The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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4. a) State the Routh stability Criterion [3.5 marks] b) The characteristic equation for a certain feedback control system is given as s4+3s3+3s2+s+K=0, determine the range of values of K, for which the system is stable.
Please help! Easy question, answer pls, 15 pts.
Answer:
360 in
Step-by-step explanation:
To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:
\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)
So, the dressmaker has 360 in of ribbon.
Express 80 as the product of its prime factors
Write the prime factors in ascending order.
Answer:
Give brainliest - the crown thingy.
2*2*2*2*5
Or
2^4 * 5
The * is the symbol on my keyboard for the multiplication symbol.
Step-by-step explanation:
What are the coefficients for the binomial expansion of (a + b)^3?
Answer:
coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively. (required coefficient)
Step-by-step explanation:
What are the domain restrictions of q^2−7q−8 divided by q^2+3q−4 ?
o q≠1 and q≠−8
o q≠−1 and q≠8
o q≠−1 and q≠4
o q≠1 and q≠−4
The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)
The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:
q² + 3q - 4 = 0
Now, we can factorize the quadratic equation:
(q + 4)(q - 1) = 0
To find the values of q, we set each factor equal to zero and solve for q:
q + 4 = 0 or q - 1 = 0
Solving these equations, we get:
q = -4 or q = 1
So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.
Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.
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Complete Question:
What are the domain restrictions of q²−7q−8/q²+3q−4?
a) q≠1 and q≠−8
b) q≠−1 and q≠4
c) q≠1 and q≠−4
d) q≠−1 and q≠8
Line AB is perpendicular to line CB.
A(2,3), B(5,7) C(x,8)
What is the value of x to make this statement true?
Answer:
Step-by-step explanation:Hly/3fcEdSxere's li\(^{}\)nk to the answer:
bit.\(^{}\)
Answer:
a 2 and 3 step by step exolaniation
Given G = 1 / 2(F - 30), find the value of F
if G = 10
Answer:
50
Step-by-step explanation:
10 = (F - 30)/2
20 = F - 30
50 = F
Translate the following arguments into symbolic form. Then determine whether each is valid or invalid by constructing a truth table for each.
Brazil has a huge foreign debt. Therefore, either Brazil or Argentina has a huge foreign debt.
Let's translate the argument into symbolic form using the following symbols:
B: Brazil has a huge foreign debt.
A: Argentina has a huge foreign debt.
The argument can be represented as follows:
B → (B ∨ A)
To determine the validity of the argument, we can construct a truth table for the expression (B → (B ∨ A)). The truth table will include all possible combinations of truth values for B and A, and we will evaluate the truth value of the entire expression for each combination.
The truth table for the argument is as follows:
B A B ∨ A B → (B ∨ A)
T T T T
T F T T
F T T T
F F F T
As we can see from the truth table, regardless of the truth values of B and A, the expression B → (B ∨ A) always evaluates to true. Therefore, the argument is valid because the conclusion is always true when the premise is true.
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Sammy wants to deposit into a 7% annual simple interest account she will also deposit twice as much in a certificate of deposit earning 5% annual simple interest to earn $390 of annual interest how much should she invest in each account?
Answer: $2294 should be invested in the simple interest account while $4588 should be invested in the certificate of deposit.
Step-by-step explanation:
Let x represent the amount that he would deposit in the simple interest account.
Let y represent the amount that he would deposit in the certificate of deposit.
she will deposit twice as much in the certificate of deposit. It means that
y = 2x
Interest from the simple interest account would be 7%. This mean that the interest would be 7/100 × x = $0.07x
Interest from the certificate of deposit account would be 5%. This mean that the interest would be 5/100 × y = $0.05y.
The total interest from both accounts would be $390. It means that
0.07x + 0.05y = 390- - - - - - - - - - 1
Substituting y = 2x into equation 1, it becomes
0.07x + 0.05 × 2x = 390
0.07x + 0.1x = 390
0.17x = 390
x = 390/0.17 = $2294
y = 2x = 2 × 2294
y = 4588
I need help with this solving equations X + 9 = -16
Answer:
Step-by-step explanation:
x + 9 = -16
Subtract 9 form both sides
x + 9 - 9 = - 16 - 9
x = -25
Answer:
X= -25
Step-by-step explanation:
Subtract 9 from both sides.
Find the measures of the complementary angles that satisfy each case.
The measure of the first angle is 40° less than the measure of the second.
Answer:
25° and 65°
Step-by-step explanation:
1. 65°-25°= 40°
2. 90°-65°=25°
3. 90°-25°=65°
Therefore 25° and 65° fit the criteria, make sure to add the degrees symbol :)
Complementary angles have a sum of 90° thus measure of the first and the second angle is 25° and 65° respectively.
