[/tex]Solving the operations:
[tex]\begin{gathered} p(4)=\frac{15!}{(11)!(4!)}(0.0256)(0.6)^{11} \\ \downarrow \\ p(4)=\frac{15!}{(11)!4!}(0.0256)(0.003628) \end{gathered}[/tex]Step 5. Solving step by step and simplifying the factorial expressions, the result is:
[tex]\begin{gathered} p(4)=\frac{15!}{(11)!4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12\times11!}{(11)!4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12}{4!}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{15\times14\times13\times12}{4\times3\times2\times1}(0.0256)(0.003628) \\ \downarrow \\ p(4)=\frac{32760}{24}(0.0256)(0.003628) \\ \downarrow \\ p(4)=(1365)(0.0256)(0.003628) \\ \downarrow \\ p(4)=0.126776 \end{gathered}[/tex]The probability is 0.126776
Answer:
[tex]P\left(4successes\right)=0.126776[/tex]Find the value of f(4).
y = f(x)
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Answer:- 4
Step-by-step explanation:
given that y = f(4)
therefore x = 4
therefore y=4
Write a recursive formula for the arithmetic sequence and identify the 8th term.a={8.9, 10.3, 11.7,...}Please share your work/thinking/calculations to earn full credit.
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An arithmetic sequence is given. It is required to find the recursive formula and the 8th term.
The given sequence is:
[tex]a=\left\lbrace8.9,10.3,11.7,...\right\rbrace[/tex]Explanations:
Recall that a recursive formula is a formula in which the next term of a sequence is defined by prior terms.
The recursive formula of an arithmetic sequence is:
[tex]a_n=a_{n-1}+d[/tex]Where n is the number of terms, a₁ is the first term, and d is the common difference of the sequence.
The common difference is the difference between each pair of consecutive terms in an arithmetic sequence.
Hence, the common difference of the given sequence is:
[tex]d=10.3-8.9=1.4[/tex]Substitute the common difference into the recursive formula:
[tex]a_n=a_{n-1}+1.4[/tex]Substitute n=4 into the formula:
[tex]\begin{gathered} a_4=a_{4-1}+1.4 \\ \Rightarrow a_4=a_3+1.4 \end{gathered}[/tex]Substitute the third term of the sequence:
[tex]a_4=11.7+1.4=13.1[/tex]Follow the same procedure of adding the common difference to the previous term to get the next term:
[tex]\begin{gathered} a_5=14.5 \\ a_6=15.9 \\ a_7=17.3 \\ a_8=18.7 \end{gathered}[/tex]Hence, the 8th term of the sequence is 18.7.
Answers:
The recursive formula of the sequence is:
[tex]a_n=a_{n-1}+1.4[/tex]The 8th term of the sequence is 18.7.
I forgot how to find the slope and y-intercept of the equation. For example y=3/4x - 5
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The slope of any equation of the curve is defined as the rate of change in y-coordinate with respect to rate of change in x- coordinate
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1_{}_{}}[/tex][tex]\text{Slope}=\frac{dy}{dx}\text{ }[/tex]Differentiate the given equation with respect to x
[tex]\begin{gathered} y=\frac{3}{4}x-5 \\ \frac{dy\text{ }}{dx}=\frac{3}{4}-0 \end{gathered}[/tex]Thus, the slope of the equation is 3/4
or Slope of the equation y=3/4x-5 is 3/4.
Now, for the y-intercept
Put x=0 in the equation
[tex]\begin{gathered} y=\frac{3}{4}x-5 \\ y=\frac{3}{4}(0)-5 \\ y=-5 \end{gathered}[/tex]The y-intercept of the equation y=3/4x-5 is y=(-5)
you drive an average of 400 miles per week in a car that gets 18 miles per gallon. With gasoline price at 4 per gallon approximately how much would you save each year on gas if you instead had a car that got 50 miles per gallon?
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Okay, here we have this:
simplify the expression 4n + 1/8 + 4 y + 1/8 + 9n - 3 y
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Solve each equation . 4^3x-3= 8^4x-4
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Answer:
x = 1
Explanation:
To solve for x in the equation,
[tex]4^{3x-3}=8^{4x-4}[/tex]We write each side as
[tex]\begin{gathered} 4^{3x-3}=(2^2)^{3x-3} \\ 8^{4x-4}=\mleft(2^3\mright)^{\mleft\{4x-4\mright\}} \end{gathered}[/tex]which gives
[tex](2^2)^{3x-3}=(2^3)^{\{4x-4\}}[/tex]Now, using the property that
[tex](A^x)^y=A^{xy}[/tex]we rewrite the above as
[tex]2^{2(3x-3)}=2^{3\{4x-4\}}[/tex]Which implies
[tex]2(3x-3)=3(4x-4)_{}[/tex]Expanding the equation gives
[tex]6x-6=12x-12[/tex]Adding 6 to both sides gives
[tex]6x=12x-12+6[/tex][tex]6x=12x-6[/tex]subtracting 12x from both sides gives
[tex]6x-12x=-6[/tex][tex]-6x=-6[/tex]Finally, dividing both sides by -6 gives
[tex]x=1[/tex]which is our answer!
what percentage of 375 is 225
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SOLUTION:
We are to find what percentage of 375 is 225.
[tex]\frac{225}{375}\text{ X 100}[/tex][tex]60\text{ percent}[/tex]In conclusion, 225 is 60% of 375.
x equal 3 true or false
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The statement:
[tex]x=3[/tex]Will be true or false depending on the value that we assign to the number x. As you can see, that will be true only then x is equal to 3 or any equivalent representation of that same number.
That statement will be false if any other number is used as the value of x.