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We are given three angles and we are asked to determine if the angles are the angles of a triangle. To do that we need to have into account that the measure of the angles of a triangle always adds up to 180, therefore, if we add up the angles and the result is 180, then these angles can be angles measures of a triangle. If the result is different from 180 the angles can't be the angle measures of a triangle. Taking the first set of three angles we get:
[tex]58+34+42=134[/tex]Since the result is different from 180 then these angles can't be the angle measure of a triangle.
The same procedure is used to determine the other sets of angles.
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2.3x + 8 = - 1.7x - 8 solve for x
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The value of x after solving (2.3x + 8) = (-1.7x-8) is -4.
According to the question,
We have the following expression:
(2.3x + 8) = (-1.7x-8)
Now, moving -1.7x from the right hand side to the left hand side will result in the change of its sign from minus to plus:
2.3x+1.7x +8 = -8
4x+8 = -8
Now, moving 8 from the left hand side to the right hand side will also result in the change of the sign from plus to minus:
4x = -8-8
4x = -16
x = -16/4 (4 was in multiplication on the left hand side. So, it is in division on the right hand side.)
x = -4
Hence, the value of x is -4.
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Line AB is tangent to circle C at B and line AD is tangent to circle C at D. What is the lenghth AB.
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Answer:
Explanation:
The Two Tangent Theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.
To be able to find AB we have to 1st of all find the value of x by equating both lengths together since both AB and AD are equal as shown below;
[tex]\begin{gathered} 2x^2+3x-1=2x^2-4x+13 \\ 2x^2-2x^2+3x+4x=13+1 \\ 7x=14 \\ x=\frac{14}{7}=2 \end{gathered}[/tex]S
find the surface area of the figure and round to the nearest
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The figure in the image is a Hemisphere.
The surface area of a hemisphere is given as:
[tex]3\text{ }\times\text{ }\pi\text{ }\times r^2[/tex]Thus, the surface area is:
[tex]\begin{gathered} 3\text{ }\times\text{ 3.142 }\times8.6^2 \\ 697.15ft^2 \end{gathered}[/tex]Hence, the surface area of the figure, to the nearest whole number is 697 square feet.
Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.
Statement 1: If Bob is Sally’s spouse, then Sally is Bob’s spouse.
Statement 2: If the light is red Northbound, then the traffic is stopped.
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Kyle has a container of flour in the shape of a cylinder.
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Answer:
Part A:
The volume of a cylinder is given below as
[tex]\begin{gathered} V_{cylinder}=\pi\times r^2\times h \\ r=\frac{d}{2}=\frac{10in}{2}=5in \\ h=8in \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} V_{cyl\imaginaryI nder}=\pi r^2h \\ V_{cyl\mathrm{i}nder}=\pi\times5^2\times8 \\ V_{cyl\mathrm{i}nder}=\pi\times200 \\ V_{cyl\mathrm{i}nder}=628.3in^3 \end{gathered}[/tex]Hence,
The volume = 628.3in³
Part B:
To determine the weight of the flour in ounces, we will use the relation below
[tex]\begin{gathered} 0.13ounce=1in^3 \\ x=628.3in^3 \\ cross\text{ multiply, we will have} \\ x=0.13\times628.3 \\ x=81.679 \\ x\approx81.7ounces \end{gathered}[/tex]Hence,
The weight = 81.7 ounces
help with this functions and equations question. please answer correctly
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The distance D(t) Maya travels in her racecar and the times taken, given in the table indicates the average rate of change of distance over the specified times are;
(a) 30.3 meters per second
(b) 25.4 meters per second
What is the average rate of change of a function?The average rate of change of a function, over an interval, gives the rate at which the function changes per unit of the interval.
The average rate of change of the distance is given by the equation;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{The \: sum \: of \: distance \: traveled }{The \: sum \: of \: the \: time taken } }[/tex]
The following values are obtained from the given table;
(a) At time t = 0 seconds, distance traveled, D(0) = 0 meters
At time t = 5 seconds, distance traveled, D(5) = 151.5 meters
Which gives the average rate of change as follows;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{(151.5 - 0) \: m }{(5 - 0 ) \: s} = 30.3 \: m/s }[/tex]
The average rate of change for distance driven is 30.3 meters per second(b) The table gives that at time, t = 7 seconds, distance traveled, D(7) = 205.1 meters and that at time t = 9 seconds, distance traveled, D(9) = 255.9 meters, which gives;
[tex] \displaystyle {Average \: rate \: of \: change = \frac{(255.9 - 205.1) \: m }{(9 - 7) \: s} = 25.4 \: m/s }[/tex]
The average rate of change of distance between the points in time of 7 seconds and 9 seconds is 25.4 meters per secondLearn more about the average rate of change of a function here:
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f(x) = x + 4 and g(x) = x - 1Step 3 of 4: Find (f 3)(x). Simplify your answer.Answer(f)(x) =
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For this problem, we are given two functions, we need to determine the composite between these two expressions.
