Answer:
As x>0 increases, f(x) increases. As x<0 decreases, f(x) increases.
1. Use the elimination strategy to solve this linear system:
(1) 12c + 28d = 12 (2) -20c + 16d = 168
2. Determine the number of solutions of this linear system:
(1) 7x − 3y = 43 (2) 7x - 3y = 13
The solution to the linear system is c = -6 and d = 3.
To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:
(1) 12c + 28d = 12
(2) -20c + 16d = 168
To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:
(1) 60c + 140d = 60
(2) -60c + 48d = 504
Now, we can add the equations:
(60c + 140d) + (-60c + 48d) = 60 + 504
188d = 564
d = 564/188
d = 3
Substituting the value of 'd' back into equation (1):
12c + 28(3) = 12
12c + 84 = 12
12c = 12 - 84
12c = -72
c = -72/12
c = -6
The solution to the linear system is c = -6 and d = 3.
Now let's analyze the second linear system:
(1) 7x - 3y = 43
(2) 7x - 3y = 13
By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.
The linear system has no solution.
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Sam and Bruno were computing how many kilometers they rode in the 3 bike trips they took last month. In order, they rode 45.7, 40.9, and 38 miles. Their solutions are shown.
Answer:
We are given number of miles the 3 bike trips they took last month = 45.7, 40.9, and 38 miles.
Sam and Bruno were computing how many kilometers.
Also one kilometer equals 0.621 miles.
From this we can see than 1 kilometer is smaller unit and a mile is a larger unit.
In order to convert number of miles into kilometers, we need to divide each number of mile by 0.621 miles.
We always divide a larger value by a smaller value to get the smaller unit.
Therefore,
Bruno is correct. When going from a larger unit to a smaller unit you need to divide.
Step-by-step explanation:
Hopefully this helped, if not HMU and I will get u a better answer.
-Have a great day! :)
To the nearest degree, what is the measure of the central angle for bathing?
The central angle of Bathing = 108 degrees.
In the given pie chart,
Since we know,
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
The whole circle is 360 degrees
which represents 100%.
It is given that,
Bathing = 30%
So have need to find 30% of 360 degrees.
Therefore,
Bathing = (30/100)x360
= (30/10) x 36
= 3x36
= 108
Hence,
The central angle = 108 degrees.
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The complete question is:
To the nearest degree, what is the measure of the central angle for bathing?
Complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and a compounded n times a year. Complete the table
The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.
To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.
The formula for calculating compound interest is as follows:
A = P(1 + r/n) ^nt,
where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.
The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &
\text{A = P(1 + r/n) }^{nt} &
\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &
\text{3100(1 + 0.04/1)}^{1*10} &
\text{\$4788.03} \\ \hline \text{2} &
\text{3100(1 + 0.04/2)}^{2*10} &
\text{\$4798.76} \\ \hline \text{4} &
\text{3100(1 + 0.04/4)}^{4*10} &
\text{\$4817.46} \\ \hline \text{12} &
\text{3100(1 + 0.04/12)}^{12*10} &
\text{\$4861.94} \\ \hline \end{array}\)
The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.
In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.
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A game Is played using one die. If the die is rolled and shows 3, the player wins $15. M the die shows any number other than 3, the player wins nothing. Complete parts (a) through (0)
a. If there is a charge of $3 to play the game, what is the game's expected value?
Answer:
0
Step-by-step explanation:
Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)
In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).
The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.
Therefore, the expected value is:
Expected Value = (1/6) x $15 + (5/6) x (-$3)
Expected Value = $2.50 - $2.50
Expected Value = $0
Simplify the expression 4(2f−5g) + 6g.
Answer:
8f-14g is the answer
Step-by-step explanation:
write each ratio as a fraction in simplest form then explain its meaning
Answer:
Step-by-step explanation:
2:5 for every 2 sandwiches there are 5 cartons of milk
sandwich to milk carton
4:10
I need to know the answer
Answer: on all of them or just a few. cuz you should only ask for one and a step by step, cuz then when you have a test or sum you won't know what to do
Answer:
Step-by-step explanation:
A) 7 B) 7
C) 31 D)640
E) 82 F) 62
G) 9 H)73
Robert has some nickels and some dimes. He has a maximum of 29 coins worth no less than $2.20 combined. If Robert has 10 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Robert's dimes are anywhere between 17 and 19.
Explanation:Nickels
are worth 5 cents, and
dimes
are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.
