The correct option is D. 2x + 7 is used for solving the equation by substitution.
What is defined as the substitution method?The substitution method is a straightforward method for algebraically solving a system of linear equations and determining variable solutions. It entails determining the value of x-variable in aspects of y-variable using the first equation and afterwards substituting or fixing the value of x-variable with in second equation, as the name implies.The following are the two given equations;
4x = 5 - 2y .......equation 1
y - 2x = 7 .......equation 2;
using substitution mean put the value of one variable from 1 equation into the other.
Consider equation 2;
y - 2x = 7
y = 2x + 7
Put this in equation 1;
4x = 5 - 2y
4x = 5 - 2(2x + 7)
Simplifying;
4x = 5 - 4x - 14
4x = 9 - 4x
8x = 9
x = 9/8
Therefore, the value of x is obtained as 9/8 for which the equation used is (y = 2x + 7).
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Help i am so confused and I need this asap!!
Answer:
25 tickets were purchased ahead of time
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1)
25
× 11
------
275
2)
625
-275
--------
350
3)
350 ÷ 14 = 25
Check:
350 (dollars from purchased ahead of time)
+275 (dollars from purchased at the door)
--------
$ 625 (total ticket sales stated in the word problem)
What is this called ,
, <--- That is called a comma
∠A and \angle B∠B are complementary angles. If m\angle A=(x-19)^{\circ}∠A=(x−19) ∘ and m\angle B=(3x+1)^{\circ}∠B=(3x+1) ∘ , then find the measure of \angle B∠B.
Answer:
∠ B = 82°
Step-by-step explanation:
complementary angles sum to 90° , then
∠ A + ∠ B = 90 , that is
x - 19 + 3x + 1 = 90
4x - 18 = 90 ( add 18 to both sides )
4x = 108 ( divide both sides by 4 )
x = 27
Then
∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°
Which of the following is not a rational number?
A) The product of 14 and 0.833333...
B) The sum of 27 and 43
C) The product of 12 and 17−−√
D) The sum of 5+5√ and 14−5√
The product of 12 and √17 is not a rational number.
Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number.
In other words, p/q, where p and q are both integers and q ≠ 0, can be used to represent a rational number.Irrational numbers are real numbers that cannot be represented as simple fractions. An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.The product of ant two rational numbers is always a rational number , but product of a irrational number and a rational number is not a rational number.
Hence only the third option is correct.
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A power company calculates a person's monthly bill from the number of
kilowatt-hours (kwh), x, used.
the function b(x)
The bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
The given functions are
b(x) = 0.15x; x ≤ 360
b(x) = 0.10(x - 360) + 54; x > 360
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
For a person who uses 560 kWh, it means that:
x > 360
So, we use the following function to determine the bill
b(x) = 0.10(x - 360) + 54
Substitute 560 for x
b(560) = 0.10(560 - 360) + 54
⇒b(560) = 74
Hence, the bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
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Your question is incomplete, probably the complete question/missing part is:
A power company calculates a person's monthly bill from the number of kilowatt-hours ( Nh), x, used. The function b(x)= 0.15x, and x≤360. 0.10(x-360)+54, and x>360 determines the bill. How much is the bill for a person who uses 560 kWh in a month? A. $84 B. $54. $64 D. $74.
Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbl
Which number sentence tells the story of how many marbles he had left ?
The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form
Total number of marbles Tran bought=25 marbles
Total number of marble Tran has before buying new marbles=10 marbles
Total number of marbles after buying new marbles=35 marbles
Given that he lost 6 marbles because of the hole in his pocket
Therefore, the Total number of marbles left=35-6
The total number of marbles left=29 marbles.
Therefore, The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
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Matt sliced a pizza into 8 equal parts and gave 4 slices to stuart. which are other ways that show the fraction of a pizza matt gave stuart? choose more than one answer:
The fraction of a pizza Matt gave Stuart is 4/8 or 2/4 or 1/2.
Given that, Matt sliced a pizza into 8 equal parts and gave 4 slices to Stuart.
We need to find the fraction of a pizza Matt gave Stuart.
What is the fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Now, the fraction=4/8
=2/4 =1/2
Therefore, the fraction of a pizza Matt gave Stuart is 4/8 or 2/4 or 1/2.
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You want to make 20 plates and have 30 bags of shredded cheese. How can you determine how much cheese to put on each plate so that each plate has the same amount of shredded cheese?
The amount of cheese in each plate = 1.5x
There are 30 bags of shredded cheese.
Let 'x' be the quantity of cheese in each bag. Then,
The total quantity of cheese in 30 bags = 30x
Number of plates = 20 plates
We need to determine the quantity of cheese put on each plate so that each plate has the same amount of shredded cheese.
