Answers
Answer:
366.6 mm²
Step-by-step explanation:
Step 1: find XY using the Law of sines.
Thus,
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
m < W = 180 - (70+43) (sum of angles in a triangle)
W = 180 - 113 = 67°
WY = 24 mm
X = 43°
XY = ?
[tex] \frac{XY}{sin(67)} = \frac{24}{sin(43)} [/tex]
Cross multiply:
[tex] XY*sin(43) = 24*sin(67) [/tex]
[tex] XY*0.68 = 24*0.92 [/tex]
Divide both sides by 0.68 to solve for XY
[tex] \frac{XY*0.68}{0.68} = \frac{24*0.92}{0.68} [/tex]
[tex] XY = 32.47 [/tex]
XY ≈ 32.5 mm
Step 2: find the area using the formula, ½*XY*WY*sin(Y).
Area = ½*32.5*24*sin(70)
Area = ½*32.5*24*0.94
= 32.5*12*0.94
Area = 366.6 mm² (nearest tenth)
Related Questions
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answers
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
w²-30w+210=0
Step-by-step explanation:
2w + 2l = 60 , w + l = 30, l = 30 - w
wl = 210
w(30-w) -210 = 0
30w - w²-210 = 0
w²-30w+210=0
Angles α and β are angles in standard position such that: α terminates in Quadrant III and sinα = - 5/13 β terminates in Quadrant II and tanβ = - 8/15
Find cos(α - β)
-220/221
-140/221
140/221
220/221
Answers
Answer:
140/221.
Step-by-step explanation:
For the triangle containing angle α:
The adjacent side is -√(13^2-5^2) = -12.
For the triangle containing angle β:
Hypotenuse = √(-8)^2 + (15)^2) = 17.
cos(α - β) = cos α cos β + sin α sin β
= ((-12/13) * (-15/17) + (-5/13)* (8/17)
= 180/221 + - 40/221
= 140/221.
A ladder is placed 8 feet away from the base of a tree. If the ladder forms a 57° angle
with the ground, how high up the tree will the ladder reaach
Answers
Answer:
3.88 feet
Step-by-step explanation:
let the length the ladder reaches be x
[tex] \tan(57) = \frac{x}{8} [/tex]
[tex]x = 8 \tan(57) [/tex]
x = 3.8775938143
Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Required
Why is the function not continuous at x = 3
First substitute 3 for x at the denominator
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Factorize the numerator and the denominator
[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]
[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]
[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]
Divide the numerator and denominator by (x - 3)
[tex]f(x) = \frac{x+2}{x+3}[/tex]
Substitute 3 for x
[tex]f(3) = \frac{3+2}{3+3}[/tex]
[tex]f(3) = \frac{5}{6}[/tex]
Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;
Then the function is continuous
Answer:
A: f is not defined at x = -3
Step-by-step explanation: EDGE 2020
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard
deviation 7.1%. What is the standardized score for a student who scores 60% on this test?
on 70
Answers
Answer:
-0.704 (corrected to 3 significant figures).
Step-by-step explanation:
Standardized score = (actual score - mean) / standard deviation
Standardized score = (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
Standardized score = (actual score - mean) / standard deviation
= (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
What is supposed by way of ordinary distribution?A regular distribution is an association of facts set in which maximum values cluster in the center of the range and the relaxation taper off symmetrically in the direction of either intense.
What are everyday distributions with examples?Peak, beginning weight, studying potential, activity satisfaction, or SAT scores are only some examples of such variables. due to the fact that commonly distributed variables are so not unusual, many statistical checks are designed for commonly disbursed populations.
Learn more about the normal distribution here: https://brainly.com/question/4079902
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There are 6 chemical elements represented by Li, Na, Mg, Rb, Cs, and Fr that
are written on separate pieces paper. You randomly choose 3 elements, one
at a time, without replacement.
Find the probability that the third element is Na.
Enter the correct answer in the box.
Answers
Answer:
1/6
Step-by-step explanation:
I think this is tricky.
when you randomly choose the 1st two times, it doesn't matter as long as Na was not chosen, otherwise the probability would become ZERO for the 3rd one be Na.
So, after 1st two is removed, there are only 4 left in the pool, so picking Na at the 3rd draw is 1/4 probability.
But, come to think of it, when 1st draw, you have to draw the other 5 out of 6, 2nd draw the 4 out of 5, then 3rd is 1 Na out of the 4.
So, 5/6 x 4/5 x 1/4 = 1/6
Determine the possible rational zeros of this polynomial function using the rational zeros theorem: p(x) = 4x^4 + 13x^3 – 49x^2 – 73x –15
Answers
Answer:
[tex]\large \boxed{\sf \ \ \ -1, \ -5, \ -\dfrac{1}{4} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:
[tex]P(x) = 4x^4 + 13x^3-49x^2-73x-15[/tex]
First of all, what is the rational zeroes theorem?