The two functions are:
[tex]\begin{gathered} f(x)=x+4\\ \\ g(x)=x-1 \end{gathered}[/tex]This composite is the product of the two functions, therefore we have:
[tex]\begin{gathered} (f\cdot g)(x)=(x+4)\cdot(x-1)\\ \\ (f\cdot g)(x)=x^2-x+4x-4\\ \\ (f\cdot g)(x)=x^2+3x-4 \end{gathered}[/tex]The answer is x²+3x-4.
i need help with this equation please there are two more possible answers that were cut off they are 17,2% and 19,5%
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Consider that the experimental probability of an event is based upon the previous trials and observations of the experiment.
The experimental probability of occurrence of an event is given by,
[tex]\text{Probability of an event}=\frac{\text{ Number of outcomes that favoured the event}}{\text{ Total number of trials or outcomes}}[/tex]As per the problem, there are a total of 1230 trials of rolling a dice.
And the favourable event is getting a 2.
The corresponding experimental probability is calculated as,
[tex]\begin{gathered} P(\text{ getting a 2})=\frac{\text{ No. of times 2 occurred}}{\text{ Total no. of times the dice is thrown}} \\ P(\text{ getting a 2})=\frac{172}{1230} \\ P(\text{ getting a 2})\approx0.13984 \\ P(\text{ getting a 2})\approx13.98\text{ percent} \end{gathered}[/tex]Thus, the required probability is 13.98% approximately.
Theref
Solve the system of equations.y= x2 - 3x + 6y = 2x + 6
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We have the following:
[tex]\begin{gathered} y=x^2-3x+6 \\ y=2x+6 \end{gathered}[/tex]We subtract the equations:
[tex]\begin{gathered} y-y=x^2-3x+6-2x-6 \\ 0=x^2-5x \\ 0=x(x-5) \\ x=0;x=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} y=2\cdot0+6 \\ y=6 \\ y=2\cdot5+6 \\ y=16 \end{gathered}[/tex]therefore, the answer is:
(0,6) and (5,16), the option D.
multiply decimals 3.76 × 4.8=this is how the problem needs worked
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18.048
Explanation:[tex]\begin{gathered} 3.76\text{ }\times\text{ 4.8} \\ \\ To\text{ make it easy, we remove the decimal points while multiplying:} \\ 376\text{ }\times\text{ 48} \end{gathered}[/tex][tex]\begin{gathered} We\text{ count the numbers of decimal points:} \\ 2\text{ decimal point in 3.46} \\ 1\text{ decimal point in 4.8} \\ \text{Total decimal points = 3} \\ We\text{ count 3 decimal points in our result} \end{gathered}[/tex]The result is 18.048
The system of equations may be solved by hand calculation or by using the crossing-graphs method.Solve the following system using the crossing-graphs method.2x - y = 04x + 2y = 48(x, y) = (_____,_____)
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The first thing you can do is graph each of the equations. To do this, you can write the equations following the form
[tex]y=mx+b[/tex]Where m is the slope of the line and b the intersection point with the y axis. Then
[tex]\begin{gathered} 2x-y=0 \\ 2x=y \\ y=2x \\ \text{ And the other equation} \\ 4x+2y=48\text{ } \\ \text{To simplify the equation, you can divide by 2 both sides of the equation} \\ 2x+y=24 \\ y=-2x+24 \end{gathered}[/tex]Graphing you have
The solution of the system of equations will be the point at which both lines intersect. Therefore, the solution is (6,2).
IF log x = 1/₂, find log (10x²)
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Answer:
2
Step-by-step explanation:
log ab = log a + log b
Similarly,
log 10x² = log 10 + log x²
log a^b = b log a
Similarly,
log 10x² = 2 log x
= 2 * 1/2
= 2/2
= 1
Note :-
The value of log 10 = 1
Hence,
log 10x²
= log 10 + log x²
= 1 + 1
= 2
Which is a perfect square?583644
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Solution:
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
Hence,
[tex]36=6^2=6\times6[/tex]Therefore, the perfect square is 36.
a gate that is 5 ft tall casts a shadow 9 ft long the house behind the gate cast a shadow of 54 ft how about how many feet tall is the house
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
gate:
hg = 5 ft
shadow = 9ft
house
hh = ?
shadow = 54 ft
Step 02:
We must apply the theorem of thales.