For this we just need to divide the total amount of shredded cheese by the number of plates.
The equal amount of cheese in each of 20 plates = 30x/20
= 3x/2
= 1.5x
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millimeters
Equal 15 centimeters 4 millimeters
154mm
we know that 1cm = 10 mm
therefore 15cm= 10*15 mm
= 150 mm
and 4 mm
we get total mm= 15cm +4mm
= 150mm+4mm
= 154 mm
mm stands for millimeters and cm stand for centimeters
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Please Help I Do Not Understand. 20+ Points!
The water level in Colorado river is 2.55 m below average. a large rainfall caused The water level to rise 0.8 m. what is the water level after the rainfall?
The water level after the rainfall is 1.75 below average.
How to calculate the difference?From the information, the water level in Colorado river is 2.55 m below average. a large rainfall caused and the water level to rise 0.8 m.
The water level after the rainfall will be:
= -2.55 + 0.8
= -1.75
Therefore, the water level after the rainfall is 1.75 below average.
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Find an equation of the line through (3,4) and parallel to y = 2x + 2: y =____. (Type your answer in slope-intercept form.)
Answer:
y = 2x - 2
Step-by-step explanation:
y = 2x + 2
4 = 2(3) + c
4 = 6 + c
c = -2
y = 2x - 2
The line is parallel so slope remains same but intercept changes.
Find the area of the region inside the circle r=4cos(theta) and outside the circle r=2.
Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3
What is the polar curve?A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.
r = 1 − cosθsin3θ
Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.
The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.
The figure attached shows the bounded region of the two graphs. The red curve is r=4cos(θ) and the blue curve is r=2.
The points of intersection of the two curves are
θ = π/3 and 5π/3
The area is calculated as follows:
Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.
A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ
=[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ
= [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]
= 4π/3 + 2√3
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help!!! 50 points!!!!
Answer:
Less than and -97
Step-by-step explanation:
Answer: -17
Step-by-step explanation:
find the value by using the systematic of expressions then exponent it then factorize it by using prime numbers
If mPQY = 4x – 7 and mRQY = 2x + 25, solve for x. Show all your work. Please help me. I would appreciate it. Thanks. x s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
The value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
Given that, m∠PQY= 4x-7 and m∠RQY = 2x+25 are linear pairs of angles.
What are linear pairs of angles?Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Now, m∠PQY+m∠RQY=180°
⇒4x-7+2x+25=180°
⇒6x+18=180°
⇒6x=162
⇒x=27°
So, m∠=PQY=4x-7
=101°
and m∠RQY=2x+25
=79°
Therefore, the value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
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Answer:
27
Step-by-step explanation:
Local time in melbourne is always 3 hours ahead of singapore time and singapore is 5 hours behind wellington, which is 12 hours ahead of london. what is the time difference between melbourne and london?
The time difference between Melbourne and London is 11.00 hours.
Here we need to find the time difference between Melbourne and London.
Here we have that the time difference between Melbourne and Singapore is 3 hours ahead.
And the Time difference between Singapore and Wellington is 5 hours behind then the difference between wellington and Melbourne is 3 hours.
Now the time difference between Wellington and London is 12 hours.
Through this we know that the time difference between Melbourne and London 11.00 hours.
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can someone answer this and fast please and thank youuu!
Answer:
Step-by-step explanation:
Find the slope of the lines containing the following points
(-2, 1) & (-5,5)
The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].
As per the question statement, two points lie (-2, 1) & (-5,5) on a line.
We are supposed to find the slope of the line.
To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].
Using these values into above mentioned formula, we get,
Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].
Slope of a line: In mathematics, the slope or gradient of a line is a value that describes both, direction and the steepness of the line.To learn more about Slope of lines, click on the link below.
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424 divided by 3243.6
What is the HCF of 8 and 12?
===============================================
Reason:
HCF = highest common factor
8 = 4*2
12 = 4*3
Both have 4 in common, and this is the largest such factor.
You can use factor trees as an alternative method.
The cost of building a storage house is $70 per square foot flooring. what will it cost to build a storage house 12 feet wide and 10 feet long and 8 feet high?$
The cost of building a storage house is $89,600.
Area of rectangle:
Area of the rectangle is defined as the amount of space covered by a flat surface of a particular shape.
The formula for the area of the rectangle is,
Area of a Rectangle = (Length × Breadth) square units
Given,
The cost of building a storage house is $70 per square foot flooring.
Length = 10 feet
Width = 12 feet
Height = 8 feet.
Here we need to find the cost to build a storage house.
To find the cost of the storage,
First, we have to find the area of the storage house,
Apply the values on the formula, to find the area of the storage house,
=> A = 10 x 12
=> A = 120 square foot.
So, the cost of building the storage house is,
=> 120 x 70
=> 89600.
