Answers
a = square root 9
a = 3
answer
3 ft
C being the hypotenuse.
a = a
b = 8 ft
c = √73 ft
a^2 + 8^2 = √73^2
a^2 + 64 = 73
a^2 = 9
a = 3
Related Questions
Jane Peter and Simon have $395 which they wish to divide between them Jane gets $20 more than Peter and Peter gets $15 more than Simon how much does each get
Answers
If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?
Answers
Answer: The values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Step-by-step explanation: For an angle [tex]\theta[/tex],
[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]
We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].
Given that
[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]
We will be using the following trigonometric properties:
[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]
The calculations are as follows:
We have
[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]
Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so
[tex]\cos\theta=-\dfrac{1}{2}.[/tex]
Now, we have
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]
Thus, the values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.
The value of cos and tan for given theta is:
[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]
How to find if the angle given lies in third quadrant?If angle lies between 0 to half of pi, then it is int first quadrant.
If angle lies between half of pi to a pi, then it is in second quadrant.
When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.
And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.
Which trigonometric functions are positive in third quadrant?Only tangent function and cotangent functions.
In first quadrant, all six trigonometric functions are positive.
In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.
We can continue as follows:
[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]
Thus, evaluating cos and tan at obtained theta:
[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]
Learn more about trigonometric functions and quadrants here;
https://brainly.com/question/25952919
red die and a black die are rolled at the same time. The probability of getting a 6 on the red die is 16, and the probability of getting a 3 on the black die is 16. Given that the two events are independent, what is their combined probability?
Answers
it should be 1/6 not 16
there are 6 numbers on a die so to get a number you have a 1/6 probability
so 1/6 x 1/6 = 1/36
the probability of getting both a 6 and a 3 is 1/36
A quadratic equation is shown below: 9x2 − 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
Find the discriminant, b^2 - 4ac, which is the same as the value of the radicand.
(-16)^2 - 4 * 9 * 60 = -1904
Since the discriminant is negative, there will be NO real solutions, and 2 complex solutions.
Part B.
4x^2 + 8x - 5 = 0
You can tell if a quadratic is factorable if you find the discriminant and it is a perfect square. The discriminant for this quadratic is 144 so it is factorable.
(2x + 5)(2x - 1) = 0
Set each factor equal to zero.
2x + 5 = 0 2x - 1 = 0
subt 5 from both sides add 1 to both sides
2x = -5 2x = 1
divide both sides by 2 divide both sides by 2
x = -5/2 x = 1/2
A fair sortition trial is carried out, and one of the candidates is assigned the number 32,041. If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, how many candidates are there?
Answers
Answer: 3125
Step-by-step explanation:
Given: A fair sortition trial is carried out, and one of the candidates is assigned the number = 32,041
If each digit can be chosen from 0-4, and if each of the possible sequences is assigned to a candidate, then the number of candidates (repetition of digits allowed)=[tex]5\times5\times5\times5\times5[/tex]
[tex]=3125[/tex]
Hence, the number of candidates there are = 3125.
There are 42 boys and girls participating in an essay-writing competition. Of the competitors, 21 are in seventh grade, 14 are in eighth grade, and 7 are in ninth grade. What is the probability of an eighth grader winning the competition? Which simulation(s) can be used to represent this situation?
Answers
simulate this by using a number generator with numbers 1 - 6.....with 1 - 3 representing 7th graders, 4 and 5 representing 8th graders, and 6 representing 9th graders
Answer: Our required probability is 0.34.
Step-by-step explanation:
Since we have given that
Number of seventh grade student s= 21
Number of eight grade students = 14
Number of ninth grade students = 7
Total number of boys and girls = 42
Probability of an eigthth grader winning the competition would be
[tex]\dfrac{14}{42}\\\\=\dfra{1}{3}\\\\=0.3333333..................\\\\\approx 0.34[/tex]
Hence, our required probability is 0.34.
The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function mc002-1.jpg. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
Answers
The average rate is the change in h divided by the change in t, mathematically:
r=(h(3)-h(0))/(t2-t1), in this case:
r=(-16*9+300-0-300)/(3-0)
r=-144/3
r= -48 ft/s
Answer:
the answer on edge is D) h(3)-h (0)/3
And, the answer to the equation is 156.
Can you please help me
Answers
Find the least number between 200 and 500 which leaves a reminder of 3 in each case when divide by 8,10,12 and 30
Answers
Assume n the number to be found.
n-3 is so a multiple of 8,10,12,30 .
The lcm of 8,10,12,30 is 2^3*3*5=120
n-3=120 or 240 or 360.... n-3=240
==> n=243
Justin is redoing his bathroom floor with tiles measuring 6 in. By 13 in. The floor has an area of 8500 in.². What is the least number of tiles he will need
Answers
8500 total in divided by 78 = 108.97 (approx)
This number needs to be rounded up for least amount of tiles
=109 tiles
A savings account earns 6% (APR) interest calculated monthly, paid into the account at the end of 6 months. Travis deposits $100 into the account at the beginning of the first month. At the end of each month, he deposits an additional $100 into the account. How much interest will Travis have earned after 6 months?
Answers
End of month 1 = 100×1.06 = 106
Beginning of month 2 = 106+100 = 206
End of month 2 = 206×1.06 = 212
Beginning of month 3 = 212+100 = 312
End of month 3 = 312×1.06 = 330.72
Beginning of month 4 = 330.72+100 = 430.72
End of month 4 = 430.72×1.06 = 455.8
Beginning of month 5 = 555.8
End of month 5 = 555.8×1.06 = 589.148
Beginning of month 6 = 689.148
End of month 6 = 689.148×1.06 = 624.49688
The amount of interest Travis will receive at the end of month 6 is
624.49688 - 600 = 24.49688 ≈ $24.50
9 1/4 - 6 2/3
Write answer as mixed number with fractional part in lowest terms.
Answers
To subtract the mixed numbers 9 1/4 and 6 2/3, first convert them to improper fractions, find a common denominator, and then perform the subtraction. The result is expressed as the mixed number 2 7/12 with the fractional part in lowest terms.
Explanation:Subtracting Mixed Numbers
The question involves subtracting mixed numbers, specifically 9 1/4 (nine and one quarter) from 6 2/3 (six and two thirds). First, we need to convert these mixed numbers into improper fractions for easier subtraction.
Convert 9 1/4 to an improper fraction: (9 × 4) + 1 = 36 + 1 = 37/4.Convert 6 2/3 to an improper fraction: (6 × 3) + 2 = 18 + 2 = 20/3.To subtract, we need a common denominator. Multiplying the denominators 4 and 3 gives us 12, the LCD.Adjust the fractions: 37/4 becomes 111/12 (since 37 × 3 = 111) and 20/3 becomes 80/12 (since 20 × 4 = 80).Now subtract the numerators: 111 - 80 = 31. So, the difference is 31/12.Finally, convert 31/12 back into a mixed number, which is 2 7/12 (since 31 divided by 12 is 2 with a remainder of 7).The answer is 2 7/12.
To subtract mixed numbers, find a common denominator. Subtract the fractional part by subtracting the numerators. Subtract the whole numbers as usual. The answer is 8 7/12.
Explanation:To subtract mixed numbers, we first need to find a common denominator. In this case, the common denominator is 12. Then, we can subtract the fractions by subtracting the numerators and leaving the denominator the same.
For the whole numbers, we simply subtract them as usual.
So, 9 1/4 - 6 2/3 = 8 7/12.
Huilan's age is two times Thomas's age. The sum of their ages is
54
. What is Thomas's age
Answers
If one store is selling 3/4 of a bushel of apples for $9, and another store is selling 2/3 of a bushel for $9, which store has the better deal? Explain you answer
Answers
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest tenth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)
Answers
V=(hπd^2)/4, and we are told that the height is 3r, r=d/2, so 3r=3d/2=h
V=(3d/2)(πd^2)/4
V=(3πd^3)/8, we know d=10 so
V=3000π/8
V=375π in^3, lastly we are told to approximate π≈3.14 so
V≈375(3.14) in^3
V≈1177.5 in^3
The volume of the cylinder is 1177.5 cubic inches.
Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.
The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.
Now, we can substitute these values into the formula for the volume of a cylinder:
[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]
Rounded to the nearest tenth.
How do you do 8.75 Times 38
Answers
x 38
---------
332.50
Find the value of a and z: (x^8)^3=ax^z
Answers
(x^8)^3=ax^z
x^24 = ax^z
so : z=24 and a= 1
A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4. Which statements about the new rectangle are true?
Check all that apply.
The dimensions of the new rectangle will be 10 cm by 12 cm.
The dimensions of the new rectangle will be 40 cm by 48 cm.
The new perimeter will be 4 times the original perimeter.
The new perimeter will be 16 times the original perimeter.
The new area will be 4 times the original area.
The new area will be 16 times the original area.
The new perimeter will be 44 cm.
The new area will be 30 square cm
Answers
Answer:
The dimensions of the new rectangle will be 10 cm by 12 cm.The new perimeter will be 4 times the original perimeter.The new area will be 16 times the original area.The new perimeter will be 44 cm.Step-by-step explanation:
Given dimensions of original rectangle , length(l)=3 cm and width(w)=2.5 cm
We know that after dilation with scale factor (k), the dimension of new figure = k times the original dimensions.
Thus width of new rectangle=[tex]4\times2.5=10\ cm[/tex]
length of new rectangle=[tex]4\times3=12\ cm[/tex]
∴The dimensions of the new rectangle will be 10 cm by 12 cm.
Now, Perimeter of original rectangle=[tex]2(l+w)=2(3+2.5)=2(5.5)=11\ cm[/tex]
Thus, Perimeter of new rectangle=[tex]2(4l+4w)=2(12+10)=2(22)=44\ cm[/tex]
⇒ Perimeter of new rectangle=44 cm=[tex]4\times11\ cm[/tex]
∴The new perimeter will be 4 times the original perimeter.
Now, Area of original rectangle=[tex]lw=3\times2.5=7.5\ cm^2[/tex]
Thus, Area of new rectangle=[tex]4l\times4w=12\times10=120\ cm^2[/tex]
Area of new rectangle=[tex]16lw=16(lw)[/tex]
⇒The new area will be 16 times the original area.
Choose the correct simplification of (5xy7)2(y2)3.
Answers
The simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex].
What is the simplified form of the expression?Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.
What are the exponent rules?The different Laws of exponents are:
[tex]x^{m} .x^{n} =x^{m+n}[/tex][tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex][tex](x^{m} )^{n} = x^{m\times n}[/tex][tex]x^{0} =1[/tex][tex]x^{-1} = \frac{1}{x}[/tex]According to the given question.
We have an expression [tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]
To simplify the above expression we use the exponent rules.
Therefore,
[tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]
[tex]= 5^{2}x^{2} y^{7\times2} y^{2\times3}[/tex]
[tex]= 25 x^{2} y^{14} y^{6}[/tex]
[tex]= 25 x^{2} y^{14+6}[/tex]
[tex]= 25 x^{2} y^{20}[/tex]
Therefore, the simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex] .
Find out the more information about the simplified form of the expression and exponent rules here:
https://brainly.com/question/14575743
#SPJ2
Find the area.
Square
A = s^2
s - side.
Answers
area = S^2
side = 12 miles
12^2 = 144
area = 144 miles
Solve for ×. show your work
30×-40=80
Answers
30x = 80+ 40
30x = 120
---- ----
30 30
x = 4
hope this helps
Find the balance in the account. $4,100 principal earning 4%, compounded monthly, after 10 years
Answers
A=p (1+r/k)^kt
A future value?
P present value 4100
R interest rate 0.04
K compounded monthly 12
T time 10 years
A=4,100×(1+0.04÷12)^(12×10)
A=6,112.41. ..answer
$4100*(1+0.04/12)^(12*10)
4100*1.490832682=
$6112.41
Deon rented a truck for one day. there was a base fee of $16.95, and there was an additional charge of 75 cents for each mile driven. Deon had to pay $220.20 when he returned the truck. For how many miles did he drive the truck?
