The value of tan(x) is [tex]-\frac{\sqrt{91}}{3}[/tex] if cos(x) = -3/10 and the angle is in the second quadrant i.e. quadrant II
How to determine the value of tan(x)?The expression is given as:
cos(x) = -3/10
Using the following trigonometry identity:
sin²(x) + cos²(x) = 1
The equation become
sin²(x) + (-3/10)² = 1
Evaluate the exponent
sin²(x) + 9/100 = 1
Subtract 9/100 from both sides
sin²(x) = 91/100
Take the square root of both sides
[tex]\sin(x) = \frac{\sqrt{91}}{10}[/tex]
Sine is positive in quadrant II.
So, the tangent is calculated using:
[tex]\tan(x) = \sin(x) \div \cos(x)[/tex]
This gives
[tex]\tan(x) = \frac{\sqrt{91}}{10} \div -\frac{3}{10}[/tex]
Evaluate
[tex]\tan(x) = -\frac{\sqrt{91}}{3}[/tex]
Hence, the value of tan(x) is [tex]-\frac{\sqrt{91}}{3}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/11967894
#SPJ1
It is believed that the best angle to fly a kite is 30 degrees. If you fly a kite at this angle and let out 200 feet of string, approximately how high above the ground will the kite be?
Answer:
200 feet of the ground at a thirty degrees angle does not make a difference .
u need to know whether it is the top or bottom of it, the kite
how do i do this?????
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve for x and y ~
Since the given triangle is a right angled triangle, we can use Trigonometric ratios here to get the required values
[tex]\qquad \sf \dashrightarrow \: \tan(45 \degree) = \dfrac{y}{2 \sqrt{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: 1= \dfrac{y}{2 \sqrt{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \:y = 2 \sqrt{2} \: \: units[/tex]
Now, let's get to x ~
[tex]\qquad \sf \dashrightarrow \: \sin(45 \degree) = \dfrac{y}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{ \sqrt{2} } = \dfrac{2 \sqrt{2} }{x} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 2 \sqrt{2}{} \times \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 2 \times 2[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 4 \: \: units[/tex]
I hope you understood the whole procedure ~
help 30 points for all ansers
The answers to the problem are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles.
c) ∠BST and ∠RSB are complementary angles.
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY.
Types of AnglesAngles are formed when two lines meet and they are of different types.
acute: this is an angle less than 90°
obtuse: this angle is greater than 90° but less than 180°
reflex: this angle is greater than 180° but less than 360°
Analysis:
∠BRS = 180 - (20X - 22) = 202 - 20X
a) To find x, sum of angles in the triangle = 202-20x + 2x+32 + 5x+10 + 120-10x = 180
364 -23x = 180
23x = 364-180
23x = 184
x = 8
b) ∠ZRB = 20x-22 = 20(8) - 22 = 138°
∠BTS = 2x+32 = 2(8)+32 = 48°
138°+48° = 186° [tex]\neq[/tex] 180°
They are not supplementary
c) ∠BST = 120-10X = 120 - 10(8) = 40°
∠RSB = 5x+10 = 5(8)+10 = 50°
50+40 = 90°. They are complementary
d) ∠ABT = 180 - ∠ABR = 180 - 100 - x = 88°
It is acute since it is less than 90°
e) SA is not an angle bisector, since it dived the angles as 40° and 50° and not equal.
In conclusion, the solution to the questions are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles
c) ∠BST and ∠RSB are complementary angles
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY
Learn more about angles: brainly.com/question/25716982
#SPJ1
What is the solution to the linear equation? 6k 10. 5 = 3k 12 k = 0. 5 k = 2 k = 7. 3 k = 9.
The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.
What is Linear Equation?Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.
Here, 6k + 10.5 = 3k + 12
6k - 3k = 12 - 10.5
3k = 1.5
k = 1.5/3
k = 1/2
Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.
Learn more about Linear Equation from:
https://brainly.com/question/11897796
#SPJ1
Please help me please help me
Solve the following equations for x.
A. 7(x)^3=243
B. 5(x)^4+7=42
The values of x given the following expression are ∛243/7 and 7^1/4
Indices expressionGiven the following expression
7x³ =243
x³ = 243/7
x = ∛243/7
For the expression
5x⁴ + 7 = 42
5x⁴ = 42 - 7
5x⁴ = 35
x⁴ = 7
x = 7^1/4
Hence the values of x given the following expression are ∛243/7 and 7^1/4
Learn more on indices here: https://brainly.com/question/8952483
#SPJ1
I have no clue, I have asked others and they don't know either.
To find the point of symmetry:
⇒ must find where the distance between the original point and the
line of symmetry and reflected point and the line of symmetry are
equally distant from each other
Based on that knowledge:
⇒ the image appears to be entirely reflected horizontally
⇒ when the line of symmetry is the y-axis
⇒ A, A' equal distant from line of symmetry
⇒ B, B' equal distant from line of symmetry
⇒ C, C' equal distant from line of symmetry
Answer: y- axis
Hope that helps!
help! Solve each triangle (find all missing sides and angles) Round each answers to the nearest tenth
Answer:
D.
Step-by-step explanation:
sin 67 = b / 2.4
b = 2.4 sin 67
= 2.2
cos 67 = a / 2.4
a = 2.4 cos 67
= 0.9
M < A = 90-67 = 23 degrees.
8 ft
6 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate i.
A = [? ] ft2
Answer:
49.12 ft squared
Step-by-step explanation:
1/2(6*8) = 24
1/2(16)pi = 8pi = 25.12
total: 49.12
Find the number that belongs
in the green box.
4
? 1°
29°
10
Round your answer to the nearest tenth.
Answer:
16.6°
Step-by-step explanation:
The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.
__
We choose to use a=10, b=4, C=29°.
c² = a² +b² -2ab·cos(C) . . . . . law of cosines
c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304
c ≈ √46.0304 ≈ 6.78457
Then angle B (opposite side b) is ...
sin(B)/b = sin(C)/c . . . . . . . . . law of sines
sin(B)/4 = sin(29°)/6.78457
B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°
The missing acute angle is about 16.6°.
Find the area of the rhombus
[tex]60cm^{2}[/tex]
Step-by-step explanation:
A=pq/2
shorter diagonal= 8cm
longer diagonal = 15cm
15*8 = 120
120/2 = 60
A = [tex]60cm^{2}[/tex]
What is the quotient? startfraction n 3 over 2 n minus 6 endfraction divided by startfraction n 3 over 3 n minus 9 endfraction
The quotient of the fraction n³ / (2n - 6) ÷ n³ / (3n - 9) is 2/3
How to solve fractionn³ / (2n - 6) ÷ n³ / (3n - 9)
multiply by the reciprocal of n³ / (3n - 9)= n³ / (2n - 6) × 1 / n³ / (3n - 9)
= 2n - 6 / 3n - 9
= 2(n - 3) / 3(n - 3)
= 2/3
Therefore, quotient of the fraction n³ / (2n - 6) ÷ n³ / (3n - 9) is 2/3
Learn more about fraction:
https://brainly.com/question/1622425
#SPJ5
Answer:
2/3
Step-by-step explanation:
HELP!!! Simplify the expression.
3√25t²
Answer:
15t
Step-by-step explanation:
if you do the sqrt of 25 you get five than multiply that by 3 to get 15 then do the sqrt of t to get t
Hope this helps! ;-)
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
4 people are going to a dinner party. Each person at the party will eat 5/6 pound of salad but you can only buy in pounds.If you can only buy whole pounds of salad, how many pounds should you buy?
Can someone help me with this please thank you.
Answer:
1) 104
2) 132
3) 110
4) 112
5) 105
Step-by-step explanation:
These questions involve the sum of interior and exterior angles.
for the first 4 questions,
Use the formula: (n-2)*180-(sum of remaining angles)
For example q1, it has 4 angles
So substitute 4 into n
(4-2)*180=360
64+99+93+x=360
x=104°
(Do the same for q2-4)
For q5,
Sum of exterior angles of ANY polygon=360°
Therefore,
88+75+92+x=360
x=105°
Pls double check the answers yourself with a calculator, hope you find it helpful! :)
25(-7)= ?
what type of equation is this?? division, multiplication, addition, or subtraction??
Answer:
multiplication
Step-by-step explanation:
the () means to multipy
please help! the questions are in the photo.
What is the Volume! ~
Answer:
108
Step-by-step explanation:
Volume of a Square Pyramid :
V = 1/3 x Base Area x HeightSolving :
V = 1/3 x (6)² x 9V = 36 x 3V = 108 cubic centimetersAnswer: Volume = 108 cm ³
Explanation:
For a square pyramid, the volume can be calculated as follows:
Volume = * area of base * height
Volume = * side² * height
We have:
side length = 6 cm
height = 9 cm
Therefore:
Volume = * 36 * 9 = 108 cm ³
Hope this helps :)
Aldo is a software salesperson. His base salary is $2500 and he makes $80 more for every copy of English is Fun he sells. His total pay, p (in dollars), after selling c copies is given by the following.
p=80c+2500
Answer the following questions.
(a)
If Aldo's total pay is $5140, how many copies did he sell?
? copies
(b)
What is Aldo's total pay if he sells 23 copies?
$
Answer:
A: He sold 33 copies
B: $4340
Step-by-step explanation:
A: p=80(33) + 2500
p=2640+ 2500
p=5140
B: p = 80(23) + 2500
p=1840+ 2500
p=4340
[tex] \sf \pink{guide \: questions}[/tex]
1. What is the average grade of Brenda in Mathematics?
2.What happened to Brenda during the second quarter?
Nonsense=auto banned/auto reported
Correct/not Nonsense=brainliest
Answer:
See below ~
Step-by-step explanation:
1. The average grade of Brenda :
sum of grades in all quarters / 486 + 82 + 84 + 88 / 4340/4852. During the second quarter, Brenda scored her lowest grade, which was an 82.
The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:
The title of the graph is Tennis Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 2 and 1, 5 and 2, 8 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 16 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 3.3 and 2, 6.8 and 4, 10 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
Part A
y-intercept: 3
It represents that after 0 months practice, the number of matches won is 3.
Part B
slope intercept form: y = mx + b
Here to find slope,
take two points: (5, 12), (0, 3)
[tex]\sf slope: \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{rise}{run}[/tex]
[tex]\rightarrow \sf slope = \dfrac{3-12}{0-5} = 1.8[/tex]
Equation:
y - y1 = m(x- x1)
y - 12 = 1.8(x - 5)
y = 1.8x - 9 + 12
y = 1.8x + 3
To find Matches won after 13 months
insert x = 13
y = 1.8(13) + 3
y = 26.4 ≈ 26 matches
The team could have won 26 matches after 13 months practice.
Answer:
See below ~
Step-by-step explanation:
Part A :
The approximate y-intercept of the line is about (0, 3)This represents that with 0 months of practice, 3 matches are wonPart B :
Finding the slopeTake two points on the line : (0, 3) and (5, 12)m = y₂ - y₁ / x₂ - x₁m = 12 - 3 / 5 - 0m = 9/5m = 1.8 (slope)Forming the equation :
y = mx + b (where m is the slope and b is the y-intercept)y = 1.8x + 3Predicting how many matches can be won with 13 months of practice :
Here, x (number of months) = 13y = 1.8(13) + 3y = 23.4 + 3y = 26.4y = 26 matches (roughly)HELPPPP THIS IS 7TH GRADE MATH AND IM CONFUSED (it’s the Jessica one btw)
40 POINTS!!!
Find the volume of this irregular figure.
Hint: Find the volume of the whole rectangular prism, then subtract the volume of the missing piece, which is also a rectangular prism.
