The length of the hypotenuse x is 36 units.
What is the hypotenuse?The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The longest side of a right triangle in mathematics is called the hypotenuse. In other words, the hypotenuse is the side that faces the right angle.So, let us assume that side x is the hypotenuse of the triangle:
Formula for hypotenuse: c=√a²+b²Now, substitute values in the formula as follows:
x =√a²+b²x =√12²+34²x = √144 + 1,156x = √1,300x = 36.05551Rounding off: 36
Therefore, the length of the hypotenuse x is 36 units.
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Answer:
36 units
Step-by-step explanation:
What is 9^p / 9^5 = 9^3. What is the p in the equation?
The value of p is 8 by the law of exponents.
What is exponents?
The base b and the exponent, or power, n, are used in the mathematical operation known as exponentiation. Its symbol is Bn, and its pronunciation is "b to the n."
An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 to the power 3, 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively.
Remember that every number multiplied by one is equal to itself. Exponents are a technique of expressing extremely large numbers in terms of powers.
The number of times a number has been multiplied by itself is the exponent, so to speak.
Given that,
9^p/9^5 = 9^3
By laws of exponents and power,
Here, p - 5 = 3
p = 3 + 5
p = 8
The value of p is 8 by the law of exponents.
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Find the common ratio of the geometric sequence:3/16, 1/4, 1/3, ...
The common ratio, r = (1/4)/(3/16)
= (1/4)(16/3)
= 4/3
OR
(1/3)/(1/4) = (1/3)(4/1)
= 4/3
The common ratio of a geometric sequence is the ratio of any two consecutive terms.
Suppose we are given a geometric sequence: a1, a2, a3, ...
The common ratio is given as:
a2/a1 = a3/a2 = ...
determine the elements of each of the following three sets explicitly, and justify your answers:
• A = {n ∈ N : cos(nπ) greater than or equal to 0};
• B = {cos(nπ) : n ∈ N};
• C = {q + r : q, r ∈ Q ∩ [0, 1]}.
Elements of following sets are
A = {1}
B = {-1, 1}
C = Q ∩ [0, 1]
Sets
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Given that
A = {n ∈ N : cos(nπ) greater than or equal to 0}
B = {cos(nπ) : n ∈ N}
C = {q + r : q, r ∈ Q ∩ [0, 1]}
Therefore elements of
A = {1}
as cos 2[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 6[tex]\pi[/tex], cos 8[tex]\pi[/tex] and so on is equal to 1.
B = {-1, 1}
as cos [tex]\pi[/tex] , cos 2[tex]\pi[/tex], cos 3[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 5[tex]\pi[/tex] and so on is equal to -1 and 1.
C = Q ∩ [0, 1]
as q and r both belongs to Q ∩ [0, 1] and their sum will be also equal to Q ∩ [0, 1].
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WILL GIVE BRAINLIEST TO FIRST ANSWER
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $21.50
10 $25.00
15 $32.50
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
The y-intercept of the total fee paid by Tyrell on his trip to Chicago when the cab travels 0 miles, the total fee will be $10.00.
What is the y-intercept?The total fee paid by Tyrell is made up of a fixed cost and a variable cost. The fixed fee is the fee that is incurred regardless of the miles travelled. The variable fee is the fee that changes with the distance travelled.
The total fee paid can be modelled as a linear function. A linear function is a single variable that is raised to the power of one.
Total fee = fixed fee + variable fee
Variable fee = (change in total fee ) / (change in total miles)
(17.50 - 13) / (5 - 2)
4.50 / 3 = 1.50
Fixed fee = $13 - (1.50 x 2)
$13 - 3 = $10
The fixed fee, $10 is equivalent to the y-intercept.
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Answer:
its a- For every additional mile the cab travels, the total fee increases by $10.00.
Step-by-step explanation:
hope this helps
Lin’s scale of 1 inch to 1 foot can be written as
Answer: 1i=1f
Step-by-step explanation:
Timed. Please help!!
Answer:
m<ABF = 34
m<FDC = 51
m<CFD = 92
Answer:
I am not sure about this.
write an perpendicular equation of y=-2x+1 that goes through the point (-1,4)
Which of the graphs on the right is the graph of C?
The graph on the right which is a graph of C is Option D. See the explanation below.
