Answer:
Angle Z = 180-32 -90 = 58 degrees
sine (32) = y / 16
y = 16 * sine (32)
y = 16 * 0.52992
y = 8.47872
x^2 = 16^2 -y^2
x^2 = 256 -71.888
x^2 = 184.112
x = 13.568
Step-by-step explanation:
Answer:
x = 13·568, y = 8·47 and z = 58
Step-by-step explanation:
I don't think the question required you to use the Pythagoras theorem but here are some pointers anyway.
Okay, the Pythagoras theorem is quite simple: a² + b² = c²Where c is always the hypotenuse, a is the height or the opposite side and b is the base or the adjacent side. (I've attached a picture just in case) (It might look confusing but the way I've lettered them is taking the 90° angle to be on the right side)The a and b doesn't actually matter so don't think too much about which side is a and which one is b, they're more or less the same.The reason I said that this question might not solely require you to use the Pythagoras theorem is because you need to have two variables for the equation to work, maybe this is what got you confused.
For this question, you're required to use Tangents, Sines and Cosines, or you can combine this method and Pythagoras method.
Looking for x and y:Method one: Using Tangents, Sines and Cosines AND the Pythagoras theorem
Step 1: Looking for x(Using Sin, Cos and Tan)
To find the length of side x, we need to use the Cosine of 32°
Cos 32° = Adjacent side ÷ Hypotenuse
0·8480 = x/16
Make x the subject and multiply both sides by 16
0·8480 × 16 = x/16 × 16
13·568 = x
∴ side x is 13·568
Step 2: Looking for y( using the Pythagoras theorem)
a² + b² = c²
a = y, b = x = 13·568, c = 16
y² + 13·568² = 16²
y² + 184·0906 = 256
y² = 256 - 184·0906
y² = 71·9094
y = √71·9094
y = 8·4799
Method 2: Using Tan, Cos and Sin only
Step 1 remains the same as shown above; x = 13·568
Step 2: Looking for y
Y can be gotten by using the Sine of 32°
Sin 32° = Opposite ÷ Hypotenuse
Sin 32° = y ÷ 16
0·5299 = y/16
Make y the subject and divide both sides by 16
0·5299 × 16 = y/16 × 16
8·4784 = y
∴ y is equal to 8·4784
(I know there's a difference in points of the two values of y, but if you round them off to 2 decimal places we see it remains 8·47
2. Looking for z:
Using addition and subtraction
The simpler method would be to just add all the internal angles.
The little square in the corner tells us that that is a 90° angleThe internal angles of a triangle ALWAYS add up to 18032 + 90 + z = 180
122 + z = 180
z = 180 - 122
z = 58
∴ z is equal to 58°
Using Tan, Sin and Cos
The cosine of Z is equal to y divided by 16, where y = 8·47
Cos z = 0·5294
Make z the subject and divide both sides by Cos.
z = 0·5294/Cos
z = 58·04° (I just used the anti-cos to get this number. Press shift, and cos on your calculator then type 0.5294 in front of it)
Here there is also a slight difference in points between the two steps but if you round off step 2 to a whole number you get 58, so it's all good :)
HOPE THIS HELPS!!! :)
x - (2x + 1) = 8 - (3x + 2)
Answer:
x=7/2
Step-by-step explanation:
Answer:
x=7/2
Step-by-step explanation:
x-(2x+1)=8-(3x+2)
x-2x-1=8-3x-2
-x-1=6-3x
+x on both sides
-1=6-2x
-6 on both sides
-7=-2x
7=2x
÷2 on both sides
7/2=x
Hope this helps =]
Julio spent $21 on a magazine and five notepads. If the magazine cost $6, then how much was each notepad?
Answer:
3
Step-by-step explanation:
15!!!! POINTSS what is the mode in the data shown below
can someone please help me with this question?
Answer:
402.12
Step-by-step explanation:
V=πr2h= π·42·8≈402.12386
Answer:
864 feet
Step-by-step explanation:
Plug numbers in
I need help with this please help me out
Answer:
A and E
Step-by-step explanation:
hope that helps
I NEED HELPI HAVE 5min
Answer:
A - s^2
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
a first number plus twice a second number is 8 twice the first number plus the second totals 25
Answer:
x=14 y=-3
Step-by-step explanation:
what is the measure of ZDEG on circle O?
Answer:
∠ DEG = 50°
Step-by-step explanation:
Angles on the circle subtended by the same arc are congruent.
∠ CFG and ∠ DEG are angles on the circle subtended by arc CD , then
∠ DEG = ∠ CFG = 50°
Answer:
50° parallel lines subtended on circumference theorem, and congruent angles seen as subtended on same arc lone examples attached.
Kim will paint all the faces of the outside of the storage trunk when it is closed. How many square feet will Kim paint?
Answer:
Step-by-step explanation:
B i don’t know
Answer:
A
Step-by-step explanation:
Just asking for the answer to this problem.
Answer:
371.26
Step-by-step explanation:
Using trig we can do tan(68)*5 to find the height of the parallelogram, after this we can do the height times 30 to find the answer
Take the function f(x)= square root of x+5 (then outside of square root) +1
And:
1. Reflect it along the x axis
2. translate it 4 units left
3. Translate it 3 units dow
What would be this functions NEW equation?
[tex]f(x) = - \sqrt{x + 5 + 4} + 1 - 3[/tex]
[tex]f(x) = - \sqrt{x + 9} - 2[/tex]
The selling price of an item is $520. It is marked down by 10%, but this sale price is still marked up from the cost of 360$. Find the markup from cost to sale price.
Answer:
30%
Step-by-step explanation:
Answer: good luck
Step-by-step explanation:
What is the area of the triangle?
