The set of side lengths that could be the sides of a right triangle must follow the Pythagoras theorem
How to determine the side lengths?The rule of the side lengths of a right triangle is:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the longest side, and a and b represent the lengths of the triangle
This in other words mean that:
All right triangles obey the Pythagoras theorem
Note that I gave a general explanation because the question is incomplete
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Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]x =\sqrt 2[/tex]
Step-by-step explanation:
Given is a 30° - 60° - 90° triangle.side x lie opposite to 30° angle[tex]\implies x = \frac{1}{2}\times \sqrt 8[/tex][tex]\implies x = \frac{1}{2}\times 2\sqrt 2[/tex][tex]\implies x =\sqrt 2[/tex]Simplify the expression to yield a quadratic trinomial in standard form.
6x(x-4)-(3x− 2)
Step-by-step explanation:
6x² - 24x - 3x + 2
6x² - 27x + 2
10 1. Use the image below to answer the following questions: Solve for the measurement of A. b. Solve for y. a. C. Solve for x. X 48 Y A
Answer:
see explanation
Step-by-step explanation:
(a)
the sum of the 3 angles in the triangle = 180° , then
∠ A = 180° - 90° - 48° = 180° - 138° = 42°
(b)
using the tangent ratio in the right triangle
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{10}[/tex] ( multiply both sides by 10 )
10 × tan48° = y , then
y ≈ 11.1 units ( to the nearest tenth )
(c)
using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{x}[/tex] ( multiply both sides by x )
x × cos48° = 10 ( divide both sides by cos48° )
x = [tex]\frac{10}{cos48}[/tex] ≈ 14.9 units ( to the nearest tenth )
The simplified ratio of 32/12 is:
Answer:
8/3
Divide both sides by the GCF, 4.
32 ÷ 4 = 8
12 ÷ 4 = 3
B. Solve the following inequalities and graph their solution sets. Use red or blue marker and ruler for the graph. 1. 3x-7 ≤ 5 Solution:
Answer:
[tex]3x \leqslant 5 + 7 \\ 3x \leqslant 12 \\ x \leqslant 4[/tex]
Step-by-step explanation:
hope it helps
How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
Please show work! Factor sin^2Θ + sin^2Θ cos^2Θ
Factorization of sin²θ + sin²θ cos²θ gives us; 2sin²θ - sin⁴θ
How to simplify Trigonometric Functions?
We want to simplify;
sin²θ + sin²θ cos²θ
Let us factorize out sin²θ to get;
sin²θ(1 + cos²θ)
Now, we know that cos²θ = 1 - sin²θ
Thus;
sin²θ(1 + cos²θ) = sin²θ(1 + 1 - sin²θ)
⇒ sin²θ(2 - sin²θ)
⇒ 2sin²θ - sin⁴θ
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How many pairs of vertical angles are shown in the drawing?
Answer:
A.0
Step-by-step explanation:
Vertical angles are angles that are opposite of each other when two lines cross
Hope This Helped
Help lolllllllllllll
Answer:
-5 or 5
Step-by-step explanation:
the absolute value of -5 is 5. The absolute value of 5 is also 5.
Hope this helps :)
Which of these can help you visualize data? Select all that apply.
bank statement
circle graph
spreadsheet
table
bar graph
Answer:
circle graph and bar graph
Step-by-step explanation:
they visualize because they are not simply just words, they make colorful graphs
How do you write y=mx+b for this equation 21-y-mx=34
Answer:
y = -mx - 13.
Step-by-step explanation:
21-y-mx=34
Add y to both sides
21 - mx = 34 + y
Subtract 34 from both sides
-13 - mx = y
Rearrange:
y = -mx - 13.
Five people, each working 8 hours a day, can assemble 400 toys in a 5-day work week. What is the average number of toys
assembled per hour, per person?
A 2
B 4
C 8
D 16
Answer:
A. 2
Step-by-step explanation:
First divide the 400 toys by the 5 people to see how many each did:
400 toys/5 people = 80 toys/person
Next let's see how many hours were worked by multiplying the hours per day by the number of days worked:
5 days x 8 hours/day
40 hours
Now to find how many toys were assembled per hour per person, let's divide the toys/person by the number of hours they each worked:
[tex]\frac{80 toys/person}{40 hours}[/tex]=2 toys/person/hour
The average number of toys per person per hour is 2.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Total number of toys assembled = 400
Total days of work = 5
Each person work daily for = 8 hrs
Total number of people = 5
Then, the total toys assembled per day
400/5= 80
The number of hours worked by the 5 workers per day = 8 × 5= 40
So, the number of toys assembled per person per hour = 80 / 40= 2
Hence, the average number of toys per person per hour is 2.
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Evaluate the expression below when x = 3 54 ÷ 2•3-x²
Answer:
72
Step-by-step explanation:
54/2(3)−3^2
= 54/2(3)−3^2
=72
Step 5: to isolate x, multiply both sides by:
To isolate x , multiply both the sides by ( 5/23 )
What is an Equation ?An equation is formed when two algebraic expressions are equated using an equal sign.