What is a graph?A graph is a graphic (such as a sequence of one or more points, lines, line segments, curves, or regions) that depicts the change of one variable in comparison to another.
What is the explanation for the above?
Note that the graph is calibrated at 25 per unit. Hence where x = 0, given the equation C(0) = 0.25x + 75
We have:
0.23 (0) + 75
Hence
C = 75
Tracing this back to the graph, by inference we see that the graph that depicts x as being on the x-axis with y on 75 is option D.
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The table shows the results of a random survey of people about their favorite movie genres. if 350 people are asked about their favorite movie genres, how many people will prefer comedies? Enter your answer, rounded to the nearest whole number, in the box.
Answer:
38.26% prefer comedies
If 350 people are asked, 134 people will prefer comedies
Explanation:
First, we need to find the percentage of people that prefer comedy. Taking into account the table, 44 people prefer comedy from the 115 people in total.
So, the percentage of students that prefer comedy is calculated as
44/115 x 100% = 0.3826 x 100% = 38.26%
Then, if 350 are asked about their favorite movie genres, the number of people that will prefer comedies is equal to 350 people times the percentage calculated before, so
350 x 38.26% = 350 x 0.3826 = 133.9 = 134
Therefore, 134 people will prefer comedies.
Solve: -2 < 5 - 2x < 2
can be written in the form A < x < B
where A= and B =
Round 3 decimal places if necessary
Answer:
-2 < 5 - 2x < 2
-7 < - 2x < -3
7/2 > x > 3/2
3.5 > x > 1.5
1.5 < x < 3.5
Which of the following is a result of shifting a circle with equation
(x-2)2 + (y - 3)2 = 25
to the left 2 units?
OA. The y-coordinate of the center of the circle decreases by 2.
OB. Both the x- and y-coordinates of the center of the circle decrease
by 2.
C. Both the x- and y-coordinates of the center of the circle increase
by 2.
D. The x-coordinate of the center of the circle decreases by 2.
The most appropriate choice of circle will be given by
x coordinate of the center decreases by 2
Fourth option is correct
What is circle?
Circle is a round two dimensional figure where all the points on the circle maintains a fixed distance from a point known as the center of the circle. The fixed distance of the point on the circle from the center of the circle is known as radius of the circle.
Equation of circle is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius of the circle.
Here,
(x-2)^2 + (y - 3)^2 = 25
(x-2)^2 + (y - 3)^2 = 5^2
This is the equation of circle with center (2, 3) and radius 5 units
On shifting the circle 2 units to the left, the coordinate of center of circle changes to (0, 2)
That means x coordinate of the center decreases by 2
So fourth option is correct
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3.) A prism with a volume of 270 m³ is dilated by a factor of 3.What is the volume of the dilated prism?4.) A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54.What is the volume of the dilated prism?5.) A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.What is the scale factor?
3) In general, a dilation is an enlargement of the sides of a shape, even if it is a 3D shape.
Furthermore, the volume of a prism is given by the formula
[tex]V=A_{\text{base}}\cdot h=l\cdot w\cdot h[/tex]Then,
[tex]V_{\text{new}}=3l\cdot3w\cdot3w=3^3(l\cdot w\cdot h)=27V_{initial}[/tex]Therefore,
[tex]\Rightarrow V_{\text{new}}=27\cdot(270)=7290[/tex]The answer to part 3) is 7290 m^3
4) Due to similar reasoning, in general, the area of a shape is given by
[tex]A=l\cdot w[/tex]If we apply a dilation to that area,
[tex]\Rightarrow A_{\text{new}}=kl\cdot kw=k^2A_{original}[/tex]Where k is the dilation factor.
