Answers
Therefore it is 8
In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Hence, if the shortest leg is 4, then the hypotenuse is 8.
Explanation:In a 30-60-90 triangle, the ratios of the sides are specific and constant. The shortest side, the one opposite the 30-degree angle, is considered to be x. The longest side (hypotenuse), directly across from the 90-degree angle, is 2x, and the remaining side is x√3. In this case, the shortest side (x) is indicated to be 4.
So, in this triangle, the hypotenuse (2x) would be 2*4 = 8.
The Pythagorean theorem, as mentioned in the reference content, will also hold, but in the case of this special triangle, the ratios of the sides simplify the process of determining side lengths.
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Related Questions
HELP ASAP!!! ill mark brainliest! Which of the following graphs represents the function ƒ(x) = 2x?
Answers
A graph that correctly represents the exponential function [tex]f(x) = 2^x[/tex] include the following; B. graph B.
How to write and graph an exponential function?In Mathematics and Euclidean Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x)=a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change or common ratio.Based on the information provided above, we would select the following exponential function to plot on a set of axes or cartesian coordinate;
[tex]f(x) = 2^x[/tex]
where:
The rate of change (b) is 2 and it represents an exponential growth.
The y-intercept (a) is 1 and it means the graph of this function would cross the y-axis at point (0, 1).
In conclusion, we can logically deduce that only graph B correctly represent an exponential function with these key features.
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Missing information:
Which of the following graphs represents the function [tex]f(x) = 2^x[/tex]?
Given the form D =ABC, what is the formula for C?
Answers
D = ABC
D/AB = ABC/AB
C = D/AB
C = D/AB is your answer
hope this helps
D
C = --------- Because you have to get C all by itself in order to set up a correct
AB formula, and you can only do so by dividing C by A and B. A and B are canceled out on the right side, but until you have numerical values for D, A, and B, you can't divide them into a number, so this equation is the result and the correct answer.
Write the first five terms of a sequence. Write both an explicit formula and a recursive formula for a general term in the sequence. recursive formula for arithmetic sequence recursive formula for geometric sequence how to write a recursive formula recursive formula calculator arithmetic sequence formula calculator geometric sequence formula recursive sequence write the first five terms of the arithmetic sequence Report inappropriate predictions
Answers
9, 12, 19, 30, ...
Therefore the whole formula for the nth term is;2n^2 + 3n - 10
Answer with explanation:
⇒Arithmetic Sequence
11,21,31,41,51,......
First term[tex]a_{1}[/tex] =11
Common Difference(d)=21-11=10
[tex]\rightarrow a_{n}=a_{n-1}+10---{\text{Recursive formula}}\\\\\rightarrow a_{n}=a_{1}+(n-1)d\\\\a_{n}=11+(n-1)\times 10\\\\a_{n}=10n+1---{\text{Explicit formula}[/tex]
⇒Geometric Sequence
First five terms of the sequence are
[tex]4,4^2,4^3,4^4,4^5,.....\\\\\text{First term}=a_{1}=4\\\\ \text{Common ratio},r=\frac{a_{2}}{a_{1}}\\\\r=\frac{4^2}{4}\\\\r=4\\\\a_{n}=4\times a_{n-1}---\text{Recursive formula}\\\\a_{n}=a_{1}\times r^{n-1}\\\\a_{n}=4\times 4^{n-1}\\\\a_{n}=4^{1+n-1}\\\\a^n=4^n-----\text{Explicit formula}[/tex]
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Answers
Answer:
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
Step-by-step explanation:
Reflection over the x-axis move point C from (-1, 1) to (-1, -1), point D from (-1, 2) to (-1, -2), point A from (-4, 2) to (-4, -2) and point B from (-4, 1) to (-4, -1). As can be seen, y-coordinate changes sign, so that, the distance between the original point and its reflection respect x-axis remains the same.
Rotation 90 degrees counterclockwise around origin means that x-coordinate and y-coordinate switches and x-coordinate is multiplied by -1. So, point (-1, -1) transforms into (1, -1) - point C' -, (-1, -2) transforms into (2, -1) - point D' -, point (-4, -2) transforms into (2, -4) - point A' - and point (-4, -1) transforms into (1, -4) - point B'.
Can anyone help me with this math problem???
Answers
Selection A is appropriate.
