Answer:
m∠2 = 94°
Step-by-step explanation:
m∠3 and m∠2 are vertically opposite angles meaning they have equal angle. They are of equal measure.
Given that m∠3 = 94°, so m∠2 = 94° as well.
Answer:
94°
Step-by-step explanation:
We know that vertically opposite angles are equal to each other.
Therefore,
<2 = <3
94° = 94°
What is the probability of getting the sum ‘10’, when you role 2 dices?
Answer:
total probability (1,1),(1,2),(1,3)(1,4) (1,5)(1,6)
(2,1) (2,2) (2,3) (2,4) (2,5)(2,6)
(3,1)(3,2)3,3 3,4) (3,5) (3,6)
(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
3/36=1/12
Step-by-step explanation:
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Answer:
Step-by-step explanation:
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Does the following system have a unique solution? why?
The required system of equation has no solution.
When the system of equation has unique solution.The more physical interpretation of the idea of two linear equations having a linear equation is that it will always have a singular solution regardless of whether the lines are parallel or coinciding.
According to question:We have,
4x + 10y = 57---------------(1)
2x + 5y = 38
Multiply 2
4x + 10y = 76----------(2)
So, above equation (1) and (2) has no solution.as values of x and y are not same for both the equation.
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Find the area of the circle shown. Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
19.63
Step-by-step explanation: area of circle=pi*r^2
3.14*2.5^2
3.14*6.25
=19.625 rounded to nearest tenth is 19.63
Driving down a mountain, Bob Dean finds that he descends 3200 feet in elevation by the time he is
3.9 miles (horizontally) away from the high point on the mountain road. Find the slope of his descent. (1 mile = 5280 feet).
Answer:
-0.155
Step-by-step explanation:
You want the slope of Bob's descent when he descends 3200 feet in a horizontal distance of 3.9 miles.
SlopeTo find the slope of Bob Dean's descent, we can use the formula:
slope = (change in elevation) / (change in horizontal distance)
ApplicationIn this case, the change in elevation is 3200 feet and the change in horizontal distance is 3.9 miles.
slope = -3200 feet / (3.9 miles)
To convert the horizontal distance to feet, we multiply by 5280 (the number of feet in a mile)
slope = -3200 feet / (3.9 * 5280 feet)
slope = -3200 / 20,592
slope ≈ -0.1554
The slope of Bob Dean's descent is about -0.155.
__
Additional comment
As a percent grade, this is a 15.5% grade, very steep. He will need to check his brakes before he starts down.
Given the graph of the function F(x) below, what happens to
F(x) when x goes from 0 to 1?
For the graph of the function F(x), when x goes from 0 to 1, F(x) is a negative number with large absolute value. Option D is correct.
What is absolute value?A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
When the value of x goes from 0 to 1 the function shifts and the value is decreased gradually, thus giving F(x) as negative number with a large absolute value.
Hence, option D is the correct answer.
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Write the equation of the line that passes at the point (-8,5) with the slope m=-1 in slope-intercept form.
Answer:
y = -x - 3
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:
y - 5 = -1(x + 8)
Simplifying, we get:
y = -x - 3
This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.
Triangle HIJ is similar to triangle KLM find the measure of side KL around your answer to the nearest tenth if necessary
The measure of side KL from triangle KLM is 22 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle HIJ is similar to triangle KLM.
From the similar triangles,
JH/MK =HI/KL
31/13.9 =49/KL
31KL=49×13.9
31KL=681.1
KL=681.1/31
KL=21.97
KL≈22
Therefore, the measure of side KL is 22 units.
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Help me find the answer for this question
The graphs of the functions f(x) and g(x) are attached with the answer.
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given are the functions f(x) and g(x).
The given functions are -
f(x) = [tex]$100(\frac{3}{5})^{x}[/tex]
g(x) = [tex]$100(\frac{2}{5})^{x}[/tex]
Refer to the graphs of the function f(x) and g(x).
Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.
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What can you say back to someone who asked: " How you been today?"
Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...
Step-by-step explanation:
How I've been today? Quite magnificent. Thank thou for your generosity.
Which of these equations is a quadratic function?
Answer:
B
Step-by-step explanation:
Quadratic Function:A quadratic function is a polynomial function which has a degree of 2, and is generally expressed in standard form: [tex]ax^2+bx+c\text{ where }a\ne 0[/tex]. The degree of a polynomial function can be determined by looking at which term has the largest exponent.
By looking at both options, B would be the correct option as it is a polynomial function with degree 2, while option A is a polynomial function with degree 1, also known as a linear equation.
b) Three interior angles of an n-sided polygon are 136', 138' and 146'. The remaining angles are 165' each. Find the value of n.
By solving a linear equation we will see that the polygon has 19 sides.
How to find the number of sides of the polygon?Remember that for a polygon of n sides, the sum of the interior angles is equal to:
(n - 2)*180°
Here we also know that 3 angles are:
136°, 138°, and 146°
And the rest of the angles (n - 3) angles are of 165° each.
Then the sum of the interior angles gives:
136° + 138° + 146° + (n - 3)*165°
And that must be equal to the expression above, so we can write the linear equation:
136° + 138° + 146° + (n - 3)*165° = (n - 2)*180°
420° + n*165° - 495° = n*180° - 360°
n*165° - 75° = n*180° - 360°
360° - 75° = n*180 - n*165
285° = n*15°
285°/15° = n
19 = n
That is the solution.
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Six years ago,the sum of the ages of two brothers was 22, find the age of the older brother
The age of the older brother is 13
How to determine the age of the elder brotherFrom the information given, let their ages by x and y
This is represented as;
x + y = 22
(x - 6) (y -6) = 21
From equation (1), make x, the subject of formula
x = 22 - y (3)
Substitute equation (3) in equation (2), we get;
(22 - y- 6)(y - 6) = 21
expand the brackets
(16 - y)(y-6) = 21
16y - 96 - y² +6y = 21
collect iike terms
-y² + 22y - 96 - 21 = 0
subtract like terms
-y² + 22y - 117 = 0
y²- 22y + 117 = 0
Find the pairs factors of 117 and substitute the values
y² - 13y - 9y + 117 = 0
(y² - 22y) - (9y + 117) = 0
factorize
y(y - 22) - 9(y - 22) = 0
Then y = 9 and y = 22
The older brothers age = x = 22 - y = 22- 9 = 13
Hence, the value is 13
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The complete question:
The sum of the ages of two brothers is 22 years. Six years ago, the product of their ages was 21 years. What is the age of the elder brother?
The chart below describes the speed of four painters. Which painter is the fastest?
A local salesman receives a base salary of $850 monthly. He also receives a commission of 11% on all sales over $500. How much would he have to sell in a month if he needed to have a monthly income of $3000?
He would need to sell $
to reach his needed monthly income needs.
For the local salesman to have a monthly income of $3,000, using mathematical operations, he would need to sell $20,045 worth.
How the total sales are determined?The sales revenue that the local salesman should generate to reach his monthly income target is determined by working backward with the mathematical operations of subtraction, division, multiplication, and addition.
Firstly, the base salary is deducted from the expected monthly earnings to obtain the amount of the sales commission.
The sales commission is equated to its commission percentage through division and multiplication operations.
The result is added to $500 to arrive at the expected sales revenue.
The monthly base salary = $850
Commission = 11% on sales above $500
Needed monthly income = $3,000
Sales commission = $2,150 ($3,000 - $850)
11% = $2,150
100% = $19,545 ($2,150/11% x 100%)
$19,545 = Sales above $500
Total target sales = $20,045 ($19,545 + $500)
Thus, if the salesman expects a monthly income of $3,000, he must generate monthly sales revenue of at least $20,045.
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Express the trig ratios as fractions in simplest terms.
The trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given triangle WVX, WV=24, WX=51 and VX=45
We know that, sinθ = Perpendicular/Hypotenuse and cosθ = Base/Hypotenuse
Here, sin X= 24/51
sin X= 8/17
cos W= 24/51
cos W= 8/17
Therefore, the trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.
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Using Squeeze/Sandwich Theorem,
Calculate the limit of : lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2))
Using Squeeze theorem, the limit of the function is 0
What is the LimitThe Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.
