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].
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:
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
Which community is more toxic
1 reddit
2 2b2t
3 dead by daylight
4 the entirety of 4chan
Can someone please answer these questions ASAP!!
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 ?
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.
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
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.
–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
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:
What is two thing you like about math
Answer:
1. Math encourages curiosity and questions.
2. Math can save you money. ...
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
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
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
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? *
13 = -4x +9 solve equation.
Answer:
-1x or -x
Step-by-step explanation:
4 divided by -4
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]
please I am struggling really bad help me
can someone please help me with this !
Find the solution in the system of equations shown below
Answer:
no solution
Step-by-step explanation:
the lines are parallel, they never intersect.
.............
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.
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.
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.
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:
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
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
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
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
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