What is an angle?Angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Let's suppose the first angle is x while the second is y.
If two angles have a sum of 90° then they will be called as complementary angles since x and y are complementary.
x + y = 90
Now given that,
The measure of the first angle is 40° less than the measure of the second.
x = y - 40
x - y = -40
By adding both equations,
(x + y) + (x - y) = 90 + (-40)
2x = 50
x = 25
y = 90 - 25 = 65
Hence "The first and the second angle is 25° and 65° respectively".
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Graph the linear inequality shown below on the provided graph. y>-3x+8
On graphing the inequality , a dotted line and the shaded area is seen which means all the values above that line is included.
What is a Linear Inequality ?When two algebraic expressions are equated using inequality operators < ,> etc , the statement formed is called Linear Inequality.
The inequality given is
y > - 3x+8
On graphing the inequality , a dotted line and the shaded area is seen which means all the values above that line is included.
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Text? I go to much going on inside of my head..
Answer:
If you need anything just let me know.
Step-by-step explanation:
Hope you have a good day.
the function g(x) is a transformation of the quadratic parent function, f(x)=x2. what function is g(x)? (from apex)
Answer:
To create function m, 5 was added to the parent function f. Adding a constant to the parent function translates it up. So, function f was translated 5 units up to create function m.
Step-by-step explanation:
PLEEEASE HELP! TEST TMRW AND I MIGHT FAIL.
Help!!!! What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.
The area of the figure is
Choose...cm².
Answer:
153
Step-by-step explanation:
You need to find the area of the triangle first which is 63. The you want to find the area of the trapezoid which is 90. Then add them together.
a) Calculate the size of angle x in the diagram
below.
b) Work out the bearing of A from B.
The angle x in the diagram is 98 degrees.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.
Therefore, let's find the angle of x using the angle relationships as follows:
The size of the angle x can be found as follows:
82 + x = 180(same side interior angles)
Same side interior angles are supplementary.
Hence,
82 + x = 180
x = 180 - 82
x = 98 degrees
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Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, they require at least 100 sushi pieces.
24 pieces of sushi had previously been ordered and paid for by Sofia.
Roll sushi is available.
Each roll = 12 pieces at $8
R = additional rolls that Sofia orders
Additional sushi = Needed sushi - ordered sushi
=100-24
=76 pieces of sushi
A roll contains 12 pieces.
76/12 = 6.33
Rolls must be ordered by Sofia.
She will therefore place 7 additional sushi rolls, each with 12 pieces.
12*7=84 pieces
Remember that they need at least 100 pieces, so there may be more than 100 in total.
84 pieces plus the 24 pieces Sofia has previously ordered.
The total number of pieces will be 108.
Therefore, using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).
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Complete question:
Sofia ordered sushi for a company meeting. They change plans and increase how many of people
will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8. How many more sushi Sofia will order and of what amount?
5. At a classroom costume party,
the average age of the b boys is
g, and the average age of the g
girls is b. If the average age of
everyone at the party (all these
boys and girls, plus their 42-
year-old teacher) is b+g, what is
the value of b+g?
Answer:
42+b+g
Step-by-step explanation:
42+b+g is the only specific answer because b (boys) and g (girls) are not specified as numbers.
The required simplified value of b + g is 21.
Given that,
At a classroom costume party, the average age of the b-boys is g, and the average age of the g girls is b.
The average age of everyone at the party (all these boys and girls, plus their 42- year-old teacher) is b+g,
The average of the values is the ratio of the total sum of values to the number of values.
Here,
The average age of the b-boys is g.
The average age of the g-girls is b.
The average age of everyone at the party (all these boys and girls, plus their 42-year-old teacher) is b+g,
Now,
average of n = 3 (b , g , b+g)
Average = g + b + 42 / 3
b + g = (b + g + 42 ) / 3
3b + 3g = b + g + 42
3b - b + 3g - g = 42
2b + 2g = 42
2 (b + g) = 42
b + g = 21
Thus, the required simplified value of b + g is 21.
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Order the following from LEAST to GREATEST: 3/5, -1/2, 0.50, -7/10, -0.75 *
Answer:
-0.75, -7/10, -1/2, 0.50, 3/5
Answer:
-0.75, -7/10, -1/2, 0.50, 3/5
Step-by-step explanation:
put all of them as a decimal first
3/5 = 0.6 (5)
-1/2 = -0.50 (3)
0.50 = 0.50 (4)
-7/10 = -0.70 (2)
-0.75 = -0.75 (1)
Topic: Determining if given values are solutions to a two variable equation
Answer:
2. a & c
3. a, b & c
Step-by-step explanation:
Substitute each solutions to the question to see if you get the answer
a. 5(2)-0=10 -- so (2,0) is the solution
b. 5(3)-0=15 -- (3,0) is not the solution
c. 5(0)-(-10)=10 -- (0,-10) is the solution
d. 5(1)-(1)=4 -- (1,1) is not the solution
a. -(-4)+ 6(1) = 10 -- so (-4,1) is the solution
b. -(-22)+ 6(-2) = 10 -- so (-22,-2) is the solution
c. -(2)+ 6(2) = 10 -- so (2,2) is the solution
d. -(10)+ 6(0) = - 10 -- so (10,0) is not the solution
Which is ⁴√81x³y⁴z8 with rational exponents?
