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].
A rectangle has a width of 2x and a length of 2x+5, what is the area?
Answer:
what ever the next person says
Step-by-step explanation:
I need Help with this
Fabiola's special seasoning mix has three ingredients. The recipe uses 4 parts thyme, 3 parts parsley, and 1 part green onion. If she is making 24 tbsp. of the mix, how many tbsp. of parsley does she need?
3
5
15
9
Answer: 9
Step-by-step explanation: First, you find how many parts are needed. 4+3+1=8
So, we then divide 24 by 8 to find out what one part is. This is 3
As she needs 3 parts of parsley, we multiply 3 by 3 (each part) to get 9 tbsp.
Fabiola's special seasoning mix of 24 tbsp. needs 9 tbsp. of parsley.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Fabiola's special seasoning mix has three ingredients. The recipe uses 4 parts thyme, 3 parts parsley, and 1 part green onion.
Let, 'x' be the ratio multiplier.
Therefore, 4x + 3x + x = 24.
8x = 24.
x = 3.
So, She needs 3×3 = 9 tbsp. of parsley.
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Only hash channel catfish typically was about 0.06 g during the first six weeks of life at weight increase about 10% each day right a exponential model for the weight how much will the catfish gain weight after six weeks
Answer:
3.225 gram
Step-by-step explanation:
Given that :
Initial weight = 0.06g
Rate of increase, r = 10% = 0.1 per day
Weight gain after 6 weeks
For an exponential model. f(x)
f(x) = a(1 + r)^x
Where ; a = initial amount ; r = growth rate ; x = period
Our model becomes :
f(x) : 0.06(1 + 0.1)^x
f(x) = 0.06(1.1)^x
Number of days in 6 weeks = 6*7 = 42 = x
f(42) : 0.06(1.1)^42
= 3.285 gram
Hence, weight gain after 6 weeks :
(3.285 - 0.06) g = 3.225 gram
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!! <3
Answer: The numbers go from left to right on the table in this order: 0, 3, 4, 3, 0, -5.
To do the problem, you put the x - value in place of where the x is in the equation above (y = 4 - x^2) and then you put what y equals in the box after you finish.
Good luck, hope this helped!!
Find the values of x and y in the equation below.
Answer:
6
18
not negatives!!!!!
Step-by-step explanation:
Write the equation of the line that passes through the points (-2, -8) and (8,-8).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
slope is 0
y-(-8)=0(x-(-2))
y+8=0(x+2) no solution
Step-by-step explanation:
[tex]\frac{-8-(-8)}{8-(-2)} =0/10[/tex]
what is the actual length?
Answer:
Step-by-step explanation:
2ft
Hey guys again please I suck at math
Answer:
the correct answer is number 2
Step-by-step explanation:
X3 - 4x - 16x-24
Answer:
the answer is B
Step-by-step explanation:
X3-4x2-16x+24
Please help will give Brain
On the first day of ticket sales the school sold 8 senior citizen tickets and 1 child ticket for a total of $97. The school took in $102 on the second day by selling 6 senior citizen tickets and 4 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
Answer:
A senior citizen ticket costs $11, and a child ticket costs $9.
Step-by-step explanation:
Let s = price of 1 senior citizen ticket, and let c = price of 1 child ticket.
First day:
8s + c = 97
Second day:
6s + 4c = 102
We have a system of 2 equations in 2 unknowns.
8s + c = 97
6s + 4c = 102
We will use the addition method to solve the system.
Multiply both sides of the first equation by -4. Write the second equation below it and add the equations.
-32s - 4c = -388
(+) 6s + 4c = 102
----------------------------
-26s = -286
Divide both sides by -26.
s = 11
Now substitute s with 11 in the first original equation and solve for c.
8s + c = 97
8(11) + c = 97
88 + c = 97
Subtract 88 from both sides.
c = 9
Answer: A senior citizen ticket costs $11, and a child ticket costs $9.
A line has a slope of 5 and y-intercept of -2. What is its equation in slope-intercept from? Write your answer using interfere, proper fraction and improper fractions in simplest form.
Y=_x - _
Answer:
y=5x-2
Step-by-step explanation:
what is the image of (8,7) after a reflection over the line y=-x?
Answer:
(-7,-8)
Step-by-step explanation:
The original point is (8,7)
To reflect it, just switch their places and change their signs.
So, (-7,-8)
For each point on the unit circle, select the angle that corresponds to it.
Click each dot on the image to select an answer.
