The number of cookies Zahra made with 4/5 kilograms of butter is 1333.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Zahra has 4/5 kilograms of butter to bake cookies.
Each batch of cookies requires 6/10 grams of butter
4/5 kilograms = 800 grams and 6/10 grams =0.6 grams
Number of cookies = Number of kilograms of butter ÷ Butter requires in each cookie
= 800 ÷ 0.6
= 800/0.6
= 1333
Therefore, the number of cookies are 1333.
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use the theorem in sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z|
The integral of f (z) around the positively oriented circle |z|
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3
What is integral?In mathematics, an integral lends numerical values to functions to represent notions like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.
With the exception of the point where z = z, where f(z) is analytic within and on C, let C be the smooth, simple closed curve except at z =z , then ,
[tex]\int\limits^_ {} \,[/tex] f(z) dz = 2πi [ res f(z)] z = [tex]z_{1}[/tex]
here f(z) is singular at z = -1,
res [tex]f(z)_{z = -1}[/tex] = [tex]\lim_{z\to \-1} z+1 f(z)_[/tex]
[tex]\lim_{z\to \-1}[/tex] [tex]z^{3}[/tex](1-3z)/(1+2[tex]z^{4}[/tex])
when z = -1 then f(z) = -4/3
Therefore [tex]\int\limits^_ {} \,[/tex]f(z) dz = 2πi (-4/3)
[tex]\int\limits^_ {} \,[/tex]f(z) dz = -8πi/3.
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jonah and haley made brownies to bring as a class treat. some were plain and some had sprinkls the class ate 3/4 of one pan and 1/6 of another pan of plain brownies they ate 5/6 of one pan and 1/10 of another pan of brownies with sprinkles. if the brownies were the same sie dud the class eat more plain brownies or more brownies with sprinkles
Answer:
5/6
Step-by-step explanation:
he class ate 3/41 = <<3/41=3/4>>3/4 of one pan of plain brownies
They also ate 1/61 = <<1/61=1/6>>1/6 of another pan of plain brownies
The total amount of plain brownies they ate is 3/4 + 1/6 = <<3/4+1/6=5/6>>5/6
The class ate 5/61 = <<5/61=5/6>>5/6 of one pan of brownies with sprinkles
They also ate 1/101 = <<1/101=1/10>>1/10 of another pan of brownies with sprinkles
The total amount of brownies with sprinkles they ate is 5/6 + 1/10 = 5/6 + 1/10 = 41/60
The class ate more plain brownies because 5/6 > 41/60. Answer: {5/6}.
100 POINTS WILL GIVE BRAINLIEST What is the target percent change for Growth Domestic Product?
A. 2-3% growth per period
B. 1-5% growth per period
C. 3-6% growth per period
Answer:A
Step-by-step explanation:
If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = 10x² + [? ]
Answer:
The missing term in the output of the function [tex]g(f(x))[/tex] is -18.
[tex]g(f(x))=10x^2-18[/tex]
Step-by-step explanation:
Function CompositionIn mathematics, function composition is a term that encompasses a relationship between two functions wherein the output of one function is used as the input for another function. This relationship combines two functions to form a single function, known as a composite function. For future reference, function composition may also be denoted by a small circle, see below:
[tex](g\circ f)(x)=g(f(x))[/tex]
In the given problem, we must evaluate the composite function [tex]g(f(x))[/tex] / [tex](g\circ f)(x)[/tex] to identify the unknown term.
With composite functions, we begin evaluating from the inside. To evaluate [tex]g(f(x))[/tex], we must substitute the output of the function [tex]f(x)[/tex] (given as the expression [tex]2x^2-5[/tex]) as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex]:
[tex]g(f(x))=g(2x^2-5)[/tex]
Now, using [tex]f(x)[/tex] as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex] (given as the expression [tex]5x+7[/tex]), we can substitute [tex]2x^2-5[/tex] into the output for the function [tex]g(x)[/tex]:
[tex]g(f(x))= 5(2x^2-5)+7[/tex]
From here, we can go ahead and distribute the 5:
[tex]g(f(x))=10x^2-25+7[/tex]
Combine like terms:
[tex]g(f(x))=10x^2-18[/tex]
With the composite function evaluated, we can identify our missing term as [tex]-18[/tex].
It says to find the surface area of the figure and to round to nearest hundredth. confused..
Find the measure of angle 2
a 50°
b 90°
c 140°
d 40°
let d be a positive integer. show that among any group of d 1 (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d.
Among any group of d+1 integers there are two with exactly the same remainder when divided by d.
What are Positive Integers?Positive integers are those bigger than 0 that don't contain any fractional portions. On the number line, these figures are located to the right of 0.
