Answers
Answer:
30 square units
Step-by-step explanation:
The area of the given right triangle can be found a couple of ways:
Pythagorean theoremThe missing side length can be found using the Pythagorean theorem relation between the sides:
c² = a² +b²
13² = a² +5²
a² = 169 -25 = 144
a = √144 = 12
Then the area is ...
A = 1/2ab = 1/2(12)(5) = 30 . . . square units
__
TrigonometryThe angle at lower right can be found from the trig relation ...
Cos = Adjacent/Hypotenuse
cos(A) = 5/13
A = arccos(5/13) ≈ 67.38°
The area can be found from these side lengths and the angle:
A = 1/2bc·sin(A)
A = 1/2(5)(13)sin(67.38°) = 30 . . . square units
_____
Additional comment
The sine of the angle can be computed from the cosine using the identity ...
sin(x) = √(1 -cos²(x))
In this case, the sine of the angle would be found to be 12/13, so the area would be computed as ...
A = 1/2(5)(13)(12/13) = 1/2(12)(5) . . . . same as using the Pythagorean theorem
Related Questions
WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The cost for a business trip for 3 people is $1,975 per person. The business trip would use 79%
of the company’s travel budget. Find the total amount of money the company has budgeted for
travel. pls show work :)
Answers
Answer:
7500
Step-by-step explanation:
3*1975=5925
5925/.79=$7500
Answer:
5175
Step-by-step explanation:
1975*3=5925
5925/79%=7500 (Take one zero off)
750
5925-750=5175
The Company will pay 5175 in total. But 1725 per each person going.
Hey, I need some help with this:
Give an example of what an inverse operation is and how they are used in solving equations
Answers
Inverse operations are an operation that undoes each other. For example, addition and subtraction, multiplication and division, squares and square roots.
For example, we have the equation:
2 + 2 = 4
The inverse of this equation is:
4 - 2 = 2
Best of Luck!
If you take out a loan that costs $561 60 over eight years at an interest rate of 9% how much was the loan for?
Answers
Answer:
The loan was $28184.81
Step-by-step explanation:
Let the loan amount be x
Rate of interest on Loan = 9%
Time = 8 years
Amount of loan over 8 years = $56160
Formula : [tex]A=P(1+r)^t[/tex]
Where A = Amount =56160
P = Principal = x
r = rate of interest = 9% = 0.09
t = time = 8 years
Substitute the values in the formula :
So,[tex]56160=x(1+0.09)^8[/tex]
[tex]\frac{56160}{(1+0.09)^8}=x[/tex]
$28184.81=x
Hence The loan was $28184.81
Of all 25 marbles in a bag, 3 of the marbles are white. What is the probability that a white marble will be randomly selected from the bag without looking? Write your answer as a percent.
Answers
Step-by-step explanation:
Total marbles = 25
Probability of white marble = 3/ 25 = 0.12
PLEASE HURRY!!IM BEING TIMED!WILL NAME BRAINLIEST!!
The table and graph show that each cracker in a package has 7 calories.
Crackers and Calories
crackers(X) calories(Y)
1 7
2 14
3 21
4 28
Which statement about the graph is true?
A.)The number of crackers is the dependent variable, and the number of calories is the independent variable.
B.)The point (42, 6) is on the line.
C.)The number of crackers are graphed on the y-axis, and calories are graphed on the x-axis.
D.)The two variables are the number of crackers and the number of calories.
(Picture not option!just a graph!)
Answers
Answer:
D.)The two variables are the number of crackers and the number of calories.
Step-by-step explanation:
The number of crackers is the independent variable, and the number of calories is the dependent variable.
The point (6, 42) is on the line
The number of crackers are graphed on the x-axis, and calories are graphed on the y-axis.
factorise 15x- 10x^3
Answers
Answer:
5x (3-2x^2)
Step-by-step explanation:
so all you have to do is 15x-10x=5x right?, then all you have to do is 15/5=3. 10x/5x=2x. then subtract 1 from the exponents. then you get the answer. okay Im sure about the fist part and the divison but not the exponents, I did use a calculator to check it though.
The factorize equation is, [tex]\rm 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0[/tex].
The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
Given that,
Equation; [tex]\rm 15x - 10x^3[/tex]
We have to determine,
Factorize the equation and factor of the equation.
According to the question,
To factorize the equation and determine the factor of the equation following all the steps given below.
Equation; [tex]\rm 15x - 10x^3[/tex]
Step1; Taking the term 5x common from the equation,[tex]\rm = 15x - 10x^3 = 0 \\\\= 5x (3-2x^2) = 0[/tex]
Step2; Simplify the equation,[tex]\rm = 5x (3-2x^2) = 0\\\\ = 5x (\sqrt{3} - \sqrt{2x}) (\sqrt{3}+\sqrt{2x}) = 0[/tex]
Step3; The roots of the equation are,[tex]\rm = 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0\\\\ The \ roots \ of \ the \ equation \ are;\\\\5x = 0, \ x = \dfrac{0}{5}, \ x =0\\\\\\[/tex]
[tex]\sqrt{3} - \sqrt{2x} = 0, \sqrt{2}x = \sqrt{3}, \ x = \dfrac{\sqrt{3} }{\sqrt{2} }\\\\ \sqrt{3} +\sqrt{2x} = 0, \sqrt{2}x = -\sqrt{3}, \ x =- \dfrac{\sqrt{3} }{\sqrt{2} }[/tex]
Hence, The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
For more details refer to the link given below.
https://brainly.com/question/11540485
Find the volume of the cone
Answers
Answer:
12π
Step-by-step explanation:
Volume of the cone is πr^2 * h / 3
r = 3
h = 4
9π * 4 / 3 = 12π
Answer: 37.6991118
Step-by-step explanation:
Pythagorean Theorem: Jason only has room for a TV that is less than 30^ prime prime wide.
Find the width of the TV
Answers
Answer:
Step-by-step explanation:
length² + width² = diagonal²
24² + width² = 40²
576 + width² = 1600
width² = 1600 - 576
width² = 1024
width = √1024 = √32*32
width = 32"
Width of the TV is more than 30"
Answer:
32
Step-by-step explanation:
First off, Bruh, 30" is not prime prime. That's 30 inches.
The base of the TV is 32. This is because A^2+B^2=C^2. 24 is A, 40 is C, and the base is B.
So that means that is we take 24^2 and the base^2, we should get 40^2. 40^2 is 1600. 24 squared is 576. So if we take the base and square it and add 576, we should get 1600. Or we could just take 1600 and subtract 576.
1600-576=1024.
So now, the root of 1024 is the base. Which is 32. Hope that helped.
The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Answer the following questions about the equation modeling the volume of the shipping box.
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If you get two solutions, are they both reasonable?
Answers
Answer:
see below
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
FOIL
8(n^2 +2n+4n+8) = 1144
Divide each side by 8
8/8(n^2 +2n+4n+8) = 1144/8
(n^2 +2n+4n+8) = 143
Combine like terms
n^2 +6n+8 = 143
Subtract 143 from each side
n^2 +6n+8 -143= 0
Combine like terms
n^2 +6n -135 =0
Factor
What two terms multiply to -135 and add to 6
-9*15 =-135
-9+15 = 6
(n-9) (n+15) =0
Using the zero product property
n-9 =0 n+15=0
n = 9 n=-15
The length cannot be negative so n = -15 cannot be a solution
n =9
Answer:
n = 9
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n² + 2n + 4n + 8 = 143
n² + 6n - 135 = 0
n² + 15n - 9n - 135 = 0
n(n + 15) - 9(n + 15) = 0
(n - 9)(n + 15) = 0
n = 9, -15
since n is a length, it can not be negative
Therefore the only solution is n = 9
The parabola opens to the right. The focus is given as
F (p,0) and directrix x = -p. The distance between the
focus and point P is equal to the distance between the
directrex and point P. Continue to simplify the equation to
solve for y2. THE ANSWER IS 4px!! :)
Answers
Answer:
Step-by-step explanation:
We have that the focus is at (p,0) and that the directrix is x=-p. Take the point (-p,0) of the directrix. We know that the vertex of the parabola is at the middle point ot the line segment that joins the points (p,0) and (-p,0). To get the middle piont, we take the average coordinate by coordinate. That is, the middle point is [tex](\frac{-p+p}{2}, \frac{0+0}{2}) = (0,0)[/tex]. The general formula of a parabola of vertex (h,k) that opens to the right or to the left is given by
[tex](y-k)^2 = 4p(x-h)[/tex]
Where |p| is the distance from the focus to the vertex. If the parabola opens to the right, then p>0 and p<0 otherwise. In our case, h =0=k, so we get that
[tex]y^2 = 4px[/tex]
Answer:
y^2 = 4px
Step-by-step explanation:
edg 2021
The change in the x-coordinates of any two points on a line in the xy-plane is
the______
A. rise
B. slope
C. angle
D. run
Answers
Answer:
D. run
Step-by-step explanation:
The slope is given by
m = (y2-y1)/ (x2-x1) = rise/ run
The change in the x coordinates is the run
If you have a cube with a side length of ¼, how many cubes can fit into your rectangular prism? Explain.
