Answer:
x = 4; y = 3; z = 2
Step-by-step explanation:
3x + 2y + z = 20
x - 4y - z = -10
2x + y + 2z = 15
6x + 4y + 2z = 40
x - 4y - z = -10
-------------------------
7x + z = 30
x - 4y - z = -10
8x + 4y + 8z = 60
----------------------------
9x + 7z = 50
z = 30 - 7x
9x + 7(30 - 7x) = 50
9x + 210 - 49x = 50
-40x = -160
x = 4
z = 30 - 7(4)
z = 2
2x + y + 2z = 15
2(4) + y + 2(2) = 15
y = 3
x = 4; y = 3; z = 2
BRAINLIEST!! HELP! 30 POINTS!
Let theta equal 17pi/12
Part A: Determine tan θ using the sum formula. Show all necessary work in the calculation. (5 points)
Part B: Determine cos θ using the difference formula. Show all necessary work in the calculation. (5 points)
The tan θ and cos θ values of 17π/12 are illustrations of trigonometry ratios
The values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively
Part A: tan θ using the sum formulaWe have:
θ = 17π/12
Express as sum
θ = 9π/12 + 8π/12
Simplify
θ = 3π/4 + 2π/3
The above becomes
tan(17π/12) = tan(3π/4 + 2π/3)
Using the sum formula, we have:
tan(A + B) = [tan(A) + tan(B)]/[1 - tan(A)tan(B)]
Substitute known values
tan(3π/4 + 2π/3) = [tan(3π/4) + tan(2π/3)]/[1 - tan(3π/4)tan(2π/3)]
Evaluate the expression
tan(3π/4 + 2π/3) = [-1 - √3]/[1 - (-1)(-√3)]
Evaluate the product
tan(3π/4 + 2π/3) = [-1 - √3]/[1 - √3]
Rationalize
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-1 - \sqrt3}{1 - \sqrt3} * \frac{1 + \sqrt3}{1 + \sqrt3}[/tex]
Evaluate the product
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + \sqrt3)^2}{1 - 3}[/tex]
This gives
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + 3 + 2\sqrt 3)}{-2}[/tex]
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(4 + 2\sqrt 3)}{-2}[/tex]
Divide
[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = 2 + \sqrt 3[/tex]
So, we have:
tan(17π/12) = 2 + √3
Part B: cos θ using the difference formula.We have:
θ = 17π/12
Express as difference
θ = 9π/4 - 5π/6
The above becomes
cos(17π/12) = cos(9π/4 - 5π/6)
Using the difference formula, we have:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
So, we have
cos(17π/12) = cos(9π/4)cos(5π/6) + sin(9π/4)sin(5π/6)
Evaluate
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} * - \frac{\sqrt 3}{2} + \frac{\sqrt 2}{2} * \frac 12[/tex]
Evaluate
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (- \frac{\sqrt 3}{2} + \frac 12)[/tex]
Evaluate the difference
[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (\frac{1 - \sqrt 3}{2})[/tex]
Expand
cos(17π/12) = (√2 - √6)/4
Hence, the values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively
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Given the quadrilateral below, What is the value of x?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
According to angle sum property of a quadrilateral, Sum of all angles of a quadrilateral measures 360°
So, let's solve for x ~
[tex]\qquad \tt \dashrightarrow \:68 + 126 + 106 + x = 360[/tex]
[tex]\qquad \tt \dashrightarrow \:300+ x = 360[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 360 - 300[/tex]
[tex]\qquad \tt \dashrightarrow \:x = 60 \degree[/tex]
Given f(x) = x2 + 1 and g(x) = |x + 31| which value of x is a
solution to the equation f(x) = g(x)?
Answer:
the answer is 30..........
Factor the expression. x2 – 10xy + 24y2
A) (x – 6y)(x – 4y)
B)(x + 6y)(x + 4y)
C)(x + 2y)(x – 12y)
D) (x – 2y)(x + 12y)
I need help.... Could someone please help me
furthering dendritic untiring s very crushed iridium rushes Rivendell ft Zarathustra
Simplify the expression
Step-by-step explanation:
for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.
you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).
(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =
= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =
= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =
= 2c / (8ab²f²) = c / (4ab²f²)
PLEASE HELP FOR BRAINLIEST, I'M DOING A TESTTT.
Find the area of the triangle below.
Be sure to include the CORRECT UNIT in your answer.
Answer:
the answer is 60 yards for the triangle
Use the distributive property to remove the parentheses.
7w3(2w5+9w)
Simplify your answer as much as possible.
Ó
Х
Х
5
?
Answer:
14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]
Step-by-step explanation:
7w³ (2[tex]w^{5}[/tex] + 9w) ← multiply each term in the parenthesis by 7w³
= 14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]
[ using rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ]
Answer:
7w⁴ (2w⁴ + 9)
Step-by-step explanation:
Given
7w³ (2w⁵ + 9w)Let's simplify.
Using the distributive property, 7w³ is distributed to 2w⁵ and 9w7w³ * 2w⁵ + 7w³ * 9w14w⁸ + 63w⁴The common factor of the two terms is : 7w⁴⇒ 7w⁴ (2w⁴ + 9)Suppose that you have been hired at an annual salary of $16,000 and expect to receive annual increase of 3%. What will your salary be when you begin your sixth year?
well, at the beginning of the 6th year, you've been there for 5 whole years, so you've gotten 5 increases hmmm
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=16000(1 + 0.03)^{5}\implies A=16000(1.03)^5\implies A\approx 18548.39[/tex]
please help me will give brainliest. look at attachment
Answer:
The correct answer is Choice C.
Step-by-step explanation:
I drew a diagram of all the triangles to compare the statements given to each other
I marked the triangle sides with lines to show congruency in length.
One line for AB = DF
Two lines for AB = GI
Three lines for BC = HI
Four lines for DE = HI
The angles are all marked for the last sentence we are given.
The first and third triangles are the only ones similar. This is because of SAS congruence as given in the Diagram. AB = GI, angle B = angle I, BC = IH
The second triangle is different from the rest, and even if we tried to rotate it ad compare it, it would still be wrong.
5x+4y=-14 3x+6y=6
Linear Combination Method
Answer:
8x+10y=-8
Step-by-step explanation:
5x+3x=8x
4y+6y=10y
-14+6=-8
HELP PLS HJJHHHJJHH
Answer:
See below ↓↓
Step-by-step explanation:
Important facts given [needed to solve]
Time period = 3 yearsLoan amount = $5000Interest rate = 8% (semi-annually - twice a year)Monthly payment = $156.68Solving :
Total amount to be repaid = Monthly payment x 3 years= Monthly payment x 3 x 12 months= $156.68 x 36= $5640.48 (a)Interest paid
Total amount repaid - Initial loan amount= 5640.48 - 5000= $640.48 (b)Find the distance between the two points in simplest radical form.
(-1,-1) and (5,-9)
[tex]\sqrt{ { (x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ = \sqrt{( {5 - ( - 1)}^{2} + {( - 9 - ( - 1)}^{2} )} \\ \\ = \sqrt{ {(5 + 1)}^{2} + {( - 9 + 1)}^{2} } \\ \\ = \sqrt{ {(6)}^{2} + {( - 8)}^{2} } \\ \\ = \sqrt{36 + 64} \\ \\ = \sqrt{100} \\ \\ = 10 \: units[/tex]
Hope it helpswhat the answer to this?
Answer:
1/5
Step-by-step explanation:
jack + 4 friends = 5 people
5 people would each get 1 slice
Which of the following is not a kind of consumer credit?
a. installment credit
b. personal loans
A
C. service credit
d.
marginal credit
Please select the best answer from the choices provided
OA
OB
OC
OD
Mark this and return
Save and Exit
Next
Submit
Answer:
D. marginal credit is right one
HELP PLEASE PYTHAGOREOM THEOREM
Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex]
Since 10 and 24 are the legs, "x" has to be the hypoteneuse. "a" and "b" are the legs (10 and 24).
Now, replace the values in.
[tex]10^2+24^2 = x^2[/tex]
[tex]x^2 = 100+576\\x^2 = 676\\x = 26[/tex]
Hope this helped! :)
Which point would be a solution to the system of linear inequalities shown below?
Answer: (-4, -6)
Step-by-step explanation:
Solving by graphing
[] See attached
() The only point in the required range is point (-4, -6)
Solving by plugging-in
I will figure out what the correct option is by plug them into the first equation. Since only one of these options is true, I do not need to do the second equation.
[✗] Let's check point (4, 10)
() 10 < (1/4)4 - 4
10 < 1 - 4
10 < -3 is false, so this answer is incorrect
[✗] Let's check point (-4, 5)
() 5 < (1/4)-4 - 4
5 < -1 -4
5 < -5 is false, so this answer is incorrect
[✗] Let's check point (-4, -4)
() -4 < (1/4)-4 - 4
-4 < -1 -4
-4 < -5 is false, so this answer is incorrect
[✓] Let's check point (-4, -6)
() -6 < (1/4)-4 - 4
-6 < -1 - 4
-6 < -5 is true, so this answer is correct
Use calculus to find the volume of the following solid S:
The base of S is the parabolic region {(x,y)|x^2≤y≤1}. Cross-sections perpendicular to the y-axis are squares.
S casts a "shadow" on the x-y plane given by the set
[tex]S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}[/tex]
Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².
The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is
[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx[/tex]
The integrand is even, so this integral is equal to twice the integral over [0, 1] :
[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}[/tex]
a+b-__=a whats the blank and whats a and b
Answer:
-c is the blank and a+b is variables of real numbers.
Step-by-step explanation:
A real number is a value of a continuous quantity that can represent a distance.
However equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
When rounded to the ten thousands place, which of the
numbers below round to 110,000? Select all that apply.
A) 113,450
B) 95,678
C) 104,298
D) 94,560
E) 106,789
Answer:
e
Step-by-step explanation:
Answer:
a, e
Step-by-step explanation:
a would round to 110,000 because 113,450 rounded to the ten thousand round down to 110,000
95,678 would round up to 100,000 not 110,000
104,298 would round down to 100,000 not 110,000
94,560 would round down to 90,000
106,789 would round up to 110,000 because 6 rounds up because 5 and up is rounded up
8 points
Find the measure of the arc or
angle indicated. Assume that
lines which appear tangent are
tangent. *
O 56
O 45
O 52
O 65
Answer:
C. 52Step-by-step explanation:
The angle formed by two secants is half the difference of intercepted arcs.
55 = 1/2(162 - x)162 - x = 55*2x = 162 - 110x = 52Correct choice is C
Let that be y
2(55)=162-x110=162-xx=162-110x=52°Option C
4. There are two numbers that add together and the result is 63. If you subtract the same number together, the result is 28.
a) Create two equations from the statement above. Make sure to specify what each variable means.
b) Solve the system of equations by Elimination.
Answer:
45.5 and 17.5
Step-by-step explanation:
a)
Let Number 1 be X and Number 2 be YX + Y = 63X - Y = 28b)
From adding 1. and 2. ,2X = 91X = 45.5Y = 63 - 45.5 = 17.5Ken drinks 730 bottles of soda a year.
How much does he drink a day.
A 12
B 4
C 2
D 5
Lesley has 180 y marbles in a bag. She gave 2/5 of the marbles to Danny. How many marbles does Lesley have left?
sheri caught twice as many fireflies as robert. jessica caught 10 more flies than robert all together they caught 150 flies. how many flies did jessica catch?
Answer:
45 fireflies
Step-by-step explanation:
Because,
Sheri caught 70 and Robert caught 35.
150-35-70= 35
35+10 is equal to 45.
Following the rules given is the right answer
Question 2 I need help
Thank youuu
Answer:
Pls help me with my questions
Step-by-step explanation:
Which decimal is greater: 4.58 or 4.5?
Answer
Since 3 is greater than 0 we know that 7.835 is greater than 7.8. We follow the same process to find that 7.35 is less than 7.358. Then we can put the number
There you go I hope that helps and have a great day
Find the axis of symmetry and the vertex of the graph of y=3x^2+2x
Answer:
Vertex is (-1/3, -1/3) and the axis of symmetry is x = -1/3
Hope this helps :)
A data set is normally distributed with a mean of 63 and a standard deviation of 10.4.
What percentage of the data is between 45 and 77?
Enter your answer as a number to the nearest whole percentage, like this: 42%
Answer:
87%
Step-by-step explanation:
The percentage of normally-distributed data between 45 and 77 in a data set with mean 63 and standard deviation 10.4 can be found by any of a number of calculators, apps, web sites, or spreadsheets.
The percentage is 87%.
Julia has 2 chemistry books and 3 math books. In her rush to get to class, she grabs two books without stopping to look. What is the probability that she pulls out a math book and a chemistry book?
Answer:
P(M &C) = 0.24
Step-by-step explanation:
Chemistry book will be denoted by C
Mathematics book will be denoted by M
5C2 = 10
There are 10 possible ways in which she can choose two books from the 5 books.
The probability of choosing a chemistry book:
P(C) = 2/5
The probability of choosing a mathematics book:
P(M) = 3/5
Probability of choosing a chemistry book and a mathematics book:
P(M &C) = (2/5) × (3/5)
P(M &C) = 0.24 or 24%
The probability that she pulls out a math book and a chemistry book will be 0.24.
What is mean by Probability?The term probability refers to the likelihood of an event occurring
Given that;
Julia has 2 chemistry books and 3 math books.
Now,
Since, Julia has 2 chemistry books and 3 math books.
Hence, Total number of books = 2 + 3 = 5
So, The probability to choosing a chemistry book = 2/5
And, The probability to choosing a math book = 3/5
Thus, The probability that she pulls out a math book and a chemistry book is,
⇒ 2/5 × 3/5
⇒ 6/25
⇒ 0.24
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