If angles a and b are supplemented, they add up to 180 degrees. If angles a and c are supplements, they add up to 180 degrees.
Since angle a is a common angle in both of these equations, you can conclude that angles b and c must also be supplemented and add up to 180 degrees. Supplemented means that two angles add up to 180 degrees. In other words, they are supplementary angles.
Supplementary angles are two angles that add up to 180 degrees. They are considered "complementary" to each other as they "complete" a straight line, which measures 180 degrees. A straight line is a geometric object with no curvature, consisting of an infinite set of points that extends infinitely in both directions. It is the shortest distance between two points and has the property of being perfectly straight. In geometry, straight lines are a basic building block to define and measure other shapes and figures.
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Factoring out 3x^2+2x-21=0
The factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.
How to solve quadratic equations?All related terms should be combined and moved to one side of the equation. Moving all of the components to one side of an equation while maintaining the x2 term positive is the first step in factoring an equation. The x2 terms, x terms, and constants (integer terms) must all be added to or subtracted from one another, and they must all be moved to one side of the equation so that nothing is left on the other. You may just write "0" on the other side of the equal sign if that side has no more words.
Given that the equation is 3x^2 + 2x -21 = 0
Using the method of expansion to solve the quadratic equation we have:
3x^2 + 2x -21 = 0
Multiply (a)(c) and find its prime factors:
(3)(21) = 63
Prime factors: 7, 9
Using the factors deduce the middle term:
3x^2 + 9x - 7x -21 = 0
Take the common in the first two and the last two terms:
3x(x + 3) -7(x+3) = 0
(3x - 7) (x + 3) = 0
Equate to 0:
(x + 3) = 0
x = -3
(3x - 7) = 0
x= 7/3
Hence, the factors of the equation 3x^2+2x-21=0 are (3x - 7) (x + 3) = 0 and x = -3 and x = 7/3.
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The domain of y = sin x is the set of _______. all real numbers > 0 real numbers all real numbers < 0 all real numbers > x
The domain of y = sin x is the set of all real numbers.
The sine function, represented by y = sin x, is defined for all real numbers, meaning that any real number can be plugged into the function as the input (x) and will produce a valid output (y). Therefore, the domain of y = sin x is the set of all real numbers.
Find the percentage error in x when it is estimated to be y and y>x
Answer:
The percentage error in x can be calculated as follows:
Percentage error = (Estimated value - Actual value) / Actual value * 100
Let x be the actual value and y be the estimated value such that y > x.
Percentage error = (y - x) / x * 100
This formula calculates the absolute error in terms of a percentage of the actual value.
Can somebody translate:
2 more than the quotient of a number and 4 is equal to 5
Answer: x/4+2=5
Step-by-step explanation:
Based on the scatter plot below, which is a better prediction for y when x = 5?
is it one or 6
According to the scatter plot below, when x = 5, the value of y is 1.
What is scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables). With a particular confidence interval, a scatter plot might imply several types of relationships between variables. Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).
Here,
Based on the scatter plot below, when x=5 then value of y is 1.
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consider the vectors a = (−1, −2, 3), b = (3, 0, −2), v = (2, −5, −4) and the plane p given by 2x y = z 13. 1. what should the real number y be, so that (1, y, −9) is perpendicular to v?
The value of y if (1, y, −9) is perpendicular to vector v is 38/5.
Given vector v = 2i - 5j - 4k and vector c = 1i + yj - 9k
In the question, we are told that we need to find y if vector v and vector c are perpendicular. So, if two vectors are perpendicular their dot product is zero
So, vector v.vector c = 0
(2i - 5j - 4k ).(i + yj - 9k) = 0
2(1) - 5(y) - 4(-9) = 0
2 - 5y + 36 = 0
5y = 38
y = 38/5
Hence, the value of y is 38/5.
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If tan (theta) = 24/10, 0 < (theta) < pi/2 then
sin(theta) equals
cos(theta) equals
sec(theta) equals
To determine the cosine of an angle, use the Cos Theta Formula in mathematics.The Answer is 3.
Find the solution ?If arctan(2)=, then let the angle be.In this case, tan = 2.
We get =63.43 when we plug the value into the arctan(x) graph.
We do this by using the x=2 line and examining where it crosses the arctan graph (x).
To determine the cosine of an angle, use the Cos Theta Formula in mathematics.