Answers
Answer:
Step-by-step explanation:
No of cubes that can fit into rectangular prism = Volume of rectangular prism
Volume of cube
Find the volume of rectangular prism and divide that by the volume of cube
What is the mean absolute deviation of 24,30,36,42,48,54
Answers
Add all the numbers together, and divide by how many numbers there are!
Area and perimeter please
Answers
Answer:
185.68 for perimeter
1652.16 for area
Step-by-step explanation:
Please give me brainliest i hope you do well.!
it me again I need help
Answers
Answer:
85%
Step-by-step explanation:
He hit it 17/20
We want that as a percent
Multiply by 5/5
17/20*5/5 = 85/100
Percent means out of 100
85%
Answer:
85
Step-by-step explanation:
P(hit) = 17/20 × 100
85%
Which choice is equivalent to the quotient shown here for acceptable values of x?
Answers
Answer:
(D)
Step-by-step explanation:
Equivalent expressions are expressions that have equal values
The equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]
The expression is given as:
[tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex]
Represent the expression as a quotient
[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x^2}{3x}}[/tex]
Evaluate the quotient
[tex]\sqrt{8x^2 } \div \sqrt{3x} = \sqrt{\frac{8x}{3}}[/tex]
Hence, the equivalent expression of [tex]\sqrt{8x^2 } \div \sqrt{3x}[/tex] is [tex]\sqrt{\frac{8x}{3}}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
plz halp meh!!!!!!!
Answers
Answer:
M=25-3D
Step-by-step explanation:
Daniel starts with 25 dollars and spends three dollars per day for a d number of days. So the amount of money in his wallet should be equal to the starting number of dollars minus the amount of money he spends. Therefore we get the equation M=25-3D, where M is the amount of money is his wallet, and D us the number of days he buys a drink and chips.
The half-life of a certain radioactive element is 35 hours. If there are 904 grams of this element, how much will be left after 70 hours? PLEASE HELP I MIGHT FAIL MATH.
Answers
===========================================================
Explanation:
The half-life is 35 hours. This means every 35 hours, the amount of the substance is cut in half. If we started with 100 grams, then 35 hours later, we will have 50 grams. Then another 35 hours later we will then have 25 grams, and so on.
In this case, we start with 904 grams and follow this sequence:
904, 452, 226, 113, ...
Each term is cut in half. Going from term to term it takes 35 hours each. The third term 226 is the result of waiting two half-lives, which is 2*35 = 70 hours that have elapsed total.
--------------
If you want to use a formula, then it would be
[tex]y = A*\left(\frac{1}{2}\right)^{x/H}[/tex]
where,
H = half-life duration (in this case, it is 35)
A = starting amount (which is 904 in this case)
x = amount of time that has elapsed (we will plug in x = 70)
y = final amount after x units of time has elapsed
note that x and H must have the same time unit. Both are in terms of hours in this case.
------------
So we will plug A = 904, x = 70, H = 35 into the formula to get...
[tex]y = A*\left(\frac{1}{2}\right)^{x/H}\\\\y = 904*\left(\frac{1}{2}\right)^{70/35}\\\\y = 904*(0.5)^{2}\\\\y = 904*(0.25)\\\\y = 226\\\\[/tex]
We see that x = 70 leads to y = 226. This means after 70 hours, there is 226 grams of the material left.
Triangle XYZ is a right triangle.
Use the drop downs to determine the length of the legs of the right triangle.
What is the length of Side X Z?
What is the length of Size Y Z?
Answers
Answer:
What is the length of Side X Z?
✔ 5
What is the length of Size Y Z?
✔ 6
The length of side XZ is 5 units.
The length of side YZ is 6 units.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To find the length of side XZ, we can use the distance formula, which is:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Substituting the coordinates of X (-2, 4) and Z (3, 4), we get:
[tex]d(XZ) = \sqrt{(3 - (-2))^2 + (4 - 4)^2}\\= \sqrt{5^2 + 0^2}\\= \sqrt{25}\\= 5[/tex]
The length of side XZ is 5 units.
To find the length of side YZ, we can again use the distance formula with the coordinates of Y (3, -2) and Z (3, 4):
[tex]d(YZ) = \sqrt{(3 - 3)^2 + (4 - (-2))^2}\\= \sqrt{0^2 + 6^2}\\= \sqrt(36)\\= 6[/tex]
The length of side YZ is 6 units.
Thus,
The length of side XZ is 5 units.