(a) 3x(¾)yz²
(b) 8x (¾) yz²
(c) 2x (⅓) yz²
(d) 9x (⅓) yz²
The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²
How to solve Laws of Exponents?The 8 laws of exponents can be listed as follows:
Zero Exponent Law: a^(0) = 1.
Identity Exponent Law: a^(1) = a.
Product Law: a^m × a^n = a^(m+n)
Quotient Law: a^m/a^n = a^(m - n)
Negative Exponents Law: a^(-m) = 1/a^(m)
Power of a Power: (a^m)^n = a^(mn)
Power of a Product: (ab)^m = a^m*b^m
Power of a Quotient: (a/b)^m = a^m/b^m
We are given the algebra expression as:
⁴√81x³y⁴z⁸
This gives us:
81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)
= 3x^(3/4)yz²
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pls help me with this
Answer: A)72.8067226km/hr (final asnwer)
b) volume of a cube= a^3 (sides^3) =4.5^3= 91.125 cm^3 (final asnwer)
c) 1 day cost= $(35.9 +11.55 + 35) =$82.45
therefore for 5 days= $82.45 * (multiplied) by 5 = $412.25 (final asnwer)
Step-by-step explanation:
Answer:
(a)≈72.8 kilometer per hour
(b)91.125 cm^3
(c)272.25$
Step-by-step explanation:
(a)speed=mile/hour
=371mile/8.2hours
=371×1.609kilometers/8.2hours
≈72.8 kilometer per hour
(b)the vol: of cube= a^3 (a=side)
=(4.5)^3
=91.125cm^3
(c) for 5 days, (35.9×5)+(11.55×5)+35 ($35 is ofor one-off charge so there is no need to multiply with 5)
=272.25$
There are n people in a room where n is an integer greater then or equal to 2. Each person shakes hands once with every other person. What is the total number of handshakes in the room
Therefore, according to the given information, the total number of handshakes in the room is n(n-1)/2.
To find the total number of handshakes in the room, we can use the formula n(n-1)/2, where n is the number of people in the room. In this case, since each person shakes hands once with every other person, we can plug in n for the number of people and get n(n-1)/2.
If there are n people in a room, where n is an integer greater than or equal to 2, and each person shakes hands once with every other person, we can use the formula n(n-1)/2 to find the total number of handshakes. This formula calculates the number of unique pairs that can be formed from n individuals. In this case, we plug in n for the number of people and get n(n-1)/2.
Therefore, according to the given information, the total number of handshakes in the room is n(n-1)/2
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translate: the sum of 1 and twice a number f is divided by 3 and then added by 2 is equal to the number f
Answer:
(1+2f)/3 + 2 = f
Step-by-step explanation:
Writing the equation
the sum of 1 and twice a number f
1 + 2f
divided by 3
(1+2f)/3
then added by 2
(1+2f)/3 + 2
is equal to the number f
(1+2f)/3 + 2 = f
Hurry please!
Which linear equation represents the graph?
A) Y= -1/3x + 3
B) y = 3x - 2
C) y= 1/3x + 3
D) y= -3x - 2
Answer:
A
Step-by-step explanation:
scientific research on popular beverages consisted of 65 studies that were fully sponsored by the food industry, and 35 studies that were conducted with no corporate ties. of those that were fully sponsored by the food industry, 13 % of the participants found the products unfavorable, 22 % were neutral, and 65 % found the products favorable. of those that had no industry funding, 36 % found the products unfavorable, 17 % were neutral, and 47 % found the products favorable. what is the probability that a participant selected at random found the products favorable? if a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry? if a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?
To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.
For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:
(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%
If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:
P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)
P(Favorable | Industry-sponsored) = 0.65
P(Industry-sponsored) = 65/100
P(Favorable) = 0.587
P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%
Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:
P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)
P(Unfavorable | No industry funding) = 0.36
P(No industry funding) = 35/100
P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413
P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%
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 please help me i wil give brainliest
Answer:
all of them
Step-by-step explanation:
If x and y are proportional, then it will create a straight (linear) line
Answer:
all of them
Step-by-step explanation:
convert -4 8/25 into a decimal HELP
Answer:
-4.32
Step-by-step explanation:
8/25 is .32
then add that to the end of -4