Can someone please help me on this question, I'm a little stuck? The question should be down below!
Answers
We have a right triangle with a missing side.
When we have two sides given sides on the right triangle and we need to find the missing side, we use the Pythagoras theorem:
The formula is given by:
[tex]a^2=b^2+c^2[/tex]Where:
a = Hypotenuse
b= Opposite side
c= Adjacent side
Now, we need to label the sides of the given triangle:
The largest side, represents the hypotenuse, in this case, a=15m.
The adjacent side is between the 90 degrees angle and the hypotenuse, in this case, c = 9m
Therefore, the missing side is the opposite side, let set b for this side:
Replacing these values:
[tex](15m)^2=b^2+(9m)^2[/tex][tex]225=b^2+81[/tex]Solve the equation for b:
[tex]225-81=b^2[/tex][tex]144=b^2[/tex][tex]\sqrt[]{144}=\sqrt[]{b^2}[/tex]Therefore, the missing side:
[tex]12=b[/tex]
Related Questions
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:
Answers
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 mSimplify the following expression.(12x-2.1)-(19x+6.9)
Answers
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]i need help with this equation please there are two more possible answers that were cut off they are 17,2% and 19,5%
Answers
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
f(x) = x + 4 and g(x) = x - 1Step 3 of 4: Find (f 3)(x). Simplify your answer.Answer(f)(x) =
Answers
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.
find the surface area of the figure and round to the nearest
Answers
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.
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
Answers
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
y varies inversely as x. y=12 when x=7. Find y when x=2
Answers
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
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.
Answers
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?
Answers
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
Write the equation as an exponential equationlog_9(2x – 7) = 2x – 3
Answers
Please help me out here. I really don’t understand
Answers
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...
2.3x + 8 = - 1.7x - 8 solve for x
Answers
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.
To know more about solving here
https://brainly.com/question/315182
#SPJ1
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
Answers
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.
multiply decimals 3.76 × 4.8=this is how the problem needs worked
Answers
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
Solve the system of equations.y= x2 - 3x + 6y = 2x + 6
Answers
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.
Which is a perfect square?583644
Answers
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.
On its website a tv station displays temperature data for each hour during the past 24 hours. The data are displayed as using two different functions on a line graph. One function shows the current temperature and the other function shows the historical average. Which quantities are represented by the y-values on the line graph
Answers
, Given the question, we are asked to find which of the quantities are represented by the y-values on the line graph .
Explanation
In the question, we are told that the tv station displays temperature data using two different functions on a line graph. One of the functions shows the current temperature and the other function shows the historical average.
A function, by definition, can only have one output value(y) for any input value. In this case the input values are the time the temperature which we result in the output value of the historical average and temperature.
Therefore,
Answer
Option D
Factor the given polynomial by finding the greatest common monomial Factor 6x^3y+9xy^3
Answers
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).
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
Answers
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]Ben, Claire and Devon are training for a triathalon. Today, they are practicing their swimming by swimming one mile. Ben swam 0.77 of the mile before stopping. Claire swam 3/5 of the mile and Devon swam 82% of the mile before stopping. Who swam the farthest distance? Who swam the shortest distance?
Answers
Given:
Ben, Claire, and Devon are swimming one mile.
Ben swam 0.77 of the mile before stopping.
So, the distance Ben swam = 0.77 x 1 = 0.77 mile
Claire swam 3/5 of the mile.
So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles
Devon swam 82% of the mile before stopping.
So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles
Arrange the distances in order from the largest to the least:
0.82, 0.77, 0.6
So, the answer will be:
The farthest distance is for Devon = 0.82 miles
The shortest distance is for Claire = 0.6 miles
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%
Answers
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]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
Answers
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
To know more about Equation check:
https://brainly.com/question/1529522
#SPJ5
IF log x = 1/₂, find log (10x²)
Answers
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
Line AB is tangent to circle C at B and line AD is tangent to circle C at D. What is the lenghth AB.
Answers
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
help with this functions and equations question. please answer correctly
Answers
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:
https://brainly.com/question/24686935
#SPJ1
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) = (_____,_____)
Answers
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).
helpppppppppppppppppppp
Answers
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)}
See photo for problem
Answers
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
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
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
Answers
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.