Answer:
x = 35, y = 26.5
Step-by-step explanation:
x = 35 ( Alternate angles are congruent )
The sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
2y - 10 + 35 + 102 = 180, that is
2y + 127 = 180 ( subtract 127 from both sides )
2y = 53 ( divide both sides by 2 )
y = 26.5
A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
multiply 1 1/4 by 180
Answer:
225
Step-by-step explanation:
1 1/4 can be put into decimal form:
1.25
So the equation would now be
1.25 times 180
use a calculator:
225
Answer: 225
1 1/4 x 180 = 225
ay - b = c solve for y
Answer:
\(Y=\frac{c}{a}-\frac{b}{a}\)
Step-by-step explanation:
Answer:
y=c+b/a (The a is under c+b)
Step-by-step explanation:
Add the b over to c.
ay=c+b
Now divide both sides by a, which will remove the a from y.
y=c+b/a
X 78° у Find the unknown angle measures
Does the system of equations below have no solution, 1 solution, or infinite solutions
= 2 − 1
= 2 + 4
Answer:
no solution
Step-by-step explanation:
y = 2x - 1 → (1)
y = 2x + 4 → (2)
substitute y = 2x - 1 into (2)
2x - 1 = 2x + 4 ( add 1 to both sides )
2x = 2x + 5 ( subtract 2x from both sides )
0 = 5 ← not possible
This indicates the system has no solution
How do I work this out?
Answer:
2×2×2×2×2×2 = 64
Raise 2 to the power of 6.
64
Step-by-step explanation:
Hope it is helpful....
Status
Exam
Convert the function from point-slope
form to slope-intercept form.
y + 3 = -2(x - 1)
y = [? ]x - [
Enter
Answer:
y = -2x - 1
Step-by-step explanation:
y + 3 = -2 ( x - 1 )
y + 3 = -2x + 2
y = -2x - 1
The propositional variables s and m represent the two propositions:
s: It is sunny today.
m: I will bring my umbrella. Select the logical expression that represents the statement: "Despite the fact that it is sunny today, I will bring my umbrella."
(A) s
(B) s∧m
(C) s∨m
The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.
The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.
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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.
To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.
In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.
The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.
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A solid with surface area 50units^2 is dilated by a scale factor of K to obtain a solid surface area 200units^2. Find the value of K.
The value of K is 2.
Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.
We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.
Using the formula for the surface area, we have:
Initial surface area * (scale factor)^2 = Final surface area
50 * K^2 = 200
Dividing both sides of the equation by 50:
K^2 = 200/50
K^2 = 4
Taking the square root of both sides:
K = √4
K = 2
Therefore, the value of K is 2.
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Pls help asap I don’t get these questions
Answer:
The answer is "d"
-3(4x-2)-2x
-12x+6-2x
-12x-2x+6
-14x+6
Hence, the answer is D.
Answer:
The would-be option number D
Step-by-step explanation:
Distribute - 3 through the parentheses
\(-12x+6-2x \\-14+6\)
Which pyramid has a greater volume and how much greater is its volume?
8 in
4 in
.
9 in
6 in.
8 in
10 in
A) The volume of the pyramid on the left is greater by 8 in
B) The volume of the pyramid on the left is greater by 24in.
C) The volume of the pyramid on the right is greater by 8 in.
D) The volume of the pyramid on the right is greater by 24 in
Answer:
A)
Step-by-step explanation:
I did the test and got it correct please mark brainliest. I know it is correct.
solve by factoring 2x^2 + 10x - 28 = 0
Answer:
x = 2, x = -7
Step-by-step explanation:
Hello!
First, let's factor the equation by grouping.
Factor2x² + 10x - 28 = 02(x² + 5x - 14) = 02(x² + 7x - 2x - 14) = 02(x(x + 7) - 2(x + 7)) = 02(x - 2)(x + 7) = 0Set each factor with x equal to 0, and solve for x.
(x - 2) = 0The solutions for x are 2 and -7.
Number 19 and 20 pleaseeeeeeeee
Answer:
19. a) yes; acute triangle
20. a) no, because 4+2<7
Answer:
You did it correct
but last it no
Step-by-step explanation:
bc i said so and i have same book at school
Was wondering how to do this im confused.
A) The equation for a line that passes through the points (8, 2) and (6, 10) is:
y = -4*x + 34
B) line that has a slope of -2 and that passes through the point (-3, 5)
y = -2*x - 1
How to write the linear equations?
A) First we want to find the equation for a line that passes through the points (8, 2) and (6, 10).
Remember that a general linaer equation is of the form:
y = m*x + s
Where m is the slope and s is the y-intercept.