The symbol for it is Cos(), and it has the following form:
adjacent/hypotenuse = cos().
f(θ) = tan(θ) = 3
Note that
tan (x+y ) = tan x +tan y/1-tan x tan y
Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
= (tanθ + tan π)/(1 -tanθ tan π)
= 3/1 = 3
Answer is 3.
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Two identical rectangular prisms and two identical cubes are joined.
Find the new solid’s surface area.
The surface area of the whole solid will be 144 square inches.
What is a surface area?The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.
The surface area will be calculated as:-
SA = SA of cuboid + SA of cube
SA = 6 x ( 11 x 2 ) + 6 x 2
SA = 132 + 12
SA = 144 square inches
Therefore, the surface area of the whole solid will be 144 square inches.
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what is the measurement of Arc FQ?
The measure of arc FQ is given as follows:
155º.
How to obtain the measure of arc FQ?The measure of arc FQ is obtained applying the two secant theorem in the context of this problem.
From the theorem we have that the angle of 40º represents half the difference between the angle measures of arcs FQ and TR = 75º.
Applying the two secant theorem, the angle measure of arc FQ is given as follows:
(FQ - 75)/2 = 40
FQ - 75 = 80
FQ = 75 + 80
FQ = 155º.
Meaning that the last option represents the correct option in the context of this problem.
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A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red. He draws out a marble at random a) what is the probability that it is either green or a blue marble? b) if the man makes two draws one of after the order from his pocket without replacement, what is the probability that; i) The first draw will be a green and the second draw, a blue marble? ii) neither is a red marble?
Answer:
Green: 5; White: 2; Blue: 3; Red: 2; Total: 12
A) 8/12
i) 5/12 and 3/11
ii) 10/12
Hope this helps!
Step-by-step explanation:
a) The probability that it is either green or a blue marble is 2/3
b) The probability that first draw will be a green and the second draw, a blue marble is 3/44
c) The probability that neither is a red marble is 15/22
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
A man has twelve identical marbles in his pockets consisting of five green, two white, three blue and two red
Now , the probability is
a)
The probability that it is either green or a blue marble is P(green or blue) = P(green) + P(blue)
P(green) + P(blue) = 5/12 + 3/12
P(green) + P(blue) = 8/12 = 2/3
Therefore , the probability is 2/3
b)
The probability that first draw will be a green and the second draw, a blue marble is P(green and blue) = P(green) x P(blue | green)
P(green) x P(blue | green) = (5/12) x (3/11)
P(green) x P(blue | green) = 15/132
c)
The probability that neither is a red marble is P(neither draw is red) = P(non-red on first draw) x P(non-red on second draw | non-red on first draw)
P ( neither red ) = ( 5/6 ) ( 9/11 )
P ( neither red ) = 15/22
Hence , the probability is solved
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Points K and M are points of tangency. Find the value of x.
Applying the two-tangents theorem, the value of x is: 5.
What is the Two-tangents Theorem?The Two-Tangents Theorem says that if a single point outside a circle is used to draw two tangent lines, they will have the same length.
Since point J is formed by the two tangents, KJ and MJ, therefore:
KJ = MJ
Substitute:
4x + 7 = 7x - 8, find x
Combine like terms:
4x - 7x = -7 - 8
-3x = -15
-3x/-3 = -15/-3
x = 5
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HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
Write a function:j(x) that represents how much you would pay if you use the store discount first followed by the mall coupon??
Answer:
j(x) = f(g(x)) = f(0.25x) = 0.75x - 5
find the domain of each function. (enter your answers in interval notation.) (a) (b) g(t) = sin(e−t) g(t) = 1 − 6t
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the given function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables. The domain is indicated by the fact that the fraction's denominator is not equal to zero and by the fact that the digit under the square root bracket is positive. (For a function that has fractional values.)
(a) The domain of the function-
[tex]g(t)=sin(e^{-t})[/tex]
is (-∞,∞)
(b) the domain of the function -
[tex]g(t)=\sqrt{1-6^t[/tex] is (-∞,0)
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what would be the answer to 23 x 10^5
Answer:
2300000
Step-by-step explanation:
projectile is fired vertically upward and has position given by s(t) = 16t^2 320t _ 336 for 0
The time when the projectile has an instantaneous velocity of zero is a = 10 seconds.