[tex]\frac{hg}{hh}=\frac{shadow\text{ gate}}{\text{shadow house}}[/tex][tex]\frac{5ft}{hh}=\frac{9ft}{54\text{ ft}}[/tex]hh * 9 ft = 5 ft * 54 ft
hh = (5 ft * 54 ft ) / 9 ft
hh = 270 ft ² / 9 ft = 30 ft
The answer is:
The house is 30ft tall.
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. How many liters of water remain in the tank after 7 minutes?
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Tank B originally had 80 liters of water.
Water is being drained off the tank at a rate of 2.5 liters per minute.
After 7 minutes have passed, the tank has lost 7*2.5 = 17.5 liters of water.
This means the tank still has 80 - 17.5 = 62.5 liters of water.
After 7 minutes 62.5 liters of water remain in the tank
Which of the equations below could be the equation of this parabola?
10-
(0,0)
Vertex
-10
O A. y--/2²2
O B. x=2²
O c. y-1/2x²
O D. x=-12²
10
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The equation of this parabola is Y = -1/2 X². So option C is correct.
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Given that,
The graph of parabola,
the vertex (0, 0)
Y - 0 = 4a (X - 0)²
Y = 4aX²
It can be seen in the graph it is downward parabola so value a should be less than zero
So possible equation could be Y = -1/2 X²
Hence, the equation is Y = -1/2 X²
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y varies inversely as x. y=12 when x=7. Find y when x=2
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We write as an inverse proportion first then make an equation by multiplying by k:
[tex]y=\frac{k}{x}\Rightarrow k=x\times y[/tex]Find the value of k:
[tex]k=7\times12=84[/tex]Then, when x = 2, y is:
[tex]y=\frac{84}{2}=42[/tex]Answer: y = 42
Theoretical Probabilities. Use the theoretical method to determine the probability ofthe following outcomes and events. State any assumptions that you make. Drawing a king from a standard deck of cards
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Recall that the theoretical probability that an event occurs is given by the following quotient:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]We know that in a standard deck there are 52 cards from which 4 are kings, therefore:
[tex]\text{Probability of drawing a king=}\frac{4}{52}.[/tex]Answer:
[tex]\frac{4}{52}\text{.}[/tex]Simplify the following expression.(12x-2.1)-(19x+6.9)
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The given algebraic expression is
[tex](12x-2.1)-(19x+6.9)[/tex]To simplify this expression, we need to solve those parentheses in the first place, multiplying the sign in front of each of them.
[tex]12x-2.1-19x-6.9[/tex]Now, we reduce like terms. Remember that like terms are those who have the same variable, and those who don't have variables at all.
[tex]12x-19x-2.1-6.9=-7x-9[/tex]Therefore, the simplest form of the given expression is[tex]-7x-9[/tex]A football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time). If the team goes for 1 point after each touchdown, what is the probability that the coach’s team wins? loses? ties? If the team goes for 2 points after each touchdown, what is the probability that the coach’s team wins? loses? ties? Can you develop a strategy so that the coach’s team has a probability of winning the game that is greater than the probability of losing
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His football team is losing 14 points near the end of the game. The team scores two touchdowns with each worth 6 points (total = 12 points).
After each touchdown, the coach must decide whether to go for 1 point with each kick(99% successful) or 2 points with a run or pass(45% successful).
Note
Two touchdown = 12 points
So, it remaining 2 point to level up and more than 2 points to win the game
a.
If the team goes for 1 point after each touchdown, the probability that the coach's team loses? wins? ties? can be computed below
[tex]undefined[/tex]helpppppppppppppppppppp
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Answer: [tex]f^{-1}[/tex] = {(17, 16), (8, 3), (3, 8), (4, 4)}
Step-by-step explanation:
To list the inverse function, we will simply switch the x- and y-values in each coordinate pair. Coordinate points are written as (x, y).
f = {(16, 17), (3, 8), (8, 3), (4, 4)}
[tex]f^{-1}[/tex]= {(17, 16), (8, 3), (3, 8), (4, 4)}
Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
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Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
Please help me out here. I really don’t understand
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Step-by-step explanation:
you have both points : (1, 1) and (5, 5).
so, we don't need to do any triangle calculations to get the height of the main triangle.
all we need to do is calculate the distance between these 2 points.
