The statements that are true about the ordered pair (−4, 0) and the system of equations include the following:
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true. The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.How to determine the solution?In order to determine which statements are true with respect to a solution of the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;
For ordered pair (-4, 0), we have:
2x + y = -8x
2(-4) + 0 = -8(4)
-8 = -32 (False)
For ordered pair (-4, 0), we have:
x - y = -4
-4 - 0 = -4
-4 = -4 (True).
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Mr. Dunston and Mr. Dolland spent $45 all
together. Mr. Dunston and Ms. Campbell
spent $65 all together. If Ms. Campbell spent
3 times as much as Mr. Dolland, how much
did Mr. Dunston spend?
The money spent by Mr. Dunston is $ 35.
Given that:-
Money spent by Mr. Dunston and Mr. Dolland = $ 45
Money spent by Mr. Dunston and Ms. Campbell = $ 65
Ms. Campbell spent 3 times as much as Mr. Dolland.
We have to find the money spent by Mr. Dunston.
Let the money spent by Mr. Dunston be $ x,
Let the money spent by Mr. Dolland be $ y and,
Let the money spent by Ms. Campbell be $ 3y
Hence, from the data given in the question, we can write,
x + y = 45 ...(1)
x + 3y = 65 ... (2)
By elimination method, we can write,
(2) - (1)
2y = 20
y = 10
x + 10 = 45
x = 45 - 10 = 35
x = 35
Hence, the money spent by Mr. Dunston is $ 35.
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4x + 10y = 2
x - 10y = 13
Answer:
x = 3
y = -1
Step-by-step explanation:
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Check:
From Eq. 1:
4x + 10y = 2
4*3 + 10*-1 = 2
12 - 10 = 2
The solution of the equation is that the value of x = 3 and y = -1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The equation will be solved as,
4x + 10y = 2 Eq. 1
x - 10y = 13 Eq. 2
The result of the sum of Eq. 1 and Eq. 2 is:
4x + x = 5x
10y - 10y = 0y = 0
2 + 13 = 15
Then the result is:
5x = 15
x = 15/5
x = 3
From Eq. 2:
x - 10y = 13
3 - 10y = 13
-10y = 13 - 3
-10y = 10
y = 10/-10
y = -1
Therefore, the solution of the equation is that the value of x = 3 and y = -1.
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Use the product-to-sum identities to rewrite the following expression as a sum or difference.
2sin(2x)sin(2x)
The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.
How to transform a product of trigonometric functions into a sum of trigonometric functions
Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:
sin α · sin β = [cos (α - β) - cos (α + β)] / 2
First, write the trigonometric function defined in the statement:
2 · sin 2x · sin 2x
Second, use the product-to-sum formula by considering α = β = 2 · x:
2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]
cos 0 - cos 4x
1 - cos 4x
Third, write the resulting expression:
2 · sin 2x · sin 2x = 1 - cos 4x
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The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
Is there a proportional relationship between the area and radius of a circle? Explain.
The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
The area of a circle with radius "r" is given as,
A = πr²
Since,π = constant.
Removing constant by proportionality.
A ∝ r²
Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".
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Kevin has $97,800 in a savings account that earns 2% interest per year. The interest is not
compounded. How much will he have in total in 4 months?
Fill in the table using the function rule y=5x-2
The table has been shown using the function rule y = 5x - 2. (Refer to the table attached below).
What is the function rule?The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.When the provided input values are applied, the function rule y = 2 x + 4 produces the output values displayed in the table. Now, the output numbers " are represented by and the input values are represented by. Consequently, the expression f (x) = 3 x + 1 can be used to represent the function rule y = 3 x + 1.So, the rule is y = 5x - 2:
Now calculate values as follows:
(A) When x = 0:
y = 0 - 2y = - 2(B) When x = 1:
y = 5 - 2y = 3(C) When x = 2:
y = 10 - 2y = 8(D) When x = 3:
y = 15 - 2y = 13Therefore, the table has been shown using the function rule y = 5x - 2. (Refer to the table attached below)
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Use Structure A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5?
