Geometry: Trig Pile Up Activity
The measure of the unknown angle is 53 degrees.
The length of the unknown side of the blue triangle is 4.43 cm
Right angle triangleRight angle triangle have one of its angles as 90 degrees.
The sum of angle in a triangle is 180 degrees.
Therefore, the measure of the unknown angle can be calculated as follows:
let
x = unknown angle
x = 180 - 90 - 37 = 53°
Therefore, let's find the unknow length of the blue triangle.
tan 53 = opposite / adjacent
tan 53 = 6.9 / a
a = 6.9 / 1.327
a = 5.1996985682
a = 5.2
The green triangle hypotenuse = 5.2 + (5.2 - 2.6) = 7.8 cm
Therefore,
sin 59 = opposite / 7.8
opposite = 7.8 × 0.8571673007
opposite = 6.68590494548
opposite side = 6.69 cm
The hypotenuse of the blue triangle = 6.69 - 2 = 4.69 cm
Therefore,
sin 71 = x / 4.69
x = 4.69 × 0.94551857559
x = 4.43448211956
x = 4.43 cm
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Help help help help math math
Answer:
No Solution
Step-by-step explanation:
-y = -2x + 8
y = 2x - 8
2x + 8 = 2x - 8
2x - 2x = -8 - 8
0 = -16
No Solution
You can also graph y = 2x + 8 and y = 2x - 8. The slope are the same and so they are parallel
Mr. Anderson decides to visit a childhood friend. His car gives him 24.82 miles to the gallon. Mr. Anderson has 4 gallons of fuel. Which of the following is true?
A.
Mr. Anderson can travel 83.28 miles.
B.
Mr. Anderson can travel 49.64 miles.
C.
Mr. Anderson can travel 115.28 miles.
D.
Mr. Anderson can travel 99.28 miles.
Answer:
D. Mr. Anderson can travel 99.28 miles.
Step-by-step explanation:
If Mr. Anderson has 4 gallons and each gallon moves him 24.82 miles you can multiply the number of miles per gallon by the gallon resulting in an equation that looks like 4*24.82=99.28.
A spinner has 16 equal-sized sections. Twelve of the sections are orange.
a. What is the probability that the spinner will land on orange?
b. Use words to describe the probability
a.
out of 16, or
.
4
b. It is
that the spinner will land on orange.
The probability that the spinner will land on orange is the likelihhood of landing on orange
The probability that the spinner will land on orange is 0.75
How to determine the probability?From the question, we have:
Spinner section = 16
Orange section = 12
So, the probability that the spinner will land on orange is:
p = 12/16
Evaluate
p = 0.75
Hence, the probability that the spinner will land on orange is 0.75
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Mrs. Williams' desk is located at (-5,2). The wireless internet box is halfway between her desk and the door. If the box is located at the coordinates (8, -8), what are the coordinates of the door?
Topic : Midpoint between points
desk = (-5,2)box = (8, -8)door = (x, y)formula:
[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]
=====================================
[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]
separate taking coefficients:
[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]
[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]
[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]
[tex]\rightarrow \sf x =21, \ y= -18[/tex]
coordinates of door: (21, -18)
Let that be (x,y)
So
[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]
(x,y)=(21,-18)Heather planted 4 times as many tulips as Sarah planted. If Heather planted 64 tulips, how many tulips (s) did Sarah plant?
Step-by-step explanation:
let, the tulips be 'x'
According to the question,
heather=4x
& sarah=x
but heather planted 64 so,
4x=64
or, x=64/4
x=16
hence, sarah planted 16 tulips
Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).
How to determine how many tulips (s) Sarah planted using algebraLet's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.
Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:
Heather's tulips = 4 * Sarah's tulips
64 = 4s
Presently, ready to fathom for s:
s = 64 / 4
s = 16
Sarah planted 16 tulips.
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Barry has two cubes of different sizes. The first cube has a volume of 1 cubic unit. The second cube has sides one-third as long as the first cube does. What is the volume of the second cube?
Answer:
1/27 units cubed or 0.037037... units cubed
Step-by-step explanation:
Volume of a cube = s*s*s : Where s is a side length.
The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)
The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.
Volume of second cube= (1/3s)(1/3s)(1/3)s
Volume of second cube= (1/3)(1/3)(1/3)
Volume of second cube= 1/27
What’s the difference between 4, 7/9 and 2 1/2
[tex]\huge \mathbb \orange{ANSWER} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]
[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]
[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]
[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]
 Find the equation of the line that is perpendicular to 4 x + 3 y = 5 and goes through the point (3, –3)
Step-by-step explanation:
the line equation
y = ax + b
gives us slope (a) and y-interception (b).