The length of side YZ is 6 units.
Learn more about triangles here:
https://brainly.com/question/25950519
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Find , to the nearest tenth of a foot , the height of the tree represented in the accompanying diagram.
Answers
Answer:
Height of tree = 28.2 ft (Approx)
Step-by-step explanation:
Given:
Angle from ground to top of the tree = 62°
Distance from a point to base of tree = 15 ft
Height of tree = [tex]X[/tex]
Find:
Height of tree = [tex]X[/tex]
Computation:
Using trigonometric application:
[tex]Tan\ 62 = \frac{Height\ of\ tree}{Distance\ from\ a\ point\ to\ base\ of\ tree} \\\\Using\ calculator\ , Tan62 = 1.88\\\\1.88=\frac{Height\ of\ tree}{15} \\\\Height\ of\ tree=28.2ft[/tex]
Height of tree = 28.2 ft (Approx)
Which of the following is equivalent to the complex number i8?
Choose 1 answer:
mi
1
-1
pl
Stuck? Watch a video or use a hint.
Report a problem
Answers
Answer:
1
Step-by-step explanation:
note that i² = - 1
Thus
[tex]i^{8}[/tex]
= i² × i² × i² × i²
= - 1 × - 1 × - 1 × - 1
= 1 × 1
= 1
The value of complex number is 1. Therefore, the option B is the correct answer.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
The given complex number is i⁸.
We know that, i²=-1
Now, i⁸ can be written as i²×i²×i²×i²
= -1×(-1)×(-1)×(-1)
= 1
Therefore, the option B is the correct answer.
To learn more about the complex numbers visit:
https://brainly.com/question/10251853.
#SPJ2
can someone help with this please,, also explain if you can..
Answers
Answer:
story 1
Step-by-step explanation:
because it says 2 higher than -2 so -2+2 is 0
Can someone pls help
Answers
Answer:
a) At what time does Bethan arrive home from school?
The answer would be C) 15:30
b) What distance does Siobhan travel each day when going to school and back?
The answer would be D) 16km
Step-by-step explanation:
Is this SAS or Not SAS?
Answers
Both triangles angles and sides are congruent
Answer:
SAS
Step-by-step explanation:
Simplify. Rewrite the expression in the form y^ny n y, start superscript, n, end superscript. y^{-4}\cdot y^{3}=y −4 ⋅y 3 =y, start superscript, minus, 4, end superscript, dot, y, cubed, equals
Answers
Answer:
[tex]y^{-4}\cdot y^3=y^{-1}[/tex].
Step-by-step explanation:
The given expression is
[tex]y^{-4}\cdot y^3[/tex]
We have to simplify the above expression. in form of [tex]y^n[/tex].
Using property of exponents, we get
[tex]y^{-4}\cdot y^3=y^{-4+3}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
After addition of exponents, we get
[tex]y^{-4}\cdot y^3=y^{-1}[/tex]
Therefore, [tex]y^{-4}\cdot y^3=y^{-1}[/tex].
find the measure of arc UT Given
a.168
b.192
c.84
d.96
Answers
Answer:
is there supossed to be a picture?
Step-by-step explanation:
Answer:
Can you please give us a picture!
Step-by-step explanation:
A man wants to hike two trails. The length of one trail is 7.709 km. The length of the other trail is 9.0309 km. What is the total length of the two trails?
Answers
Answer:
Its addition I think so the answer would we 16.7399km for both trials
Step-by-step explanation:
A city has an elevation of –752 feet. Which statement describes the city’s elevation?
–752 above sea level
–752 below sea level
752 above sea level
752 below sea level
Answers
Answer:
752 bellow sea just did that
Answer:
Its 752 below see level!
Step-by-step explanation:
I am doing the assignment right now and got it right!, if you want can you guys mark brainliest that would help a lot!!
Find the interquartile range (IQR) of the data plot below
Answers
Answer:
3.5
Step-by-step explanation:
0 1 1 3 3 3 4 5 7
median= 3
Q1= 1
Q3= 4.5
4.5-1= 3.5
Answer:3.5
0,1,1,3,3,3,4,5,7
What is the solution of the inequality shown
below?
c+2 < -1
Answers
Answer: c < -3
Step-by-step explanation: To solve for c in this inequality, your goal is the same as it would be you were solving an equation, to get c by itself on one side of the inequality.
Since 2 is being added to c, subtract
2 from both sides of the inequality.
On the left, the +2 and -2 cancel out
and on the right, -1 - 2 is -3.
So we end up with c < -3.
I have also graphed this for you below.