Answer:
470 cm³
Step-by-step explanation:
Volume of rectangular prism = width × length × height
⇒ Volume of whole rectangular prism = 9 cm × 10 cm × 8 cm
= 720 cm³
Side lengths of the missing piece:
width = 5 cmlength = 10 cmheight = 8 cm - 3 cm = 5 cm⇒ Volume of the missing piece = 5 cm × 10 cm × 5 cm
= 250 cm³
⇒ Volume of irregular figure = 720 cm³ - 250 cm³
= 470 cm³
I need help with this math question please!
Answer:
x < 0
( x is less than 0 )
Explaination:
That open circle point means the answer will not be equal to, which would be options including <(less than) or >(greater than).
If the circle was closed you would use these symbols, ≤(less than or equal to) and ≥(greater than or equal to)
The open circle lands on 0 and the arrow points to the left into the negative numbers. The answer should be x<0 or x is less than 0.
A way to help remember less than vs greater than on a line like this is that the arrow points in the same direction as the symbol! For example, your question shows an arrow going to the left, and the symbol used for it is less than (<) which also looks like a left pointing arrow.
Hope this helps out! :D
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the
students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter
of his or her name, answer each of the following questions.
What is P(A), the probability that the first student is a girl?
What is P(B), the probability that the second student is a girl?
What is P(A and B), the probability that the first student is a girl and the second student is a girl?
Answer:
what is P(A), the probability that the first student is a boy? 3/5
what is P(B), the probability that the second student is a girl? 3/4
what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2
No, évents A and B are not independent events
Step-by-step explanation:
The probability that the first student is a girl P(A)= 3/4.
The probability that the second student is a girl P(B)= 3/4.
The probability that the first student is a girl and the second student is a girl P(A and B)=9/16.
Given that there are three girls (Sandra, Marta, Jane) and one boy (Franklin), and the sample space of possible outcomes is:
{SA, SM, SJ, SF, MA, MS, MJ, MF, JA, JS, JM, JF, FA, FS, FM, FJ}
P(A): Probability that the first student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the first student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A) = Number of favorable outcomes / Total outcomes = 3 / 4
P(B):
Probability that the second student is a girl (Sandra, Marta, or Jane).
Number of favorable outcomes where the second student is a girl: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(B) = Number of favorable outcomes / Total outcomes = 3 / 4
P(A and B):
Probability that the first student is a girl and the second student is a girl.
Number of favorable outcomes where both students are girls: 3 (Sandra, Marta, Jane)
Total outcomes: 4 (total number of students)
P(A and B) = P(A).P(B)
= 3/4 × 3/4
=9/16
Hence, P(A)=3/4
P(B)=3/4
P(A and B)=9/16
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ3
This figure shows the dimensions of an A frame house.
What is the volume of the house?
Enter your answer in the box.
V =
ft³
Find the area of the trapezoid
Answer:
A = 7.5 units^2
Step-by-step explanation:
A = (a+b)/2 * h
A and B are both bases of the trapezoid (top and bottom)
H is the height
A is 1
B is 4
H is 3
Plug that into the trapezoid equation and we get
(1+4)/2 * 3 = 7.5 units ^2
16.38 divided by 0.06
Answer:
273
Step-by-step explanation:
Answer: 273
Step-by-step explanation: when you divide 16.38 by 0.06 you get 273.
Which function can be used to model the graphed geometric sequence? f(x 1) = five-sixthsf(x) f(x 1) = six-fifthsf(x) f(x 1) = five-sixths superscript f (x) f(x 1) = six-fifths superscript f (x)
The function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
Exponential functionsThe standard exponential function is expressed as y = ab^x
Using the coordinates (3, 900) and (4, 750)
Create the equations
900 = ab^3 ............. 1
750 = ab^4 ................. 2
Divide
900/750 = 1/b
b = 75/90
b = 5/6
Determine the value of "a"
900 = a(5/6)^3
900 = (125/216)a
a = 1555.2
Determine the required equation
y = 1555.2(5/6)^x
Hence the function that can be used to model the graphed geometric sequence is y = 1555.2(5/6)^x
Learn more on exponential function here: https://brainly.com/question/12940982
#SPJ4
Answer:
a
Step-by-step explanation:
