The required length of LM and LK are given as 4.709 cm and 3.151 cm respectively.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
Here,
Let LM = x and LK = y
Applying trig operators,
(1)
tan48 = 3.5 / y
y = 3.5 / tan48
y = 3.151 cm
(2)
sin48 = 3.5 / x
x = 3.5/sin 48
x = 4.709 cm
Thus, the required length of LM and LK are given as 4.709 cm and 3.151 cm respectively.
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PLEASE HELP ASAP!!!!!!
The simplified form of the expression y⁻³/4y⁶ is option B: - 1/4y⁹
How to simplify expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication, division etc. Therefore, let's simplify the expression.
The simplified form of the expression y⁻³/4y⁶ is:
To simplify this expression, you can use the rule of simplifying the powers of a variable.
It can be done by:
Divide the exponents of y in the numerator and denominatorIn the numerator, y has an exponent of -3, in the denominator y has an exponent of 6.Subtracting the exponents of y in the numerator and denominator you get -3-6 = -9Now, the simplified form is: -1/4y⁻9Therefore, The final step is to simplify the coefficient, 1/4 is a fraction, but to make it simpler we can divide 1 by 4, getting -1/4
Thus option B is correct.
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70.50 - 45.50 + 0.15x - 0.09x =
Therefore , the value of the given problem of linear equation comes out to be x = -250.
Define a linear equation.In algebra, a mathematical model is just one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since x and y are variables, the previous sentence is frequently referred to as a "mathematical expression with 2 variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many different situations. Once an issue has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.
Here,
Given : 70.50 - 45.50 + 0.15x - 0.09x =0
To find the value of x,
Thus,
We do : 70.50 - 45.50 + 0.15x - 0.09x =0
=> 15 + 0.06x =0
=> 6/100 *x = -15
=> 6x = -1500
=> x = -1500/6
=> x = -250
Therefore , the value of the given problem of linear equation comes out to be x = -250.
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A group of friends wants to go to the amusement park. They have $134.50 to spend on parking and admission. Parking is $14.50, and tickets cost $24 per person, including tax. How many people can go to the amusement park?
What does the fundamental theorem of algebra state about the equation 2x 2 â 4x 16 0?
The fundamental theorem of algebra states that every polynomial equation of degree n, where n is a positive integer, has at least one root in the complex number system.
The Fundamental Theorem of Algebra states that any polynomial equation of degree n, with real or complex coefficients, has at least one root (real or complex).
In the case of the equation 2x^2 - 4x + 16 = 0, the Fundamental Theorem of Algebra implies that there is at least one real or complex root. In fact, this equation has two real roots: x=4 and x=-2.
This theorem provides an important foundation for many branches of mathematics, as it proves that solutions to equations exist.
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find the range of g
choose one answer
-4(x)9
the g(x) values -4,0,&9
-5(x)4
the g(x) -values -5, -2, 1, 3, and 4
In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7, but we can figure it out.
What is the value of x in 4 =- 9?Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
To determine the value of X in a multiplication operation, the usual form is
Product = Multiplicand x Multiplier
Consider Multiplier as x.
Product = Multiplicand x
The equation to determine the value of x is then
X = product/multiplier
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four positive whole numbers add up to 93
One of the numbers is a multiple of 19
the other three numbers are equal
write the four numbers in ascending order
Answer: 12...12...12...57
Help please I’m struggling
Answer:
Step-by-step explanation:
Attached are the formula. (Ignore the point slope formula not needed)
For second part, just know that m= slope and b = y intercept in the slope-intercept formula. Just plug those in for each of those, I will do one for you and you try the rest ok
Slope = 1/3 and y-intercept = -1
Slope intercept formula is y = mx + b
y = 1/3 x + (-1)
y= 1/3 x -1
Now you try the rest.
X~N(570, 103). Find the z-score corresponding to an observation of 470.
A. 0.97 B. -0.97 C. 0.64 D. -0.64
The z-score corresponding to an observation of 470 is -0.97.