4x + 3y = 5
3y = -4x + 5
y = -4/3 × x + 5/3
the slope of the original line is therefore -4/3.
a perpendicular slope flips x and y upside-down and flips the sign.
so, the perpendicular slope of -4/3 is 3/4.
the desired line looks like
y = 3/4 × x + b
b we get by using the given point and its coordinates :
-3 = 3/4 × 3 + b = 9/4 + b
-12/4 = 9/4 + b
b = -21/4
so our full line equation is
y = 3/4 × x - 21/4
or
4y = 3x - 21
-3x + 4y = -21
I am struggling on this and I need help
Answer:
I think so Last 3 figured are the correct answer
I have a question whats 2+2
Answer:
22
Step-by-step explanation:
You add the to numbers together and the answer will be 22
I hope it helps! Have a great day!
Muffin ^^
What is the equation of a circle with center (−5, −8) and radius 2?
(x − 5)2 + (y − 8)2 = 4
(x + 5)2 + (y + 8)2 = 4
(x + 5)2 + (y + 8)2 = 2
(x − 5)2 + (y − 8)2 = 2
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Standard equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of centre k = y - coordinate of centrer = radius of the circle
Now, let's plug in the values ~
[tex]\qquad \sf \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]
Therefore, the correct choice is B
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4
How to determine the circle equation?The center of the circle is given as:
Center (a,b) = (-5, -8)
The radius is given as:
Radius, r = 2
The equation of the circle is calculated using:
(x - a)² + (y - b)² = r²
Substitute values for r and (a,b)
(x + 5)² +(y + 8)² = 2²
Evaluate the square of 2
(x + 5)² +(y + 8)² = 4
Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4
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41. Henry stands on a platform and shoots a rocket in his 10th
grade science class. He found that the motion of the rocket can be
described by the equation y = 60 + 28x – x2, where y is the
vertical distance and x is the horizontal distance traveled. If this
trajectory equation were to be graphed, find the x-intercepts of the
equation. (Fun fact: The positive x-intercept is how far away from
the platform the rocket hits the ground!)
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
What are the x-intercepts of a quadratic equation?A quadratic equation is modeled by:
y = ax² + bx + c.
The x-intercepts are the values of x when y = 0, given by:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is:
y = 60 + 28x - x².
Hence the coefficients are a = -1, b = 28, c = 60.
Then:
[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]
[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]
[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
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The Length Of A Room is two time its breadth and breadth is two time its height If The volume of room is 512m2 what is the cost of plastering its wall at rs 5.50 per m2
Answer:
Rs 2464
Step-by-step explanation:
Given:
The length of a room is 2 times its breadth and breadth is 2 times its height. The volume of the room is 512 cubic metre.To find:
The cost of plastering it's wall at Rs 5.50 per square metre.Solution : A/C to given data;
[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (2)
A/C to given data let, structure of room is cuboidal.
Now, we have to find out the height of the room, so we use formula of volume of the cuboid.
[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]
[tex]512 = 2B * 2H * H[/tex]
[tex]512 = 2 * 2H * 2H * H[/tex]
[tex]512 = 4H * 2H^{2}[/tex]
[tex]512 = 8H^{3}[/tex]
[tex]H^{3} = \frac{512}{8}[/tex]
[tex]H^{3} = 64[/tex]
[tex]H = \sqrt[3]{64}[/tex]
[tex]H = 4 m[/tex]
[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]
[tex]B = 2 * H[/tex]
[tex]B = 2 * 4[/tex]
[tex]B = 8 m[/tex]
[tex]\\[/tex]Now, put value of B in eq. {1}
[tex]L = 2 * B[/tex]
[tex]L = 2 * 8[/tex]
[tex]L = 16 m[/tex]
Now, we have to find out area of the room, so we use formula of total surface area of cuboid.
[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]
[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]
[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]
[tex]Area of the room = 256 + 128 + 64[/tex]
[tex]Area of the room = 384 + 64[/tex]
[tex]Area of the room = 448 m^{2}[/tex]
Now, to find out room wall plastering cost
[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]
[tex]Room wall plastering cost = 448 * 5.50[/tex]
[tex]Room wall plastering cost = Rs 2464[/tex]
[tex]ence, the room wall plastering cost is Rs 2464.[/tex]
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
Which verb form correctly completes this sentence?
No estoy convencido de que ellos ___________ lo que significa esta fiesta.
A.
comprenden
B.
comprendemos
C.
comprendan
D.
comprendes
Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine.
The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 5:30 a.m. until 1:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 6:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below.
Based on the times that the machine produces cookies that have the optimal amount of chips, the proportion produced daily with the optimal number of chips is 62.5% or 0.625.