If P(x) is a polynomial with integer coefficients
and if (p and q being integer)
[tex]\dfrac{p}{q}[/tex]
is a zero of P(x), meaning
[tex]P(\dfrac{p}{q})=0[/tex]
then p is a factor of the constant term of P(x) and
q is a factor of the leading coefficient of P(x).
How to apply it here?
The constant term of P(x) is -15
The leading coefficient of P(x) is 4
so p is a factor of -15
q is a factor of 4
15 = 1 * 5 * 3
4 = 2 * 2 * 1
q can be 1, 2, 4
-p can be 1, 3, 5, 15
so it gives the following potential solutions
-1, -3, -5, -15
[tex]\dfrac{-1}{2}, \dfrac{-3}{2}, \dfrac{-5}{2}, \dfrac{-15}{2}[/tex]
[tex]\dfrac{-1}{4}, \dfrac{-3}{4}, \dfrac{-5}{4}, \dfrac{-15}{4}[/tex]
Let's compute P(x) for x in this list of potential solutions
x P(x)
-1 0
-3 -264
-5 0
-15 148680
-0.5 7.875
-1.5 -39.375
-2.5 -185.625
-7.5 4948.125
-0.25 0
-0.75 7.96875
-1.25 -15.9375
-3.75 -324.84375
It gives -1, -5 and -0.25
Conclusion
The possible rational zeroes of P(x) are
-1
-5
[tex]\dfrac{-1}{4}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A metal cube
of
side 4.4cm was melted
and the molten material used to make a Sphere
Find to 3 significant figures the radius of
the
sphere [take It - 22/7].
Answers
Answer: 2.73 cm
Step-by-step explanation:
Given that :
Side (a) of cube = 4.4cm
Volume of a cube (V) = a^3
V = 4.4^3
V = 85.184cm^3
Therefore, volume of the sphere made = 85.184cm^3
Volume of sphere = 4/3 πr^3
Where r = radius
85.184 = (4/3)*(22/7)*r^3
85.184 = (88/21)*r^3
85.184 = 4.1905 * r^3
r^3 = 85.184 / 4.1905
r^3 = 20.327884
Take the cube root of both sides
r = 2.73 cm
PLEASE HELP ME GUYS Consider adjacent angles that measure (2x + 45)° and (3x + 55)°. The sum of the measures of these two angles is 135°. Write and solve and equation to find the value of x and the measure of the two angles.
Answers
Answer:
x=7
2x+45=59
3x+55=76
Step-by-step explanation:
Answer:
7°, 59°, 76°
Step-by-step explanation:
The equation for the sum of the angles:
(2x + 45)° + (3x + 55)° = 135°Solving for x:
(5x + 100)°= 1355x= 35x= 35°/5x= 7°The angles:
(2x + 45)°= 2*7°+45° = 59°(3x+55)°= 3*7° + 55° = 76°Based on the table, which best predicts the end
behavior of the graph of f(x)?
As x, f(x) —, and as x->-0, f(x) →..
As x 700, f(x) →, and as x -→-00, f(x) →--.
As x, f(x) →-00, and as x———00, f(x)
As x -+-0, f(x) →-00, and as x->-00, f(x) -
->
-→-00
Answers
Answer:
The correct option is;
As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞
Step-by-step explanation:
The values given are;
x, f(x)
-4, 18
-3, 9
-2, 6
-1, 3
0, 0
1, -3
2, -6
3, -9
4, -18
Based on the table, as the magnitude of x increases in the positive direction, the magnitude of f(x) increases in the negative direction
Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞.
John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at speed of 42mph. On the way back the rain was over so his speed was 54mph. What was John's average speed, for the whole trip?
Answers
Answer:
48 mph.
Step-by-step explanation:
You need to calculate the average. So,
42 + 54 = 96
Because there are two quantities, 42 and 54, divide 96 by 2.
The average speed is 48.
help me plz its math plz help
Answers
Hi there! :)
Answer:
a = 12 units.
Step-by-step explanation:
Using the Pythagorean Theorem (c² = a² + b²), where
c = length of the Hypotenuse
a = length of the shorter leg
b = length of the longer leg
We can calculate the length of "a" by substituting in the values into the equation:
c = 15
a = "x"
b = 9
----------------
15² = x² + 9²
Simplify the squares:
225 = x² + 81
225 - 81 = x²
144 = x²
Take the square root of both sides:
√144 = x
x = 12 units.
Therefore, the length of a = 12 units.