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M is the midpoint
of CD. A iş a point
not on CD. If AMC = 2x + 1" and AMD = 5x – 13, find the value of x.
The value of x given that M is the midpoint of CD is 14/3
How to determine the value of x?The given parameters are:
AMC = 2x + 1
AMD = 5x – 13
From the question, we understand that:
M is the midpoint of CD
This means that:
The segments are congruent
i.e. AMC = AMD
Substitute the known values in the above equation
So, we have
2x + 1 = 5x - 13
Collect the like terms in the above equation
So, we have
5x - 2x = 13 + 1
Evaluate the like terms in the above equation
So, we have
3x = 14
Divide both sides of the equation by 3
So, we have
x = 14/3
Hence, the value of x given that M is the midpoint of CD is 14/3
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Calvin estimated he would need 8 hours to
complete his science project. It actually took
him 12 1/2 hours to get everything done. What
was his percent error?
Answer:45%
Step-by-step explanation:
please answer need help
Find the radius of a circle with area 345 square centimetres
30 pts need in like 10 mins!!
Please say the answer like-
… divided by … = ……
Or
… times … = …..
Answer:
5.9
Step-by-step explanation:
It's because area is 345
Formula , A=πr2Find the √ of 34518.6=3.14×f2fR = 5.9Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
State the groups of shapes
Answer:
The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.
Step-by-step explanation:
The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.
It says. Use the graph of f to determine whether the following statement is true or false. The range of f is [-5,1]
The statement is false because the range is [-5, 1)
EXPLANATION
The range of a function is the set of y-values for which the function is defined.
From the graph given the range is:
-5≤ x < 1
This can be represented by interval notation as :
[ - 5, 1)
Therefore, the statement is false because the range is [-5, 1)
HELP PLS ASAPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C; 5.32
Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!
There are 4 pink, 5 yellow, 2 violet and 3 gray marbles
in a hat. You pick 2 marbles from the hat. Marbles are
NOT returned to the hat.
P(pink, then violet)
P(gray, then gray)
P(not yellow, not yellow)
P(yellow, not yellow)
================================================
Work Shown for problem 1
P(pink, then violet) = P(pink)*P(violet given 1st was pink)
= (4/14)*(2/13)
= 8/182
= 4/91
------------------------------
Work Shown for problem 2
P(gray, then gray)
= P(gray)*P(gray given 1st was gray)
= (3/14)*(2/13)
= 6/182
= 3/91
-------------------------------
Work Shown for problem 3
P(not yellow, not yellow)
= P(not yellow)*P(not yellow given 1st was not yellow)
= (9/14)*(8/13)
= 72/182
= 36/91
-------------------------------
Work Shown for problem 4
P(yellow, not yellow)
= P(yellow)*P(not yellow given 1st was yellow)
= (5/14)*(9/13)
= 45/182
In ΔOPQ, PQ = 17, QO = 9, and OP = 15. Which statement about the angles of ΔOPQ must be true?
Answer:
All angles are different.
Internal angles can be acute, obtuse, or right angle.
The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.
Step-by-step explanation:
Given - In ΔOPQ, PQ = 17, QO = 9, and OP = 15.
To find - Which statement about the angles of ΔOPQ must be true?
Proof -
As given,
In ΔOPQ, PQ = 17, QO = 9, and OP = 15.
As all the sides of the given triangle is different, So the given triangle is a Scalene triangle.
Now,
We know that , In Scalene triangle -
All sides are different.
All angles are different.
Internal angles can be acute, obtuse, or right angle.
The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.
Smallest angle: ∠P
Opposite shortest side.
Middle angle: ∠O
Opposite middle side.
Largest angle: ∠Q
Opposite longest side.
Therefore:
m∠P<m∠O<m∠Q
Less than symbol goes from smallest to largest
Here's a better Explanation!!!!!!
Use the diagram to calculate the measure of angle 5
Answer:
m∠5=22 °
Explanation:
In the diagram:
• Angles 4 and 90 degrees, are ,vertical angles,.
,• Angles 2 and 68 degrees, are ,vertical angles,.
Since the measure of vertical angles is equal:
\(\begin{gathered} m\angle4=90\degree \\ m\angle2=68\degree \end{gathered}\)In the triangle:
\(m\angle2+m\angle4+m\angle5=180\degree\text{ (sum of angles }in\text{ a triangle)}\)Substitute the measures of angle 2 and 4 obtained earlier:
\(\begin{gathered} 90\degree+68\degree+m\angle5=180\degree \\ 158\degree+m\angle5=180\degree \\ Subtract\text{ }158\degree\text{ from both sides of the equation.} \\ m\angle5=180\degree-158\degree \\ m\angle5=22\degree \end{gathered}\)The measure of angle 5 is 22 degrees.
