Eliminating c first is easiest:
• adding equations 1 and 2 together gives
(4g + 12f - c) + (10g - 14f + c) = 40 + (-74)
14g - 2f = -34
[7g - f = -17]
• adding equations 1 and 3 together gives
(4g + 12f - c) + (12g + c) = 40 + (-36)
16g + 12f = 4
[4g + 3f = 1]
Multiply the first equation wrapped in [] above by 3, then add it to the other one. This eliminates f :
3 (7g - f ) + (4g + 3f ) = 3 (-17) + 1
(21g - 3f ) + (4g + 3f ) = -51 + 1
25g = -50
Solve for g :
g = -2
Plug this into the first equation in [] and solve for f :
7 (-2) - f = -17
-14 - f = -17
f = 3
Plug these both into any of the original 3 equations. The third one has no f term, so that's simplest. Solve for c :
12 (-2) + c = -36
-24 + c = -36
c = -12
Given the following equations, determine the relationship of the lines they represent: y = 5 and x = 6.
Answer:
2x2/er5
Step-by-step explanation:
Andrew left his house at time zero and drove to the store, which is 10 blocks away, at a
speed of 5 blocks per minute. Then he stopped and went into the store for 2 minutes.
From there, he drove in the same direction at a speed of 5 blocks per minute until he
got to the bank, which is 10 blocks away from the store. He stopped at the bank for 3
minutes. Then he drove home at a speed of 4 blocks every minute. Make a graph of
showing the number of blocks away from home that Andrew is 2 minutes after he
leaves his house, until he gets back home.
the graph of Andrew's distance from home will look like this: Time (x-axis) 0 1 2 3 4 5 6 7 8 9 10 Distance (y-axis) 0 5 10 10 15 20 20 24 28 32 0
What is graph?Graph is a data structure which is used to represent relationships between objects or data points. It is composed of nodes and edges, where nodes are the objects and edges are the connections between the objects. Graphs are used to represent mathematical equations, networks, and data structures such as trees. They are also used to represent relationships between data points in large datasets. Graphs can be used to represent both directed and undirected relationships, and are commonly used in many fields including computer science, engineering, mathematics, and data science.
From the given information, we can create a graph that shows Andrew's distance from home as he drives to the store, to the bank, and back again. The x-axis will represent time (in minutes), and the y-axis will represent the number of blocks away from home.
At time zero, Andrew is at his home, so the graph will begin with a point at (0, 0). As he travels to the store, the graph will move up 5 blocks for every minute he drives. Therefore, after 2 minutes, he will be 10 blocks away from home, so the graph will be at (2, 10). After he stops at the store for 2 minutes, he will still be 10 blocks away from home, so the graph will stay at (2, 10).
When he leaves the store and drives to the bank, he will move 5 blocks each minute. After 5 minutes, he will be 25 blocks away from home, so the graph will be at (5, 25). After he stops at the bank for 3 minutes, he will still be 25 blocks away from home, so the graph will remain at (5, 25).
Finally, when he drives home, he will move 4 blocks for each minute he drives. After 5 more minutes, he will be back at his home, so the graph will be at (10, 0).
Therefore, the graph of Andrew's distance from home will look like this:
Time (x-axis) 0 1 2 3 4 5 6 7 8 9 10
Distance (y-axis) 0 5 10 10 15 20 20 24 28 32 0
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John bought a shirt at ksh 500 and marked it at Ksh 600. A customer bought it at ksh 550. What was the percentage discount?
Answer:
The original price of the shirt was Ksh 500 and it was sold for Ksh 550.
The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.
To find the percentage discount, we can use the formula:
percentage discount = (discount ÷ original price) × 100%
percentage discount = (-50 ÷ 500) × 100%
percentage discount = -10%
Therefore, the percentage discount is 10%.
The general form of the equation of a circle is a X squared plus BY squared plus 3X plus 3Y plus Z equals zero wear a equals B does not equal zero is the circle has a radius of three units in the center lies on the Y axis, which set of values of a B C,D and E my correspond to the circle
The set of values that corresponds to the circle with a radius of three units and the center lying on the Y axis is:
A = 1, B = 1, C = 0, D = 3, E = 0.
The general equation of a circle is given by:
x^2 + y^2 + 2gx + 2fy + c = 0
In this case, since the circle has a radius of three units and the center lies on the Y axis, we can deduce the following information:
The center of the circle lies on the Y axis, which means the x-coordinate of the center is zero.
The radius of the circle is three units, which means the distance from the center to any point on the circle is three units.
Using the information above, we can substitute the values into the general equation to solve for the corresponding values:
Substituting the x-coordinate of the center (zero) into the equation, we have:
0^2 + y^2 + 2g(0) + 2fy + c = 0
y^2 + 2fy + c = 0
Since the center lies on the Y axis, the x-coordinate is zero, so the term with x (2gx) becomes zero.