Answer:
a= 12
Step-by-step explanation:
Pythagorean Theorem: a²+b²=c²
b= 9
c= 15
a= x = what we are looking for
For this problem, we need to set c² equal to x² and b², which would look like:
15²= x²+9²
225= x²+81
Subtract 81 from both sides
144=x²
Square root both sides
x=12
a= 12
Simplify.
B2 x b6=??
Answers
Answer:
b^8
Step-by-step explanation:
When multiplying exponents with the same base, we can add the exponents
b^2 * b^6
b^ (2+6)
b^8
Answer:b8 x
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "b6" was replaced by "b^6". 1 more similar replacement(s).
STEP
1
:
Multiplying exponential expressions
1.1 b2 multiplied by b6 = b(2 + 6) = b8
Final result :
b8x
Omar has a new credit card.He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points, how much money did he spend?Easy question for easy points
Answers
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
The hardcover version of a book sells for 15 dollars and the paperback sells for 11.50. If a store sells 70 copies of the book in one month and charges 917 dollars how many hardcover versions were sold
Answers
Answer: 32 copies of hardcover version.
Step-by-step explanation: Suppose the quantity of hardcover version copies sold is H and the paperback copies is P.
1) A store sells a total of 70 copies:
H + P = 70
2) One hardcover is sold for $15 and one paperback for $11.50. In one month was charged $917:
15H + 11.5P = 917
Solving the system of equations:
H + P = 70 (I)
15H + 11.5P = 917 (II)
Since it is asked for the hardcover version, find H.
Multiply equation (I) by -11.5:
-11.5H - 11.5P = - 805 (III)
Add (II) and (III):
-11.5H - 11.5P = - 805
15H + 11.5P = 917
3.5H = 112
H = 32
In one month, it was sold 32 hardcover version of a book.
i cant see the answers does anyone else have this problem
Answers
Answer:
yeah....same!
Step-by-step explanation:
I'm having the same problem I thought it was just me
Triangle TQRS Find the value of x.
O x = 2
O x = 3
O x= 33
O x= 52
Answers
Answer:
x=3
Step-by-step explanation:
To solve for x, we will follow the steps below:
First note that exterior angle =two opposite interior angle
From the diagram below
(25x) ° + (57 + x)° = (45x)°
25x° + 57° + x° = 45x°
next step is to collect the like term
45x° - 25 x° - x° = 57°
19x° = 57°
Divide both-side of the equation by 19
19x°/ 19 = 57° /19
On the left-hand side of the equation 19 will cancel out 19 leaving us with just x° while on the right-hand side of the equation 57 will be divided by 19
x = 3
Please explain: Find the measure of angle A. a. 32 b. 57 c. 59 d. No angle exists.
Answers
Answer:
The answer is option B.
57°Step-by-step explanation:
To find Angle A we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The adjacent is 14
The hypotenuse is 26
So we have
cos A = 14/26
cos A = 7/13
A = cos-¹ 7/13
A = 57.42
A = 57° to the nearest degreeHope this helps you
Answer:
57 deg
Step-by-step explanation:
(see attached for reference)
we are given a right triangle together with the lengths of one side (= 14 units) and the hypotenuse (= 26 units)
Using the trigonometry formulas, we can find angle A
cos A = adjacent length / hypotenuse
cos A = 14 / 26
A = cos⁻¹ (14/26) (use calculator)
A = 57.42 deg
A = 57 deg (rounded to nearest whole degree)
1. In your own words please describe a Relations vs. Function
2. please describe the mathematical order of operation(photo attached)
Answers
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
1. Relations are the set of y (output) and x (input) values that are related. A function is when each input has a relation with one output.
2. The mathematical formula is the formula of Pythagoras theorem. Where the length c (hypotenuse) is equal to the square root of the sum of the legs squared.
Solve for X and determine the measure of each angle.
X
(x - 35)
X
(2x - 75°)
Answers
it's a quadrilateral
interior angles add up to 360
x + 2x - 75 + x + x - 35 = 360
5x - 110 = 360
5x = 360 + 110
x = 470 ÷ 5
x = 95
and x - 35 = 60
2x - 75
= 190 -75
= 115
Answer:
see explanation
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Sum the given angles and equate to 360
x + x + x - 35 + 2x - 75 = 360, that is
5x - 110 = 360 ( add 110 to both sides )
5x = 470 ( divide both sides by 5 )
x = 94 , then
x - 35 = 94 - 35 = 59
2x - 75 = 2(94) - 75 = 188 - 75 = 113
Thus
The 4 angles are 59°, 94°, 94°, 113°
30% of a number is 45 what is the number ?
Answers
Hey there! I'm happy to help!
When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D
0.3n=45
To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.
0.3n÷0.3=45÷0.3
n=150
Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!
Have a wonderful day! :D
In AABC, which trigonometric ratio has the value a/c?
Answers
Answer:
tan A has the ratio a/c
Step-by-step explanation:
Pleased to help u...