7 cameras cost $308. The cost of each camera is the same. What is the cost of each camera?
Answer:
$44
Step-by-step explanation:
Hello!
It said that 7 cameras cost $308, right?
If each camera costs the same, it means that 7 cameras with the same value equal $308.
If we use this in an equation, and if x is a variable we want to solve, it would be:
7x = 308.
If 7x = 308, it would be
308/7 =
44.
So, $44 is the answer.
please help! Write the equation of line that has a y-intercept of -6 snd a slope of 3
Answer:
y=3x+6
Step-by-step explanation:
the equation of a line in
slope-intercept form
is.
xy=mx+b
6x + 4y = 7Kx + 8y = 7What is the value of K?
The value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
What are equations?Two things are equal, according to an equation.
It will be written with the equals sign "=" as in x+2=6.
What is on the left (x + 2) is equal to what is on the right ((6)), according to that equation.
A remark like "this equals that" can be compared to an equation.
So, we have the equations:
6x + 4y = 7
Kx + 8y = 7
Now, we know that both equations are equal to 7. so, we can write it as:
6x + 4y = Kx + 8y
Solve with subject K as follows:
6x + 4y = Kx + 8y
Kx - 6x = 4y - 8y
(K-6)x = -4y
k-6 = -4y/x
k = (-4y/x) + 6
Therefore, the value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.
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Mary spends 2 2 3 hours on math homework every week. She also spends 3 1 3 hours on art homework every week. How much time does Mary spend in total on math and art over 4 weeks?
Answer: This is the answer. please give me the brainliest. Thanks
Find the derivative of g(y)=(y-4)*(2y+y^2)
Answer:
\(g'(y)=3y^2-4y-8\)
Step-by-step explanation:
start by foiling out the given function
\(g(y)=(y-4)(2y+y^2)\\=2y^2+y^3-8y-4y^2\\=y^3-2y^2-8y\)
next, use the power rule to find the derivative
power rule: To use the power rule, multiply the variable's exponent n, by its coefficient a, then subtract 1 from the exponent. If there's no coefficient (the coefficient is 1), then the exponent will become the new coefficient.
\(g'(y)=3y^2-4y-8\)
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
,
,
The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3
How to determine the x-coordinates where the graphs of the equations intersect?From the question, we have the following parameters that can be used in our computation:
y = 2x
y = x² - 3
The x-coordinates where the graphs of the equations intersect is when both equations are equal
So, we have
x² - 3 = 2x
Rewrite the equation as
x² - 2x - 3 = 0
When the equation is factored, we have
(x + 1)(x - 3) = 0
So, we have
x = -1 and x = 3
Hence, the x-coordinates are x = -1 and x = 3
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Question
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
y = 2x
y = x² - 3
How do I make an equation on a graph?
to get the equation of any straight line, we simply need two points off of it, let's use the points in the picture below.
\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-10 +4}{6 +3} \implies \cfrac{ -6 }{ 9 } \implies - \cfrac{2 }{ 3 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{2 }{ 3 }}(x-\stackrel{x_1}{(-3)}) \implies y +4 = - \cfrac{2 }{ 3 } ( x +3) \\\\\\ y+4=- \cfrac{2 }{ 3 }x-2\implies {\Large \begin{array}{llll} y=- \cfrac{2 }{ 3 }x-6 \end{array}}\)
What is the slope of the line segment that passes through
points (1,3) and (5, 13)?
Answer: 5/2
Step-by-step explanation:
slope equation: (y2-y1)/(x2-x1)
13-3/5-1 = 10/4 or 5/2
Answer:
2.5
Step-by-step explanation:
Gradient (slope) =
\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)
reduce 4/36 to simplest termrs
If 2x-y=9 and 3x+4y=19, then y=
Answer:
x = 5
y = 1
Step-by-step explanation:
2x - y = 9
3x + 4y = 19
We multiply the first equation by 4
8x - 4y = 36
3x + 4y = 19
11x = 55
x = 5
Now we put 5 in for x and solve for y
2(5) - y = 9
10 - y = 9
-y = -1
y = 1
Let's Check the answer
2(5) - 1 = 9
10 - 1 = 9
9 = 9
So, x = 5 and y = 1 is the correct answer.