The given equation is
(3/5)(x-10) = 18-4x-1
(3/5)x - 6 = 18-4x-1
(3/5)x - 6 = 17-4x
(3/5)x = 23 -4x
(23/5)x = 23
Step 5 says To isolate x , multiply both the sides by (5/23)
x = 5
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Andy wrote the equation of a line that has a slope of Step 2: y plus 2 equals StartFraction 3 Over 4 EndFraction x minus StartFraction 9 Over 4 EndFraction. and passes through the point (3, –2) in function notation.
Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)
How to determine the equation of the line?The given parameters are:
Slope, m = 3/4
Point, (x,y) = (3,-2)
The equation of the line is calculated using:
y - y1 = m(x - x1)
Substitute the known parameters
y + 2= 3/4(x - 3)
From the question;
Andy's equation is y + 2 = 3/4(x - 9/4)
The above equation is different from the actual equation y + 2= 3/4(x - 3)
Hence, Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)
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The nearest hundred to 83,752,245 is?
Answer:
83,752,000
Very positive with this answer
Answer:
83,752,200
Step-by-step explanation:
please give me brainlist
You wish to take a flight from Nevada to New York. Use the point (-4, 0) to represent Nevada, and the (5, 2) to represent New York. The airline has partitioned the flight so that you have a layover. The flight distance is partitioned in a ratio of 3:1. Determine the ordered pair that represents the location of the layover.
Using proportions, it is found that the ordered pair that represents the location of the layover is (3.75, 1.5).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The flight distance is partitioned in a ratio of 3:1, hence, for both the x and y coordinates, we have that:
L - Nv = 3/4(Ny - Nv)
For the x-coordinate, we have that:
[tex]x + 4 = \frac{3}{4}(5 + 4)[/tex]
[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]
[tex]x = \frac{11}{4}[/tex]
x = 3.75
For the y-coordinate, we have that:
[tex]y = \frac{3}{4}(2)[/tex]
[tex]y = \frac{6}{4}[/tex]
y = 1.5.
The ordered pair that represents the location of the layover is (3.75, 1.5).
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Fred's teacher gave the class the
quadratic function f(x) = 4x² + 16x+9
State two different methods Fred could use to solve the equation f(x) = 0.
Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest
tenth.
Two methods Fred could use to solve the equation are
The completing the square method The formula methodThe solution for the function is x ≅ -0.7 OR x ≅ - 3.3
Solving quadratic equationsFrom the question, we are to solve the given quadratic equation
Two methods Fred could use to solve the equation are
The completing the square method The formula methodThe given quadratic function is
f(x) = 4x² + 16x+9
Now, we are to solve f(x) = 0 for x
That is,
4x² + 16x+9 = 0
Using the formula method to solve the equation
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the equation,
a = 4, b = 16, and c = 9
∴ [tex]x =\frac{-16 \pm \sqrt{16^{2}-4(4)(9) } }{2(4)}[/tex]
[tex]x =\frac{-16 \pm \sqrt{256-144 } }{8}[/tex]
[tex]x =\frac{-16 \pm \sqrt{112 } }{8}[/tex]
[tex]x =\frac{-16 \pm 10.58 }{8}[/tex]
[tex]x =\frac{-16+ 10.58 }{8}[/tex] OR [tex]x =\frac{-16- 10.58 }{8}[/tex]
[tex]x =\frac{-5.42 }{8}[/tex] OR [tex]x =\frac{-26.58 }{8}[/tex]
x = -0.6771 OR x = - 3.3229
x ≅ -0.7 OR x ≅ - 3.3
Hence, the solution for the function is x ≅ -0.7 OR x ≅ - 3.3
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Which equation represents a line that is parallel to the line that passes through the points (-6,9) and (7,-17)?
Answer:
y = -2x-3
Step-by-step explanation:
Slope = - 2 C = - 3y =-2x-3Please help!! Need help asap.
guys help just with part b for number 2!
Answer:
22 8th graders
Step-by-step explanation:
if 25% of the 88 kids are 8th graders then do this.
88x.25=22
88x.75=66
there are 22 eighth graders
and 66 seventh graders.
Estimate the amount of time she spent at ballet to the nearest hour
The amount of time that Lila spent at Yoga and Ballet are approximately equal to 26 hours and 13 hours respectively.
How to calculate the time spent?First of all, we would calculate the amount of time that Lila spent at Yoga by multiplying the total time spent by the percentage of time spent on Yoga as follows:
Yoga time = 92 × 28/100
Yoga time = 92 × 0.28
Yoga time = 25.76 ≈ 26 hours.
Part B.Next, we would calculate the amount of time that Lila spent at Ballet by multiplying the total time spent by the percentage of time spent on Ballet as follows:
Ballet time = 92 × 14/100
Ballet time = 92 × 0.14
Ballet time = 12.88 ≈ 13 hours.
