Which trigonometric ratios are correct for triangle ABC? Check all that apply
Answers
Let
OPP denote the length of the side opposite to M,
ADJ denote the length of the side adjacent to M, and
HYP denote the hypotenuse.
then:
Sin(M) = OPP/HYP
Cos(M)= ADJ/HYPP
Tan(M)=OPP/ADJ
Back to our problem,
using the Pythagorean we can find the length of AB:
[tex]|AB|^2+|AC|^2=|BC|^2\\\\|AB|^2+9^2=18^2\\\\|AB|^2=18^2-9^2\\\\|AB|^2=(18-9)(18+9)=9 \cdot 27=9 \cdot 9 \cdot3\\\\|AB|=9 \sqrt{3} [/tex]
[tex]Sin(C)= \frac{OPP}{HYP}=\frac{9 \sqrt{3} }{18}= \frac{ \sqrt{3} }{2}[/tex]
[tex]Cos(B)= \frac{ADJ}{HYP}= \frac{9 \sqrt{3}}{18}= \frac{ \sqrt{3}}{2} [/tex]
[tex]Tan(C)= \frac{OPP}{ADJ}= \frac{9 \sqrt{3} }{9}= \sqrt{3} [/tex]
[tex]Sin(B)= \frac{OPP}{HYP}= \frac{9}{18}= \frac{1}{2} [/tex]
[tex]Tan(B)= \frac{OPP}{ADJ}= \frac{9}{9 \sqrt{3}}= \frac{1}{ \sqrt{3} }= \frac{ \sqrt{3}}{3} [/tex]
Answer: 1, 3, 4
Related Questions
Which number line correctly shows 4.5 – 2.5?
Answers
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
[tex]4.5-2.5[/tex]
According to the number line,
First we go 4.5 units towards the positive axis of x from the origin.
And then back by 2.5 units from there towards the negative axis of x to show the subtraction.
So, it will interpretate the subtraction of 2.5 from 4.5.
Numerically, it is expressed as
4.5-2.5=2
So, It should reach at 2 in the positive axis of x.
Hence, First option is correct.
A number line that correctly shows 4.5 – 2.5 is: A. number line A.
What is a number line?In Mathematics and Geometry, a number line refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
This ultimately implies that, every number line would primarily increase in numerical value towards the right from zero (0) and decrease in numerical value towards the left from zero (0).
Based on the information provided above, we have:
4.5 - 2.5 = 2.
Solution = 2.
Therefore, number line A is the correct representation of 4.5 - 2.5 = 2.
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Let a and b be irrational numbers. Is (ab)^2 always rational, sometimes rational, or never rational?
Answers
Final answer: never rational
Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 toher savings. How long will it take her to save enough money to buy the bike?
Answers
A stadium has 20,000 reserved seats and 25,000 general admission seats. If reserved seats are $17.50 and general admission seats are $10.75, how much money would be taken in if tickets for all the seats were sold?
Answers
20,000 multiplied by $17.50 is $350,000
General seats -
25,000 multiplied by 10.75 is $268,750
$268,750 added with $350,000 is $618,750.
The total amount of money would be $618,750.
Hope this helps!
What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)?
Answers
Answer:
The sum of of the polynomials (m + n + 3) + (m + n + 4) is 2m + 2n +7
Step-by-step explanation:
The given expression is (m + n + 3) + (m + n + 4)
we need to find the sum of this expression
so, first we add the similar terms
m + n + 3 + m + n + 4
first write the like term together and then constant,
⇒ m + m + n + n +3 + 4
⇒ 2m + 2n +3 + 4
⇒ 2m + 2n +7
Therefore, The sum of of the polynomials (m + n + 3) + (m + n + 4) is 2m + 2n +7
What is the range of the following set of numbers? 114, 90, 83, 101, 97, 142, 117, 87, 72
Answers
Answer:
The answer is 70
Step-by-step explanation:
Monique Fournier deposited $12,500 into a savings account paying 6.5% annual interest compounded monthly. What amount will she have in her account after 3 years
Answers
A = P(1 + r/n)^nt
A (Amount)
P (Principal)
r (Interest rate)
n (Times per year the interest is compounded)
nt (time in years)
A = 12500(1 + 0.065/12)^3(12)
A = 12500(1.005)^3(12)
A = 12500(1.005)(^36)
A = 12500(1.20)
A = 15,000
Hope I helped :)
Follow below steps;
Monique Fournier wants to find out how much her $12,500 savings account, with an annual interest rate of 6.5% compounded monthly, will grow to after 3 years. To calculate the future value of this investment, we can use the compound interest formula:
FV = P times (1 + r/n)^(nt)
Where:
FV is the future value of the investmentP is the principal amount ($12,500)r is the annual interest rate (6.5% or 0.065 as a decimal)n is the number of times interest is compounded per year (12, since it's compounded monthly)t is the number of years the money is invested (3 years)Plugging the numbers into the formula gives us:
FV = $12,500 times (1 + 0.065/12)^(12 imes 3)
After calculating, Monique's account balance after 3 years will be:
FV = $12,500 times (1 + 0.0054167)^(36)
FV = $12,500 times 1.0054167^36
FV ≈ $12,500 times 1.214669
FV ≈ $15,183.36
After 3 years, Monique Fournier will have approximately $15,183.36 in her savings account
help........me pls.........
Answers
5 Mountain Image stamps
2 Mountain Image Stamps and 6 Flower Image Stamps
Sorry it took so long, but hope this helps!
angles a and b are complementary if the measure of angle A is 27 degrees more than measure of angle b, what is the measure of angel b ?
Answers
a= x +27
b= x
2x+27=90°
2x= 90-27
2x=63
x=63/2
x= 31.5 or 31°30'
b= 31°30'
a= 31.5+27= 58.5---->58°30'
If the shadow of a tree is 14 m long and the shadow of a person who is 1.8 m tall is 4 m long, how tall is the tree?
Which of the following proportions could not be used to solve the problem?
a: 14/1.8=x/4
b: x/14=1.8/4
c: x/1.8=14/4
Answers
Answer: [tex]\frac{x}{14}=\frac{1.8}{4}[/tex]
Step-by-step explanation:
Let 'x' be the height of tree.
The length of shadow of a tree = 14 m
The length of shadow of a person =4 m
The height of person = 1.8 m
Since both man and tree are standing vertical to the ground.
Assume the formation of shadow is happening at the same time then the angle that the sun hits the earth making shadows of both person and tree will be equal.
By direct proportion , we have
[tex]\frac{\text{height of tree}}{\text{length of shadow of tree }}=\frac{\text{height of person}}{\text{length of shadow of person}}\\\\\Rightarrow\frac{x}{14}=\frac{1.8}{4}[/tex]
The correct answer would be:
14/1.8 = x/4
I just finished with that assignment and it said it was correct :-)
What are the next 3 numbers in the number sequence? 5, 11, 18, 26, 35, 45, ? ? ?
Answers
It increases by 1 everytime first 6 then 7 then 8 then 9 and etc
Is 12,000,000 the standard form of 1.2 times 10 to the negative 7 power?
Answers
"1.2 times 10 to the POSITIVE 7 power.
That is; "12,000,000 = 1.2 * 10⁷ " .
____________________________________________
Use a table to compute the product below. (8x2 - 2x - 5)(2x + 7) A. 16x3 + 60x2 - 24x - 35 B. 16x3 - 52x2 + 24x + 35 C. 16x3 + 52x2 - 35 D. 16x3 + 52x2 - 24x - 35 its D but thx yall bc you guys don't know how to help!!!
Answers
16x^3+52x^2-24x-35
the answer is d
Help with rate of sales tax
Answers
so, if we take 18.99 to be the 100%, how much is 1.52 in percentage off of it?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 18.99&100\\ 1.52&t \end{array}\implies \cfrac{18.99}{1.52}=\cfrac{100}{t}\implies t=\cfrac{1.52\cdot 100}{18.99}[/tex]
How many more people attended the Magic's games than attended the pacers' games? 582,295 pacers 715,901 magic
Answers
715901-582295=133606
Answer:
133606 persons
Step-by-step explanation:
Number of persons attended the Magic's game= 715,901 games
Number of persons attended the Pacer's game= 582,295 persons
We have to find the number of persons who attend the Magic's game more than Pacer's game.
To find this, we have to find the difference
Number of persons attended the Magic's game= 715,901 games
Number of persons attended the Pacer's game= 582,295 persons
Number of persons who attended More Magic's game= 715901- 582295
Number of persons who attended More Magic's game= 133606 persons
Hence, the correct answer is 133606 persons
Nicholas bicycled 15.8 kilometers each day for 18 days last month. how many kilometers did he bicycle last month?
Answers
so he biked a total of (15.8 * 18) = 284.4 km <==
Write a quadratic function f whose zeros are 2 and 9 .
Answers
For this system, x=2 and x=9 are the zeros.
Therefore (x-2) and (x-9) are the binomials which solve to those zeros.
Multiply the binomials together to get the quadratic:
(x-2)(x-9) = x² - 11x + 18
f(x) = x² - 11x + 18
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
A quadratic equation is of the form:
f(x) = x² - (Sum of roots)x + (product of roots)
The given roots are 2 and 9
Sum of roots = 2 + 9
Sum of roots = 11
Product of roots = 2 x 9
Product of roots = 18
Substituting these values into the general form of a quadratic equation
f(x) = x² - 11x + 18
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What is the value of 6 in 342.76?
A six ten-thousandths
B six thousandths
C six tenths
D six hundredths
Answers
the second digit to the right of the decimal point is the hundredths place
so it is D. 6 hundredths.
5. Triangle ABC is a right triangle with CD and AB angle C is a right triangle.
By the ,(.......) △ACB∼△ADC and △ACB∼△CDB. Since similar triangles have (........) sides, BCBA=BDBC and ACAB=ADAC . Using cross multiplication gives the equations (BC)2=(BD)(BA) and (AC)2=(AD)(AB). Adding these together gives (BC)2+(AC)2=(BD)(BA)+(AD)(AB). Factoring out the common segment gives (BC)2+(AC)2=(AB)(BD+AD). Using (........) gives (BC)2+(AC)2=(AB)(AB), which simplifies to (BC)2+(AC)2=(AB)2 .
First paranthese
SAS or AAS or SSS
Second paranthese
Congruent or proportional
Third paranthese
SA or CPCTC
Answers
The second parenthesis would be "proportional". Any time you have similar triangles, the sides form a ratio. For example if ABC is similar to DEF, then AB/DE = BC/EF
Finally the third parenthesis would be "Segment Addition Postulate" possibly shorted and abbreviated to simply SA. This idea is that we can glue two lines together to form a larger line. In this case, AD+DB turns into AB.
Answer:
AAS
Proportional
Segment Addition Postulate
Step-by-step explanation:
Confirming that the other answer on here is correct! :D
What is the value of n?
−6.5(n−5)=18.2
Answers
Evaluate the expression (x-2y)^2where x=3and y=2
Answers
y = 2
[tex](x-2y)^2 = (3-(2*2))^2 = (3-4)^2 = (-1)^2 = -1*-1 = 1[/tex]
Hence, the answer is 1.
To evaluate the expression (x-2y)² where x=3 and y=2, substitute the values of x and y into the expression and simplify.
To evaluate the expression (x-2y)² where x=3 and y=2, we substitute the values of x and y into the expression.
Substituting x=3 and y=2 into the expression, we get (3-2*2)².
Solving this expression, we have (3-4)^2 which simplifies to (-1)².
Finally, (-1)² equals 1.
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Name a pair of whole number factors whose product is 8
Answers
Those would be: 1 and 8
2 and 4
so there are two solution to this question: 1 and 8, 2 and 4!
we can also include negative numbers:
-1 and -8
-2 and -4
because a multiplication of two negative numbers gives a positive result!
Use the table below of the function f(x)=x4-2x3 to answer this question
X F(x)
-1 3
0 0
1 -1
2 0
3 27
What is the average rate of change from x=-1 to x=2? -3, -1, 1, 24
Answers
(-1,3) and (2,0)
Slope=(y2-y1)/(x2-x1)
m=(0-3)/(2-(-1))
m=(-3)/(3)
m=-1
The average rate of change of the given function from x = -1 to x = 2 is -1.
The average rate of change of a function between two points, x = a and x = b, is calculated as the difference in the function values at these points divided by the difference in x-values, which is similar to the slope formula for a linear function (gradient).