Is 0 a Positive Integer?Since it is neither positive nor negative, 0 is not a positive integer. Positive integers are defined as numbers greater than 0 in mathematics.
The possible remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The number of remainders that can be obtained is d, or |0, 1, 2,..., d-1|=d0,1,2,...,d-1=d.
According to the Pigeonhole Theory:
objects are the number of integers in d+1.
"holes" = "remainders" + "d"
[d+1/d]=2
According to the Pigeonhole Principle, there are always two d+1 integers in every group that have precisely the same residual after being divided by d.
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There are always two d+1 numbers in any group that have the exact same residual after division.
Examples of integers and what they are:An integer, pronounced "IN-tuh-jer," is an entire number which can be positive, minus, even zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, among 3,043. 1.43, 1 3/4, 3.14, and other values which aren't integers seem to be some examples.
Briefing:The potential remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The possible number of remainders is d, or I{0,1,2,.......d-1}I = d
By the Pigeonhole Principle:
Objects = umber of integers = d+1
Holes = number of remainders = d
[tex]\frac{d+1}{d} = 2[/tex]
According to the Pigeonhole Principle, there are always two d+1 numbers in every group that have precisely the same residual after being divided by d.
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Could someone help me answer this multiple-answer question? I'm stuck
Answer:
x = 2
<1 = 28
Step-by-step explanation:
The two angles equal each other.
4x + 20 = 5x + 18 Subtract 4x from both sides
20 = x + 18 Subtract 18 from both sides
2 = x
4x + 20
4(2) + 20
8 + 20
28
Tommy does 28J of work to push the pencil over 4m. How much force did he use?
Answer:
Given that,
Tommy does 28 joules of work for pushing up the pencil.And, the distance is 4 meter.We know that
Work = Force × distance
So, the force = work ÷ distance
= 28 ÷ 4
= 7 newtonsTherefore we can conclude that the force that he used is 7 newtons.
Good afternoon! I have a survey for you guys to take. I would appreciate it if you do, because I use it for my schoolwork.
Knowing that the Bacon Cheeseburger meal is about 1000 calories and that you are supposed to consume between 2000 and 3000 calories per day, would you still eat Jack in the Box? Thank you beforehand!
1. I would eat there often
2. I would eat there sometimes
3. I would eat there rarely
4. I would not eat there ever
Answer:
Step-by-step explanation:
2, i would eat there sometimes!
Answer:
3. I would eat there rarely.
Step-by-step explanation:
Please give brainliest!!!
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 3(1.09)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)
The solution is
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is given by
f ( a ) = 3 ( 1.09 )ᵃ
A)
To find the domain of the function f ( a )
The length of the fish was approximately 5.98 cm
So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,
And , f ( a ) = 5.98 cm
So , 5.98 = 3 ( 1.09 )ᵃ
Solving for a , we get
Divide by 3 on both sides of the equation , we get
1.9933 = ( 1.09 )ᵃ
a = 8
So , the value of a is 8
So , the domain of the function is [ 0 , 8 ]
B)
The y-intercept of the graph is given by substituting the value of a = 0,
So , f ( a ) = 3 ( 1.09 )ᵃ
when a = 0 , we get
f ( 0 ) = 3 ( 1.09 )⁰
f ( 0 ) = 3 cm
Therefore, the value of f ( 0 ) = 3 cm
C)
The average rate of change from m =2 to m = 8 is given by the equation ,
when m = 2 ,
f ( a ) = 3 ( 1.09 )ᵃ
f ( 2 ) = 3 ( 1.09 )²
f ( 2 ) = 3 x 1.1881²
f ( 2 ) = 3.5643
And , when a = 8
f ( a ) = 3 ( 1.09 )ᵃ
f ( 8 ) = 3 ( 1.09 )⁸
f ( 8 ) = 3 x 1.99256
f ( 8 ) = 5.97768
So , the average rate of change is the slope of the graph
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )
Slope = ( 5.97768 - 3.5643 ) / 6
Slope = 2.4133879 / 6
Slope = 0.40223 cm per month
Therefore ,
The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month
Hence ,
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
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Samson opened a bank account with 2.25% simple interest. The total amount of interest Samson will earn after 30 years is $812.50. How much did Samson deposit when he opened the account? Round if necessary.
Answer: The equation for simple interest is:
Future interest = Principal*(interest rate*number of years). Remember to write the interest rate of 1.25% as 0.0125 (rather than directly as 1.25)
812.50 = x(0.0125*20)
812.5 = x(0.25)
x = $3250
This means that Samson deposited $3250 when he opened the account.