If the line passes through (a, b) and (c, d), then the slope is given by:
m = (d - b)/(c - a)
Then in this case, the slope is:
m =(2 - 10)/(8 - 6) = -8/2 = -4
Replacing that we get:
y = -4*x + s
To find the value of s we use the fact that the line passes through (8, 2), this means that:
2 = -4*8 + s
2 + 32 = s
34 = s
The linear equation is:
y = -4*x + 34
B) Now we want to find a line that has a slope of -2 and that passes through the point (-3, 5)
Here we already know the slope, so we can write:
y = -2*x + s
Again, to find the value of s, we replace the values in the point in the linear equation:
5 = -2*-3 + s
5 = 6 + s
5 - 6 = s = -1
We conclude that this linear equation is:
y = -2*x - 1
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Which expression is not equivalent to
Answer:
B i think I'm kinda sure tho
b
let f(x)=∫x1sin(t)tdt. find the indicated derivative.
The function F(x) has a derivative f'(x) = sin(x) - xcos (x). This is accomplished by employing the chain rule and the basic calculus theorem.
The calculus fundamental theorem can be used to derive the derivative of f(x).
Let x1sin(t)dt equal F(x). The fundamental theorem of calculus states that F'(x) = sin (x).
Let g(x) now equal x. The chain rule then states that f'(x) = g' (x) F'(x)= g'(x)sin(x)=cos (x).
Therefore, f'(x) = sin(x) - xcos is the derivative of f(x) (x).
F(x) has a derivative f'(x) = sin(x) - xcos (x). Applying the chain rule and the calculus's fundamental theorem will get this result. The integrand assessed at the integral's upper limit is equivalent to the derivative of a definite integral, according to the calculus fundamental theorem. According to the chain rule, the derivative of a function made up of two functions is equal to the sum of the derivatives of the inner and outer functions. The inner function in this instance is sin(t), while the outer function is x. Thus, by using the chain rule and the fundamental theorem of calculus, we can determine that f'(x) = sin(x) - xcos (x)
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what is 6.8 percent of 9.95
Answer:
0.6766
Step-by-step explanation:
6.8%*9.95=0.6766
The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 20ln(40t − 1200), where t is measured in years. Find the equation to model the population.
P = 2t + 60
P equals 1 over 40 times e to the power of the quantity five hundredths times t end quantity plus 30 where P 0 equals 30
P equals 1 over 40 times ln of the quantity five hundredths times t end quantity plus 30 where P 0 equals 30
P equals 1 over 800 times e to the power of t plus 30 where P 0 equals 30
The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.An equation is a formula that expresses the equality of two expressions.Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)
where t is measured in years.
We need to find an equation to model the population.
let y = \(p^{-1}\)(t)
where t is measured in years.
We need to find an equation to model the population.
20\(ln\)(40y - 1200) = t
\(ln\)(40y - 1200) = t/20
\(e^{ln(40y - 1200)}\) = \(e^{0.05t}\)
(40y - 1200) = \(e^{0.05t}\)
40y = \(e^{0.05t}\) + 1200
y = \(\frac{1}{40}\) \(e^{0.05t}\) + 30
Now, we determine the initial value.
P(0) = \(\frac{1}{40}\) + 30
P(0) = 30
The equation to model the population is P = \(\frac{1}{40}\) \(e^{0.05t}\) + 30
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CAN ANYONE HELP ME WITH THIS QUICKKKKK!
Step-by-step explanation:
You can mention the main values like N = 50 , Efm= 2640 in the answer box and put the formula for calculating mean Efm/N and simply show the answer. Goodluck
125 is 30% of what number
Answer:
24
Step-by-step explanation:
Answer:
125 is 30% of the number 24, hope this helps
Step-by-step explanation:
We have, 125% × x = 30
or, 125/100 × x = 30
Multiplying both sides by 100 and dividing both sides by 125,
we have x = 30 × 100/125
So your answer is X=24
An inchworm is 1.2 inches long 4 days after hatching. It is 3.5 inches long 11 day after hatching. What is it's average rate of growth in inches
per day?
The average rate of growth is
inches per day. (Round to the nearest hundredth)
Consider the problem of finding a plane αTx=β (i.e. α1x1+α2x2+α3x3+α4x4=β with α=(0,0,0,0)) that separates the following two sets S1 and S2 of points (some points from S1 and S2 might lie on the plane αTx=β) : S1={(1,2,1,−1),(3,1,−3,0),(2,−1,−2,1),(7,−2,−2,−2)}, S2={(1,−2,3,2),(−2,π,2,0),(4,1,2,−π),(1,1,1,1)}. 1.1 Formulate the problem as a linear optimization problem (LO). 3p 1.2 Find a feasible solution (α,β) for (LO) if it exists, or show that no feasible solution exists. 2p
All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.
