You have a 32-foot fence around a square garden. You paint 1/3 of one side of the fence. What fraction of the fence did you paint?
Which situations can be represented by a linear function?
Select each correct answer.
Every day, the number of bacteria in the dish is 3 times what it was the previous day.
Every year, Luisa puts $10 into her savings account.
A country's population increases by 0.8% each year.
The barrel leaks 0.5 L of water each day.
The barrel leaks 0.5 L of water each day.
Every year, Luisa puts $10 into her savings account.
Linear functions represent situations with a constant rate of change. Saving $10 every year and a barrel leaking 0.5 L of water each day are examples of linear relationships due to this constant change.
Situations that can be represented by a linear function are those where the rate of change remains constant. Let's analyze the given situations according to this condition:
Every year, Luisa puts $10 into her savings account. This describes a constant rate of change, with $10 being added each year, which can be represented by a linear function.The barrel leaks 0.5 L of water each day. Here, the change in water level is constant (0.5 L per day), also indicative of a linear relationship.These two scenarios fit the criteria for being linear because they involve a constant rate of change over time. On the other hand, scenarios like the exponential growth of bacteria or percentage-based population growth are not linear since the rate of change is not constant; these would be represented by exponential functions.
Pablo is buying chips and salsa for a party and has a budget of no more than $36.Chips cost $3 per bag and a container of salsa costs $4
m∠6 is (2x – 5)° and m∠8 is (x + 5)°. What is m∠3?
Answer:
m∠3=115°.
Step-by-step explanation:
It is given from the figure that line q is parallel to s and r is the transversal.
Since, m∠6 and m∠8 forms a linear pair as they are on the straight line r, therefore using the linear pair property, we have
m∠6+m∠8=180°
⇒[tex]2x-5+x+5=180^{\circ}[/tex]
⇒[tex]3x=180^{\circ}[/tex]
⇒[tex]x=60^{\circ}[/tex]
Thus, the measure of ∠6 is [tex]2x-5=2(60)-5=120-5=115^{\circ}[/tex]
Now, m∠3=m∠6=115° as both m∠3 and m∠6 forms the alternate interior angle pair.
Therefore, the measure of m∠3=115°.
in one week there are 10,080 minutes. what is this number in scientific notation?
The temperature, t, in Burrtown starts at 21°F at midnight, when h = 0. For the next few hours, the temperature drops 4 degrees every hour. Which equation represents the temperature, t, at hour h?
A. t = 21h + 4
B. t = 4h + 21
C. t = –4h + 21
D. t = –21h + 4
Answer:
C. t = –4h + 21
Step-by-step explanation:
We know that when h = 0, t = 21°F. Replacing h = 0 in equation A and D we get:
A.
t = 21h + 4
t = 21(0) + 4
t = 4
D.
t = –21h + 4
t = –21(0) + 4
t = 4
So, none of them are correct.
The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in equation B and C we get:
B.
t = 4h + 21
t = 4(1) + 21
t = 25
C.
t = –4h + 21
t = –4(1) + 21
t = 17
In consequence, C is the correct option.
Write an equation of a line that is parallel to x=8 and that passes through the point (-3,-2)
Answer:
The answer is x=-3.
Step-by-step explanation:
I'm not sure how to word it, but I did this question on khan, and got this answer and it was right.
What is the length of chord in O below?
A. 5 units
B. 5.70 units
C. 2.5 units
D. 10 units
The length of chord CD is 5 unit.
What is Chord?The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle. It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.
We have,
As, the distance to both chords are 5.70 unit.
and, both chords are 90 degrees from the line then the chords are identical.
As, the length of Chord AB = 5 unit then the length of chord CD =5.
Thus, the length of chord CD is 5 unit.
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Find the exact value of sin(11pi/8).
Choices are in the attachment.
Is 5 a prime composite or neither
Answer:
Prime
Step-by-step explanation:
Its factors are:1 and itself.
ALL prime numbers have the same 2 factors: 1 and itself.
Write 796.384 in expanded form
Given a polynomial f(x), if (x + 3) is a factor, what else must be true?
What applies here is one of the laws of the factorization of polynomials, called the factor theorem and it states that:
For a polynomial f(x) , if for any value a, f(a) =0 then (x-a) is factor of f(x)
Example:
Consider the polynomial
[tex]f(x) = x^{3} - 3x^{2} - 8x+4[/tex]
For a =3,
[tex]f(a) = (3)^{3} - 3(3)^{2} - 8(3)+24[/tex]
= 27-27-24+24 = 0
f (3)= 0
which means (x-3) is a factor of f(x)
Applying the above rule to the question:
if (x + 3) is a factor of a polynomial f(x), then f(-3) = 0
note that (x+3) can also be written as (x- (-3)).
use the table below to find (FoG)(1)
x 0 1 2 3 4 5 6 7
f(x) 5 7 9 11 13 15 17 19
g(x) 3 6 9 12 15 18 21 24
Answer:
value of [tex](f o g)(1)[/tex] is, 17
Step-by-step explanation:
We have to find the [tex](f o g)(1)[/tex]
Using the given tables;
[tex](f o g)(1) = f(g(1))[/tex] ......[1]
At x = 1
g(1) = 6
Substitute this in [1] we have;
[tex](f o g)(1) = f(6)[/tex]
At x = 6
f(6) = 17
then;
[tex](f o g)(1) = 17[/tex]
Therefore, the value of [tex](f o g)(1)[/tex] is, 17
Which of the following quadratic functions has a graph that opens downward?
Check all that apply.
A. y=2x-x^2
B. y= 1/3x^2-8x-13
C. y=2/3x^2-13x+5
D. y= -(3+x^2)
...?
D. Y=-(3+x^2)
A. Y=2x-x^2
Answer:
The answers are a) y=2x-x^2 and d) y=-(3+x^2) and in the attached file are the graphs.
Step-by-step explanation:
Quadratic equations are those where the exponent of the unknown term is squared, that is, the unknown is elevated to exponent 2. They have the general form of a trinomial:
ax2 + bx + c = 0
where a, b and c are real numbers and are called coefficients. Thus, a is the coefficient of x2, b is the term or coefficient of x and c is the independent term.
Which is NOT a way to state the meaning of the expression h + 7?
A-7 more than a number
B-A number added 7 times
C-A number increased by 7
D-7 is added to a number
Which of the following points are solutions to the system of inequalities shown below? Check all that apply. x + y 5 + 2 y > 2 A. (1, 1) B. (5, 2) C. (2, 5) D. (3, 6) E. (1, -1) F. (2, -5)
The points that are solutions to the system of inequalities x + y 5 + 2 y > 2 below are (5, 2), (3, 6), (1, 1). Options B, C, A, and D. For is mathematically given as
What are inequalities?Generally, inequalities are simply defined as the relationship between two non-equal expressions using a symbol like "not equal to," "greater than," or "less than."
In conclusion, The points (5, 2), and (2, 5), (1, 1) are the ones that are the solutions to the system of inequalities x + y 5 + 2 y > 2 below (3, 6).
For (5, 2),
5 + 2* 5 + 2 *2 > 2
19>2
For (2, 5)
2 + 5* 5 + 2*5 > 2
37>2
For (3, 6).
3 + 6*5 + 2*6 > 2
45>2
For (1, 1)
1 + 1* 5 + 2*1 > 2
8>2
For (1, -1)
1 + -1* 5 + 2 *-1 > 2
-6<2
For (2, -5)
2 + -5* 5 + 2*-5 > 2
−33<2
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How many steps does it take to complete 0.1 km?
Answer:1250
Step-by-step explanation:
Find the equation of the line tangent to the graph of y = cos(2x) at x = pi/4 ...?
How many grains of sand fit in a 5 gallon bucket?
To estimate the number of grains of sand that fit in a 5-gallon bucket, we can calculate the volume of the bucket and the volume of a grain of sand. By assuming the grains are approximately the same size and shape, we can use the formula for the volume of a sphere to estimate the number of grains.
Explanation:To answer this question, we need to make some assumptions. Let's assume that the grains of sand are roughly the same size and shape. We can estimate the number of grains of sand that fit in a 5-gallon bucket by considering the volume of the bucket and the volume of a grain of sand. The volume of a grain of sand can be approximated as a sphere.
Using the formula for the volume of a sphere (V = (4/3)πr³), we can find the volume of a grain of sand. If the grain of sand has sides that are 1.0 mm long, the radius of the sphere would be 0.5 mm (half of the side length).
Now, we can calculate the volume of the 5-gallon bucket, convert it to cubic millimeters, and divide it by the volume of a grain of sand to estimate the number of grains that fit in the bucket.
A 5-gallon bucket can hold approximately 36 million grains of sand.
To estimate the number of grains of sand that can fit into a 5-gallon bucket, we need to start with the volume of the bucket and an average sand grain.
A standard 5-gallon bucket is approximately 18.927 liters (since 1 gallon = 3.78541 liters).
An average grain of sand has a diameter ranging from 0.063 mm to 2 mm. We'll use an average grain size of 1 mm for our calculations. The volume V of a sphere (which we can use to approximate a sand grain) is given by the formula:
V = 4/3 π r³
For a grain of sand with a 1mm diameter, the radius r is 0.5 mm or 0.0005 meters. Therefore:
V = 4/3 π (0.0005)³ ≈ 5.24 x 10-10 m³
The volume of the 5-gallon bucket in cubic meters is:
18.927 liters = 0.018927 m³
Dividing the volume of the bucket by the volume of a single grain of sand gives us:
Number of grains = 0.018927 / 5.24 x 10-10 ≈ 3.613 x 107 grains
Therefore, approximately 36 million grains of sand can fit into a 5-gallon bucket.
Ryan's gas tank is 1/10 full. After he buys 11 gallons of gas, it is 3/5 full. How many gallons can Ryan's tank hold?
What is the quotient and remainer for 32÷6?
Four less than the quotient of a number and 3 is - 10
To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.
Explanation:To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:
x/3 - 4 = -10
To solve for x, we can start by adding 4 to both sides:
x/3 = -6
Next, we can multiply both sides of the equation by 3 to isolate x:
x = -18
Therefore, the solution to the equation is x = -18.
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How to solve this please help
Blake has more than five friends.
Let f represent the number of Blake's friends.
Which inequality describes the number of Blake's friends?
f < 5
f > 5
f ≤ 5
f ≥ 5
Answer: The correct option is (B) [tex]f>5.[/tex]
Step-by-step explanation: Given that Blake has more than five friends.
We are to select the inequality that describes the number of Blake's friends.
The number of Blake's friends is represented by f.
According to the given information, we have
the inequality that describes the number of Blake's friends is given by
[tex]f>5.[/tex]
Thus, (B) is the correct option.
A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100?
f(n) = f(n - 1) • 0.3 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.3 + 25, n > 0
f(n) = f(n - 1) • 0.7 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.7 + 25, n > 0
Which equation can be simplified to find the inverse of y = x2 – 7?
To find the inverse of the function y = x² - 7, interchange x and y to get x = y² - 7, then solve for y to get the inverse function y = (x + 7), taking into account both the positive and negative square roots.
To find the inverse of the function y = x² − 7, we need to swap the x and y variables and then solve for y. Here's a step-by-step process:
Replace y with x and x with y to get the equation x = y² − 7.Add 7 to both sides to isolate the y² term: x + 7 = y².Take the square root of both sides, remembering to consider both the positive and negative roots: y = ±√(x + 7).This results in the inverse function y = ±√(x + 7), but typically, we only take the principal square root for the inverse function, which would be y = √(x + 7) assuming x ≥ -7.
How to get my mother to celebrate her birthday, she thinks that it is not important and that she should not celebrate her birthday, how do i convince her to celebrate her birthday? Please help me...!
if h(x)=-1/2x+3, find h(-29)
Which of these problem types can not be solved using the Law of Sines?
A. SSS
B. ASA
C. AAS
D. SAS
Answer: The correct option are A, B and D.
Explanation:
The law of sine states that,
[tex]\frac{\sin A}{a} =\frac{\sin B}{b}=\frac{\sin C}{c} [/tex]
Where A, B, C are interior angles of the triangle and a, b, c are sides opposite these angles respectively as shown in below figure.
Since we need the combination of two angles and one side or two sides and one angle.
The Law of sine is useful for AAS and SSA type problems.
Reason for correct option:
In option A three sides are known but no angle is not given, therefore the SSS problem can not be solved by Law of sine and the option A is correct.
In option B a side is known and two inclined angle on that line are known. But to use Law of sine we want the line and angle which in not inclined on that line, therefore the ASA problem can not be solved by Law of sine and the option B is correct.
In option D two sides and their inclined angle is known. But to use Law of sine we want the side and angle which in not inclined on that line, therefore the SAS problem can not be solved by Law of sine and the option D is correct.
Reason for incorrect option:
In option C, the two consecutive angles are given and a side which makes the second angle with base side, therefore the first angle is opposite to the given side, so the law of sine can be used for AAS problems.
Therefore, option C is incorrect.
Which equation can be used to solve the problem?
How many 12-packs of juice boxes contain a total of 84 juice boxes?
A.
12 + b = 84
B.
12 ÷ b = 84
C.
12b = 84
D.
b ÷ 12 = 84