Multiple choice question.
cross out
A)
yes; The packs of socks are marked up to $7 and then discounted to $5.
cross out
B)
yes; The packs of socks are marked up to $9 and then discounted to $5.
cross out
C)
no; The packs of socks are marked up to $7 and then discounted to $4.20.
cross out
D)
no; The packs of socks are marked up to $5.20 and then discounted to $4.99.
The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.
How to calculate the price?In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:
= Original price + Markup
= 5 + (40% × 5)
= 5 + 2
= $7
Then, the store decides to discount the packs of socks by 40%. This will give a price of:
= 7 - (40% × 7)
= 7 - 2.8
= $4.2
The price isn't discounted to $5.
In conclusion, the correct option is C.
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the cost of 2kg carrots is £7 work out the cost of 5kg carrots.
Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.)
Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.4, 0).
(x, y) =
Answer:
(x, y) ≈ (3.4, 1.8)
Step-by-step explanation:
You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).
GraphThe first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...
(x, y) ≈ (3.42, 1.8)
(x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place
__
Additional comment
For each pair of points, the equation of the line can be written as ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
(2 -1)(x -0) -(4.3 -0)(y -1) = 0 ⇒ x -4.3y +4.3 = 0
and
(0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0 ⇒ -3x -3.3y +16.2 = 0
The calculator result in the second attachment shows the exact solution to be ...
(x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)
solve the following inequality
x³-5x² < 4x-20
The final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
What is factorization?
Factorization, also known as factoring, is the process of breaking down an object (such as a number, a matrix, or a polynomial) into a product of another object, or factors, which when multiplied together yield the original object (such as the number or matrix) in question.
What is inequality?
A relationship between two expressions or values that are not equal to each other is called an inequality.
Here, we have
Factor out the greatest common factor from each group
x²(x+5) - 4(x+5) = 0
Factor the polynomial by factoring out the greatest common factor, (x+5)
(x+5)(x²-4) = 0
Rewrite 4 as 2².
(x+5)(x²-2²) = 0
(x+5)(x+2)(x-2) = 0
Now,
x+5 = 0
x-2 = 0
x+2 = 0
set x+5 =0 then we get
x = -5
set x+2 =0 then we get
x = -2
set x-2 =0 then we get
x = 2
Hence, the final solution is all the values that make (x+5) (x+2) (x−2)=0 true.
x = −5,−2,2
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Current Attempt in Progress
Monty Corp. purchased a new machine on October 1, 2022, at a cost of $124,000. The company estimated that the machine will have
a salvage value of $15,000. The machine is expected to be used for 10,000 working hours during its 5-year life.
(a)
Compute the depreciation expense under straight-line method for 2022.
Depreciation expense $
2022
The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.
What is the straight-line depreciation method?Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.
The quotient is the depreciation expense for each year. However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.
Note that the depreciable amount is the difference between the cost of the asset and its salvage value.
Cost of new machine = $124,000
Purchase date = October 1, 2022
Estimated salvage value = $15,000
Depreciable amount = $109,000 ($124,000 - $15,000)
Estimated useful life = 5 years
Estimated working hours = 10,000 hours
Depreciation method = Straight-line
Annual Depreciation Expense = $21,800 ($109,000/5)
October 1, 2022, to December 31, 2022, = 3 months
Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)
Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.
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If f(x) = 4x² and g(x)=3x, what is (fg)(x)?
(fg)(x)=
(Simplify your answer.)
The multiplication of the given function is (fg)(x) = 12[tex]x^3[/tex]
What is operations of the function ?
Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:
Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )
It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.
The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).
Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).
Here the given function ,
=> f(x) = 4[tex]x^2[/tex]
=> g(x)= 3x
Now (fg)(x) = f(x)*g(x)
=> (fg)(x)= 4[tex]x^2[/tex]*3x
=> (fg)(x) = 12[tex]x^3[/tex]
Hence the (fg)(x) = 12[tex]x^3[/tex].
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Alan has 229 songs on a playlist. He's categorized them in the following manner: 11 rock, 21 Latin American, 46 gospel, 30 country, 39 rap, 25 classical, and 57 pop. If Alan begins listening to his playlist on shuffle, what is the probability that the first song played is a rock song?
The probability of the event that the first song played by Alan is a rock song is 0.01.
What is probabilityThe probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes. But the probability of an event say event "a" not occurring is 1 - a.
We shall calculate for the probability of the event that Alan's first song to be played is a rock song as follows:
probability of playing a rock song = 11/229
probability of not playing a Latin American song = 208/229
probability of not playing a gospel song = 183/229
probability of not playing a country song = 199/229
probability of not playing a rap song = 190/229
probability of not playing a classical song = 204/229
probability of not playing a pop song = 172/229
So,
The probability that the first song played is a rock song = (11/229) × (208/229) × (183/229) × (199/229) × (190/229) × (204/229) × (172/229)
The probability that the first song played is a rock song = 0.05 × 0.91 × 0.80 × 0.67 × 0.83 × 0.89 × 0.75
The probability that the first song played is a rock song = 0.01
Therefore the probability of the event that Alan's first song played is calculated to be 0.01 approximated to 2 decimal places.
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Write a coordinate rule for the dilation.
Answer: 584390
Step-by-step explanation: the r4u819
Find a formula for the nth term in this
arithmetic sequence:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
an =?n+
Answer: an=4n+5
Step-by-step explanation:
a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...
A formula for the nth term of the arithmetic sequence:
[tex]a_n=a_1+d(n-1)[/tex]
where: a₁ - is the first term of the arithmetic sequence
d - is the difference between the terms of the arithmetic sequence
d=a₂-a₁=a₃-a₂=a₄-a₃= ...
d=13-9=17-13=31-17= ...
d=4
n - is the number of the arithmetic sequence term
[tex]a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5[/tex]
Solve 2x2 + 20x + 8 = 0 by completing the square.
Answer:
x=−5+ 21 ,−5− 21
Step-by-step explanation:
x= 4−20+4= 214−20−4 =21
Which expression is equivalent to 5x - 5x + 3x - 3x?
Answer:
0
Step-by-step explanation:
subtracting same numbers give you zero
rita class has 14 girls and 16 boys how does the ratio 14:30 describe ritas class
Answer:
The ratio shows that there are 14 girls to 30 students in total
Step-by-step explanation:
14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students
Helppp it’s due tomorrow
……..
By using a trigonometric relation we will see that FD = 32, the correct option is C.
How to find the length FD?We can see a right triangle, such that FD is the hypotenuse.
We also know one angle of this triangle, and the adjacent cathetus to that angle.
Now remember the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Replacing the values we know we get:
cos(30°) = 28/hypotenuse
Solving the equation for the hypotenuse we get:
hypotenuse = 28/cos(30°) = 32.3
Rounding to the next whole number we get FD = 32
The correct option is C.
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What do this mean on this work
Answer:
The answer should be 13.928
Step-by-step explanation:
You do A square + B square = C square
For each chart below, identify the output rule and classify the function as exponential, linear or neither.
The classification and the output rule for each function in this problem is given as follows:
1. Output rule: y = 5x + 11. Classification: Linear.
2. Output rule: y = 2^x. Classification: Exponential.
3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.
What defines a linear function?A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:
y = mx + b.
In which:
m is the addition to y when x increases by one.b is the value of y when x = 0.Hence, for the first table, as 5 is added to x when x increases by one, the rule is:
y = f(x) = 5x + 16.
What defines an exponential function?An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:
y = a(b)^x.
In which:
b is the addition to y when x increases by one.a is the value of y when x = 0.Hence, for the second table, the rule is:
y = 2^x.
For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.
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help pleas now...............math
The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.
According to the question,
We have the following expression:
q/3+2/3 = 8q/3-5/3
Now, taking 3 as the denominator on both the sides:
(q+2)/3 = (8q-5)/3
Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:
q+2 = 8q-5
Now, changing the sides of this expression:
8q-5 = q+2
Moving q from the right hand side to the left hand side:
8q-q-5 = 2
7q -5 = 2
Moving 5 from the left hand side to the right hand side:
7q = 2+5
7q = 7
q = 7/7
q = 1
Hence, the value of q after solving the given expression is 1.
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What is the sum -10 + (-9) + (-8) + ... + 9 + 10 +11 + 12?
Answer:
23
Step-by-step explanation:
the numbers from -10 to 10 cancel out, so all that is left is 11+12=23
Finding missing side length given two similar triangles
Value of BC is 36 in triangle's similarity .
What is the triangle's similarity?
If one of the following conditions is satisfied by two triangles, they are comparable. There is equality between two sets of matching angles. It is proportionate to have three sets of comparable sides. In addition to being proportional and having equal corresponding angles, two pairs of corresponding sides are also identical.ΔABC and ΔPQR are similar .
so all sides are equal in ratio .
let BC is x .
AB/BC = PQ/QR
18/x = 2/4
18 * 4 = 2 * x
x = 18 * 4/2
x = 18 * 2
x = 36
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Mr.Marx has been in the journalism industry for 24 years. She has worked at her current job 8 of those years. What fraction of her career has she been at her current job? What is this fraction as a decimal?
Fraction of her career has she been at her current job is 1/3 or 0.333.
Given:
Mr.Marx has been in the journalism industry for 24 years.
She has worked at her current job 8 of those years.
Fraction = number of year in current job/number of years in journalism industry.
= 8 years/24 years
= 8/24
= 1/3 ≈ 0.333.
Therefore fraction of her career has she been at her current job is 1/3 or 0.333.
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The average December temperature in Salt Lake City, Utah is 10 degrees Farenheit. The actual December
temperture can vary in Salt Lake City by 5 degrees Farenheit either above or below the average. What is the
minimum temperature of Salt Lake City in December?
The minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
The average December temperature in Salt Lake City, Utah, is 10 degrees Fahrenheit. The actual December temperature can vary in Salt Lake City by 5 degrees Fahrenheit either above or below the average.
We need to find out the minimum temperature in Salt Lake City in December. Let the temperature be denoted by the variable "M". The minimum temperature is the difference between the average temperature and the variation in the temperature.
M = 10 - 5
M = 5
Hence, the minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.
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Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. At this rate, when will Cassidy and Calvin have the same amount of money? How much will they each have?
Cassidy and Calvin have the same amount of money in 11 months.
The amount is $370.
How to illustrate the equation?Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:
= 425 - 5m
Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:
= 95 + 25m
where m = number of months
The equation will be:
425 - 5m = 95 + 25m
Collect like terms
425 - 95 = 25m + 5m
330 = 30m
Divide
m= 330/30
m = 11
The number of months is 11.
The amount will be:
= 425 - 5m
= 425 - 5(11)
= 425 - 55.
= 370
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Question 4
Simplify the expression: (7x + 2)²
A 49x² + 4
B 49x² + 28x + 4
C 49x² - 4
D 25x² + 9
Answer:
B
Step-by-step explanation:
(7x+2)(7x+2)
7x×7x=49
7x×2+2×7x=28x
2x2=4
One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.
The percentage decrease in population is 17%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply it by 100. percentage . The word per cent means per 100. It is represented by the symbol “%”.
percentage decrease in population= (0riginal population- new population)÷ original population × 100
%decrease in population = (181000 - 150230) ÷ 181000× 100
=( 307770×100)/181000
= 17%
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17%
Step-by-step explanation:
i tried it it worked