Determine if the function below is continuous.
Answers
Answer:
No
Step-by-step explanation:
I believe at the point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous.
Continuous means that there is no abrupt changes (google) and im sure you know this already (im just saying no offence to anyone's intelligence)
The given function is not continuous. The correct option is D.
What is a continuous function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value.
The point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous. Continuous means that there are no abrupt changes.
It is shown in the graph that the function is reducing continuously at the point ( 1,-1) and after that, there is a sudden change in the function after that it becomes constant or parallel to the x-axis.
Because there is a sudden change in the function it will be termed a discontinuous function.
Hence, the function is not continuous, and the correct option is D.
To know more about continuous function follow
https://brainly.com/question/18102431
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what is
[tex] \frac{2ax + 3}{ax + 3} = - 1[/tex]
x value
Answers
[tex]\dfrac{2ax+3}{ax+3}=-1[/tex]
Rewrite -1 as a fraction
[tex]\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}[/tex]
Cross multiply
[tex]2ax+3=-1(ax+3)[/tex]
Distribute the -1
[tex]2ax+3=-ax-3[/tex]
Add both sides by ax
[tex]3ax+3=-3[/tex]
Subtract both sides by 3
[tex]3ax=-6[/tex]
Divide both sides by 3a
[tex]x=-\dfrac{6}{3a}[/tex]
Simplify
[tex]=-\dfrac{2}{a}[/tex]
That's the value of x respect to a. Let me know if you need any clarifications, thanks!
Answer:
Step-by-step explanation:
[tex]\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}[/tex]
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=-6+(n-1)(1/5) A)-6,-5 1/5, -4 B)5, -5 1/5,1 4/5 C)-6, -5 2/5, -4 1/5 D) 0, 3/5, 1 4/5
Answers
Step-by-step explanation:
An arithmetic sequence is given by relation as follows :
[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]
For the first term, put n = 1. So,
[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]
For fourth term, put n = 4. So,
[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]
For tenth term, put n = 10. So,
[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]
Hence, the correct option is (C).
Answer:
the answer in C)-6, -5 2/5, -4 1/5
How
are in
3 5 dozens ?
many eggs
6
Answers
Answer: 46 eggs
Step-by-step explanation:
There are 12 eggs in a dozen. Thus, there are 3 5/6*12, or 46 eggs.
Hope it helps <3
M
Which angle is an adjacent interior angle to ZJKM?
LJKL
ZMKL
J
K
ZKLM
L
LMK
Answers
Answer:MLK
Step-by-step explanation:
The angle that is placed sideways with <JKM is <MKL
Interior adjacent angle of a triangleThe adjacent interior angle of a triangle are angles placed sideways with each other.
For the given diagram attached, you can see interior angles of the triangle are <LMK, <MKL and <KLM
Among the listed interior angles, the angle that placed sideways with <JKM is <MKL
Learn more on interior angles here: https://brainly.com/question/24966296
Lucy is going to invest in an account paying an interest rate of 7% compounded daily. How much would Lucy need to invest, to the nearest dollar, for the value of the account to reach $84,000 in 6 years?
Answers
Answer:
Lucy needs to invest $55,194.16
Step-by-step explanation:
The given information are;
The interest rate of the account = 7% compounded daily
The amount at the end of 6 years = $84,000
The time duration = 6 years
The amount Lucy
The formula for compound interest is
[tex]A(t) = P \times \left ( 1 + \dfrac{r}{n} \right )^{n \times t}[/tex]
Where;
r = The interest rate = 7% = 0.07
n = The number of times a year = 365
t = The number years = 6 years
A(t) = The amount after 6 years = $84,000
P = The initial amount invested
Therefore, we have;
[tex]\$ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}[/tex]
[tex]P = \dfrac{\$84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\$84,000}{1.522} = \$55,194.16[/tex]
Therefore, Lucy needs to invest $55,194.16.
If a field researcher wanted to learn a political organization's pattern of recruitment over time, the researcher mightbegin by interviewing a fairly recent recruit and ask who introduced that person to the organization. Then theresearcher might interview the person named and ask who introduced that person to the political organization.This would be an example of: systematic sampling. accidental sampling. snowball sampling. quota sampling deviant cases sampling.
Answers
Answer:
C. snowball sampling
Step-by-step explanation:
Snowball sampling also known as referral sampling or chain sampling is a sampling method in research where the participants in the research are recruited to find new participants. This is a non-probability sampling method because participants choose other participants through their own insight. Just as a ball takes up more snow as it rolls by, so also this research method takes up more participants as it progresses.
So, when the field researcher who wanted to learn about a political organization's recruiting pattern begins by interviewing a participant who in turn suggests another participant, he has applied the snowball sampling method.