(-9,17); slope= -4/3
Answers
You get: y-17=-4/3(x-(-9))
Simplify: y-17=-4/3(x+9)
Distribute: y-17=-4x/3-(36/3)
Simplify Fraction: y-17=-4x/3-12
Add “17”: y=-4x/3 +5
An equation of the line in slope-intercept form that passes through the point (-9, 17) and has a slope of -4/3 is y = -4x/3 + 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-9, 17) and a slope of -4/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 17 = -4/3(x - (-9))
y - 17 = -4x/3 - 12
y = -4x/3 - 12 + 17
y = -4x/3 + 5
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Complete Question:
Write an equation in slope-intercept form of the line that passes through the point (-9,17) and had a slope of -4/3.
Which of the binomials below is a factor of this trinomial?
x2 + 4x + 4
A. x - 2
B. x + 2
C. x - 4
D. x + 4
Answers
B. x + 2
Part 1.] The attached picture
Part 2.] What is the probability of getting 4 heads when tossing a coin 6 times (rounded to the nearest tenth).
Part 3.] A.) Describe the connection of the pattern of outcomes to Pascal’s triangle.
B.) Look at the increase in values. What is the pattern in the number of total possible outcomes?
Part 4.] Complete the table for powers of 11.
11^0=____
11^1=____
11^2=____
11^3=____
Using the pattern, what is the value of 11^4? _____
Calculate 11^5? _____
Calculate 11^6? _____
Part 5.] Can you use the values in Pascal’s triangle to find the powers of 11? Explain.
Answers
HTH, THH, HHT
TTH, THT, HTT
We consider the same for four tosses (answer provided in order with respect to the supplied given in the number of outcomes):
HHHH
THHH, HTHH, HHTH, HHHT
HHTT, HTHT, THHT, TTHH, THTH, HTTH
HTTT, THTT, TTHT, TTTH
TTTT
For the total possible outcomes we just add the number of outcomes in the third column. For three tosses we'll have a total of 8 possible outcomes and for four tosses we'll have 16 possible outcomes.
Part 2. From the answers in part 1 we can determine a pattern for the total possible outcomes based on the number of tosses. It's [tex] 2^{x} [/tex] where x is the number of tosses. So for 6 tosses we'll have 64 possible outcomes.
To find how many outcomes would have exactly 4 heads, we determine the number of outcomes with HHHHTT. This will be a simple permutation problem with the equation: [tex] \frac{6!}{4!2!} =15[/tex]. Therefore, there will be 15 outcomes with exactly 4 heads.
We just divide the number of outcomes with exactly 4 heads over all possible outcomes to determine the probability.
[tex] \frac{15}{64}=0.2 [/tex]
ANSWER: The probability would be 0.2.
Part 3-a. A Pascal's triangle is a triangle of numbers where the first and last numbers in every row are 1 and the rows at the middle are determined by getting the sum of the two nearest rows above it. Attached here is an image of the triangle.
We can observe that the pattern of outcomes is exactly like the numbers appearing in the rows of the Pascal's triangle (with the exception of the first row of the triangle)!
Part 3-b. As mentioned earlier, the pattern for the total possible number of outcomes is just [tex] 2^{x} [/tex] where x is the number of tosses. We know this because we are familiar with the fact that the answers supplied in the table in Part 1 are powers of 2.
Part 4. We first use the calculator to determine these powers:
[tex] 11^{0}=1 [/tex]
[tex] 11^{1}=11 [/tex]
[tex] 11^{2}=121 [/tex]
[tex] 11^{3}=1331 [/tex]
[tex] 11^{4}=14641 [/tex]
[tex] 11^{5}=161051 [/tex]
[tex] 11^{6}=1771561 [/tex]
We just used the calculator to find these values easily but we can actually use a pattern to find the values. The pattern is evident for the first 5 exponents (0-4). We can see that the first 5 answers all look like the Pascal's triangle values!
Part 5. Yes, you can find the values for the powers of 11 using Pascal's triangle. As stated earlier, the first 5 powers (including 1) are evidently following the pattern. For exponent 5 and up, this is still actually following the triangle but the double digit answers are just carried over to the next digit.
For example, 1 5 10 10 5 1 became 161,051 since the two 10s in the middle had to be carried over.
This pattern will hold true for any powers of 11.
A nautical mile is a unit of distance frequently used in ocean navigation. It is defined as the length of an arc s along a great circle on the earth when the subtending angle has measure 1' = "one minute" = 1/60 of one degree. Assume the radius of the earth is 3,960 miles.