Answer:
A. ~30°
B. ~240°
C. ~330°
Step-by-step explanation:
each unit cube measured 1 inch3. what is the maximum volume of the prims
Answer:
1 x 3 x 1 = 3
Step-by-step explanation:
In a bag of marbles, 1/2 are red, 1/4 are blue, 1/6 are green and 1/12 are yellow. You pick a marble without looking. What color marble are MOST likely to be choose?
Answer:
Its red becasue 1/2 is greater than all of them
The most likely color of the marble that will be chosen is red.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Number of red marbles in the bag=1/2
Number of blue marbles in the bag=1/4
Number of green marbles in the bag=1/6
Number of yellow marbles in the bag=1/12
Now,
To determine the most likely color of the marble that will be chosen, we need to calculate the probability of selecting each color. The probability of selecting a red marble is 1/2, the probability of selecting a blue marble is 1/4, the probability of selecting a green marble is 1/6, and the probability of selecting a yellow marble is 1/12.
To compare the probabilities, we need to find a common denominator. The common denominator for 2, 4, 6, and 12 is 12. So, we can rewrite the probabilities as:
Probability of selecting a red marble = 6/12
Probability of selecting a blue marble = 3/12
Probability of selecting a green marble = 2/12
Probability of selecting a yellow marble = 1/12
Since the probability of selecting a red marble is the highest among all the colors, it is the most likely color to be chosen.
Therefore, by probability the answer will be red marble.
Learn more about probability here;
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Find the height of a cone with a diameter of 12 m and whose volume is 133 m.
A. 2 m
B. 9 m
C. 3 m
D. 1 m
Answer:
D
Step-by-step explanation:
Here, we want to get the height of the cone
radius = diameter/2
r = 12/2 = 6 m
To get this, we use the formula for the volume
V = 1/3 * pi * r^2 * h
133 = 1/3 * 3.142 * 22/7 *6^2 * h
h = 1.12 m
Silver scored 48 points in 4 basketball games. If Silver scored the same amount in each game how many points would he score in 10 games?
Answer: 120
Step-by-step explanation: He scores 12 points each game. 12 x 10 = 120 Good luck! :D
Markus buys an old bike for £50. He cleans it up and sells it for £60. What is his percentage profit?
i’ll mark brainliest
Dane needs to cut 4 strips of border for his rectangular project board. The project board has a length of 12 1/2 inches and a width of 6 1/4 inches. How much border will Dane have left if the border comes in a 60-inch roll?
What is 234475 x 45678 =?
13 = -4x +9 solve equation.
Answer:
-1x or -x
Step-by-step explanation:
4 divided by -4
If angle 10 and angle 15 are congruent, which lines are parallel
Answer:
Line a is parallel with line b
Step-by-step explanation:
Solve
7 + X = 2x-5
3
Answer:
the exact form is 22/5
decimal form is 4.4
mixed number form is 4 2/5
Step-by-step explanation
isolate the variable by dividing each side by factors that don't contain the variable
Help will mark Brainliest
Answer:
To find the slope, use the formula rise/run or change in y/change in x
In this case, the slope is 5
To find y-intercept, substitue values for x and y
Step-by-step explanation:
-3 = 5(2) + b
-3 = 10 + b
-10 -10
-13 = b
Therefore, b is -13
So here's how the equation looks in slope-intercept form
y = 5x + -13
Write an equivalent expression by distributing the "_" sign outside the parentheses-(6p-7.2)
identify the percent of change as an increase or a decrease 3/8 to 7/8
Answer:
133.5
Step-by-step explanation:
Can one of y’all please help me this is Urgent
Answer:
B
Step-by-step explanation:
It’s the only one with sides that correlate
Use the fraction strips to compare 2/4 and 5/8
Answer:
Step-by-step explanation:
We are given 2 fractional numbers:
We have to use fraction strips to compare to the fractional numbers.
Let we are Comparing with the length of number of sections.
i.e.
Let we are Comparing with the length of number of sections.
i.e.
Now, let us have a look at 3rd part of question:
The sections of 2/4 is _____ the length of 5/8. Therefore, 2/4 < 5/8
Let the answer be .
So, the equation becomes:
So, the answers are:
2
5
Answer:
1) two
2)five
3)less than
4)<
Step-by-step explanation:
i took the test on iready :)
A quantity with an initial value of 380 decays exponentially at a rate of 1% every 4 hours. What is the value of the quantity after 174 minutes,
Answer:
377.24
Step-by-step explanation: