Answer: not factorable with rational numbers.
Step-by-step explanation: No explanation because it is not factorable.
Find an equation of variation in which y varies directly as x and y=1 when x=0.5. Then find the value of y when x = 14.
An equation of variation is y= ___.
When x=14, the value of y is ___.
Part 1
The value of y is twice that of x, so the equation is y = 2x.
Part 2
Substituting in x = 14, we get y = 2(14) = 28.
What is the length of CB on the number line?
A 1
B −2
C −3
D 3
Norman has a coin collection. There are 2 dimes for every 3 quarters in his collection. If Norman has a total of 68 dimes, how many quarters does he have?
34
45
102
136
Answer: Option C, 102
Step-by-step explanation:
x = 102 (C)
Let the quarters be x
So, 2 dimes = 3 quarters
1 dime = 3/2 quarters
68 dimes = 68×3/2
= 204/2
= 102
Pleaseeeeeeeeeeeee help!
The symbolic quantified statement is given as:
For all real integers x and y, if x³ = y³, then x = y.
Using quantifiers, this can be written as:
∀x,y∈ℝ, (x³ = y³) → (x = y)
What is the explanation for the above?
The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.
The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.
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Evaluate 3x2 + 3x - 9, when x = 2
Answer:
9
Step-by-step explanation:
3x^2 + 3x - 9
Substitute x = 2 into the equation.
3(2)^2 + 3(2) - 9
3(4) + 6 - 9
12 + 6 - 9
18 - 9 =
9
Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals. Determine the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament is 20.
What is a linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0.
In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.
Here, we have
Given: Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals.
we have to determine the number of players the team can bring to the tournament.
So to make an equation, the bus charge would be the y-intercept (If no member went, they still paid for the bus fee) and the meals would be the slope (since it is dependent on how many members ride the bus.)
The total would add up to be 2412.50, so the equation would be:
2412.50 = 67x+1072.50
where x = the number of players the team can bring to the tournament without going outside of their budget.
After solving this, we get
2412.50 = 67x+1072.50
2412.50 - 1072.50 = 67x
1340 = 67x
x = 20
Hence, the number of players the team can bring to the tournament is 20.
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Which step brings you closest to getting the variable alone on one side of the equation
16 = 7x-5?
Answer:
Adding 5 from both sides then dividing by 7
Step-by-step explanation:
The best way to isolate x is to add 5 to both sides first:
21 = 7x
Then to isolate x by itself divide both sides by 7
x = 3
That would be the value of x and your final answer.
can i have help with this pls, no one will teach me it
Answer:
x = 21
Step-by-step explanation:
As stated in the hint: When angles form a linear pair, their sum is 180° in other words, these are supplementary angles:
3x + 18 + 4x + 15 = 180 add like terms
7x + 33 = 180 subtract 33 from both sides
7x = 147 divide both sides by 7
x = 21
Find the difference. Write the answer in simplest terms. 2/3- 3/9
Answer:
1/3
Step-by-step explanation:
2/3=6/9
6/9-3/9=3/9
3/9=1/3
Answer:
1/3
Step-by-step explanation:
2/3 -3/9= 6/9 -3/9=3/9
=1/3
Someone plss help I tried and I still can't get it plss help me
Answer:
-18 is an integer but not a whole number
Step-by-step explanation:
a whole number is only positive numbers and 0 itself while an integer is basically any number that isn't a decimal or a fraction. -18 is an integer, but it can't be a whole number because it is a negative number.
Determine whether each relation is a function.
Answer:
Each relation is a function because none of the domain repeats.
I NEEDD HELPPP ASAPPPPPPPP
The value of sin (α + β) is,
⇒ sin (α + β) = - 135/377
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.
Angle α in quadrant 3:
y = opposite = 21 and x = adjacent = 20
Then, hypotenuse = √( 21² + 20²)
= √ ( 441 + 400)
= sqrt( 881)
So, sin α = 21/√881
= 21 × sqrt(881)/881
And, cos α = 20/sqrt(881) = 20sqrt(881) / 881
Since, Angle β in Quadrant 2:
Hence, adjacent = -5 and hypotenuse = 13
Then, by Pythagorean,
y = opposite = 12
So, sin β = 12/13, cos β = -5/13
as given,
And, tan β = -13/12
Since, We know that;
sin (α + β) = sin α cos β + cos α sin β
= 21/√881 × - 5/13 + 20/√881 × 12/13
= 1/√881 (- 105/13 + 240/13)
= - 1/√881 (135/13)
= - 135/377
Hence, The value of sin (α + β) is,
sin (α + β) = - 135/377
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What is the missing side length?
y = 1/3x -1
x-intercept (3,0)
How did they get this answer? Somebody please help
Answer:
Step-by-step explanation:
x-intercept is where the line cuts the x-axis. That is, when y=0.
Substitute y=0 and we get:
\(0=\frac{1}{3} x-1\)
\(1=\frac{1}{3} x\)
\(x=3\)
So x-intercept is the point (3,0).
4. To ship a package, it costs $5 for shipping supplies and $0.75 for each pound the piece weighs. If Tori
wants to ship a 12-pound package, how much would it cost?
Pls answer report if wrong
Answer:
III
Step-by-step explanation:
It is expanded by an uneven scale factor.
The speed of hair growth for humans is about 1, centimeters per month. Susan's hair has grown 3 centimeters since the last time she got it cut. Let z be the number of months she has been growing her hair. Write a number model to show how many months she has been growing her hair. Then solve the problem.
Answer: z = 3
Step-by-step explanation: 1 centimeter = 1 month so 3 centimeter = 3 months
The difference between the areas of the figures is less than 4.
An absolute value inequality that represents this situation is ___
The solution of the inequality is ___
Thank you!
What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).
The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.
In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.
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Which number doesn't share the same pattern as
2,20, 4,8,300
Micheal records the number of miles he runs each week for nine weeks.
6,11,13,8,15,9,11,5,9
Which box plot represents the data?
Answer:
... c
Step-by-step explanation:
Carbon 14 is a radioactive isotope of carbon, the most common isotope of carbon being carbon 12. Carbon 14 is created when cosmic ray bombardment changes nitrogen 14 to carbon 14 in the upper atmosphere. The resulting carbon 14 combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis. Animals acquire carbon 14 by eating plants. When an animal or plant dies, it ceases to take on carbon 14, and the amount of isotope in the organism begins to decay into the more common carbon 12. Carbon 14 has a very long half-life, about 5730 years. That is, given a sample of carbon 14, it will take 5730 years for half of the sample to decay to carbon 12. The long half-life is what makes carbon 14 dating very useful in dating objects from antiquity.
Consider a sample of material that contains A(t) atoms of carbon 14 at time t. During each unit of time a constant fraction of the radioactive atoms will spontaneously decay into another element or a different isotope of the same element. Thus, the sample behaves like a population with a constant death rate and a zero birth rate. Make use of the model of exponential growth to construct a differential equation that models radioactive decay for carbon 14.
Solve the equation that you proposed in to find an explicit formula for A(t).
Answer:
Differential equation: \(\frac{dA}{dt} = k\cdot A(t)\), \(k < 0\), \(k = -\frac{1}{\tau}\), \(\tau > 0\).
Solution: \(A(t) = A_{o}\cdot e^{-\frac{t}{\tau} }\)
Step-by-step explanation:
Let suppose that rate of change of the amount of Carbon-14 atoms are directly proportional to the current amount of Carbon-14 atoms. That is:
\(\frac{dA}{dt}\propto A(t)\)
\(\frac{dA}{dt} = k\cdot A(t)\)
Where:
\(A (t)\) - Amount of Carbon-14 atoms, dimensionless.
\(k\) - Proportionality constant, measured in \(\frac{1}{yr}\).
\(k\) must be negative as death rate is constant and birth rate is zero. (\(k< 0\)). Dimensionally, we can rewritte this constant as following:
\(k = -\frac{1}{\tau}\)
Where \(\tau\) is the time constant (\(\tau > 0\)), measured in years.
We can find the solution of the ordinary differential equation by separating each variable:
\(\frac{dA}{dt} = -\frac{1}{\tau}\cdot A\)
\(\int {\frac{dA}{A} } = -\frac{1}{\tau} \int \, dt\)
\(\ln A(t) = -\frac{t}{\tau} + C\)
\(A(t) = e^{-\frac{t}{\tau}+C }\)
\(A(t) = e^{C}\cdot e^{-\frac{t}{\tau} }\)
\(A(t) = A_{o}\cdot e^{-\frac{t}{\tau} }\)
Where \(A_{o}\) is the initial amount of atoms of Carbon-14.
Solve the formula for the given variable
-2x-6=4x
Helppp mee
Last year, The Lakewood Times had a total of 4,770 subscribers. This year, after the paper
was bought out, it had 6,201 subscribers. What is the percent of increase in the number of
subscribers?
%
The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
What is the percentage increase?
Percent increase is a way of measuring how much something has increased relative to its original value. It is expressed as a percentage, and it is calculated by taking the difference between the new value and the original value, and then dividing that difference by the original value, and then multiplying by 100.
Formula: % increase = (new value - original value) / original value x 100
To find the percent increase, you can use the formula:
% increase = (new value - old value) / old value x 100
In this case, the percent increase would be:
% increase = (6201 - 4770) / 4770 x 100 = 30.4%
Hence, The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
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What are the solutions of the equation (2x + +3)2 +
+ 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to
solve.
-40V5
O X=
-7± √5
OX=
O x= -7 and x = -2
O x= -1 and x = 4
Answer:
b
Step-by-step explanation:
By using the substitution method the solution to the given equation is
x = ±7/2 + √5/2
System of equationGiven the equation expressed as:
(2x +3)^2 + 8(2x + 3) + 11 = 0
Expand the equation
4x^2 + 12x + 9 + 16x + 24 + 11 = 0
4x^2 + 28x + 44 = 0
x^2 + 7x + 11 = 0
Factorize the result to have:
On factorizing the values of x are
x = ±7/2 + √5/2
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If a car is going 100 m/s and slows down to 50 m/s in 20 s, what is the rate
of acceleration?
How many 2 1/3 m lengths of rope can be cut from a rope of length 21 m?
Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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Find the missing side lengths, put answer as radical in simplest form
Look at picture for reference
The value of the missing side lengths x and y are 5√2 and 5 respectively.
What is the value of side length x and y?The figure in the image is a right triangle.
Angle θ = 45 degree
Hypotenuse = x
Opposite to angle θ = y
Adjacent to angle θ = 5
To solve for side x and side y, we use the trigonometric ratio.
Note that:
Cosine = adjacent / hypotenuse
tangent = opposite / adjacent
Solving for x:
Cosine = adjacent / hypotenuse
Plug in the values
cos( 45 ) = 5/x
x = 5 / cos( 45 )
x = 5√2
Solving for side y:
tangent = opposite / adjacent
Plug in the values
tan( 45 ) = y/5
y = tan( 45 ) × 5
y = 5
Therefore, the value of side length x is 5 units.
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I need to finish this quick!!!!!!!!!!!!!!
Answer:
-4??
Step by step explanation:
i believe