Find the length of one nautical mile to the nearest 10 feet.
Answers
s = rФ
Radius is given to be = 3960 miles
We are to find the arc length in feet, so we convert the miles to feet.
1 mile = 5280 feet.
So,
Radius = 3960 x 5280 feet = 20908800 feet
Angle = 1/60 degree
The angle must be in radians before, we use its value in the equation given above.
So, 1/60 degrees in radians will be:
[tex] \frac{1}{60} * \frac{ \pi }{180} = \frac{ \pi }{10800} [/tex]
Now we can use this value of angle in above equation to find the arc length.[tex]s = 20908800 * \frac{ \pi }{10800} = 6080 feet[/tex]
So, rounded of to nearest 10 feet, the length of one nautical mile is 6080 feet.
The value of one nautical mile to the nearest feet is [tex]\boxed{6080{\text{ feet}}}[/tex].
Further Explanation:
The arc, radius and the angle are related to each other.
The angle can be obtained as the ratio of an arc of the circle to the radius of the circle.
The formula for the angle can be expressed as,
[tex]\boxed{{\text{Angle = }}\frac{{{\text{length of an arc}}}}{{{\text{radius of circle}}}}}[/tex]
The length of an arc can be obtained as,
[tex]\boxed{{\text{Length of an arc}}=\left({{\text{radius}}\times{\text{angle}}}\right)}[/tex]
Given:
The angle is one minute represented by 1'.
One minute is equal to [tex]{\left({\frac{1}{{60}}}\right)^\circ}[/tex].
The radius of earth is 3960 miles.
Explanation:
One mile is equal to 5280 feet.
[tex]\boxed{1{\text{ mile}}=5280{\text{ feet}}}[/tex].
The radius in feet can be expressed as follows,
[tex]\begin{aligned}Radius&=3960\times5820\\&=20908800{\text{ feet}}\\\end{aligned}[/tex]
Convert the angle into radian.
[tex]\boxed{1{\text{ degree}} = \frac{\pi }{{180}}{\text{ radian}}}[/tex]
The value of [tex]\frac{1}{{{{60}^ \circ }}}[/tex] can be obtained as follows,
[tex]\begin{aligned}{\text{Angle}}&=\frac{1}{{60}}\times\frac{\pi }{{180}}\\&=\frac{\pi }{{10800}}\\\end{aligned}[/tex]
The length of an arc of the earth can be obtained as follows,
[tex]\begin{aligned}{\text{length of an arc}}&=20908800\times\frac{\pi }{{10800}}\\&=6080{\text{ feet}}\\\end{aligned}[/tex]
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Unit and Measurement
Keywords: Nautical mile, unit distance, earth, radius of earth, great circle, one degree, length of nautical unit, feet.
please help idk this one !!Which represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answers
y+4=x² Equation 1
y-x=2 Equation 2
Isolate y from equation 2.
y=x+2 Substitute value of y in equation 1.
x+2+4=x²
x+6=x²
x²-x-6=0
Solve for x.
x²-3x+2x-6=0
x(x-3)+2(x-3)=0
(x-3)(x+2)=0
x-3=0 or x=3
and
x+2=0 or x=-2
Substitute value of x in y=x+2
y=-2+2=0
and
y=3+2=5
So solutions are (-2,0) and (3,5)
Answer: (-2,0) and (3,5)
Answer:
[tex](-2,0)[/tex] and [tex](3,5)[/tex]
Step-by-step explanation:
we have
[tex]y+4=x^{2}[/tex] -----> equation A
Is a vertical parabola open upward
[tex]y-x=2[/tex] ----> equation B
Is the equation of a line
we know that
The solution of the system of equations is the intersection point both graphs
Using a graphing tool
The intersection points are [tex](-2,0)[/tex] and [tex](3,5)[/tex]
see the attached figure
my sister needs help on this! right answer ill choose as an "brainliest" person:)
Answers
[tex]\sf V=lwh[/tex]
[tex]\sf V=(12)(6)(8)[/tex]
[tex]\sf V=576in^3[/tex]
Now the gap:
[tex]\sf V=lwh[/tex]
[tex]\sf V=(2)(6)(6)[/tex]
[tex]\sf V=72in^3[/tex]
Subtract the two volumes to find the volume of the entire figure:
[tex]\sf 576-72=\boxed{\sf 504in^3}[/tex]
How many distinct and real roots can an nth-degree polynomial have?
Answers
An n-th degree polynomial may have up to n distinct real roots.
Fred played golf and for the past 5 times had a score of 82, 79, 83, 71, and 80. What was his average score?
Answers
Which expression represents the sum of (2x-5y) and (x+y)?
A. 3x-4y
B.3x-6y
C.x-4y
Dx-6y
Answers
= (2x+x) + (-5y+y)
= 3x + (-4y)
= 3x-4y
So option A is the correct one.
If the area of an equilateral triangle is 9√3 sq ft, how long is a side?
6 ft.
9 ft.
18 ft.
Answers
[tex]Area= \frac{ \sqrt{3} }{4}s^2 \ \ \ \ \ \text{[s= length of a side] } \\ \\ \\ \frac{ \sqrt{3} }{4}s^2=9 \sqrt{3} \\ \\ s^2=9 \sqrt{3}: \frac{ \sqrt{3} }{4}= 9 \sqrt{3} \cdot \frac{ 4 }{ \sqrt{3} }=36 \\ \\ s= \sqrt{36}=6 \ \text{ft } [/tex]
The answer is 6 ft.
Answer:
6ft.
Step-by-step explanation:
What is the measure of AC? Enter your answer in the box. ___°
Do not answer for points. If so, you WILL be reported and points be taken BACK. -.-
Answers
2(3x - 1.5) = 3x + 9
6x - 3 = 3x + 9
3x = 12
x = 4
arc AC = 3(4) + 9 = 12 + 9 = 21
answer
21
Answer:
AC = 21⁰
Step-by-step explanation:
arc AC has central angle 3x+9 n its inscribed angle <ABC is 3x-1.5
central angle = 2 * inscribed angle
3x+9 = 2 * (3x-1.5)
3x+9 = 6x -3
3x = 12
x = 4
so arc AC = (3*4 + 9) = 21⁰
15) Which equation does not represent a function?
A) y = 2x + 3
B) x = 4y + 7
C) 6x - 5y = 8
D) y2 = -5x - 8
Answers
PLEASE HELP STEP BY STEP
Answers
[tex]= \frac{z^{2}-6}{z-5} \times \frac{z^{2}+z-18}{z+2}[/tex]
[tex]= \frac{(z^{2}-6)(z^{2}+z-18)}{(z-5)(z+2)}[/tex]
Ordinarily, with a problem of this sort, there would be factors that would cancel, making the result simpler than what you get by multiplying things out. Here, there are no common factors and the numerator factors are all irrational. Of course, the denominator cannot be zero, so the restrictions are
.. z ≠ -2 or +5
[tex]= \frac{z^{4}+z^{3}-24z^{2}-6z+108}{z^{2}-3z-10}[/tex]
You are going to movies friday night (not a matinee). which of the theaters will cost the least, if you intend to have soda and popcorn? theater a theater b theater c adults $6.25 $7.25 $5.25 children $3.50 $3.75 $4.25 soda $2.00 $2.00 $2.50 popcorn $2.50 $2.00 $2.50
Answers
Theater C is the least expensive option for an adult going to the movies on Friday night with the cost of tickets, soda, and popcorn totaling $10.25.
To find out which theater will cost the least for a movie on Friday night including soda and popcorn, we need to calculate the total cost for each theater and then compare the costs. Let's assume you are an adult going to the movie.
Theater A: Movie ($6.25) + Soda ($2.00) + Popcorn ($2.50) = $6.25 + $2.00 + $2.50 = $10.75Theater B: Movie ($7.25) + Soda ($2.00) + Popcorn ($2.00) = $7.25 + $2.00 + $2.00 = $11.25Theater C: Movie ($5.25) + Soda ($2.50) + Popcorn ($2.50) = $5.25 + $2.50 + $2.50 = $10.25Comparing the total costs, Theater C has the lowest cost at $10.25.
write an equation that is parallel to y = -4x - 1 and passes through (-2 , 4)
Answers
In order for a function to be parallel to another, they must have the same slope but different intercepts (or else they'd be the same line).
This equation has the same slope and the same intercept, so it is parallel.
Hope this helps!