2 points in a coordinate grid create a right-angled triangle.
the direct distance is the Hypotenuse (the side opposite of the 90° angle). and the legs are the x- and the y-coordinate differences (one up or down the other left or right).
and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse a and b being the legs.
so, how long are these legs here ?
the x-difference is 5 - 1 = 4.
also the y-difference is 5 - 1 = 4
so,
distance² = 4² + 4² = 16 + 16 = 32
distance = sqrt(32) = sqrt(16×2) = 4×sqrt(2) =
= 5.656854249...
the distance of P to the line RQ is 5.656854249...
The area of a rectangle is 28m^2, and the length of the rectangle is 5 meters less than three times the width. Find the dimensions of the rectangle. L:W:
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The area of a rectangle is given by the formula
[tex]A=L*W[/tex]where
A=28 m2
L=3W-5
substitute given values in the formula
[tex]\begin{gathered} 28=(3w-5)W \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \end{gathered}[/tex]Solve the quadratic equation
Using the formula
we have
a=3
b=-5
c=-28
substitute
[tex]w=\frac{-(-5)\pm\sqrt{-5^2-4(3)(-28)}}{2(3)}[/tex][tex]w=\frac{5\pm19}{6}[/tex]The solutions for w are
w=4 and w=-2.33 ( is not a solution because is a negative number)
so
The width w=4 m
Find out the value of L
L=3w-5=3(4)-5=7 m
therefore
L=7 mW=4 mSee photo for problem
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Answer:
possible outcome= {H,T}
number of possible outcome=2
obtaining a tail(T)=1
n(T)=1
P(T)=n(T)/number of possible outcome
=1/2
Factor the given polynomial by finding the greatest common monomial Factor 6x^3y+9xy^3
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Answer:
(3xy)(2x² + 3y²)
Step-by-step explanation:
Hello!
The greatest common factor for the coefficients is 3, as both terms have a coefficient with the greatest factor of 3.
The greatest common factor for the x-terms is x, as both terms has x to a minimum of the first power.
The greatest common factor for the y terms is y as both terms has y to a minimum of the first power.
Factor out 3xy:6x³y + 9xy³3xy(2x²) + 3xy(3y²)(3xy)(2x² + 3y²)The factored form is (3xy)(2x² + 3y²).
in health class, the students were asked what grain they prefered in their breakfast cereal. The results are shown in the table. what's the probability that a randomly chosen student in the health class listed oats as their favorite grain?A. 20%B. 25%C. 35%D. 14%
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To find the probability of a randomly choosen student listing oats as its favorite grain, divide the number of students that chose oats by the total number of students and multiply the fraction by 100%.
To find the total number of students, add the numbers under each cereal:
[tex]12+14+8+6=40[/tex]The number of students who chose oats, is 14. Then, the requested probability, is:
[tex]\frac{14}{40}\times100=35\text{ \%}[/tex]A rectangle with an area of 20 square units is dilated by the scale factor of 3.5. find the area of the new rectangle
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We are given the area of a rectangle. The area of a rectangle is the product of the length and the height. Therefore, we have:
[tex]A=lh[/tex]If we scale the rectangle by a factor of 3.5 this means that we multiply the length and the height by 3.5, like this:
[tex]A^{\prime}=(3.5l)(3.5h)[/tex]Solving the product:
[tex]A^{\prime}=12.25lh[/tex]Since "lh" is the original area we have:
[tex]A^{\prime}=12.25A[/tex]Now, we substitute the value of the original area:
[tex]A^{\prime}=12.25(20)[/tex]Solving the operations:
[tex]A^{\prime}=245[/tex]Therefore, the new area is 245 square units.
Subtract the expressions. (10y - 2) - (8y + 3)
Answers
SOLUTION
We want to solve the expression
[tex]\mleft(10y-2\mright)-(8y+3)[/tex]Now, use the minus sign to multiply the other part
That is
[tex]-(8y+3)[/tex]We have
[tex]\begin{gathered} (10y-2)-(8y+3) \\ 10y-2-8y-3 \\ \text{collecting like terms } \\ 10y-8y-2-3 \\ 2y-5 \end{gathered}[/tex]Hence the answer is 2y - 5
Write the equation as an exponential equationlog_9(2x – 7) = 2x – 3