Given:
In a right angled triangle ABC the perpendicular and the base measure 3 cm.
To find:
The hypotenuse and three trigonometric ratios.
Solution:
Pythagoras theorem:
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Use Pythagoras theorem in triangle ABC.
[tex]Hypotenuse^2=(3)^2+(3)^2[/tex]
[tex]Hypotenuse^2=9+9[/tex]
[tex]Hypotenuse=\sqrt{18}[/tex]
[tex]Hypotenuse=3\sqrt{2}[/tex]
The three trigonometric ratios are
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin \theta=\dfrac{3}{3\sqrt{2}}[/tex]
[tex]\sin \theta=\dfrac{1}{\sqrt{2}}[/tex]
Similarly,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos \theta=\dfrac{3}{3\sqrt{2}}[/tex]
[tex]\cos \theta=\dfrac{1}{\sqrt{2}}[/tex]
And,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan \theta=\dfrac{3}{3}[/tex]
[tex]\tan \theta=1[/tex]
Therefore, the hypotenuse is [tex]3\sqrt{2}[/tex] cm and three trigonometric ratios are [tex]\sin \theta=\dfrac{1}{\sqrt{2}}, \cos \theta=\dfrac{1}{\sqrt{2}}, \tan \theta=1[/tex].
HELP ASAP 40 POINTS
What is the equation for the nth term of the sequence
And what is the 52nd term of the sequence. -8,-12,-16
Given:
The sequence is -8, -12, -16.
To find:
The nth and 52th term of the given sequence.
Solution:
We have,
-8, -12, -16
It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is
[tex]r=a_2-a_1[/tex]
[tex]r=-12-(-8)[/tex]
[tex]r=-12+8[/tex]
[tex]r=-4[/tex]
The nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
Where, a is first term and d is common difference.
Putting a=-8 and d=-4, we get
[tex]a_n=-8+(n-1)(-4)[/tex]
[tex]a_n=-8-4n+4[/tex]
[tex]a_n=-4-4n[/tex]
Putting n=52, we get
[tex]a_{52}=-4-4(52)[/tex]
[tex]a_{52}=-4-208[/tex]
[tex]a_{52}=-212[/tex]
Therefore, the equation for the nth term of the given sequence is [tex]a_n=-4-4n[/tex] and the 52nd term of the sequence is -212.
n + 5 = n +7 Find a value of n that makes the equation true.
Answer:
This equation has no solution.
Step-by-step explanation:
n should equal some value that makes the statement true, and there is none. To prove this, solve for n and you'll get a nonsensical answer.
n + 5 = n + 7
n = n + 2
0 = 2 ?
Find the solution in the system of equations shown below
Answer:
no solution
Step-by-step explanation:
the lines are parallel, they never intersect.
.............
find the nth term of 5 9 14 18 5 23
first of all it is not in the form of A. P because d=a2-a1=9-5=4,a3-a2=14-9=4,a4-a3=18-14=4,a5-a4=5-18= -13,a6-a5=23-5=18
Which community is more toxic
1 reddit
2 2b2t
3 dead by daylight
4 the entirety of 4chan
this picture sucks I know but help me please :))
Answer:
See step by step
Step-by-step explanation:
The student found the cosine of angle A not the sine. Sine is Opposite/Hypotenuse. This student found Adjacent/Hypotenuse. The correct answer is Sin A= 12/13.
Explain how you would determine the slope and y-intercept of a line
when given a table, graph and an equation.
I KISS YOUR TOES IF YOU HELP ME
Answer:
slope is m= y_2-y_1/x_2-x_1 and the y-intercept is where the line crosses over the x-axis
Step-by-step explanation:
fill in the points and do the equation m= rise(y points)/ run(x points)
m=slope
(x_1, y_1) =coordinates of first point in the line
(x_2, y_2)=coordinates of second point in the line
Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 18. Using the empirical rule, what percentage of IQ scores are between 50 and 158?
Answer:
78
Step-by-step explanation:
I NEED HELP ASAP!!! 100 POINTS
If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?
f=3
f=4
f=5
f=6
Answer:
A
Step-by-step explanation:
We are given:
[tex]\cos(22f-1)=\sin(7f+4)[/tex]
Recall the co-function identity:
[tex]\sin(\theta)=\cos(90-\theta)[/tex]
Let θ = 7f + 4. So:
[tex]\sin(7f+4)=\cos(90-(7f+4))[/tex]
Substitute:
[tex]\cos(22f-1)=\cos(90-(7f+4))[/tex]
Remove the cosine:
[tex]\displaystyle 22f-1=90-(7f+4)[/tex]
Distribute:
[tex]22f-1=90-7f-4[/tex]
Subtract:
[tex]22f-1=-7f+86[/tex]
Add 7f and 1 to both sides:
[tex]29f=87[/tex]
Therefore:
[tex]f=3[/tex]
Can someone please answer these questions ASAP!!
13 = -4x +9 solve equation.
Answer:
-1x or -x
Step-by-step explanation:
4 divided by -4
In city W, the average cost for a gym membership is given by the equation y = 34.99x +49, where y is the total cost, in dollars, for x months of membership. What is the meaning of the y-value when x = 1? *
What is two thing you like about math
Answer:
1. Math encourages curiosity and questions.
2. Math can save you money. ...
There are 195 adults and 320 children at a zoo. The zoo makes a total of $6,515 from the entrance fees, and the cost of an adult and a child to attend is $27, how much does it cost each for a parent and a child? Let a represent an adult. Let c represent a child. Enter a system of equations to represent the situation, then solve the system.