To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.
1.1 Formulation:
The problem can be formulated as follows:
Minimize: 0 (since it is a feasibility problem)
Subject to:
α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1
α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2
α1, α2, α3, α4 are unrestricted
β is unrestricted
y_i ≥ 0 for all points in S1
z_i ≥ 0 for all points in S2
The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.
1.2 Finding a feasible solution:
To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.
Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.
For S1:
(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible
(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible
(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible
(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible
For S2:
(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible
(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible
(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible
(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible
Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.
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A batch of 150 iPads is inspected by choosing a sample of four iPads. Assume that 8 of the 150 iPads do not conform to specifications. How many samples of four contain exactly one non-conforming iPad
The given statement can be formulated as follows: A batch of 150 iPads is inspected by choosing a sample of four iPads. Eight of the 150 iPads do not conform to specifications.
How many samples of four contain exactly one non-conforming iPad?
Let's solve the given problem step by step.
Step 1: We have 8 non-conforming iPads and 142 conforming iPads in the batch of 150 iPads. We need to find the number of ways to choose 4 iPads that include exactly one non-conforming iPad.
Step 2: We choose one non-conforming iPad in 8 ways and choose 3 conforming iPads in 142C3 ways, where nCk is the number of ways to choose k objects from n distinct objects without regard to order.
Thus the total number of ways to choose 4 iPads with exactly one non-conforming iPad is given by:
=8 × 142C3
\(8 \times \frac{142 \times 141 \times 140}{3 \times 2 \times 1}\)
= 2,107,280
Therefore, there are 2,107,280 samples of four that contain exactly one non-conforming iPad.
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face north. do a 1/4 turn clockwise which way will i be facing
Answer:
You will be facing in a 90 degree angle.
Step-by-step explanation:
Did you mean like on a compass?
Answer:
East
Step-by-step explanation:
Determine the LCM and HCF of 250 and 350
Answer:
Step-by-step explanation:
LCM: 1750
GCD: 50
Clare spent $5.17 on apples. How many pounds of apples did Clare buy?
(round to the nearest tenth)
Answer: complete the question please
Step-by-step explanation:
How much is a pound/lb? Then do 5.17 divided by (however much is a pound/lb)
PLEASE HELP WILL GIVE BRAINLIEST
Find the value of that makes the trinomial, 2 − 23 + , a perfect square. Show your work for full credit
A perfect square trinomial can be written as the square of a binomial. The value of c that makes the trinomial a perfect square is c = 529/8.
To find the value that makes the trinomial 2x^2 - 23x + c a perfect square, we need to determine the value of c.
A perfect square trinomial can be written as the square of a binomial. In this case, we want the trinomial to be the square of a binomial in the form (ax + b)^2.
Expanding (ax + b)^2 using the binomial square formula, we get:
(ax + b)^2 = a^2x^2 + 2abx + b^2
Comparing this with the given trinomial 2x^2 - 23x + c, we can deduce the values of a, b, and c.
From the coefficients of x^2, x, and the constant term:
a^2 = 2, 2ab = -23, and b^2 = c
Solving for a, we find a = √2 or -√2.
Solving for b using 2ab = -23, we find b = -23/(2a).
Since a cannot be determined uniquely, we will use a = √2 for simplicity.
Substituting a = √2 and b = -23/(2a) into b^2 = c, we get:
(-23/(2√2))^2 = c
529/8 = c
Therefore, the value of c that makes the trinomial a perfect square is c = 529/8.
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What is the reason or purpose of solving system of equations?
The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
What is solving system?Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.
There are three methods used to solve systems of equations such as:
GraphingSubstitution EliminationTherefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
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How to solve a polynomial?
To begin solving a polynomial problem, express it in standard form. When it reaches zero, factor it and then set each variable factor to zero. The answers to the resultant equations are the original solutions. Factoring cannot solve all polynomial problems.
Polynomials are sums of terms of the form where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. A primer on polynomials. This video defines words such as degree, standard form, monomial, binomial, and trinomial.
A polynomial may be categorized into four categories based on its degree. There are four types of polynomials: zero polynomial, linear polynomial, quadratic polynomial, and cubic polynomial.
A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.
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How many total cups of orange paint will this mixture yield?
Answer:
At least 6 but are there answer choices or at least a picture of the mixture
~ Zachary