What is the proportion of cookies with optimal chocolate chips?This can be found by the formula:
= (Hours that optimal cookies are produced) / Hours that the machine runs per day
5:30 am is the same as 5.5 hours because 30 minutes is half an hour.
1:30 pm is also the same as 13.5 hours by the above rule and in 24 hour notation.
Proportion of optimal cookies is therefore:
= (11 am - 6am) / (13.5 - 5.5)
= 5 / 8
= 0.625
= 62.5%
Find out more on optimal production at https://brainly.com/question/6348653.
Find the distance between (4,-5) and (-3,-5).
Answer:
7 units
Step-by-step explanation:
Since the two points have the same y-coordinate of -5, the distance between them is due to the difference of their x-coordinates.
Distance
= 4-(-3)
= 4 +3
= 7 units
Note:
Should the two points have different x and y coordinates, you may use the distance formula below.
[tex]\boxed{\textcolor{steelblue}{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
write balanced chemical equation for the process of photosynthesis giving the physical state of all the substances involved in the conditions of the reaction
Answer:
The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.
Step-by-step explanation:
CAN SOMEBODY HELP ME SOLVE THIS EQUATION
Step-by-step explanation:
Slope m=4
Y intercept b=(-5)
formula f(x)=4x-5
If u need how to solve do let me know
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
About (blank) employees took a break that lasted between 37 and 41 minutes.
36
90
120
180
Answer:
on k12 im pretty sure its 90
Step-by-step explanation:
there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped
pls help
Letf(x)=(x+2)2.
Letg(x)=3(x+2)2.
Which statement describes the graph of g(x) with respect to the graph of f(x)?
It is compressed horizontally by a factor of 3.
It is translated up 3 units.
It is stretched vertically by a factor of 3.
It is translated right 3 units.
find the product 4 (-9 1/8)
Answer:
4/8=2
-91/2=-45.5
by eliminate 4 by dividing by 8
given that 10022bse 3 is equal to 155base n find the value of n show all workings
Step-by-step explanation:
log 3 (10022)
= 8.38561
log n (155)= 8.38561
n^8.38561=155
log 10 (n)= log 10 (155)
lpg 10 (155)= 2.190331698
8.38561 log10 (n)=2.190331698
log10 n = 2.190331698÷8.38561
lo^-1 (0.2612012)
=1.825
n=1.825
There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7 correct? (b) What is the probability that the student gets exactly 8 correct? (c) What is the probability that the student gets exactly 9 correct? (d) What is the probability that the student gets exactly 10 correct? (e) What is the probability that the student gets more than 6 correct?
Answer:
Probability getting 7 correct :- 1/10Probability getting 8 correct :- 1/10 Probability getting 9 correct :- 1/10Probability getting 10 correct :- 1/10 → Probability getting more than 6 :- 4/10
I need help with this question please
Answer:
Step-by-step explanation:
As ABCD is a rectangle, ∠A = 90°.
Diagonal BD will be the hypotenuse.
[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]
Length = AB = 33.8 cm
[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]
Width = 25.5 cm
What is the value of log625^5
Answer:
13.979
Step-by-step explanation:
log 625^5 = 5 log 625 = 5*2.79588=
Answer:
Exact Form:
1/4
Decimal Form:
0.25
Step-by-step explanation:
Exercise: 6.68 'Cat Owners': According to the American Veterinary Medical Association, 30% of Americans own a cat. Find the probability that exactly 2 out of 8 randomly selected Americans own a cat. In a random sample of 8 Americans, find the probability that more than 3 own a cat.
Using the binomial distribution, it is found that there is a:
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.0.4482 = 44.82% probability that more than 3 own a cat.What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
30% of Americans own a cat, hence p = 0.3.A sample of 8 Americans is taken, hence n = 8.The probability that exactly 2 out of 8 randomly selected Americans own a cat is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.
The probability that more than 3 own a cat is given by:
[tex]P(X > 3) = 1 - P(X \leq 2)[/tex]
In which:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.3)^{0}.(0.7)^{8} = 0.0576[/tex]
[tex]P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0576 + 0.1977 + 0.2965 = 0.5518[/tex]
[tex]P(X > 3) = 1 - P(X \leq 2) = 1 - 0.5518 = 0.4482[/tex]
0.4482 = 44.82% probability that more than 3 own a cat.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
What is the factorization of the trinomial below?
3x^3 + 6x^2 - 24x
A. 3x(x - 2)(x + 4)
B. 3x(x - 2)(x - 4)
C. 3(x - 2)(x + 4)
D. 3(x^2 - 2)(x + 4)
Multiply (2 – 7i)(–1 + 4i).
Answer:26 + 15i
Step-by-step explanation: 26+ 15i is the answer because i did the assignemnt