We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).
We can see that
(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)
As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.
Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.
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The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 180 calories, and 108 calories are from fat. What percent of the total calories is from fat?
Answer:
60% of the total calories is from fat
Step-by-step explanation:
We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1Y =
108
180
By multiplying both numerator and denominator by 100 we will get:
STEP 2Y =
108
180
×
100
100
=
60
100
STEP 3Y = 60
Could you please verify this answer ?
Answer:
The equation that this graph corresponds to is y -3/4x + 8
Step-by-step explanation:
The answer choice you chose is correct.
Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answer:
D
Step-by-step explanation:
ANYONE PLEASE ANYONE WHO GOOD AT MATH PLEASE HELP
Answer:
f(g(f(1))) = 45 — needs to use the equationg(f(g(0))) = 3Step-by-step explanation:
You want to use the graph to evaluate the compositions ...
f(g(f(1)))g(f(g(0)))where f(x) = x² -2x -3, and g(x) = x -2.
Reading the graphTo find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.
f(g(f(1)))Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:
f(x) = (x -2)x -3
f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45
The value of f(g(f(1))) is 45. The equation must be used for this.
g(f(g(0)))Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.
The value of g(f(g(0))) is 3.
__
Additional comment
A suitable calculator or spreadsheet can evaluate these expressions for you.
4.1.5 Quiz: Solving Linear Equations
Question 1 of 5
How many solutions does 5 + = +6+ have?
A. Infinitely many solutions
B. No solutions
OC. One solution
D. Two solutions
The given system of equations has infinitely many solutions. Option A is correct.
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Given equation,
- 6x - 2y = 10 - - - -1
y = - 3x - 5 - - - -2
From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10
Divide the above equation by -2,
y = -3x - 5
Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.
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What is the answer of this triangle congruence question.
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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Assuming a Perfectly Competitive firm has the following cost function: TC = 1000 + 600Q – 10Q2 + 0.05Q3 . Minimum AVC is
Therefore , to calculate the average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.
How are AVC, AFC, and TC calculated?The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.
Here,
Total cost is equal to total fixed cost plus total variable cost, or TC.
In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.
AVC is now equal to VC divided by Q.
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A coefficient is a number that is blank by a blank or an expression
A coefficient is a number that is multiplied by a function or an expression.
What is a coefficient?A coefficient is a multiplier to a function or an expression.
For example, in a polynomial function, the coefficients are the terms that multiply the powers of x.
Taking the standard quadratic function as follows:
y = ax² + bx + c.
The coefficients are a, b and c.
Considering this concept, the blanks are completed on the answer at the beginning.
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In an elastic collision, momentum and kinetic energy are conserved.T or F?
Answer: True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.
Step-by-step explanation:
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The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.
The rate of change is $ 0.75 per attraction.
The table on the number of tickets and total cost is:
Number of tickets 1 5 10 15
Total cost $ 10. 75 $ 13.75 $17.50 $ 21. 25
How to find the cost of tickets ?The number of tickets that Sam can buy when he has $ 37 is:
= (Amount to spend - Cost of admission ) / Cost per ticket
= ( 37 - 10 ) / 0.75
= 36 tickets
The rate of change is therefore the $ 0.75 charged per ticket per event.
The number of tickets for $ 10. 75 is:
= ( Total cost - Cost of admission ) / cost per ticket
= ( 10. 75 - 10 ) / 0.75
= 1 ticket
The cost of 5 tickets :
= ( Number of tickets x cost per ticket) + cost of admission
= (5 x 0. 75 ) + 10
= $ 13. 75
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Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
(x, y) = (_, _)
To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.
For this one, let's pick x = 3. We'll then substitute 3 in for x in the equation:
- (3) + 2y = 7
and then solve for x:
-3 + 2y = 7
Add 3 to both sides:
2y = 10
Divide by 2 on both sides:
y = 5
This shows that (3,5) is a solution for the equation.
Again, you could pick any x-value and solve for y OR pick any y-value and solve for x. There are an infinite number of solutions.
A landscape supply business charges $35
20/04 cash deposit balance 29 385 48 how was it calculated