Step-by-step explanation:
Consider the following graph:
What is the slope/rate of change between the inputs of 0 and 4? _______.
What is the slope/rate of change between the domain values of 4 and 8? ______.
Is the slope/rate of change constant (not changing/the same)? ______.
Is the function linear? _______.
The solution is
a) The slope/rate of change between the inputs in m = -1/2
b) Slope/rate of change between the domain values of 4 and 8 is m = -1/2
c) The slope/rate of change is constant
d) The function is a linear function
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be = A
Now , the value of A is
a)
when the inputs are 0 and 4 , the values of x = 0 and x = 4
So , the values of y = 5 and y = 3 respectively
Let the first point be P = P ( 0 , 5 )
Let the second point be Q = Q ( 4 , 3 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 5 ) / ( 4 - 0 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
b)
when the domain values are 4 and 8 , the values of x = 4 and x = 8
So , the values of y = 3 and y = 1 respectively
Let the first point be Q = Q ( 4 , 3 )
Let the second point be R = R ( 8 , 1 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 1 - 3 ) / ( 8 - 4 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
c)
The slope of the line m = -1/2 and it is constant
d)
The function is a linear function and the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = -1/2 ( x - 0 )
On simplifying the equation , we get
y - 5 = -1/2 ( x )
Adding 5 on both sides of the equation , we get
y = ( -1/2 )x + 5
Therefore , the equation of line is y = ( -1/2 )x + 5 and it is linear
Hence , the equation of line is y = ( -1/2 )x + 5 and it is linear where the slope of the line is m = -1/2
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Triangle KLM is formed by connecting the midpoints of the side of triangle HIJ.
The lengths of the sides of triangle KLM are shown. What is the length of HJ?
Figures not necessarily drawn to scale.
Applying the triangle midsegment theorem, the length of HJ is: 8 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that when a line connects the midpoints of two sides of a triangle, it is parallel to the third side and also has a length that is half of the length of the third side.
In the image attached below, segment LK is a midsegment of the triangle which is parallel to a third side, segment HJ.
Therefore:
LK = 1/2(HJ) [triangle midsegment theorem]
Substitute
4 = 1/2(HJ)
Multiply both sides by 2
4 × 2 = 1/2(HJ) × 2
8 = HJ
Length of HJ = 8 units.
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Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place. Please hurry!!!
The area of the given figure is 68.6
Calculating the area of a figureFrom the question, we are to determine the area of the given figure.
Area of the given figure = Area of the semicircle + Area of the rectangle + Area of the semicircle
Area of a semicircle = 1/2πr²
Where r is the radius
Area of a rectangle = Length × Width
From the given diagram,
The diameter of the semicircle is 4
Thus,
Radius, r = 4/2 =
r = 2
Length of the rectangle is 14
and the width of the rectangle is 4
Therefore,
Area of the figure = 1/2π(2)² + 14 × 4 + 1/2π(2)²
Area of the figure = 1/2π×4 + 14 × 4 + 1/2π×4
Area of the figure = 2π + 56+ 2π
Area of the figure = 4π + 56
Area of the figure = 68.566
Area of the figure ≈ 68.6
Hence, the area is 68.6
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Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing. How much material remains for the blanket?
The remaining material for sewing is 5/2 material.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing.
1/6 of 3 = 3x1/6 = 1/2
The remaining material = 3-1/2
= 5/2
Hence, The remaining material for sewing is 5/2 material.
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5 Bob is 5 years younger than twice Mark's age. Bob is 31. How old is Mark?
Answer:
57 years old
Step-by-step explanation:
Bob=31
Mark= 31 x 2 - 5
31 x 2= 62
62- 5 = 57
Mark is 57 years old
Answer:
Mark is 18
Step-by-step explanation:
third-degree, with zeros of -3,-2, and 1, and y-intercept of -8
The polynomial y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8 is the cubic equation whose zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and intercept is - 8.
How to derive a cubic equation associated with a given set of zeros and a intercept
Herein we must derive a cubic equation such that the zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and its intercept is - 8. Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients.
If we know that (x₁, y₁) = (- 3, 0), (x₂, y₂) = (- 2, 0), (x₃, y₃) = (1, 0) and (x₄, y₄) = (0, - 8), then we solve the following system of linear equations to determine all real coeffcients by numerical methods:
- 27 · a + 9 · b - 3 · c + d = 0
- 8 · a + 4 · b - 2 · c + d = 0
a + b + c + d = 0
d = - 8
(a, b, c, d) = (4 / 3, 16 / 3, 4 / 3, - 8)
The cubic equation is y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8.
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How many square feet of tiles do you need to purchase to cover the floor of a 10.5 foot by 8.5 foot bathroom
You would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
To determine the number of square feet of tiles needed to cover a 10.5-foot by 8.5-foot bathroom floor, we can use the formula for the area of a rectangle, L × W
As per the question, the length of the floor is 10.5 feet and the width is 8.5 feet, so the total area of the floor is 10.5 feet × 8.5 feet = 89.25 square feet.
Therefore, you would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
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How to solve-2–(-12)
Answer:
10
Step-by-step explanation:
[tex]-2-(-12)\\=-2+12\\=12-2 \\=10[/tex]
The sphere is a geometric body generated by turning a semicircle around its diameter ?
The theory tells us that the sphere is a three-dimensional body that arises by rotating a semicircle around its diameter.
¿What is the sphere?The sphere has been a three-dimensional body. The main characteristics of this body are:
All the points that make up the surface of the sphere are at the same distance from a particular point known as the center. It is a geometric field that arises when a semicircle rotates around its own diameter.In the attached image let's see an example of a sphere.
¡Hope this helped!
MATHEMATICAL CONNECTIONS In Exercises 23 and 24,
use the given information to write and solve a system of
linear equations to find the values of x and y.
23. LMN = PQR, L = 40°, M = 90°,
P = (17x − y)°, R = (2x + 4y)º
The value of x and y are 3 and 11.
What is the congruent triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Given that,
△LMN = △PQR
Thus ∠L = ∠P, ∠M = ∠Q, and ∠N = ∠R.
Also, ∠L = 40°, ∠M = 90°, ∠P = (17x − y)°, ∠R = (2x + 4y)°.
The sum of interior angles of a triangle is 180°.
∠L + ∠M + ∠N = 180°
40° + 90° + ∠N = 180°
∠N = 50°.
Therefore,
17x − y = 40 .....(i)
2x + 4y = 50 .....(ii)
Multiply equation (i) with 4 and add with equation (ii)
68x - 4y = 160
2x + 4y = 50
_________
70x = 210
x = 210/70
x = 3
Putting x = 3 in equation (ii)
6 + 4y = 50
4y = 44
y = 11
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What is the range of the data set below? * Data Set 13 44 54 2 25 17 7
Answer: 52
Step-by-step explanation:
To find the range of a data set, we subtract the smallest value from the largest value.
54 - 2 = 52
and are right triangles. Find h. Use a proportion and show work.
In a triangle, The value of ''h'' will be;
⇒ h = 2.7 m
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
The triangle is right triangle.
The values are,
AB = 6 m
BD = 12 m
BC = 0.9 m
DE = h m
Now,
Since, The triangle is right triangle.
Hence, By using definition of proportional we get;
⇒ AB / BC = AD / ED
Substitute all the values, we get;
⇒ 6/0.9 = (6 + 12) / h
⇒ 6 / 0.9 = 18 / h
⇒ h = 18 × 0.9 / 6
⇒ h = 2.7 m
Thus, The value of h = 2.7 m
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what is the slope of a line that is parallel to the line shown on the graph?
PLEASE HURRY!
Answer:
-3
Step-by-step explanation:
A (0,2)
B (2,-4)
slope = (-4-2)/(2-0)
-6/2
-3
a parallel line has the same slope
Order these number from least to greatest. 33 1/3%, 0.3125, 17/48
In triangle DEF, line DE is congruent with line FD and the measurement of angle F is 55. Find the measurement of angle E. (isosceles triangle)
Step-by-step explanation:
because it is an isoceles triangle (both legs are equally long), E and F are the side angles in the baseline.
and because both leg sides are equally long, also both side angles must be equally large
therefore,
angle E = angle F = 55°.
find the length and the slope of each side of the triangle below. then, find the coordinates of the midpoint of each side. when the slope is undefined, write undefined in the response box.
The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2
how to determine the length and slope of the side of a triangle?suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).
slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)
according to trigonometric ratio, tanα = opposite side/base = x/y
tanα is the slope of hypotenuse.
the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.
the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.
When does a slope is defined?As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.
hence, the triangle is right-angled, and the biggest side has a slope only.
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3(6x-4y)-5. Help i do not know how to do this it’s very confusing I need help
Answer:
3(6x-4y) -5 18x-12y-5MAY BE IT'S HELP UHHH=^._.^
Answer:
The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.
Step-by-step explanation:
To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.
In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.
Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.
Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.
9
LBCA and LACD form a linear pair. LBCA is
represented by (2x - 5)° and LACD is
represented by (3x + 10)°.
What is the mLACD?
A. 35°
B. 61°
C. 65°
D. 115°
Answer:
D
Step-by-step explanation:
[tex]m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}[/tex]