Thus, in our case,
[tex]\begin{gathered} \Rightarrow A_{\text{new}}=(54)^2\cdot8=23328 \\ \text{and} \\ h_{\text{new}}=54\cdot6=324 \end{gathered}[/tex]Therefore,
[tex]\Rightarrow V_{\text{new}}=A_{\text{new}}\cdot h_{\text{new}}=23328\cdot324=7558272[/tex]The answer to part 4) is 7558272 cm^3
5) From the answer to question 3)
[tex]V_{\text{new}}=k^3\cdot V_{original}_{}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow3125=k^3\cdot200 \\ \Rightarrow k^3=\frac{3125}{200}=\frac{125}{8} \\ \Rightarrow k=\frac{5}{2}=2.5 \\ \Rightarrow k=2.5 \end{gathered}[/tex]The answer to part 5) is 2.5
A line has an x-intercept of -20 and a y-intercept of 15. What is the equation of theline
ok
P1 = (-20, 0)
P2 = (0, 15)
slope = (15 - 0) / (0 + 20)
slope = 15/20
slope = 3/4
Equation of the line
y - 0 = 3/4(x + 20)
y = 3/4x + 3/4(20)
y = 3/4x + 15
Result y = 3/4x + 15
Two dice are rolled. Determine the probability of the following. (Enter your probabilities as fractions.)(a) rolling an even sum _____(b) rolling a sum greater than 7 ______(c) rolling an even sum and a sum greater than 7 ______(d) rolling an even sum or a sum greater than 7 ______
First, we need to find the sample space for two dice. Since each dice has 6 faces, the sample space is
which consist in 36 elements.
Part A.
In this case, we need to find the combinations where the sum of the 2 dice is even. The combinations are:
for instance, in the upper left corner, the sum is 1+1=2, which is an even number and similarly for the other cases.
As we can note, there are 18 possible combinations. Then, the probability is
[tex]P(\text{ even sum)=}\frac{18}{36}=\frac{1}{2}[/tex]Part B.
In this case, we need to find the possible combinations where the sum of the 2 dices is greater than 7. The possible combinations are:
Since there are 15 possible combinations, the probability is given by
[tex]P(\text{ Sum greater than 7)=}\frac{15}{36}[/tex]Part C.
This case is the intersection of the two cases from above. The possible combinations are:
Since there are 9 possible combinations, the probability is
[tex]P(\text{Even sum and sum greater than 7)=}\frac{9}{36}=\frac{1}{4}[/tex]Part D.
We need to find the possible combinations where the sum is even or the sum is greater than 7. Then, this case is the union of case A and B. Then the possible combinations are:
Since there are 18+6=24 combinations, the probability is
[tex]P(\text{Even sum or sum greater than 7)=}\frac{24}{36}=\frac{4}{6}=\frac{2}{3}[/tex]The displacement of a particle from a reference point at any instant is given by s = 3 t 2 - 4 t + 5 , where s is in metres and t is time in seconds. calculate the average velocity of the particle in the time interval between 3 s and 5 s, and its instantaneous velocity at 4 s.
The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.
How to determine average velocity and instantaneous velocity?
Average velocity is defined as the body's overall displacement divided by its time of motion. While instantaneous velocity is defined as a body's speed at a certain instant in time, or its displacement at that instant. When the velocity is constant, average and instantaneous velocities will equalize at just one condition.
The definition of instantaneous velocity is the rate of change of position over a relatively brief time period (almost zero). Simply said, the speed of an object at that precise moment. The definition of instantaneous velocity is "The velocity of an item in motion at a certain point in time." The instantaneous velocity of an object may be equal to its standard velocity if it has uniform velocity.
Mathematically, average velocity = [s(t₂) - s(t₁)]/[t₂ - t₁]
Instantaneous velocity at time, t is = (ds/dt) at time = t
Given, the displacement for the particle is given by s = 3t² - 4t + 5
Time interval, t₁ = 5s and t₂ = 3s;
Using formula in literature, average velocity of the particle in the time interval between 3s and 5s is:
Average velocity = (s(5) - s(3))/(5 - 3) = (60 - 20)/2 = 20 ms⁻¹
Instantaneous velocity at t = 4 is ds/dt at that time-frame:
Now, v = ds/dt = 6t -4
Now, v(4) = 6(4) - 4 = 20 ms⁻¹
The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.
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Instructions: Find the missing side. Round your answer to the nearest tenth. stion 54° 29 х
Recalling the definition of the sine of an angle in a right triangle, we know that:
[tex]\sin (54)=\frac{x}{29}[/tex]Isolate x from this equation:
[tex]x=29\sin (54)[/tex]Use a calculator to find the numerical value of x:
[tex]x=23.46149284[/tex]Therefore, to the nearest tenth:
[tex]x=23.5[/tex]gold watch
The original price of a gold watch was $500. The dealer sells this item for $620. What percentage did the dealer mark up from the original price?
The mark up percentage was %.
The percentage of the dealer markup from the original price will be; 1.24 %
What is the percentage of the total value?Suppose the value of which a thing is expressed in percentage is "a Suppose the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part into 100 parts; then we multiply it by b so that we collect b items per 100 items(that is exactly what b percent means).
Given that the original price of a gold, watch was $500. And the dealer sells this item for $620.
Then the percentage of the dealer markup from the original price will be;
The change = amount/ original x 100%
= 620/ 500 x 100%
= 1.24 x 100%
Therefore, The markup percentage was; 1.24 %.
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Find the symmetric point of the given point (-2,-2) on a parabola with vertex (-3, 1).
The symmetric point on parabola is x = -3
What is symmetric point in parabola ?
The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.
The vertex form of a parabola's (or a quadratic) equations is given by the following formula:
y = a(x - h)² + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.
Where, vertex is given (h, k) = (-3, 1)
so the axis of symmetry is,
=> x = -3
Therefore, The symmetric point on parabola is x = -3
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A system of equations is made up of an ellipse and a hyperbola.
Ok, so
We want to find the equation of an ellipse centered at the origin with a horizontal major axis of 8 units and a minor axis of 6 units.
For this, let's remember the form of the equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where the center of the ellipse is located at the point (h,k).
If the ellipse is centered at the origin, then, h=0 and k=0, so the form of our equation will be:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]Now, we're given that our ellipse has a horizontal major axis of 8 units and a minor axis of 6 units. Since the major and minor axis are given by the parameters 2a and 2b, then, a=4 and b=3. the greater number will divide the x² term and a>b.
So, the equation of this ellipse is:
[tex]\frac{x^2}{16}+\frac{y^2}{9}=1[/tex]The graph of this ellipse will be something like:
what is the recursive formula if the sequence is 4,7,10,13...?
The recursive formula if the sequence is 4,7,10,13 is aₙ = 3n - 2.
What is a Sequence?This is referred to as the list of the things or items in mathematics in which repetitions are allowed and a certain order is followed and an example of a sequence is 1,3,5,7...etc.
The formula for arithmetic sequence is aₙ = a₁ + d ( n -1) in which a is the first term while d is the common difference. a₁ is referred to as the first term while d is the common difference which is 7 - 5 = 2 or 5 - 3 = 2.
aₙ = a₁ + d ( n -1)
= 4 + 3 ( n - 1) --- expand the bracket
= 4 + 3n - 3 = 4 -3 + 3n
aₙ = 3n + 1
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the hotel room tax junction city is calculated using the function T(x) = 0.06x + 4.5, where x is the cost in dollars of the room and T(x) is the tax in dollars. What is the original price of the hotel room if the tax on the room was $11.70? I NEED HELP ASAP
T(x) = 0.06x + 4.5
We are meant to find 'x' when T(x) = $ 11.70
Substitute for T(x) = $ 11.70 in the given function
Thus,
11.70 = 0.06x + 4.5
11.70 -4.5 = 0.06x
7.2=0.06x
[tex]\begin{gathered} \frac{7.2}{0.06}=x \\ x=120 \end{gathered}[/tex]Hence, the original price of the hotel room if the tax on the room was $1170 is $120
Please refer to the picture and pleaseeeeeeeeeeeeeeeeeee just get to the answer :D
Given
-6 is less than x , 3 is greater than x
Find
Write the inequality
Explanation
-6 is less than x
this implies , -63 is greater than x
this implies , 3>x....................2
from 1 and 2 , we obtain
-6Final Answer
the inequality is - 6 < x < 3
A scientist observes and counts 155 bacteria in a culture. Later, the scientist counts again and finds the number has increased 40%
The number of bacteria after the increase is 217
Bacteria in a culture when the scientist first observed = 155
Percentage: Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Increase in number of bacteria post observation = 40%
Bacteria after increase:
= 155 + 40% of 155
= 155 + 0.40*155
= 155 + 62
= 217
So, bacteria after the increase is 217
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I need help please this is geometry
The correct options for the intersecting line EF are-
C) BC ≅ EFD) EB ≅ DFWhat is termed as the intersecting line?Lines that intersect or cross one another in a plane are known as intersecting lines. Non-intersecting lines, on the other hand, are formed when two or even more lines do not intersect at any point.The characteristics of intersecting lines are listed below to help us identify them quickly.Intersecting lines can only intersect at one point; they cannot intersect at more than a point.Intersecting lines intersect at any angle greater than 0° as well as less than 180°.For the given question;
Line EF intersects the lines AB and DC,
Where, AB = DC
Thus, from the given figure it is shown that;
BC ≅ EFEB ≅ DFThus, the statement true about the given diagram are found.
