Answers
=========================================================
Work Shown:
We see that one of the legs is unknown. We'll call this 'a'.
The other leg is b = 2, which becomes b^2 = 4
The hypotenuse (always opposite the 90 degree angle) is c = sqrt(58). This turns into c^2 = 58 when you square both sides.
---------
Use the pythagorean theorem to get
a^2+b^2 = c^2
a^2+4 = 58
a^2 = 58-4
a^2 = 54
a = sqrt(54)
a = sqrt(9*6)
a = sqrt(9)*sqrt(6)
a = 3*sqrt(6)
The third side in simplest radical form is x=3[tex]\sqrt{6}[/tex]
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios, metric relationships, or the Pythagorean Theorem.
For solving this question, you need to apply the Pythagorean Theorem that says: (hypotenuse)²= (leg1)²+(leg2)².
The question gives:
Hypotenuse= [tex]\sqrt{58}[/tex]Leg1= 2Leg2= third side = unknowApplying the Pythagorean Theorem, you have:
([tex]\sqrt{58}[/tex])² = 2²+ x²
58=4+x²
x²=58-4
x²=54
x=[tex]\sqrt{54}[/tex]
x=[tex]\sqrt{2*3^3}[/tex]
x=[tex]\sqrt{2*3^2*3}[/tex]
x=3[tex]\sqrt{2*3}[/tex]
x=3[tex]\sqrt{6}[/tex]
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Related Questions
A certain virus is dying off at a rate of 18% per hour. Initially there were
40,000 grams of the strain. If this continues at this rate, how much of the
strain would still be alive after 48 hours? (Round your answer to the
nearest whole number.) *
Answers
Answer:
3 strain would still alive after 48 hours
Step-by-step explanation:
Initial population of virus = 40000 grams
A certain virus is dying off at a rate of 18% per hour.
We are supposed to find how much of the strain would still be alive after 48 hours
Formula : [tex]N(t)=N_0(1-r)^t[/tex]
[tex]N_0[/tex]=Initial population
N(t)= Population after t hours
r = rate of decrease = 18% = 0.18
t = time = 48 hours
So,the strain would still be alive after 48 hours=[tex]40000(1-0.18)^{48}=2.91 \sim 3[/tex]
Hence 3 strain would still alive after 48 hours
Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (2) minus 6 = negative 30. The expressions are not equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (3) minus 6 = negative 42. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (negative 2) minus 6 = 18. The expressions are equivalent because Negative 3 (2) (5 minus 4) + 3 (2 minus 6) = negative 18 and Negative 12 (1) minus 6 = negative 18.
Answers
Answer:
The expressions are not equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(2)-6=-30
Step-by-step explanation:
Two expressions are said to be equal if after a number is substituted to the expression, they produce the same result (that is they have the same value).
To determine whether -3x(5-4)+3(x-6) is equivalent to -12x-6, we have to substitute the same number to the expression and see if it produces the same result.
Substituting 2 to the first expression gives:
-3×2(5-4) + 3(2 - 6) = -6 - 12 = -18
Substituting 2 to the second expression gives:
-12(2) - 6 = -24 - 6 = -30
Since -3×2(5-4) + 3(2 - 6) = -6 - 12 = -18 and -12(2) - 6 = -24 - 6 = -30, the expressions are not equivalent because they do not produce the same result.
The correct procedure that justifies their equality is the expressions are equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(1)-6=-18
Expressions and valuesEquations are written by equating two expressions
Given the following equation -3x(5-4)+3(x-6)
Expand
-15x + 12 + 3x - 18
Collect the like terms
-15x + 3x + 12 - 18
-12x - 6
Hence the correct procedure that justifies their equality is the expressions are equivalent because -3(2)(5-4)+3(2-6)=-18 and -12(1)-6=-18
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Find x 4sqrt3 2sqrt3 8 8sqrt3
Answers
Answer:
8
Step-by-step explanation:
sin 30° = 1/2
sin is opponent/hypotenuse
so
opp/hyp = 4/x = 1/2
x = 4 * 2 = 8
Answer:
[tex]\displaystyle x=8[/tex]
Step-by-step explanation:
[tex]\displaystyle x=\frac{sin(90) \times 4 }{sin(30)}[/tex]
[tex]\displaystyle x=8[/tex]
Find the circumference of this circle:
7 cm
Write appropriate units with your answer, and round your answer to 2 decimal places.
Answers
Answer: 43.96
Reasoning/Work:
(formula): C= 2(pie, 3.14)r
2x3.14x7
43.96
What is the volume of this rectangular prism? 30.75 cm^3
61.5 cm^3
147.6 cm^3
295.2 cm^3
Answers
This question is incomplete. Because it lacks the diagram of the Rectangular prism. Find attached to this answer the appropriate diagram.
Answer:
295.2 cm³
Step-by-step explanation:
A Rectangular Prism is a 3 dimensional geometric shape.
The formula used to calculate the volume of the Rectangular Prism = Length × Width × Height
Length = 15cm
Height = 4.8cm
Width = 4.1cm
Volume of the Rectangular Prism = 15cm × 4.8cm × 4.1cm
= 295.2 cm³
Answer:
295.2
Step-by-step explanation:
Got it right on the test. Your welcome and have a great day and God bless you all.
If trapezoid JKLM is translated according to the rule (x,y)—> (x+2, y - 6), what are the coordinates of point L
Answers
Answer:
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Step-by-step explanation:
Explanation:-
Type of transformation change to co-ordinate point
vertical translation up 'd' units (x,y) changes to (x , y+d)
vertical translation down 'd' units (x,y) changes to (x , y-d)
Horizontal translation left 'c' units (x,y) changes to (x-c , y)
Horizontal translation right 'c' units (x,y) changes to (x+c , y)
Now by use above table
given data ( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Final answer:-
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Can someone plz help me out! With this problem I really need help ASAP! I will mark you as brainiest! Help help ASAP!
Answers
Answer:
John = 82 Billy = 82 Gregg = 80 Bob = 55
Step-by-step explanation:
John = (3x38)+(2x0)-(2x8)-(2x8)
Billy = (3x30)+(2x4)-(2x3)-(2x5)
Gregg = (3x30)+(2x3)-(2x4)-(2x4)
Bob = (3x25)+(2x6)-(2x9)-(2x7)
he factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot: 1 is labeled + x, 1 is labeled negative. 5 tiles are in the Factor 2 spot: 1 is labeled + x and 4 are labeled +. 10 tiles are in the Product spot: 1 is labeled + x squared, 1 is labeled negative x, the 4 tiles below + x squared are labeled + x, and the 4 tiles below the negative x tiles are labeled negative. What are the factors of x2 + 3x – 4? (x + 4) and (x – 4) (x + 3) and (x – 4) (x + 4) and (x – 1) (x + 3) and (x – 1)
Answers
Answer:
x-1 and x+4. srry if i am wrong
Step-by-step explanation:
The graph of g(x) = (x+2)^2 is a translation of the graph of f(x) ___by___units
Answers
Answer:
The graph of g(x)=(x+2)^2 is a translation of the graph of f(x) LEFT by TWO units.
∠A and ∠B are complementary. If m∠B = 64° , what is the measure of ∠A?
26°
36°
11°
64°
Answers
Answer: 26
Step-by-step explanation:
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then
∠A + ∠B = 90
∠A =90- ∠B
∠A = 26
Answer:
The measure of [tex]\angle A[/tex]:
[tex]\angle A = 26\textdegree[/tex]
Step-by-step explanation:
Since both [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary (Which they both add up to 90°), and you want to find the measure of
Measure of [tex]\angle A[/tex]: unknown
Measure of [tex]\angle B[/tex]: 64°
Finding the measure of [tex]\angle A[/tex]:
[tex]90 - 64 = 26[/tex]
[tex]\angle A = 26\textdegree[/tex]
So, the measure for [tex]\angle A[/tex] is [tex]26\textdegree[/tex].
f(1)=3
f(n)=f(n−1)+5.5
f(3)=
Answers
Answer:
f(3) = 14
Step-by-step explanation:
Using the recursive formula and f(1) = 3 , then
f(2) = f(1) + 5.5 = 3 + 5.5 = 8.5
f(3) = f(2) + 5.5 = 8.5 + 5.5 = 14
Answer:
14
Step-by-step explanation:
Jeremy analyses one of his parachute jumps. He draws a graph showing his velocity up to the opening of his parachute. a) Estimate Jeremy's acceleration at t = 10s to 1 decimal place. b) Estimate his average speed for this part of the jump. Give your answer to two significant figures.
Answers
Answer:
Jeremy's acceleration is about [tex]1\,\frac{m}{s^2}[/tex] at t =10 s
His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)
His average speed is about 46 m/s if using the tangent line (over estimate)
Step-by-step explanation:
Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.
These points are : (6, 42) and (14,50) which using the slope formula give:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}[/tex]
So his acceleration at that point is about [tex]1\,\frac{m}{s^2}[/tex]
Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:
[tex]v_{average}=\frac{area}{interval\,\,length}[/tex]
and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.
The area of this trapezoid is: approximately:
[tex]Trapezoid\,\, area=(49+40)\,8/2=356[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}[/tex]
If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):
[tex]Trapezoid\,\, area=(50+42)\,8/2=368[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}[/tex]
while his actual instantaneous velocity seems to be about 46 m/s from the graph
Answer:
a) 1.0
b) s=45
Step-by-step explanation:
Two lines are guaranteed to be coplanar if they?
Answers
Answer:
If they lie in the same plane
g(x) = 1/3 * (2/9)^x. Does the function model growth or decay?
Answers
x -> infinity, y-> 0
Answer:
It Decays
Step-by-step explanation:
Why because Kahn Acadmey said so
please help me on this!
Answers
Answer:
The rocket reached its maximum height at 1.25 seconds.
Step-by-step explanation:
A factory makes 750 cakes every day. The cakes are orange cakes or lemon cakes. Each day Aadil takes a sample of 25 cakes to check. The proportion of the cakes in his sample that are orange is the same as the proportion of the cakes made that day that are orange. On Monday Aadil calculated that he needed exactly 7 orange cakes in his sample. a) What is the total number of orange cakes that were made on Monday
Answers
A) 210
B) 0.18
Step-by-step explanation:A) On Monday, 7/25 of the 750 are orange cakes. 7/25 x 750 = 210
B) If the proportion of orange cakes is 5/25 where 5 is correct to the nearest whole number, then the 4.5 would be the lowest number that would still be rounded up to 5. 4.5/25 = 0.18
If someone could help me thank you it’s geometry :(
Answers
Answer:
<1 = 119
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
<1 = 57+62
<1 = 119
Answer:
119
Step-by-step explanation:
Simplify 7(A-6)
A-6
7A-42
7A-6
Answers
Answer:
7A - 42
Step-by-step explanation:
7(A-6)
Distribute
7*A - 7*6
7A - 42
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 3) ← 2 points on the line
m = [tex]\frac{3-2}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]
If 3 inch square is covered with 1inch squares how many of the 1 inch squares are needed? What is the area of the larger square
Answers
Answer:
9 1-inch squares will cover the bigger square. Its area is the same as the amount of squares needed, 9 inches.
the larger Area will be 9 square inch.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To cover a 3 inch square with 1 inch squares, we can arrange the 1 inch squares in a 3 by 3 grid.
So, we need 9 of the 1 inch squares to cover the 3 inch square.
The area of the larger square can be found by squaring the length of one of its sides.
Since the side length of the 3 inch square is 3 inches, the area of the larger square is:
Area = (side length)² = 3² = 9 square inches
Therefore, the larger Area will be 9 square inch.
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the middle number; put the values in order from lowest to highest, then find the number that is exactly in the middle
Answers
john has × marbles and max has twice as many.max give gives john 5 of his marbles does max now have
Answers
Answer: 2x -5
Step-by-step explanation:
Hi, to answer this question we have to write equations with the information given:
John has × marblesJohn=x
Max has twice (multiplied by 2) as many.max give gives john 5 of his marbles.We have to multiply by 2 the number of marbles that John has (x), and subtract 5.
Max = 2x -5
Feel free to ask for more if needed or if you did not understand something.
choose the definition for the function
Answers
Answer:
The answer above is wrong it actually b
The function shown in the graph is option b.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
We have from the graph that graph touches the x axis at 2 and at a point between 0 and 1.
That is,
f(x) = 0 when x = 2
Substitute the value of x as 2 in the functions given in the option when x > 1 and find those functions which give y = f(x) = 0.
It is only possible for options 'a' and 'b'.
When x = 2, -2 + 2 = 0.
Also we have the point, when x = 1, y = 1.
x = 1, then -2x + 2 = 0 ≠ 1
x = 1, then -x + 2 = -1 + 2 = 1
So when x = 1, f(x) should be of the form f(x) = -x + 2.
Correct option is option b.
Hence the correct definition of the function is option b.
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Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won't the van catch up when the distances are equal?
Answers
Answer:
It takes 0.619 hours (approximately 37 minutes) for the van to catch up with the storm.
They have driven 33.43 miles
They will catch up when their distances are equal.
Step-by-step explanation:
The speed of the van is 54 mph, and the speed of the storm is 33 mph. They are going in the same direction, so the relative speed is the difference of their speeds:
relative speed = 54 - 33 = 21 mph
Now, to find the time when the van reaches the storm, we just need to use the equation:
distance = speed * time
13 = 21 * t
t = 13 / 21 = 0.619 hours
The distance traveled by the van is:
distance = 54 * 0.619 = 33.43 miles
The van will catch up when the distances are equal (the distance of the storm is 13 + 33*0.619 = 33.43 miles)
Communication Methods Among Teens
Frequency Two-Way Table
Which answer shows the relative frequency by the row
of girls?
O 52.5%, 23.0%, 24.6%, 100%
O 57.0%, 12.2%, 27.8%, 100%
O 60%, 12.2%, 27.8%, 100%
O 62.8%, 44.0%, 62.5%, 100%
Text
e-Mail
IM
Total
Boys
32
14
15
61
Girls
54
11
25
90
Total
86
25
40
151
Answers
Answer:
it’s c i think
Step-by-step explanation:
Answer C
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below?
3(5x + 7) – 6(4 – 2x)
270 - 3
27r - 12
12r + 3
12. + 27
ha
Answers
Answer:
[tex] \boxed{27x - 3} [/tex]
Step-by-step explanation:
[tex] = > 3(5x + 7) - 6(4 - 2x) \\ \\ = > (3 \times 5x) + (3 \times 7) - (6 \times 4) - (6 \times ( - 2x)) \\ \\ = > 15x + 21 - 24 - ( - 12x) \\ \\ = > 15x - 3 + 12x \\ \\ = > 27x - 3[/tex]
Answer: 27x=3
Step-by-step explanation: 3(5x+7) -6(4-2x) = 3(5x+7) + (-6)(4+(-2x)) = 15x + 21 + (-24) + 12x =15x + 12x + (-24) + 21 =27x + (-3) =27x-3 hope this helps
What is the equation for the graph shown?
Answers
Answer:
y = -2x + 6Step-by-step explanation:
The graph is a line Then it has an equation of the form : y = my + p
where m is the slope and p is the y-intercept.
the line crosses the y-axis at the point (0,6) then
p = 6
the line is going down then
m is negative
the only provided equation that verify: m < 0 and p = 6 is y = -2x + 6
Answer:
y = -2x + 6
Step-by-step explanation:
Anyone know how this can be solved?
Answers
Answer:
127.235cm^2
Step-by-step explanation:
A = πr²/2 = 40.5 * π [cm²] ≈ 127.235 [cm²]
Answer:
[tex]127.251 {cm}^{2} [/tex]
Step-by-step explanation:
[tex] \frac{180}{360} \times \pi {r}^{2} \\ \frac{1}{2} \times 3.142 \times 9 \times 9 \\ = \frac{254.502}{2} \\ = 127.251 {cm}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
How much is $100 U.S. dollars in Canadian dollars?
Answers
Answer:
133.98
Step-by-step explanation:
Step by Step Explanation:
Can someone help me please?
Answers
Answer:
Inverse Variation
Step-by-step explanation:
y = k/x