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Complete Question:
The circle graph shows how Lila spent her after-school time during the month of October. Lila’s Activities Part A If Lila spent a total of 92 hours on these activities in the month of October, estimate the amount of time she spent at Yoga, to the nearest hour.
Part B. Estimate the amount of time she spent at Ballet, to the nearest hour.
Question 9 of 10
If you vertically compress the absolute value parent function, F(x) = |x|, by
multiplying by 3/4 what is the equation of the new function?
A: G(x)= |x+3/4|
B: G(x)= 3/4 |x|
C: G(x)= |x|-3/4
D: G(x)= |3/4 x|
Answer:
B. g(x) = 3/4|x|
Step-by-step explanation:
Multiplying the function by a number in front will stretch, compress, and/or reflect the function over the x-axis.
So if the number in front is negative that will flip it upside down, over the x-axis.
If the number is greater than 1, the function will be vertically stretched, narrower, slimmer, skinnier, taller.
In this case, the graph is vertically compressed, making it flatter, fatter, wider smashed. In this case is where the number multiplied in front of the parent function is LESS than one.
g(x) = 3/4 |x|
Suppose that the water level of a river is 4 feet and is increasing at a rate of 0.15 foot per day. Write the
variable expression to represent the depth of the river in terms of d, the number of days.
Answer:
The answer would be 4+0.15d.
Step-by-step explanation:
I hope this helps! :) I am so sorry if this is not right!
The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:
Part A: What is the approximate y-intercept of the line of best fit and what does it represent?
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope.
Answer:
(a) (i) y-intercept = 3
(ii) Represents that the team won 3 matches without any practice.
(b) (i) Equation: y = 1.8x + 3,
(ii) 26 matches won
The approximate y-intercept can be determined by seeing when the best fit line crosses the y axis.
Part AHere the best line crosses the y-axis when y = 3. So coordinates: (0, 3)
Part BTake two best points touching the line: (0,3), (5, 12)
[tex]\sf slope \ (m) = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{12-3}{5-0} = 1.8[/tex]
Equation:
y - y₁ = m(x - x₁)
y - 3 = 1.8(x - 0)
y = 1.8x + 3
So, after 13 months of practice: y = 1.8(13) + 3 = 26.4 ≈ 26 matches won.
#1
The y intercept should represent how much matches the team won without practice
Here its 3
(0,3)#2
(0,3)(5,12)Slope
m=12-3/5m=9/5Equation in point slope form
y-3=9/5xy=9/5x+3After 13 months
y=9/5(13)+3=117/5+3Approximately 26matches
PLEASE HELP ILL MAKE YOU THE BRAINIEST
Find the value of x
Answer:
12.04
Step-by-step explanation:
add 8 and 9 by the power of two: 8^2+9^2
that equals to 145
find the square root of 145 and that equals to 12.04
Describe a situation that can be represented by an equation and a situation that can be represented by an inequality. What features determine how the situation should be represented?
The inequality sign can be used when referring to two quantities that are not the same size.
What is an inequality?An inequality is used to express a condition whereby the two quantities are not the same.
For instance, if we have the same number of students inside and outside a classroom, we can use the equality sign. In a case where we do not have the same number of students inside and outside the classroom, we can use the inequality sign.
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Using synthetic division, find (2x4 − 3x3 − 20x − 21) ÷ (x − 3).
A.
2x3 + 3x2 + 9x + 7
B.
2x4 + 3x3 + 9x2 + 7x
C.
2x4 + 3x2 − 11x − 54
D.
2x3 + 3x2 − 11x − 54
The correct option for the synthetic division is A. 2x³ + 3x² + 9x + 7
How to solve the division?
Write down the first coefficient without changes and multiply the entry in the left part of the table by the last entry in the result.
Then, add the obtained result to the next coefficient of the dividend, and write the sum. All the coefficients are the coefficients of the quotient, and the last coefficient is the remainder.
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James surveyed 120 voters at random out of 12,600
registered voters in his town. based on the results of the
survey, what is the total number of registered voters
expected to vote for miss frizzle in the upcoming election
The expected number of votes for Miss Frizzle in the election is 4725
How to determine the expected number of votes for Miss Frizzle?The data that completes the question is as follows:
Miss Frizzle = 45
Miss Reynolds = 75
The expected number of votes for Frizzle is:
Frizzle = 45/120 * 12600
Evaluate
Frizzle = 4725
Hence, the expected number of votes for Miss Frizzle in the election is 4725
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evaluate the expression and enter your answer in the box below |98|
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate [tex]\pmb{|98|}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The notation |x| denotes absolute value.The absolute value of a number is its distance from zero.
Absolute value is always positive; distances can't be negative, right?
So we need to find the absolute value of 98, which is:
[tex]\star~\star\mathrm{98}~\star~\star[/tex]
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{The\;absolute\;value\;is\;a\;number's\;distance\;from\;zero}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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