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there is a $30 fee to rent a tool from the local hardware store plus $6 per day. if joe rents a jackhammer for 5 days, what is his total bill? The correct function for this situation is f (x) = 30x +6.
True or false?
The problem is false
Step-by-step explanation:
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I need help on a question involving graphing a sine function
Solution
[tex]y=sin\text{ x on the \lbrack0,2}\pi][/tex]Find the greatest common factor for the group of numbers. 20. 12, 24
Search for the numbers that divide all of the given set.
Notice that all three of them can be divided by two:
[tex]\begin{gathered} \frac{20}{2}=10 \\ \frac{12}{2}=6 \\ \frac{24}{2}=12 \end{gathered}[/tex]Therefore, 2 is the first common factor. Now, take the numbers 10, 6 and 12 and repeat the procedure. Notice that all of them are divisible by 2:
[tex]\begin{gathered} \frac{10}{2}=5 \\ \frac{6}{2}=3 \\ \frac{12}{2}=6 \end{gathered}[/tex]Therefore, 2 is the next common factor. Now, take the numbers 5, 3 and 6 and repeat the procedure. Notice that 3 is not divisible by 2 and 5 is not divisible by 3. Since there are no more numbers lower tan 3 that divide all of the numbers, there are no more common factors.
The common factors were 2 and 2. Multiply all the common factors to find the greatest common factor:
[tex]2\cdot2=4[/tex]Therefore, 4 is the greatest common factor of 20,12 and 24.
Answer this you are a pro (try your best)
There are a specific quantity of $5 bills, and Brad has 6 boxes. In order to ensure that no two boxes contain the same amount of money, he wants to place his bills into some or all of the boxes. The least amount of money he needs to do $30 is within each box.
How do you tell whether an equation has an unlimited number of solutions?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 If you use a formula with infinite solutions to simplify the equation A set of two or more linear equations with two or more variables constitutes a system of linear equations.
If all the equations in the system are taken into account simultaneously, or if you use the approach where you obtain both sides equal, the system has an infinite solution.
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help meeeeeeeeeeeeeeeeeeeeeee
thank you
a. The linear equation that models the price-sales relationship is: y = -500x + 5000
b. daily sales: $1,250.
How to Write a Linear Equation that Models a Relation?To write the linear equation for a relationship, find the unit rate/slope (m) and the starting value/y-intercept, then substitute the values into y = mx + b.
a. Using two points from the problem, (6, 2000) and (8, 1000), find the unit rate (m):
Unit rate (m) = change in y / change in x = (2000 - 1000)/(6 - 8)
Unit rate (m) = 1000/-2
Unit rate (m) = -500
Find the y-intercept (b) by substituting m = -500 and (x, y) = (6, 2000) into y = mx + b:
2000 = -500(6) + b
2000 = -3000 + b
2000 + 3000 = -3000 + b + 3000
5000 = b
b = 5000
To write the linear equation, substitute m = -500 and b = 5000 into y = mx + b:
y = -500x + 5000
b. Substitute x = 7.5 into y = -500x + 5000:
y = -500(7.5) + 5000
y = -3750 + 5000
y = 1,250
The daily sales would be $1,250.
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Each data set contains one outlierWhat are the values of the two outliers? Explain how you determined the value of the outliers .
An outlier is a value that is outside the expected limits of the data. It Is usually more than 3 standard deviation from the mean.
In the league A, we see an outlier in the minimum value (26) and, in the league B, the maximum value (256).
The outliers can be spotted in the graph by looking at points does seem to be too far of the group of data. Also, mathematically, looking at the distance from the mean: if the difference between the value and the mean is more than 3 standard deviations, we are talking about an outlier.