Substituting the radius of the circle (three) into the equation, we have:
(3)^2 = 9
Therefore, the equation becomes:
y^2 + 2fy + c = 9
Comparing this equation with the general form of the circle equation, we can deduce the values of A, B, C, D, and E as follows:
A = 1 (coefficient of x^2)
B = 1 (coefficient of y^2)
C = 0 (constant term)
D = 3 (coefficient of x)
E = 0 (coefficient of y)
Hence, the set of values that corresponds to the circle is A = 1, B = 1, C = 0, D = 3, and E = 0.
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What are the coordinates of the endpoints of the midsegment for A RST that is parallel TS? Enter your answer by filling in the boxes. (_ , _) and (_ , _)
Answer:
2,4 3,5
Step-by-step explanation:
a regular deck of playing cards is shuffled what would probability of not drawing an ace
Answer:44/52
Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =
Which of the following shapes are polygons with more than 444 sides?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Hexagon
(Choice B)
B
Pentagon
(Choice C)
C
Triangle
(Choice D)
D
Rectangle
Answer:
It's the hexagon and pentagon.
Which function has a greater maximum?
�
(
�
)
=
−
2
(
�
+
4
)
2
+
1
f(x)=−2(x+4)
2
+1f, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, plus, 4, right parenthesis, squared, plus, 1
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.
The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.
1. The given function is f(x) = \(-2(x+4)^2\) + 1.
2. To find the maximum of the function, we need to determine the vertex of the parabola.
3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.
4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.
5. The x-coordinate of the vertex is given by h = -4.
6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.
7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.
8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).
9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.
10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.
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Combine like terms in each expression
1. 1/4k+1/4m-2/3k+5/9m
2. -4b + 2w + (-4b) + 8w
3. 6- 5z + 8 - 4z + 1
Answer:
5/12k = 29/36m
8b = 10w
9z = 15
Step-by-step explanation:
Combining the like terms in these sets of equations is quite easy and straightforward. All we do is carry the like terms to either of the side of the equation, and question is solved. As in below
1/4k + 1/4m - 2/3k + 5/9m =
1/4k - 2/3k + 1/4m + 5/9m = 0
-5/12k + 29/36m = 0
5/12k = 29/36m
-4b + 2w + (-4b) + 8w =
-4b - 4b + 2w + 8w = 0
-8b + 10w = 0
8b = 10w
6- 5z + 8 - 4z + 1 =
6 + 8 + 1 - 5z - 4z = 0
15 - 9z = 0
9z = 15
500 ML = __ L
Perform numerical calculations
Answer:
500*10^6 L or 5.00*10^8 L.
Step-by-step explanation:
Capital M shows mega which equal to 10^6.
So, 500 ML = 500*10^6 L
or 5.00*10^8 L.
Answer:
0.5
Step-by-step explanation:
Step 1:
1 L = 1000 ML
Step 2:
500 ML ÷ 1000
Answer:
0.5 L
Hope This Helps :)
am i doing this right
Please look at the pic and help!!
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
If the perimeter of a sector is 4 times its radius, then the radian measure of the central angle of the sector is (A) 2. (B) 4.(C)2/π.(D)4/π.(E) impossible to determine without knowing the radius.
Answer: (B) 4
Step-by-step explanation: first, we know the perimeter is 4 times the length of the radius. So, we can make the equation: P=4r
Now, we can plug this into the arc length equation:
S=πrθ/180
Solve for θ(theta):
4r=πrθ/180
720/π = θ
720/π degrees = 4 radians
θ = 4 radians
Option A is the correct answer. the radian measure of the central angle of the sector is two(2)
The circumference of a circle: It is defined as the linear distance around it, a circle is opened to form a straight line, then the length of that line will be the circle’s circumference.
There is a formula to calculate the perimeter or circumference of a circle given by=2*pi*r
Where r is the radius.
If the perimeter of a sector is 4 times its radius, then the arc measure of the sector is
4r-2r=2r
so if 2*pi radians (full circle) has a length=2*pi*r
X radians contains 2*r
Then the X value is defined as:
X=2*r*(2*pi)/(2*pi*r)
X=2
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Which expression dose NOT represent the amount shaded in the grid.
The expression that does not represent the amount shaded in the grid is 0.078. Option C is the correct answer.
The expression represents a decimal value of 0.78, which is not equivalent to the shaded amount in the grid. It is different from the numbers provided in the question. The expression represents a decimal value of 0.7800, which is also not equivalent to the shaded amount in the grid. It is different from the numbers provided in the question. Option C is the correct answer.
The expression represents a decimal value of 0.078, which is not equivalent to the shaded amount in the grid. It is different from the numbers provided in the question.
Let's simplify ((1/10) × 7 + (1/100) × 8) expression. (1/10) × 7 equals 0.7, and (1/100) × 8 equals 0.08. Adding these together, we get 0.7 + 0.08 = 0.78. This expression is equivalent to option A.
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solve pls brainliest
Answer:
82.89 grams
Step-by-step explanation:
17.5+65.39=82.89
The answer to the image above is 82.89 grams of salt in the bowl
dividing 1/9 is equal to multiplying by
Answer: 9
Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:
10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.
Now lets try it with 1/9.
X divided by 1/9 = X times 9/1.
So dividing by 1/9 is equal to multiplying by 9.
Ella stacks two boards under a table to make it level. One board is į inch thick. The
other board is inch thick. Which equation most closely estimates the thickness of
5
12
the two boards?
Step-by-step explanation:
the problem description is incomplete or wrongly copied.
we don't know the thickness of the boards, and we cannot understand what we need to calculate, and what the answer options are.
-7 times what equals 2? i’ll give brainliest
Answer:-3.5
Step-by-step explanation:
Each side length of a triangle is 4 cm. What type of triangle is it?
☐ right
□acute
Equilateral
Isosceles
Answer: Equilateral
Step-by-step explanation:
It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.
Hope you understood.
I need help please!!!
Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.
I prefer Wills method because it is easier and less complicated.
How to solve differences?Wills method:
(5x + 6x) - (2x - 1)
Subtract both 2x and -1
5x + 6x - 2x - - 1
5x + 4x + 1
In conclusion, Wills method is preferred when both methods are compared.
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help!!!! please <33333
Hello!
For this you would just need to multiple straight across. Here's how you would set it up:
3/4 ·1/8
Then you would multiple 3 x 1 = 3
And 4 x 8 =32
Your answer should be 3/32, it cannot be simplified so that is the final answer :).
On Monday, 405 Students went on a trip to the zoo. All 9 uses were filled and 9 students had to travel in cars. How many students were in each bus?
Answer:
Step-by-step explanation:
n = 41
There are 41 students on each bus.
What is the slope of the line parallel to the line below?
Answer:
-3/4
Step-by-step explanation:
Please help!! Thank youuu
Answer:
Angle 2 = 140
Angle 3 = 40
Angle 4 = 140
EXPLANATION:
So all of these angles are going to add up to 360 degrees. The angle on the opposite side is going to be equal
angle 2 = angle 4
angle 3 = angle 1
40+40= 80
360-80= 280
280/2= 140
what does new thousand mean?
We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.
What is a thousand?A thousand is a number that denotes the sum of 1,000 units or ten hundreds.
The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."
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Enter the terms and the coefficients of the expression.
4x - 50y - 40
The terms are
and
The coefficients are
and
Answer:the terms are 4x,50y, and 40 the coefficients are 4 and 50
Step-by-step explanatio
Poppy gets semi-monthly paycheck of $2,375. What is her annual income?
Answer:
57,000
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!!
Answer:
1710
Step-by-step explanation:
simplify | 1×10^3 + 7×10^2 + 4×10 = 1710
8 + __ = 4(2+4) I need help on this also can you explain it to me so I know next time
Answer:
16.
Step-by-step explanation:
We need 8 + a number to equal 24. We need it to equal 24 because 2 + 4 = 6 and 6 x 4 = 24. To find the missing number we need to subtract 8 from 24. 24 - 8 = 16. Let's plug 16 into the equation.
8 + 16 = 4(2 + 4)
24 = 4(2 + 4)
24 = 4(6)
24 = 24
Therefore, 16 is the correct answer.
Suppose I am rolling a standard 6-sided dice. Let A be the event I roll a prime number, Let B be the event I roll a number less than or equal to 4. I ran a trial 10 times and got the results 2, 4, 3, 1, 5, 6, 1, 3, 2, 1
What is the experimental P(B)
The experimental probability of rolling a number less than or equal to 4 is 0.7.
How is conditional probability calculated? What does it mean?The likelihood that an event (A) will occur given the occurrence of another event (B) is known as conditional probability. P(A|B), which stands for "the probability of A given B," is used to express it. You must first determine P(A and B) by multiplying the odds of A and B happening together. Next, you may compute P(A|B). The conditional probability of A given B is then obtained by dividing the result by P(B).
Several situations in everyday life, including medical diagnosis, industrial quality control, and risk assessment in insurance, call for the usage of conditional probability.
Given that, the trial was run 10 times.
Thus,
P(B) = (number of times B occurred) / (total number of trials)
= 7 / 10
= 0.7
Therefore, the experimental probability of rolling a number less than or equal to 4 is 0.7.
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