13
12
Units 2
Help me
Answer:
30
Step-by-step explanation:
i believe that the 13 is there to throw you off. anyway to solve just do 5•12=60
60÷2=30 so 30 is area of triangle
area of triangle =1/2×base×height
area of triangle=1/2×12×5
area of triangle=30 unit²
Find the one of the following sets of side lenghts could represent a right triangle
Answer:
B
Step-by-step explanation:
Using the pythagorean theorem A^2 + B^2 = C^2 the only numbers that work are those in choice B. 8 short leg, 15 long leg, 17 hypotenuse.
8^2 + 15^2 = 17^2 = 64 +225=289 = 289=289 therefor proving these set of numbers are a right triangle.
Which correctly describes how the graph of the inequality 5x + 2y = 13 is shaded?
Answer:
The answer is above the solid line.
Step-by-step explanation:
Find the area of each regular polygon. Round your answer to the nearest tenth if necessary
Answer:
Step-by-step explanation:
13). Area of a square = (Side)²
= (BC)²
Since, diagonals of a square bisect each other at 90°,
ΔBOC is a right triangle.
By applying Pythagoras theorem in the given triangle,
BC² = OB² + OC²
BC² = 2(OB)²
BC² = 2(7√2)²
BC = [tex]\sqrt{196}[/tex]
Area of square ABCD = (BC)²
= (√196)²
= 196 units²
14). Measure of interior angles of the regular hexagon = 120°
Area of the regular hexagon = [tex]\frac{3\sqrt{3}}{2}(\text{side})^2[/tex]
From the given picture,
m∠BAC = m∠ABC = m∠ACB = 60°
Therefore, ΔABC is an isosceles triangle.
And all sides of this triangle will be equal in measure.
AB = AC = BC = 9 units
Area of the given regular hexagon = [tex]\frac{3\sqrt{3}}{2}(9)^2[/tex]
= 210.44 square units
≈ 210.4 square units
60 minutes is what percentage of 1 hour?
Answer:
100%
Step-by-step explanation:
Answer: 100 is your answer hope this helped
plz make brainly
Step-by-step explanation:
what is it what is it what is it?!
Answer:
1.0 g element will be remaining after 19 minutes
Step-by-step explanation:
Answer:
1.0 g element will be remaining after 19 minutes
Step-by-step explanation:
use the model below to write and solve equation
Answer is:
X is 1, very simple
A cube root function has a turning point located at (-2,3). Write an equation that could represent this function
Answer:
f(x) = A*∛(x + 2) + 3
Step-by-step explanation:
Suppose a generic cube as:
f(x) = A*∛(x - b) + C
We will have a turning point at the x value:
x = b
Then if we have a turning point at (-2, 3)
This means that the turning point is at x = -2 and y = 3
Then b = -2
And our cube root function will be something like:
f(x) = A*∛(x - (-2)) + C
f(x) = A*∛(x + 2) + C
And we know that f(-2) = 3
then:
f(-2) = A*∛(-2 + 2) + C = 3
f(-2) = A*∛(0) + C = 3
= C = 3
Then the general equation will be something like:
f(x) = A*∛(x + 2) + 3
A laptop has a listed price of $801.98 before tax. If the sales tax rate is 8.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer 870.15
Step-by-step explanation:
What 1+1 help i'll give 15 points
Answer:
11
Step-by-step explanation:
am so smart
Plz help its due by 1
11.5
Step-by-step explanation:
The possibility of a power outage seems to grow every year because of demand and aging infrastructure. What can/should companies do to mitigate this risk?
Math help help help answer all 4 pls
Answer:
a) 2,350,000,000
b) 25,000,000
c) B
Step-by-step explanation:
a) 2350 X 1,000,000 = 2,350,000,000
b) 25 X 10^6 = 25,000,000
c) sqrt(90000) =300
Hurry need help on number 1 fast pls pls pls!!!
Answer:
the second answer is the answer
There are 40 students in the 5th grade. 22 of them play soccer. What percentage of the students in the class do NOT play soccer? Please show work i need help
Step-by-step explanation:
If there are 40 kids and 22 of them play soccer that leaves you to subtract 22 from 40 which gives you 18. After that, you put the rest of the 18 students over a total of 40 and divide to get the decimal .45 and if you convert that into a percent you are left with 45%.
1. 40-22=18
2.18/40=.45
3.45=45%
Find the volume of the given figure.
Answer:
5/18
Step-by-step explanation:
Volume= length•width•height
5/6•1/2= 5/12
5/12•2/3= 10/36= 5/18
Find the probability that a randomly selected points within a square falls in the blue shaded area (circle)
Answer:
78.8 %
Step-by-step explanation:
From the question,
Area of the square = L²
A = L²
Where L = Length of the square.
From the diagram,
L = 4 in
Therefore,
A = 4²
A = 16 in².
Also,
Area of the circle (A') = πr²
Where r = radius of the circle.
Given: r = 2 in
Therefore,
A' = 22/7(2²)
A = 12.6 in²
Hence,
The probability that a randomly selected points within a square falls in the blue shaded area (Pr) = A'/A
Pr = 12.6/16
Pr = 0.7875
Pr(%) = 78.75
Pr(%) = 78.8 %
38% of 60 is?
NEED HELP
Answer:
Step-by-step explanation:
38% of 60 = [tex]\frac{38}{100}*60 = 0.38*60 = 22.8[/tex]
Answer:
Step-by-step explanation:
38% * 60
[tex]\frac{38}{100} * 60\\\\\frac{38}{5} * 3\\\\114/5 = 22.8[/tex]