Answer:
a+c=27
195a+320c=6515
Step-by-step explanation:
adult (a): 195
children (c): 320
total $: $6515
child $: 27
a+c=27 --> c=-a+27
195a+320c=6515
sub the first equation into the 2nd equation to get a=17
sub a=17 into c=-a+27 to get c=10
so, an adult ticket is $17 and a child ticket is $10.
–19w + 11 = –17w − 19
w=?
Answer:
W = 15. I hope this helped.
Step-by-step explanation:
Steps:
1.Add 19w to both sides.
11=−17w−19+19w
2.Simplify -17w-19+19w to 2w-19
11=2w−19
3.Add 19 to both sides.
11+19=2w
4. Simplify 11+19 to 30.
30=2w
5.Divide both sides by 2.
30/2 = w
6.Simplify 30/2 to 15.
15=w
7.Switch sides.
w=15
d: 11
A food company is designing boxes for several products. Each box is a rectangular prism.
15
The company makes a single serving cereal box that contains 1.2 ounces of cereal. They plan to make an extra large box for school
cafeterias. The extra large box will be a dilation of the single serving box using a scale factor of 4. How many ounces of cereal will
the extra large box contain?
I need step by step
How many ounces of cereal will the extra large box contain is 76.8 ounces.
Number of ounces of cereal?Using this formula
Number of ounces of cereal=Number of ounces×Scale factor
Let plug in the formula
Number of ounces of cereal=1.2×4×4×4
Number of ounces of cereal=1.2×64
Number of ounces of cereal=76.8 ounces
Therefore how many ounces of cereal will the extra large box contain is 76.8 ounces.
Learn more about number of ounces of cereal here:https://brainly.com/question/19263252
#SPJ2
The ratio of boys to girls in a class is 5:7 There are 36 students in the class. How many more girls than boys?
Answer:
The answer is 6.
Step-by-step explanation:
This is how I do it, there are other ways too but,
add up the ratio 5+7=12
36 (students total) divided by 12 = 3
find the difference between the ratio, which is 2.
multiply 2 by 3 and you get 6.
I need help finding out the area of this shape plz help me.
Answer:
hi
Step-by-step explanation:
glizzy
Answer:
Step-by-step explanation:
Area = l x w
i dont know if you are trying to find the area of the whole shape but the area of the shape all together is 25.6
Solve the system of linear equations by substitution.
y = -2x + 10
y = x +1
Step-by-step explanation:
y=14
y=1
thats the answer.
HELP “The vertical supports in this truss bridge are built so that
AABO=AOCD. Which of the following statements
is NOT true?”
Answer:
The statement that is not true is;
c) m∠ABO = m∠ODC
Step-by-step explanation:
With the assumption that the lengths AO, and OD are equal, we have that in ΔABO and ΔOCD, the following sides are corresponding sides;
Segment AO on ΔABO is a corresponding side to segment OD on ΔOCD
Vertices B and C on ΔABO and ΔOCD are corresponding vertices
Therefore;
Segments AB and OB on ΔABO are corresponding sides to segments OC and OD on ΔOCD respectively
Therefore, ∠ABO on ΔABO is the corresponding angle to ∠OCD on ΔOCD
Given that ΔABO ≅ ΔOCD, we have that ∠ABO ≅ ∠OCD
Therefore;
m∠ABO = m∠OCD by definition of congruency
Answer:
DStep-by-step explanation:
Can someone answer this question i am having an issue to how to figure it out
Answer:
explanation below
Step-by-step explanation:
f(x) = 3x + 2
f(8) : replace x with 8 f(8) = 3 * 8 + 2 = 26
g(x) = 5x
g(a+2) : replace x with a+2 g(a+2) = 5 (a+2) or 5a + 10
HELP PLS IM not smart it’s due tonight ♀️
Answer:
Option 3
Step-by-step explanation:
SAS Triangle Congruence Theorem
Answer:
option- 3 which is sas theorum
tell whether each equation has one solution no solution or infinitely may solutions 2x+5=5x-1
Answer:
2x+5=5x-1 =2 so it sould be one soulution
Step-by-step explanation:
Pls help me!!
A circular running track is
1/8
mile long. Elena runs on this track, completing each lap in
1/24
of an hour.
What is Elena's running speed, in miles per hour?
Answer:
It is 5mmxb3m
Step-by-step explanation:
It is what it is
can someone please help me with this !
determine if the sequence below is arithmetic or geometric and determine the common difference/ ratio in simplest form. 3, 12, 48,
Answer:
i think
3 ,
12
12 ,
48
48 ,
192
192 ,
768
768
what is the slope of a line that has a y-intercept but no x-intercept
Answer:
A line that crosses the y-axis but not the x must be horizontal. Therefore, it has no slope.
ansswer plz i been stuck on this for 10 min help ??
9514 1404 393
Answer:
33 ft²
Step-by-step explanation:
Each triangle's area is given by the formula ...
A = (1/2)bh
A = (1/2)(3 ft)(4 ft) = 6 ft²
The square base area is given by ...
A = s²
A = (3 ft)² = 9 ft²
__
The total area of the pyramid is the area of the base plus the area of four triangular faces.
Total Area = (9 ft²) + 4(6 ft²) = (9 +24) ft²
Total Area = 33 ft²
Determine the mean, median, mode, and range for the data set:
5, 6, 12, 7, 8, 10, 8
Mean-
Median-
Mode-
Range-
That’s the question
Answer:
Step-by-step explanation:
Mean (Average): 8
Median (Middle): 8
Mode (Most Common): 8
Range (Biggest - Smallest): 7
please I am struggling really bad help me