Three cubes of edge 12 cm are joined together (end to end).Find the volume of the resultng cuboid
Answers
Which of the following interpretations for the given expression is correct?
the cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
the difference of the cube of 5 times the square of y and 7 divided by 2 times the square of y
the cube of the difference of the square of 5 times y and 7 divided by the square of 2 times y
the cube of the difference of 5 times the square of y and 7 divided by 2 times the square of y
Answers
(5y² -7)³/(2y)²
I believe the best answer is the first option; the cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y.
Answer:
The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y.Step-by-step explanation:
The give expression is:
[tex]\frac{(5y^{2}-7)^{3} }{(2y)^{2} }[/tex]
In words, this expression would have all these statement referring to each operation:
The cube of the difference, because the difference is inside the cubic power.Of 5 times the square of y and 7, because these are the terms that are being subtracted.Divided by, because the expression described before is in a quotient.The square of two times y, because the both factor are inside the squared power.Therefore, the first statement is correct.
look at the question below // 50 points // please help!!
Answers
Hi there!
I believe your answer is A. Asymptote. It wouldn't be focus or axis, those just don't make sense. This means it could be either asymptote or directrix. Directrix is a fixed line describing a curve or surface. An asymptote is a line that continually approaches a given curve but does not meet it at any finite surface. Therefore, your answer is asymptote.
Hope this helps!
- Chris
Simplify:
(x^3-8)
ok i know it simplifies to (x-2)(x^2+2x+4)
but i don't know why
Answers
The Difference of Cubes formula shows up frequently in mathematics courses and should be memorized.
The formula for factoring the difference of cubes is (a^3 - b^3)= (a-b)(a^2+ab+b^2). It works because if (a-b)(a^2+ab+b^2) is multiplied it out, then it becomes a^3 - b^3. This was probably originally determined by trial and error a long time ago.
Since x is cubed and 8 is 2^3 it factors with the Difference of Cubes Formula. (x^3-2^3)=(x-2)(x^2+2x+2^2)=(x^2+2x+4)
Solve the inequality.
–12m < –24
Answers
Solving for m.
Divide both sides by 12.
-12m/12 < -24/12
-m < - 2
Multiply both sides by -1 and reverse the inequality.
- 1x -m > -1 x - 2
m > 2
Answer: m > 2
The base of a triangle is 9 inches more than 3 times the height. if the area of the triangle is 105 square inches, find the base and height.
Answers
The function h(x)=x^2+3 and g(x)=x^2-6.If g(x)=h(x)+k, what is the value of k
Answers
-x²-3 -x²-3
k=-9
Answer:
g(x) = (x – 9 )2 + -8
Step-by-step explanation:
please help 1.Bryce started with $450 in a bank account that does not earn interest. In the middle of every month, he withdraws 1/2 of the account balance. Which recursive function rule models Bryce’s balance at the end of each month?
Answers
The following recursive function represents the Brye's balance at end of each month:
[tex] a_{n}= \frac{1}{2}* a_{n-1} [/tex]
where [tex] a_{n-1} [/tex] is the account balance of previous month. And [tex] a_{n} [/tex] is the account balance of current month.
Paul, Colin and Brian are waiters. One night the restaurant earns tips totalling £71.10. They share the tips in the ratio 2:3:4. How much more does Colin get over Paul?
Answers
the total money to be shared is £ 71.10
Altogether the money could be divided into (2 + 3 + 4) 9 portions
1 portion comes to £ 71.10 / 9 = £ 7.9
Paul receives 2 portions, which equals to 7.9 * 2 = 15.8
Colin receives 3 portions , this equals to 7.9 * 3 = 23.7
Therefore the difference between the 2 portions is 23.7 - 15.8 = 7.9
hence, Colin receives £7.9 over Paul
The amount that Colin will get more than Paul is $7.90.
From the information given, Paul's share will be:
= 2/9 × $71.10
= $15.80
The share of Colin will be:
= 3/9 × $71.10
= $23.70
The difference between Colin's share and Paul's share will be:
= $23.70 - $15.80
= $7.90
Therefore, the amount that Colin will get more than Paul is $7.90.
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Using the figure below, select the two pairs of alternate interior angles.
1 and 4
2 and 3
6 and 7
5 and 8
Answers
2 and 3
6 and 7
Answer
Options second and third
Reason
From the figure we get l and m are two parallel lines and t is the traversal.
There are two pairs of alternate interior angles
The pairs of alternate interior angles are equal
pairs of alternate interior angles
2 and 3
6 and 7
Similarly there are alternate exterior angles are there. Other two options are alternate exterior angles