Given that the observation x is 470.
mean, is 570
standard deviation, σ is 103
For the occurrence score,
z = (x - μ)/σ
z = (470 - 570)/103
z = -0.97
The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalizing is the process of transforming a raw score into a standard score (however, "normalizing" can refer to many types of ratios; see normalization for more).
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a man travels from a to b at 4km/h and from b to a at 6km/h . IF HE TAKES 45 MIN TO COMPLETE ENTIR journey .find the distance travelled?
Answer: avg speed for the round trip is 2*4*6/(4+6) = 4.8 km/hr
RT distance = 4.8*0.75 = 3.6 km
sorry if this is wrong answer
9. The cost (in dollars) of producing x sneakers in a factory is given by C(x) = 25x+400. The number of
sneakers produced in t hours is given by x(t) = 20t. Find C(x(t)). Then evaluate C(x(8)).
According to the linear cost function sneakers are produced in 8 hours is 4400.
What is the linear cost function?Businesses employ a mathematical technique called a linear cost function to calculate the overall costs related to a certain level of production. When the cost of producing each item is constant regardless of the number of units produced, this approach of cost estimating can be used.
According to the given information:Given :
C(x) = 25x + 400
x(t) = 20t
∴ C(x) = 25(20t) + 400
∴ C(x) = 500t + 400
Now,
C(x(t)) = C(x(8)) = 500t + 400
= 500(8) + 400
= 4400
∴ C(x(8)) =4400
sneakers are produced in 8 hours = 4400
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Yasmine is serving ice cream with the birthday cake at her party. She has purchased 19 1/2 pints of ice cream. She will serve 3/4 of a pint to each guest. Will there be any ice cream left?
If Yasmine's guests at her birthday party are exactly 26, based on the division operation, there will not be any ice cream left.
What is a division operation?A division operation involves dividing the dividend (the numerator) by the divisor (the denominator) to obtain the quotient.
The quantity of ice cream purchased = 19¹/₂ (19.5).
The quantity of ice cream per guest = ³/₄ (0.75)
The number of guests that can be served = 26 (19¹/₂ x ⁴/₃) or (19
5/0.75)
Thus, using division operation, no ice cream will be left if the guests are not less than 26.
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An athletics competition can be entered by juniors,
seniors and veterans.
Last year 57 juniors, 209 seniors and 86 veterans
entered the competition.
This year 25% fewer people entered the
competition in total.
Work out the total number of people who entered
the competition this year.
Answer:
juniors- 43, seniors-155, veterans- 65, total-263
Step-by-step explanation:
so you divide each my 4 then subtract that from the original number and that's your answer
Juniors- 57 divide by 4=14, 57-14=43
Seniors- - 209 divide by 4=52, 209-52=155
veterans- 86 divide by 4=21, 86-21=65
Than add all 3 numbers together
:)
identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 64
Which of the following is not equal to .01?
10-2
1%
1/10
one one-hundredth
The number 1/10 is not equal to the 0.01.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equivalent number is,
⇒ 0.01
Now, We will check all the expression as;
1) 10⁻²
⇒ 1/10²
⇒ 1/100
⇒ 0.01
2) 1%
⇒ 1/100
⇒ 0.01
3) 1/10
⇒ 0.1
4) One hundredth
⇒ 1/100
⇒ 0.01
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Carbon-14 has a half life of approximately 5700 years. How much of a 1000g sample will be left undecayed and still radioactive after 11,400 years?.
In a 1000g sample, 250g will be left undecayed and still radioactive after 11,400 years.
The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay). The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite of life's exponential growth is time's doubling.
Carbon-14 has a half-life of approximately 5700 years, which means that after 5700 years, half of the original amount of Carbon-14 will remain undecayed and still radioactive. After 11,400 years, there will be 1/4 of the original amount remaining, because two half-lives have passed. So, in a 1000g sample, 250g will be left undecayed and still radioactive after 11,400 years.
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The compound interest on Rs. 5000 at 4% p.a. for 2 years
The Answer is Rs.408
step by step solution:
Given, P=5000
R=4%
T=2 years
Amount A=P ( 1+ R/100 )^T
A=5000(1+ 4/100)^2
5000 (104/100)^2
= Rs.5408
Compound interest =A−P
=5408−5000=Rs.408
What is the range of this exponential function?
y = 7*
The range of this exponential function y=7ˣ is (0,∞), {y|y>0}
What is Range?The range of a function is the set of its possible output values
The given function is y=7ˣ
Now we need to find the range of y=7ˣ
Let us take few values of x and y
x -2 -1 0 1 2
y 1/49 1/7 1 7 49
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=0. Horizontal Asymptote: y=0
The Range is: (0,∞), {y|y>0} from the graph
Hence, the range of this exponential function y=7ˣ is (0,∞), {y|y>0}
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Help asap :)
Are the following functions inverses of one another ?
Use function composition to explain your answer :)
Given functions are inverse of each other.
What are inverse functions?
A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.
Here, we have
Given: f(x) = 5x + 2
g(x) = (x-2)/5
We have to inverse one another function.
f(x) = 5x + 2
g(x) = (x-2)/5
f(g(x)) = f( (x-2)/5)
f(g(x)) = 5×(x-2)/5 + 2
f(g(x)) = x - 2 + 2
f(g(x)) = x these functions are inverse of each other.
Hence, given functions are inverse of each other.
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What are the vertex and range of the function?
The vertex of the data set of the table: (-3, 0) and the range is {y I 0 ≤ y < ∞}. The correct answer is A.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
From the table,
we interpreted the graph of data set.
Which is given in the attached image.
And from the graph,
we have the vertex = (-3, 0)
To find the range:
y have the value y = 0
And never take the value from negative y.
And expands to over positive infinity.
So, the range is 0 ≤ y < ∞
Therefore, the vertex = (-3, 0) and the range is 0 ≤ y < ∞.
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An equilateral triangle is similar to a scalene triangle, because we can map one onto the other using only dilations and rigid transformations.
No, an equilateral triangle is not similar to a scalene triangle.
Two triangles are similar if they have the same shape, but they can be different sizes. In order for two triangles to be similar, the angles in the triangles must be congruent (equal in measure) and the sides of the triangles must be proportional. An equilateral triangle has three congruent angles, each measuring 60 degrees, and three congruent sides. A scalene triangle, on the other hand, has three sides that are all different lengths and three angles that are all different measures. Because the angles and sides of an equilateral triangle are not proportional to the sides and angles of a scalene triangle, the two triangles are not similar.
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The two triangles are not similar.
Now, According to the question:
An equilateral triangle is not similar to a scalene triangle because an equilateral triangle has all equal sides and the same angle measures, and a scalene triangle's sides are all different measures and the angles don't measure the same angle.
An equilateral triangle has three congruent angles, each measuring 60 degrees, and three congruent sides. A scalene triangle, on the other hand, has three sides that are all different lengths and three angles that are all different measures. Because the angles and sides of an equilateral triangle are not proportional to the sides and angles of a scalene triangle, the two triangles are not similar.
Hence, The two triangles are not similar.
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3. What is a polynomial function in standard form with zeroes 1, 2, -3, and -1? (1 point)
Og(x)=x4+x³-7x²-x+6
Og(x)=x4+x³ + 7x²-x+6
Og(x)=x4+x³-7x²-x-6
Og(x)=x²-x³-7x²-x+6
The polynomial function would be [tex]g(x)=x^4 + x^3 -7x^2 -x -6[/tex].
Option (C) is correct.
What is a polynomial function?
A polynomial function is a function of the form:
[tex]f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0[/tex]
Where n is the degree of the polynomial, x is the variable, and [tex]a_0, a_1, a_2, ... a_n[/tex] are the coefficients. The degree of a polynomial is the highest power of the variable in the function.
A polynomial function in standard form with zeroes 1, 2, -3 and -1 is
g(x)=(x-1)(x-2)(x+3)(x+1)
So, (x-1)(x-2)(x+3)(x+1)
= (x^2 -3x +2)(x^2 +4x +3)
=[tex]x^4 + x^3 -7x^2 -x -6[/tex]
Hence, the polynomial function would be [tex]g(x)=x^4 + x^3 -7x^2 -x -6[/tex].
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26
Date:
The height of a building is 145 feet (ft).
Round the height of the building to the
nearest tens place.
_________ft
Answer:
140 feet.
Step-by-step explanation:
Hope its correct and it helps!
What is 6/7 x 14 pls help me
Answer:
[tex] \sf \: \frac{6}{7} \times 14 = 12[/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: \frac{6}{7} \times 14[/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: \frac{6}{7} \times 14[/tex]
[tex] \sf \rightarrow \frac{6}{\cancel{ \: 7 }} \times \cancel{14}[/tex]
[tex] \sf \rightarrow \: 6 \times 2[/tex]
[tex] \sf \rightarrow \: 12[/tex]
Hence, the answer is 12.
A system of equations is given.
−5y = 10 − 5x
−2y = 8 − 4x
Solve for (x, y) using the elimination method. Write your solution in (x,y) form.
Answer:
(2, 0 )
Step-by-step explanation:
- 5y = 10 - 5x → (1)
- 2y = 8 - 4x → (2)
multiplying (1) by - 2 and (2) by 5 and adding will eliminate y
10y = - - 20 + 10x → (3)
- 10y = 40 - 20x → (4)
add (3) and (4) term by term to eliminate y
0 = 20 - 10x ( add 10x to both sides )
10x = 20 ( divide both sides by 10 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
- 5y = 10 - 5(2)
- 5y = 10 - 10 = 0 , then
y = 0
solution is (2, 0 )
y=3x-2 y=2x-5 whats the answer
Answer:
x = -3
y = -11
Step-by-step explanation:
The expression 62.4d-21062.4d−21062, point, 4, d, minus, 210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange.
How many Indian rupees do you receive when you exchange \$13$13dollar sign, 13?
The Indian rupees do you receive when you exchange $13 will be 601.2 rupees.
How to calculate the number of rupees?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The expression 62.4d-210 gives the number of Indian rupees you receive when you exchange dollar d at the local currency exchange.
The Indian rupees do you receive when you exchange $13 will be:
= 62.4d - 210
= 62.4(13) - 210
= 601.2 rupees
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6X -24 in simplest form
Answer:
Step-by-step explanation:
x=4
What is the result when the number 89 is decreased by 9.6%?
Answer:
80.456 is a 9.6% decrease of 89.
Step-by-step explanation:
Answer:
Step-by-step explanation:
89×(1-9.6%)
=89×(1-0.096)
=89×0.904
=80.456
≈80
the answer is 80 if you have to round it.
Which statement defines the horizontal asymptote?
m < n, so y = 0 is the horizontal asymptote.
m = n, so y = am / bn is the horizontal asymptote.
m = n, so y = 0 is the horizontal asymptote.
m > n, so there is no horizontal asymptote.
The horizontal asymptote is y = 0 because m = n. A function's graph has a line known as a horizontal asymptote.
A horizontal asymptote is a line that the graph of a function approaches as x tends to either positive or negative infinity. If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote of the function is the line y = a/b, whereThe leading coefficients in the denominator and numerator, respectively, are a and b. Therefore, if m = n, then the horizontal asymptote is y = a/b, which reduces to y = 0.
The statement that defines the horizontal asymptote is that if m = n, then the horizontal asymptote is y = 0.
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Please Help I cant seem to do this one!
The best scale for the length axis is 10 cm to represented 1 unit on the graph
Using this scale the value of A and B are 60 and 110 respectively
What is scale in graph plot?All conceivable data for the graph is represented by the numbers on the X and Y axes.
There are major and minor axes, the major axes contains smaller divisions of 5, the smaller divisions are the minor axes
The scale are based on the major axes. The scale of a graph is the units that the distance in the major axes stands for
The scale should go beyond the values to be plotted so as to contain all the possible values
Applying the scale of 1 unit on graph for 10 units points A = 60 and point B = 110
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