Therefore, the cost for building the storage is $89,600.
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A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.
the five prime number are 19,29,29,37,41
mean =sum of observations / total number of observation
= 19+29+29+37+41 /5
= 155/5
=31
median = (n+1) / 2 th term n is number of term and n is odd
= (5+1) /2 th term
= 3 rd term
= 29
mode = the value that appears most in the data
= 29
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Translate the sentence into an equation.
Four times the sum of a number and 3 is 2.
Use the variable w for the unknown number.
The problem is:
y = -2(x-3)^2
Please help me find the;
Vertex,
X-Intercepts,
and the Axis of Symmetry
Alg 2, Intercept, Vertex form.
The Vertex is at (3, 0)
The Axis of symmetry is; x = 3
The x-intercept is; x = 3
What is the Vertex and Axis of Symmetry?
We are given the quadratic equation as;
y = -2(x - 3)²
Expanding this gives us;
y = -2(x² - 6x + 9)
y = -2x² + 12x - 18
x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
y coordinate of vertex = f(3) = -2(3)² + 12(3) - 18 = 0
Vertex is at (3, 0)
Axis of symmetry is the x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
x-intercepts is gotten by finding the roots which are; x = 3 and 3
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8. Olivia's brother is twice her age
minus 9 years. He is also as old
as half the sum of the ages of
Olivia and both of her 12 year-
old twin brothers. Write and
solve an equation to find the
ages of Olivia and her brother.
The ages of Olivia and her brother are 10 years and 11 years respectively
Let x₁, and x₂ be the ages of Olivia and her brother respectively.
Given that Olivia's brother is twice her age minus 9 years.
⇒ x₂ = 2x₁ - 9 → equation 1
Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.
⇒ x₂ = 1/2 × (x₁ + 12) → equation 2
Using equation 1 in equation 2, we get
2x₁ - 9 = 1/2 × (x₁ + 12)
⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)
⇒ 4x₁ - x₁ = 12 + 18
⇒ 3x₁ = 30
⇒ x₁ = 10 (dividing by 3 on both sides)
Using the value of x₁, in equation 1,
⇒ x₂ = 2(10) - 9
⇒ x₂ = 20 - 9
⇒ x₂ = 11
Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.
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Joe works as a pianist in a local restaurant. He makes $8.50 an hour. He was able to work 45 hours last week. How much money did he make that week?
Answer: $382.50
Step-by-step explanation:
8.50 x 45 = 382.50
A bookstore offered mystery bags each containing 12 books. The quantity of each type of book was the same in
each mystery bag. A shopper bought 3 mystery bags and found that 6 books were spy novels.
Based on this information, which prediction can the shopper make about buying mystery bags in the future?
A.There will be 4 more spy novels in 8 bags than in 6 bags
B.There will be 2 more spy novels in 6 bags than in 4 bags.
C.There will be 1 more spy novel in 9 bags than in 8 bags.
D.There will be 6 more spy novels in 10 bags than in 8 bags.
The prediction thay the shopper can make about buying mystery bags in the future is A.There will be 4 more spy novels in 8 bags than in 6 bags.
How to calculate the value?Since the shopper bought 3 mystery bags and found that 6 books were spy novels, it means that there are 6/3 = 2 spy novels in each bag.
There, the prediction thay the shopper can make about buying mystery bags in the future is that there will be 4 more spy novels in 8 bags than in 6 bags.
This is because there's an extra 2 bags which will be equal to 4 spy novels
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What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light i_0i 0 ?
The maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀ is given as -
When unpolarized light is polarized with 2 polarizers, this same intensity I = I₀cos2(Ф) (Malus' law) is obtained. When unpolarized light is polarized with just one polarizer, its intensity is reduced to half that of unpolarized light.What is polarization?Polarization is the property of wave oscillations having a definite direction relative to the wave's propagation direction. Transverse waves that can be polarized are EM waves. The polarization direction is defined as the direction parallel to the EM wave's electric field.
The effect of a polariser on polarised light is described by Malus' law, which states that-
One starts with unpolarized light.The first polariser suppresses the unaligned component of the unpolarised light and produces polarised light (at half the intensity of the input). In your notation, the intensity of this polarised output is I₀.The second polariser lets through a fraction (cos)²Ф of the polarised output from the first polariser, where is the angle between the polarisers' axes. So, once again,I₀ is the intensity of the polarised input to the second polariser, not the intensity of the unpolarised input to the two-polariser system. The output intensity is limited by this provision; I = I₀cos2(Ф)To know more about the polarization, here
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The correct question is -
What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀.
Which table represents an exponential function?
Answer: Where are the tables?
Write two ratio that are equivalent to 4:5
Answer:
8:10, 12:15
Step-by-step explanation:
