Answer:
[tex]\begin{aligned}{&\cos \theta=\frac{10}{26} \\\bf{&\tan \theta=\frac{24}{10}}\end{aligned}[/tex]
Step-by-step explanation:
Since the angle is in the first quadrant, the values of all trigonometric functions are positive. Also. the formulas for the trigonometric functions we need to find from the problem are shown below:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\\tan \theta &=\frac{y}{x}\end{aligned}[/tex]
Based on the formulas listed, the value of y and r are y = 24 and r = 26 respectively. This means that in order to determine the value of the other functions, we need In compute for the value of x using the Pythagorean Theorem:
[tex]\begin{aligned}r^{2} &=x^{2}+y^{2} \\r^{2}-y^{2} &=x^{2}+y^{2}-y^{2} \quad\left[\text { \text{Subtracting \ both \ sides \ of \ the \ equation\ by} } y^{2}\right] \\r^{2}-y^{2} &=x^{2} \\\sqrt{r^{2}-y^{2}} &=\sqrt{x^{2}} \\\sqrt{r^{2}-y^{2}} &=x \\\sqrt{26^{2}-24^{2}} &=x \\10 &=x\end{aligned}[/tex]Then, substituting this to the formula to determine the answers yields:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\&=\frac{10}{26} \\\tan \theta &=\frac{y}{x} \\&=\frac{24}{10}\end{aligned}[/tex]
Therefore, the answers are:
[tex]\begin{aligned}&\cos \theta=\frac{10}{26} \\&\tan \theta=\frac{24}{10}\end{aligned}[/tex]
Answer:
See below
Step-by-step explanation:
We are here given that ,
[tex]\longrightarrow \sin\theta =\dfrac{24}{26}[/tex]
And we would like to find out other trigonometric ratios ( since it is not mentioned about which two I will find out all 6 ) . As we know that ,
[tex]\longrightarrow \sin\theta =\dfrac{perpendicular}{hypotenuse} =\dfrac{p}{h}[/tex]
So that ,
[tex]\longrightarrow \dfrac{p}{h} =\dfrac{24}{26}[/tex]
Let us assume the given ratio to be 24x : 26x .
So we can say that ,
hypotenuse = 26xperpendicular = 24xNow let's find out the value of base , so that we can find out the other ratios .
By Pythagoras Theorem ,
[tex]\longrightarrow (perpendicular) ^2+(base)^2=(hypotenuse) ^2[/tex]
Substitute the respective values ,
[tex]\longrightarrow (26x)^2=(24x)^2+b^2\\[/tex]
[tex]\longrightarrow 676x^2 = 576x^2+b^2\\ [/tex]
[tex]\longrightarrow b^2=100x^2\\[/tex]
[tex]\longrightarrow b =\sqrt{100x^2}\\[/tex]
[tex]\longrightarrow \boldsymbol{ b = 10x } [/tex]
Now we may find the other ratios as ,
[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{10x}{26x}=\boxed{\boldsymbol{\dfrac{5}{13}}}\\[/tex]
[tex]\longrightarrow \tan\theta =\dfrac{perpendicular}{base}=\dfrac{24x}{10x}=\boxed{\boldsymbol{\dfrac{12}{5}}}\\[/tex]
[tex]\longrightarrow \cosec\theta =\dfrac{hypotenuse}{perpendicular}=\dfrac{26x}{24x}=\boxed{\boldsymbol{\dfrac{13}{12}}}\\ [/tex]
[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{26x}{10x}=\boxed{\boldsymbol{\dfrac{13}{5}}} \\[/tex]
[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{10x}{24x}=\boxed{\boldsymbol{\dfrac{5}{12}}} [/tex]
And we are done !
Ashley ate Mexican food 4 out of 7 days on her vacation. If her vacation was 35 days, how many days did she eat Mexican food?
31
21
20
28
The number of days Ashley ate Mexican food while on vacation is 20 days.
How many days did Ashley eat mexican food?
The first step is to determine the fraction of the number of days Ashley atae Mexican food. In order to do this, divide 4 by 7
4/7.
The second step is to multiply 4/7 by 35
4/7 x 35= 20 days
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help pls asap
answer:
explain:
rate of change:
[tex]\sf \bold{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
coordinates taken: (0, 0), (2, 1)
[tex]\rightarrow \dfrac{1-0}{2-0}[/tex]
[tex]\rightarrow \dfrac{1}{2}[/tex]
Take 2 points
(-2,-1)(2,1)[tex]\\ \rm\rightarrowtail m=\dfrac{1+1}{2+2}[/tex]
[tex]\\ \rm\rightarrowtail m=\dfrac{2}{4}[/tex]
[tex]\\ \rm\rightarrowtail m=\dfrac{1}{2}[/tex]
Juana invests $1,500 in an account accumulating 3% interest according to the equation v = 1500(1.03), where v
represents the value of the account after y years. Marquez and Calvin invest the same amount of money at the sam
rate. Marquez invests three years before Juana, and Calvin invests two years after Juana. By what factor would
Calvin's investment need to be increased to equal Marquez's investment at any time after Calvin's investment is
made?
A.86.3%
B. 97.1%
C. 115.0%
D. 115.9%
Answer:
d 115.9
Step-by-step explanation:
The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D)
How to determine the investment needed by Calvin to equal Marquez's investment at any time
In this question we must apply the concept of compound interest to derive the initial investment to be done by Calvin. According to the statement, Calvin invests money five years later than Marquez.
To determine the initial investment to be deposited by Calvin such that his investment equals Marquez's investment at any time we resort to the following expression:
[tex]1500\cdot (1+0.03)^{t+5} = C_{C}\cdot (1+0.03)^{t}[/tex] (1)
Then, we simplify the required initial investment:
[tex]C_{C} = 1500\cdot (1+0.03)^{5}[/tex]
[tex]C_{C} = 1738.911[/tex]
And the increase factor is:
[tex]r_{C} = \frac{1738.911}{1500}\times 100\,\%[/tex]
[tex]r_{C} = 115.927\,\%[/tex]
The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D) [tex]\blacksquare[/tex]
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What is the solution of the inequality 9 - x^2<0?
Answer:
[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]
Step-by-step explanation:
Given:
[tex]9-x^2 < \:0[/tex]
Solve:
[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}[/tex]
[tex]9-x^2-9 < 0-9[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-x^2 < -9[/tex]
[tex]Multiply\:both\:sides\:by\:-1\:[/tex]
[tex]\left(-x^2\right)\left(-1\right) > \left(-9\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x^2 > 9[/tex]
[tex]\mathrm{For\:}u^n\: > \:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\: < \:-\sqrt[n]{a}\:or\:u\: > \:\sqrt[n]{a}[/tex]
[tex]x < -\sqrt{9}\quad \mathrm{or}\quad \:x > \sqrt{9}[/tex]
[tex]\sqrt{9}=3[/tex]
[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]
~lenvy~
The diagram shows a convex polygon. What Is The Value Of T?
Answer:
t = 9
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
sum the exterior angles and equate to 360
10t + 16t + 53 + 73 = 360 , that is
26t + 126 = 360 ( subtract 126 from both sides )
26t = 234 ( divide both sides by 26 )
t = 9
2 If a hockey team loses 33% of the games they play, what is the probability that this team will win exactly 10 games out of their next 15?
a. 0.6%
b. 21.4%
c. 19.8%
d. 11.1%
So
P(A)=0.33P(A')=0.67Now
They win from 15games=10They lose=5The required probability
[tex]\\ \rm\rightarrowtail P(A')^{10}\times P(A)^5\times ^{15}C_{10}[/tex]
[tex]\\ \rm\rightarrowtail (0.33)^{5}\times (0.67)^{10}\times \dfrac{15!}{5!10!}[/tex]
[tex]\\ \rm\rightarrow 0.0039(0.0182)\times\dfrac{15(14)(13)(12)(11)10!}{5!10!}[/tex]
[tex]\\ \rm\rightarrowtail 0.00007098\times \dfrac{360360}{120}[/tex]
[tex]\\ \rm\rightarrowtail 0.00007098(3003)[/tex]
[tex]\\ \rm\rightarrowtail 0.213[/tex]
So probability
0.213(100)=21.3%Option B
Answer:
b. 21.4 % (nearest tenth)
Step-by-step explanation:
P(lose) = 33% = 0.33
P(win) = 1 - 0.33 = 0.67
Using binomial distribution X ~ B(n, p)
where n is the number of trials and p is the probability of success
⇒ X ~ B(15, 0.67)
Binomial probability formula:
[tex]\sf P(X=x)= \ _nC_x\cdot p^x \cdot(1-p)^{n-x}[/tex]
[tex]\sf \implies P(X=10)=15C10\cdot 0.67^{10} \cdot(1-0.67)^{15-10}[/tex]
[tex]\sf =3003 \cdot 0.67^{10} \cdot 0.33^5[/tex]
[tex]\sf =0.214226434...[/tex]
Converting to percentage:
0.214266434... x 100% = 21.4 % (nearest tenth)
solve the system of equations 2y - 3x = -27 5y + 3x = 6 PLEASE EXPLAIN STEPS!
(photo included)
Answer:
x=7 y= -3
Step-by-step explanation:
When you ADD both the x variable is cancelled
since -3x + 3x = zero
then you solve for y And when you plug the value of y you will solve x
2y-3x =-27
5y+3x =6
ADD BOTH
7y = -21
y = -3
PLUG y
5(-3)+3x = 6
-15 + 3x = 6
3x = 21
x=7
Can someone help me?
Answer:
Min = 2
Q1 = 4
Median = 11
Q3 = 16
Max = 18
Step-by-step explanation:
2, 4, 4, 7, 10, 11, 12, 13, 16, 17, 18
Q1 Q2 Q3
Min (minimum value) = 2
Q1 = 4
Median (middle value Q2) = 11
Q3 = 16
Max (maximum value) = 18
5. A ball is thrown into the air. It went 14 inches into the air is represented by the equation
h = -14t2 + 28t, where h represent the height and t represents the time. Determine when
the ball is thrown and how long it takes to hit the ground?
By defining that h(t) = 0 means that the ball is in the ground, we conclude that the ball is thrown at t = 0, and hits the ground again at t = 2.
When the ball is thrown?The height equation is:
h(t) = -14*t^2 + 28*t
When t = 0, we have: h(0) = 0
So it is in the ground, meaning that it is thrown at the time t = 0.
How long does it take to hit the ground?We need to find the other root of the quadratic equation, so we need to solve:
-14*t^2 + 28*t = 0
We can rewrite this as:
t*(-14*t + 28) = 0
The parenthesis is zero when:
-14*t + 28 = 0
t = 28/14 = 2
So at t = 2, the ball hits the ground.
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Copare use <,>, or =
Answer:
0.125 = ⅛
Step-by-step explanation:
Both are equal.......
Which expressions represent rational numbers? select all the apply. startroot 100 endroot startroot 100 endroot 13.5 startroot 81 endroot startroot 9 endroot startroot 729 endroot startroot 64 endroot startroot 353 endroot one-third startroot 216 endroot three-fifths 2.5
The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
1. √100 × √100
→ √100 × √100
→ 10 × 10 = 100
This is a rational number.
2. 13.5 + √81
→ 13.5 + √81
→ 13.5 + 9 = 22.5
This is a rational number.
3. √9 + √729
→ √9 + √729
→ 3 + 27 = 30
This is a rational number.
4. √64+ √353
→ √64 + √353
→ 8 + √353
This is an irrational number.
5. 1/3 + √216
→ 1/3 + √216
→ 1/3 + √216
This is an irrational number.
6. 1/5 + 2.5
→ 1/5 + 2.5
→ 0.2 + 2.5 = 2.7
This is a rational number.
More about the rational number link is given below.
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Answer:
A, B, C, F
Step-by-step explanation:
edge
Given that PO and overline WE are equidistant from the center, determine the value of m and n in the circle below.
US = 3m + 2
RU = -m + 9
PO = 20 - 14
EW = -2(2m + 1)
Based on the equidistant chords theorem, the value of m and n in the circle are:
m = 7/4 = 1.75
n = 1/2 = 0.5
What is the Equidistant Chords Theorem?The equidistant chords theorem states that, two chords are congruent if they are equidistant to the center of the same circle.
Given:
US = 3m + 2 RU = -m + 9 PO = 20 - 14 EW = -2(2m + 1)Thus, since US = RU, therefore chords PO and EW are congruent based on the equidistant chords theorem.
Therefore:
3m + 2 = -m + 9
Add like terms
3m + m = -2 + 9
4m = 7
m = 7/4
m = 1.75
20n - 14 = -2(2n + 1)
20n - 14 = -4n - 2
20n + 4n = 14 - 2
24n = 12
n = 12/24
n = 1/2 = 0.5
Therefore, based on the equidistant chords theorem, the value of m and n in the circle are:
m = 7/4 = 1.75
n = 1/2 = 0.5
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in which quadrant is point (-4,5) located?
find the area of this circle. Use 3.14 as (pie symbol) click the photo to see the circle ! Please help <3 if you can’t see, the diameter is 76
Answer:
[tex]\displaystyle 4536,4597918...\:cm.^2 = A[/tex]
Step-by-step explanation:
Split the diametre in half before proceeding:
[tex]\displaystyle \pi{r}^2 = A \\ \\ 38^2\pi = A \hookrightarrow 1444\pi = A \\ \\ \boxed{4536,4597918... = A}[/tex]
I am joyous to assist you at any time.
Rose is 60 inches tall. how many feet tall is Rose
Answer:
5 feet
Step-by-step explanation: 60 divided by 12 inches is 5 feet
What is the difference between a factor of a number and a multiple of a number? use the number 25 has an example
Answer:
factor: a submultiple; an integer value that gives an integer quotient when the number is divided by it.multiple: the product of the number and another integerStep-by-step explanation:
FactorsA set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:
f1 × f2 × f3 × ... = N
Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.
When N = 25, the prime factors are {5, 5}. That is ...
5×5 = 25
__
DivisorsA "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.
Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.
__
MultiplesFor an integer k, the value k×N is called a multiple of N, often, the k-th multiple of N.
Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.
__
Another example
When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....
Find the length of side a.
A. 4
B. 2
C. 34
D. 16
Answer:
Side A is 4
Step-by-step explanation:
Answer:
A.4
Step-by-step explanation:
a = √(c² - b²)
a= √(5² -3b²)=4
hey, could you help me real quick?
solution:
[tex]\frac{299}{6}=49\frac{5}{6}[/tex]
decimal result:
[tex]49.833[/tex]
1. Simplify the expression
[tex]26/3*23/4[/tex]
Multiply the fractions:
[tex]\frac{\left(26\cdot23\right)}{\left(3\cdot4\right)}[/tex]
Cancel terms:
[tex]\frac{\left(13\cdot23\right)}{\left(3\cdot2\right)}[/tex]
Simplify the arithmetic:
[tex]\frac{299}{\left(3\cdot2\right)}[/tex]
Simplify the arithmetic:
[tex]\frac{299}{6}[/tex]
Simplify the fraction:
[tex]\frac{299}{6} =49\frac{5}{6}[/tex]
[tex]==========================================[/tex]
First, let's convert the mixed numbers into improper fractions:-
[tex]\bf{8\displaystyle\frac{2}{3}[/tex]
Step 1:-Multiply the whole number (8) times the denominator (3). The product is 24.Add the numerator (2). The sum is 26.The denominator stays the same.Thus, the fraction is[tex]\displaystyle\frac{26}{3}[/tex]
Now, do the same for the second fraction:-
Multiply 5 times 4. The product is 20Add 3. The sum is 23.The denominator stays the same.Thus, the fraction is[tex]\displaystyle\frac{23}{4}[/tex]
Now, the formula for the area is
[tex]\bold{A=bh}[/tex]
We know both b and h, so we can just plug in the values and solve:
[tex]\bold{A=\displaystyle\frac{26}{3} *\frac{23}{4} }}[/tex]
Actually, we can reduce some fractions here (we can divide 26 and 4 by 2)
[tex]\bold{\displaystyle\frac{13}{3} *\frac{23}{2}}[/tex]
Multiplying 13 times 23 is easier than multiplying 26 times 13.
Now, this can only be done if the numbers do have some common factors. Both fractions are now in simplest form; 13, 23, 3 & 2 don't have common factors.
Multiply:
[tex]\bold{\displaystyle\frac{13*23}{3*2}}}[/tex]
The answer is
[tex]\bold{\displaystyle\frac{299}{6}}[/tex]
Convert to a Mixed Number:-
[tex]\bold{49\displaystyle\frac{5}{6}}[/tex]
[tex]==================================[/tex]
Notes:-Hope everything is clear.Let me know if you have any questions!Always remember: [tex]\boxed{Knowledge~Is~Power!}[/tex]Good luck & enjoy your day!Answered by:-Nickname:- [tex]\mathbb{DiAmOnD}[/tex]
[tex]\boxed{An~emotional~helper}[/tex]
Bob’s rectangular TV is 40 inches wide and 30 inches high. What is the length of the diagonal of Bob’s TV?
a.35 in.
b.45 in.
c.50 in.
d.70 in.
The length of the diagonal of Bob’s TV will be 50 in.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
Bob’s rectangular TV is 40 inches wide and 30 inches high.
Now,
Since, TV is in rectangular shape.
Hence, It satisfy the Pythagoras theorem.
Let the length of the diagonal of Bob’s TV = x
So, We can formulate;
⇒ x² = 40² + 30²
⇒ x² = 1600 + 900
⇒ x² = 2,500
⇒ x = √ 2,500
⇒ x = 50 in
Thus, The length of the diagonal of Bob’s TV = 50 in.
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which equation is equivalent to the expression (-2x to the power of two) (3x to the power of 5)?
A. 6x to the power of 7
B. -6x to the power of 10
C. 6x to the power of 10
D. -6x to the power of 7
Answer: pretty sure the answer is D
Step-by-step explanation:
Car #1 travels 288 miles in 4 hours. Car #2 travels 276 miles in 3
hours. What is the speed of car #1 in miles per hours
PLEASE HELP AURGENT
Step-by-step explanation:
288÷60(60 minutes in an hour) = 4.8
is this what you asked for?
Whats the mean of 72+72+72+79+82+82+88?
Answer:
78.1428571429
Step-by-step explanation:
What is the probability of rolling a sum of 8 with a pair of dice?
Answer:
[tex]\frac{5}{36}[/tex]
Step-by-step explanation:
the total number of possible combinations of rolling two dice is 36 because a side has 6 sides and [tex]6^{2}=36[/tex]
and possible combinations that sum to 8 are
2 and 63 and 54 and 45 and 36 and 2which are 5 possible combinations which gives [tex]\frac{5}{36}[/tex]
One number is two times greater than another number. if the greater number is x what is the other number?
Answer:
[tex]\frac{1}{2}x[/tex]
Step-by-step explanation:
If the greater number is x and it is two times greater than the other number then the other number is half as big. This is true because 2*[tex]\frac{1}{2}[/tex]x = x
The other number is equal to x/2.
What is a Fraction?A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator.
As per the given data:
We are given the relationship between 2 numbers, It's given that One number is two times greater than another number.
The greater number = x
Let's assume that the smaller number is y.
From the given data in the question:
One number is two times greater than another number
= x = 2y ...(i)
The other number that is the smaller number is given by:
By dividing eq (i) by 2 from both sides.
y = x/2
The other number is equal to x/2
Hence, The other number is equal to x/2
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Carmen went for a drive in her new car. She drove 437.5 miles in 7 hours. What was her speed?
Please help!!!!
Answer:
62.5 miles per hour
Step-by-step explanation:
Assuming she had the same speed the whole time and never stopped, just divide the miles driven by the time to get miles per hour. 437.5/7 = 62.5, so she drove 62.5 miles per hour.
Hopefully this helps- let me know if you have any questions!
Jin's family took a road trip to Niagara Falls. Jin slept for the last 24 miles of the trip. If the total length of the trip was 400 miles, what percentage of the total trip had they travelled when Jin fell asleep?
Answer:
94%
Step-by-step explanation:
400-24=376
Find 376 out of 400 as a decimal:
376/400 = 0.94
0.94x100 = 94%
1. What number, when substituted for x in the following problem, will make the problem true?
6X + 8% = 107
Answer:
x = 17.82
Step-by-step explanation:
6x + 8% = 107
-8% -8%
or
107 - 0.08 = 106.92
-----------------------------------
6x = 106.92
÷6 ÷6
x = 17.82
------------------------------------
I hope this helps!
90 pounds =. Ounces
I need help
Answer:
1440 ounces
Step-by-step explanation:
there are 16 ounces in a pound so multiply 90 by 16 and you get 1440 hope this helps!
PLEASE helpppppppp!!!!!!
Answer:
the correct answer is the second
Help find tqs I’ll give brainlist
Answer:
91 degrees
Step-by-step explanation:
Angle RT = 46 degrees
Angle RU = 180 degrees
Angle RS = 89 degrees
So 46 + 89 = 135
180 - 135 = 45
So Angle UT = 45 degrees
Which means that Angle QR = 45 degrees also because they are vertical from each other
So you add 45 + 46 = 91
Angle TQS = 91 degrees