The instantaneous velocity of a projectile at time t can be found by taking the derivative of its position function with respect to time. The velocity function is given by:
v(t) = ds(t)/dt = -32t + 320
The time at which the projectile has an instantaneous velocity of zero is when the velocity function is equal to 0. We can find this time by solving the equation:
-32t + 320 = 0
32t = 320
t = 10
Therefore, the time at which the projectile has an instantaneous velocity of zero is a = 10.
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--The given question is incomplete; the complete question is
"A projectile is fired vertically upward and has a position given by s(t) = -16T^2+320t+336 for 0 ≤ t ≤ 21.
Identify the time at which the projectile has an instantaneous velocity of zero; call this time = a."--
3. The Erie Canal runs 584 kilometers from Albany to Buffalo. Salvador travels on the canal from Albany. He
must travel 396 kilometers more before he reaches Buffalo. How many kilometers has he traveled so far?
Answer:
Salvador has traveled 584 - 396 = 188 kilometers so far.
a bag contain red, yellow, and green sweets, in theses ratios = red : yellow = 3:2, yellow : green = 1:5, find the ratio of red : green
Answer:
3:10
Step-by-step explanation:
In order to find the ratio of red to green sweets, we first need to find the ratio of yellow to green sweets. We know that the ratio of yellow to green is 1:5 and we also know that the ratio of red to yellow is 3:2.
We can use this information to find the ratio of red to green by cross-multiplying the ratio of red to yellow and the ratio of yellow to green.
So (3:2) x (1:5) = (3:10)
This means the ratio of red to green is 3:10.
Alternatively, we can find the ratio of red to green by using the following formula:
(red:yellow) x (yellow:green) = (red:green)
So (3:2) x (1:5) = (3:10)
The ratio of red to green is 3:10.
Answer:
Step-by-step explanation:
The ratio of red : yellow = 3:2 and yellow:green = 1:5
So, the ratio of red : yellow : green = 3:2:5
To find the ratio of red: green, we can find the ratio of red : yellow : green and then divide the red and green portions.
So, the ratio of red: green = (3/(3+2+5)) : (5/(3+2+5)) = 3/10 : 5/10 = 3:5
ms. avila got blue ribbons to give to participants at the school science fair. she ordered 120 blue ribbons from the smart start school supplier. since this was a bulk order, smart start reduced the price of each blue ribbon by $0.75. the total came to $60. which equation can you use to find the amount of money, b, smart start normally charges for a blue ribbon?
The equation 120(b - 0.75) = 60 can you use to find the amount of money, b, smart start normally charges for a blue ribbon
Ms. Avila ordered 120 blue ribbons from the smart start school supplier.
Smart start reduced the price of each blue ribbon by $0.75.
The total came to $60.
To express the problem in equation we have to read the question carefully and write the equation according to question.
Let the price of 1 blue ribbon = b
If he reduce the price by 0.75, then the price of blue ribbon = (b - 0.75)
She buy total blue ribbons = 120
So the price of 120 blue ribbons = 120(b - 0.75)
But the total cost is $60.
So the equation is:
120(b - 0.75) = 60
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HELP ASAP HURRY WILL MARK BRAINLIEST ID CORRECT
Answer:
a
Step-by-step explanation:
Answer:
a. a student who was not absent during unit should score about 98
machine builds 300 bobble-head toys in 5 hours. The machine builds the same number of bobble-head toys each hour. Which table shows the relationship between the amount of time the machine runs and the number of bobble-head toys built?
Answer: Graph A is your answer
Step-by-step explanation:
Graph A becuase since it makes the same bobble-heads each hour and in 2 hours it made 120 then it makes 60 an hour. So 60x5 is 300 so Graph shows the relationship between the amount of time the machine runs and the number of bobble-head toys built.
You have the option of buying 20 tickets at the fair for $15 or 45 tickets for $27. Which is the best deal?
Answer:
the 45 tickets
Step-by-step explanation:
In the 20 tickets deal, you'll spend USD 1.333333333333333 per ticket; in the 45 tickets deal, you pay USD 0.6 per ticket.
please help me with this question.
Answer: The last option.
Step-by-step explanation:
The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;
m∠1 + m∠2 = m∠2 + m∠3
This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.
Please answer the question in the picture! ( the cylinder one)
The volume of the cylinder is 1413 cubic cm. Then the mass of the carbon will be 2741.22 grams.
What is density?The density is the ratio of mass to volume of any substance. Let m be the mass of the object and v be the volume of the object.
Then the density D will be
D = m / v g/cm³
The volume of the cylinder is given as,
V = (π/4) d²h
V = (π/4) x 10² x 18
V = 1413 cm³
Then the mass of the carbon is given as,
1.94 = m / 1413
m = 2741.22 grams
The mass of the carbon will be 2741.22 grams.
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a paper company needs to ship paper to a late printing business. the paper will be shipped in small boxes and large boxes. the volume of each small box is 8 cubic feet and the volume of each large box is 21 cubic feet. a total of 20 boxes of paper were shipped with a combined volume of 264 cubic feet. determine the number of small boxes shipped and the number of large boxes shipped.
If a paper company needs to ship paper to a late printing business. 12 small boxes were shipped and 8 large boxes were shipped.
How to find the number of boxes shipped?Using a system of equations to represent the problem.
Let x represent the number of small boxes shipped
Let y represent the number of large boxes shipped.
We know that:
x + y = 20 (the total number of boxes shipped)
8x + 21y = 264 (the combined volume of all boxes )
Solving the first equation for y: y = 20 - x
Substituting this expression for y into the second equation:
8x + 21(20 - x) = 264
8x + 420 - 21x = 264
-13x = -156
x = 12 (small boxes)
So,
y = 20 - x
y = 20 -12
y = 8 (Large boxes)
Therefore 12 small boxes were shipped and 8 large boxes were shipped.
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4. Which type of data is displayed below? Create a tal ly chart out of it. 10 19 17 14 11 18 16 17 18 15 13 12 14 15 16 18 19 20 16 15 11 10 15 2o 12 14
Step-by-step explanation:
The data displayed below is numerical data.
Tally Chart:
10 |
19 |
17 |
14 |
11 |
18 |
16 |
17 |
18 |
15 |
13 |
12 |
14 |
15 |
16 |
18 |
19 |
20 |
16 |
15 |
11 |
10 |
15 |
20 |
12 |
14 |
Note: The above tally chart is just a representation of the data, the actual tally chart should be made on paper with tally marks.
find f if f'(x) = 1/x^2
The function f(x) is 3/x³ if f'(x) is 1/x²
Given that,
f'(x) is 1/x²
To find : f(x)
Differentiation is the opposite of integration. In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:: y = x2 => dy/dx = 2x. So, ∫ (dy/dx) dx = ∫ 2x dx = x2 together represent the integration of the function with respect to the x.
f(x) ---> differentiation ------> f'(x)
f'(x)---> integration ------> f(x)
f(x) = ∫ f'(x)
f(x) = ∫ 1/x²
f(x) = 3/x³
Therefore, function f(x) is is 3/x³ if f'(x) is 1/x² .
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pls help meee i dont understand this
Answer:
I think the y= (-7)
A bank charge a 10$ fee to open an account. Which are the following equation bet repreent the total amount in account,m, when tarting with d, in dollar
The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.
Although the question does not specify the options, but I have specified my answer as follows:
Given:
The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.
Account Opening Charges: $10
Starting amount: $d
The total amount in the account: $m
Let us say the depositor deposits an amount $k for 'i' number of months
Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.
I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.
The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time
⇒m=d-10+k×i
This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.
Therefore, the following equation is m=d-10+k×i.
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help :')
[tex]help[/tex]
Step-by-step explanation:
What we have is...
[tex]4(-4.6+w) = 22.24[/tex]
What we'll first do is distribute the 4 into the -4.6 and w
-18.4+4w = 22.24
Next we add 18.4 to both sides to get rid of it on the right side
4W = 22.24+ 18.4
4W = 40.64
Last thing to get W alone, we will divide both sides by 4
W = 10.16
solve please (image attached)
Answer:
x = 1/a
Step-by-step explanation:
To solve 7ax + 8ax = 9ax + 6 for x, we can start by combining like terms on both sides of the equation:
7ax + 8ax = 9ax + 6
becomes
15ax = 9ax + 6
Next, we can subtract 9ax from both sides of the equation:
15ax - 9ax = 9ax + 6 - 9ax
becomes
6ax = 6
Finally, we can divide both sides of the equation by 6a to find the value of x:
6ax / 6a = 6 / 6a
becomes
x = 1/a
So, the solution for x is x = 1/a.