In this case, we are looking for the average rate of change of f(x) = x^4 - 2x^3 from x = -1 to x = 2. Using the table provided:
f(-1) = 3
f(2) = 0
So, the average rate of change is:
(f(2) - f(-1)) / (2 - (-1)) = (0 - 3) / (2 - (-1)) = (-3) / 3 = -1.
A certaint plant grows 1 and 1/6 inches every week.how long will it take the plant to grow 6 and 1/6 inches?
Answers
divide 6 1/6 by 1 1/6
6 1/6 = 37/6
1 1/6= 7/6
37/6 / 7/6 =
37/6 * 6/7 = 222/42 = 5 12/42 = 5 2/7 weeks
David played a video game 5 times. The list shows his scores.
4975,5275,4825,5100,4950
What is the difference between the mean and median of the data ?
A.25
B.50
C.75
D.200
E.400
Answers
The difference between the mean and median of the data is 50.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
David played a video game 5 times.
The list shows his scores:
4975,5275,4825,5100,4950.
To find the median:
The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. To find the median, firstly arrange the data points in ascending order.
4825, 4950, 4975, 5100 and 5275.
So, the middle number is 4975.
The median is 4975.
To find the mean;
The mean = the sum of the scores / 5
The mean = 25125 / 5
The mean = 5025
The difference:
5025 - 4975 = 50
Therefore, the required difference is 50.
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China's population is 1.446×10^9 . Marshall Islands' population is 6.025×10^4 . How many times larger is China's population than Marshall Islands' population? Fill in the blanks.
1.) 0.024
2.) 2.4
3.) 240
4.) 10^4
5.) 10^5
6.) 10^13
___ x ___ times larger
Answers
Final answer:
The population of China is approximately 240 times larger than the population of the Marshall Islands. This is calculated by dividing China's population (1.446×[tex]10^9[/tex]) by the Marshall Islands' population (6.025×[tex]10^4[/tex]). (Option 3)
Explanation:
The question asks us to determine how many times larger China's population is compared to the population of the Marshall Islands. To find the answer, we divide the population of China by the population of Marshall Islands:
1.446×[tex]10^9[/tex] (China's population) ÷ 6.025×[tex]10^4[/tex] (Marshall Islands' population).
Carrying out this division, we get a result of approximately 240 times larger. Thus, the population of China is 240 times larger than that of the Marshall Islands.
In how money ways can a five-letter license plate be made with the letters from April if none of the letters are repeated ?
Answers
linear or nonlinear x-3y=10
Answers
What is the difference between the ratio AP:PB and the ratio of AP:AB?
Answers
A line segment can be divided into subsegment using ratios. The difference between [tex]AP:PB[/tex] and [tex]AP: AB[/tex] is that:
Ratio [tex]AP:PB[/tex] compares the two subsegments of AB while Ratio [tex]AP: AB[/tex] compares a segment of AB to the whole length of AB.Given:
[tex]AP:PB[/tex] and [tex]AP: AB[/tex]
In [tex]AP:PB[/tex], we can see that AP and PB has a common point (P).
This means that:
[tex]AB = AP + PB[/tex]
i.e. AP and PB are two subsegments of line segment AB.
So, the ratio [tex]AP:PB[/tex] compares the two subsegments of AB
Because AP and PB are two subsegments of line segment AB.
Then, ratio [tex]AP: AB[/tex] compares a segment of AB to the whole length of AB.
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Which functions have graphs that are less steep than the graph of f(x)= -4x^2
SELECT EACH CORRECT ANSWER
m(x)=5x2
k(x)=4x2
h(x)=−3x2
j(x)=−x2
g(x)=−5x2
Answers
So h(x) and j(x) are the answers.
The quadratic equations that are less steep than f(x)= -4x² are:
h(x) = -3x² j(x) = -x² Which functions have graphs that are less steep than the graph of f(x)= -4x²?Here we want to identify which equations have graphs less steep than the graph of the quadratic f(x) = -4x²
To identify those, we just need to see which equations have a leading coefficient with a smaller absolute value than |-4| = 4
These equatios are:
h(x) = -3x² ---> With a leading coefficient of -3, absolute value of 3.
j(x) = -x² ---> with a leading coefficient of -1, absolute value of 1.
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