Answers
220.20-16.95=203.25
203.25/.75=271
0.75*271=203.25
203.25+16.95=220.20
Need help solving this equation please 5w+8-12w=16-15w
Answers
-7w+8=16-15w
Add 15w to both sides
8w+8=16
Subtract 8 from both sides
8w=8
Divide both sides by 8
w=1
Final answer: w=1
Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
Answers
All of the items found in set A can be found in set B. The other way is not true (eg: 8 in set B is not found in set A)
If you are drawing a venn diagram, all of circle A is inside circle B
Answer:
A ⊆ B
Step-by-step explanation:
what is the ratio of x to y (simplest form)
x= 2 y=6
x=5 y=15
x=8 y=24
Answers
The diagonals of rhombus FGHJ intersect at point K. If side GH is equal to x + 9 and side JH is equal to 5x – 2, find x.
Answers
Answer: Rhombus
I have all of the properties of the parallelogram PLUS
- 4 congruent sides
- diagonals bisect angles
- diagonals perpendicular
3x - 10 = 6x - 19
3x - 6x = -19 + 10
-3x = -9
x = -9/-3
x = 3
Answer:
x = 2.75
Step-by-step explanation:
5x - 2 = x + 9
5x = x + 11
4x = 11
List the discontinuities for the function f(x) = cot(2x over 3)
Answers
As [tex]\sin x=0[/tex] whenever [tex]x=n\pi[/tex] for any integer [tex]n[/tex], we have
[tex]\sin\dfrac{2x}3=0\implies\dfrac{2x}3=n\pi[/tex]
[tex]\implies x=\dfrac{3n\pi}2[/tex]
where [tex]n[/tex] is any integer.
Answer:
Step-by-step explanation:
cot(x) can be written as
[tex]cot(x) =\frac{cosx}{sinx}[/tex]
Here we have [tex]cot(\frac{2x}{3}[/tex]
so It will be undefined whenever
[tex]sin(\frac{2x}{3}) = 0[/tex]
As we cannot have a 0 in the denominator .
so to point all the discontinuties we need to identify the x values where
[tex]sin (\frac{2x}{3} ) = 0[/tex]
[tex]\frac{2x}{3} = 0 + \pi k[/tex] where k is any integer
[tex]x= \frac{3\pi }{2} k[/tex]
It means f(x) is discontinuous at all the values of [tex]x = \frac{3\pi }{2}k[/tex]
for k = 0 , 1 ,2.....
Identify the number that does not belong with the other three. Explain your reasoning.
-10/2, -13.4, square root of 18, 22.7 repeating
Answers
How do I solve this problem: -2(7-y)+4=-4?
Answers
-2(7-y) = - 8
7 - y = = 4
y = 7 - 4
y = 3
1. Use the distributive property.
If there is any parentheses in your equations, you can simplify them with the distributive property.
a(b + c) = ab + ac
2. Combine like terms.
Make sure to combine all like terms on both sides of the equation.
3. Use The Addition Principle of Equality if needed.
The Addition Principle of Equality states that if you add an expression to both sides of the equation, you will get a second equation that is equivalent to the original equation. Or in other words, they will both have the same solution set.
4. Use The Multiplication or Division Principle of Equality if needed.
Similar to the above rule. If you multiply or divide both sides of an equation with the same expression, the resulting equation will have the same solution set as the original equation.
Now that I showed you the rules necessary to solve an algebraic equation, let's solve the one you asked us to solve.
-2(7 - y) + 4 = -4
I see parentheses and we can use the distributive property to get rid of them.
-2(7 - y) + 4 = -4
-14 + 2y + 4 = -4
On the left-hand side, we have like terms that we can combine.
-14 + 2y + 4 = -4
-10 + 2y = -4
Now use The Addition Principle of Equality by adding 10 to each side of the equation.
-10 + 2y + 10 = -4 + 10
2y = 6
Awesome! The -10 constant term disappeared on the left-hand side.
Finally, use The Multiplication or Division Principle of Equality.
Divide both sides by the coefficient of the term 2y.
2y / 2 = 6 / 2
y = 3
So, y is equal to 3.