the output of a relation is the difference of three times the input and five?
Answers
Answer:
The equation that represents this relation is y = 3x - 5
The relation is a function
If the domain of the relation is x > 2, the range of the relation is y > 1
Answer:
The equation that represents this relation is y = 3x - 5 .
The relation is a function.
If the domain of the relation is x > 2, the range of the relation is y > 1 .
Step-by-step explanation:
The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.
Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.
To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:
When x = 2, y = 3(2) − 5 = 6 − 5 = 1.
Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.
Related Questions
If the rate, in gallons per minute continues, how many gallons of water will flow from the hose in 45 minutes
Answers
Answer:
Step-by-step explanation:
45 gallons but your questtion doesnt make sense because you dont give us the number in gallons per minute
Which is the solution to the inequality? y minus 27 greater-than-or-equal-to negative 13
Answers
Answer:
y is greater than or equal to 14
Step-by-step explanation:
Answer:
y ≥ 14
Step-by-step explanation:
y - 27 ≥ -13
you manipulate this inequality like it is an equation. Only take care that the inequality swaps if you multiply by a negative. In this case, that is not needed.
y - 27 +27 ≥ -13+27
y ≥ 14
What is the difference between the measure of an arc and the arc length? Explain.
Answers
The measure of an arc is the degree/radian measure. You measure the central angle to find the measure of an arc.
The arc length is the actual length (like 2pi inches or 7 cm, etc.). You find the length of the curved part (the arc), not the straight distance between the 2 points given.
If Bill has 5 apples and eats 3 of them, how much is left.
Answers
Answer:
2 apples Follow me if u have any more request next time
Step-by-step explanation:
5-3=2
Total amount of rain each county received for five days. Palm Beach 2.3., Broward 3.5,and Dade 3.0. On average,how many inches of rain did each county received each day.
Answers
Answer: On average, each country receives 2.93 inches of rain each day.
Step-by-step explanation:
Since we have given that
Palm Beach = 2.3
Broward = 3.5
Dade = 3.0
So,the average inches of rain each country would receive each day would be :
[tex]\dfrac{2.3+3.5+3.0}{3}=\dfrac{8.8}{3}=2.93\ inches[/tex]
Hence, on average, each country receives 2.93 inches of rain each day.
The combined volume of all the things and aquarium is 1.25×10 to the six power gallons the aquarium plants to install a new dolphin take with a volume of 250,000 gallons what was the total volume of all the tanks at the aquarium after the new dolphin tank is installed
Answers
Answer:
1,500,000 gallons
Step-by-step explanation:
In this question, we are to calculate the total volume of the aquarium after installing a new dolphin tank.
Mathematically, to calculate this, we simply need to add the the volume of the new dolphin tank to the volume of the things in the aquarium before bringing the dolphin tank.
The volume of all the things in the aquarium before installing the dolphin tank is 1.25 * 10^6 = 1,250,000 gallons
now let’s add the volume of the dolphin tank which is 250,000 gallons
that would be 1,250,000 + 250,000 = 1,500,000 gallons or 1.5 * 10^6 gallons
What is an expression to represent the equation
Answers
Answer:
8 + [tex]\frac{x}{4}[/tex]
Step-by-step explanation:
I'm assuming you want an answer to the top section of the question.
We can start with 8.
8
When a problem asks for the sum, it's looking for addition, so we use the + sign.
8 +
The problem says "a number," so let's represent that with x. Basically, x just means a number we don't know.
8 + x
The "number" is divided by 4, so we'll just put x/4 as our second term.
8 + [tex]\frac{x}{4}[/tex]
What percent of 80 is 32?
Answers
Answer:
40%
Step-by-step explanation:
multiply 80 by.40 you will get 32 hope this helps god bless
You are ordering a burrito with two main ingredients and three toppings. The menu below shows the possible choices. How many different burritos are possible?
(the number of combinations)
Answers
Answer:
840
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
In the menu, there are 6 main ingredients and we take 2 at the same time, so the possible outcomes is:
[tex]C^{6} _{2}[/tex] = [tex]\frac{6!}{(6-2)!*2!}[/tex] = 15
In the menu, there are 8 toppings and we take 3 at the same time, so the possible outcomes is:
[tex]C^{8} _{3}[/tex] = [tex]\frac{8!}{(8-3)!*3!}[/tex] = 56
=> the total number of combinations :
=[tex]C^{6} _{2}[/tex]*[tex]C^{8} _{3}[/tex]
=15 * 56 = 840
Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1.5 m/s, how fast is the area of the spill increasing when the radius is 30 m?
Answers
Answer:
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
Step-by-step explanation:
Derivative Rule:
[tex]\frac{d}{dx}x^n=nx^{n-1}[/tex] [tex]\frac{d}{dx}(y^n)=ny^{n-1}\frac{dy}{dx}[/tex]Given that
The radius of the oil spill increases at a rate 1.5 m/s.
i.e [tex]\frac{dr}{dt}= 1.5\ m/s[/tex]
We need to find the rate of area increase i.e [tex]\frac{dA}{dt}[/tex] .
We know,
The area of the oil spills A = [tex]\pi r^2[/tex] ( since it spreads in circular pattern)
[tex]\therefore A=\pi r^2[/tex]
Differentiating with respect to t
[tex]\frac{dA}{dt}=\pi. 2r\frac{dr}{dt}[/tex]
Plug the value of [tex]\frac{dr}{dt} =1.5 \ m/s[/tex]
[tex]\frac{dA}{dt}=\pi. 2r(3\ m/s)[/tex]
[tex]\Rightarrow \frac{dA}{dt}=6\pi r \ m/s[/tex]
Plug r= 30 m
[tex]\Rightarrow \frac{dA}{dt}=6\pi (30\ m) \ m/s[/tex]
=180 π m²/s
The area of the oil spill is increasing at a rate 180 π m²/s, when the radius is 30 m.
The number of hours of daylight y for day x (x = 1 to 365) in Anchorage, Alaska, can be modeled by y=7.0sin(2π365x−1.4)+12.4. What is the minimum number of hours of daylight in Anchorage?
Answers
Answer:
5.4 hours
Step-by-step explanation:
As the number of hours of daylight y is modeled as a function of sin, and sin has the minimum value of -1. Therefore
[tex]sin(2\pi 365x-1.4) \geq -1[/tex]
[tex]7sin(2\pi 365x-1.4) \geq -7[/tex]
[tex]7.0sin(2\pi 365x-1.4)+12.4 \geq 5.4[/tex]
[tex]y \geq 5.4[/tex]
So the minimum number of hours of daylight in Anchorage is 5.4 hours
Final answer:
The minimum number of hours of daylight in Anchorage, Alaska, can be found using the equation provided. By considering the minimum value of the sine function, we determine that Anchorage experiences a minimum of 5.4 hours of daylight.
Explanation:
The minimum number of hours of daylight in Anchorage, Alaska, can be determined by examining the mathematical model y=7.0sin(2ω⁄365x−1.4)+12.4.
The amplitude of the sine function in this equation is 7.0, which determines the maximum variation above or below the average value.
Since the sine function oscillates between -1 and 1, the minimum value of the sine part of the equation will be -1.
Therefore, the minimum number of hours of daylight, y, occurs when the sine function is at its minimum value. By substituting -1 into the equation, we get y=7.0×(-1)+12.4, which simplifies to y=5.4.
This means that the minimum number of hours of daylight in Anchorage is 5.4 hours.
Help meeeeeeeeeeereeee
Answers
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
1/2( 4^3 - 6 * 3^2)
PEMDAS says parentheses first
( 4^3 - 6 * 3^2)
Exponents
(64 - 6 * 9)
Multiply and divide from left to right
64 - 54
Add and subtract from left to right
10
Substitute back into the expression
1/2(10)
5
What situation could the
integer - 5 represent?
Answers
Answer:
What is the average temperature in degrees Celcius of Alaska in the winter?
The integer -5 can represent a loss or debt of 5 in real-world situations like owing someone 5 dollars, or a temperature drop 5 degrees below zero. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
Explanation:
In Mathematics, an integer can represent various scenarios. The integer -5 could symbiotically stand for a loss or debt of 5 in real-world situations. For example, if you owe someone 5 dollars, your net balance would be -5 dollars. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
Learn more about Negative Integer here:
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What is 6/ 8 equal to
Answers
Answer:
1216 is equivalent to 68 because 12 x 8 = 16 x 6 = 96.
Step-by-step explanation:
EXPLANATION: if you divide 6/8 by 2 you will get 3/4
6/2= 3
8/2=4
Leah is measuring the weight of adult rhinos at the zoo. Which unit of measurement should she use to eliminate the need to write the values in scientific notation
Answers
Answer:
TONS!!!!!!!!!!!!Step-by-step explanation:
The tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
It is given that Leah is measuring the weight of adult rhinos at the zoo.
It is required to find the unit of measurement she should use to eliminate the need to write the values in scientific notation.
Given options:
1) grams
2) feet
3) gallons
4) tons
What is measurement?It is defined as the numerical quantity that gives an idea about an object's weight, length, width, and many more. It can be used to compare two objects.
We know the feet are the unit of measuring the length and gallons are the unit of measuring the volume.
The grams and tons are the units of measuring the weight.
Grams would use to measure a small amount of weight whereas we would use the tons to measure a large amount of weight. Ton is a metric unit that equals 1000 kilograms.
Thus, the tons should be used to measure the weight of the rhino to eliminate the scientific notation option fourth is correct.
Learn more about the measurements here:
brainly.com/question/4725561
What is the value of 4/15 divided 2/3
Answers
Answer:
⅖
Step-by-step explanation:
4/15 ÷ 2/3
4/15 × 3/2
2/5
Answer: 2/5 or 0.4
Step-by-step explanation: When dividing a fraction by another fraction you will always find the reciprocal of the second fraction and then multiply to get your answer.
4/15 divided by 2/3
4/15 multiplied by 3/2
0.4 or 4/10 or 2/5 is the value of 4/15 divided by 2/3
to display The number of female members in band class over the past five years use a
Answers
Answer:
For the 1st row its Line Graph and Changes over time.
For the 2nd Row its Bar Graph and Categorical.
Step-by-step explanation:
Can someone please help me on this
Answers
Answer:
28.4 miles less
Step-by-step explanation:
1. Find the length of the third side of the triangle with the pythagoream theroum
2. Pythagorean theroum= a^2+b^2=c^2
3. 45^2+ 55^2=c^2
4. 2025+3025=c^2
5. 5050=c^2
6. 71.06=c
7. Instead of driving 100 miles to work, Evelyn will now drive only 71.06 miles to work
7. That is 28.4 miles less than before
Answer:30 miles you save 30 miles
Step-by-step explanation: if you go around its 48+55=103 miles
Do formula a^2+ b^2= c^2
48^2+ 55^2=c^2
2304+3025= c^2
5329=c ^2
Sq rt of 5329 is 73
103-73=30
Need help I’m stuck on this one. I should ask my teacher but I get help from here faster. Need the answer ASAP. Thank you guys so much
Answers
Answer:
(0, 15/6) (15/7,0)
Step-by-step explanation:
Just set the other value to 0 and you can very quickly solve these.
What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)
Answers
Given:
Given that the two sides of the triangle are x, 4.0 and 5.6
We need to determine the range of possible sizes for the side x.
Range of x:
The range of x can be determined using the triangle inequality theorem.
The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".
Thus, applying the theorem, we have;
[tex]x=4.0+5.6[/tex]
[tex]x=9.6[/tex]
Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".
Thus, we have;
[tex]x=5.6-4.0[/tex]
[tex]x=1.6[/tex]
Thus, the range of possible values for x are [tex]1.6<x<9.6[/tex]
In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.
Explanation:In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.
Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.
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) Jennifer and Krystal have to stuff and mail 1000 envelopes for a new marketing campaign. Jennifer can do the job alone in 6 hours. If Krystal helps, they can get the job done in 4 hours. How long would it take Krystal to do the job by herself?
Answers
Answer:
12 hours
Step-by-step explanation:
Let's call the Jennifer's speed J, and the Krystal's speed K.
If Jennifer works alone, she can do the job in 6 hours, so:
J*6 = 1000
J = 1000/6 = 500/3
If Jennifer and Krystal work together, they can do the job in 4 hours, so:
(J+K)*4 = 1000
J+K = 250
Using the value of J, we can find K:
500/3 + K = 250
K = 250 - 500/3 = 250/3
Now, to find the time that Krystal would take if she works alone:
K * time = 1000
250/3 * time = 1000
time = 1000/ (250/3) = 1000*3/250 = 12 hours
Answer:
12 hours
Step-by-step explanation:
please check the attached files for explanation
A certain triangle has a 30° angle in a 60° angle. Which must be a true statement about the triangle
Answers
Answer:
It is a right triangle.
Step-by-step explanation:
A right triangle is a triangle with at least one angle with 90 degrees.
We know that every triangle has 180 degrees. The other unknown angle is 180 - (30+60) = 180 - 90 = 90. That means that the other angle is 90 degrees. Therefore, it is a right triangle
We also know that in this triangle, that the square of one side plus the square of another is side is equal to the square of the hypotenuse of the triangle. (According to Pythagorean theorem)
Answer:
The second-longest side is the square root of 3 times as long as the shortest side.
3(x+2)^2=48
Show steps
Answers
A. Apply special formula (ax^2+2bx+c^2)
3 (x^2+2[2x]+2^2) = 48
3(x^2+4x+4)=48
B.Multiply the coefficient with the trinomial
3x^2+12x+12=48
C. Set the equation to zero by subtracting 48 from both sides.
3x^2+12x-36=0
D. Factor using either trial and error or ac method of cross method
I'll choose trial and error.
a. Right away we can see 3(1) will be the beginning of your factors.
Why? Because nothing else multiplies to make 3.
(3x+?) (x+?)
b. Now check that -36 out. What multiplies to -36?
Remember, when using trial and error you're building off standard form, ax^2+bx+c^2 so you also have to apply whatever numbers you choose to multiply into the c^2 = -36 to add or subtract into bx=12x.
So for this problem I chose -2 and 18 because 3(-2)=-6 and 18-6=12.
Thus...
3x^2+12x-36=0
(3x+18)(x-2)
E. Set both binomials to zero and solve for X. I'll leave this to you.
c=1 when a randomly chosen card out of a standard deck of 52 playing cards is a heart and c=2 otherwise. draw a histogram showing probibility distribution for the random variable
Answers
Answer:
The possible values of c are 1 or 2. There are 13 hearts in a deck of cards and 52-13 = 39 cards that are not. There are a total of 52 cards to choose from, so the possibilities for each value of c are found by dividing the number of results for that value by 52. (Image 1)
Histogram is attached for your reference.
What is the surface area of a cylinder with base radius 4 and height 7?Either enter an exact answer in terms of \pi or use 3.14 for \piπpi and enter your answer as a decimal
Answers
Answer:
The surface area is 88*pi square units.
Step-by-step explanation:
The surface area of a cylinder is given by two times the area of the base plus the area of the sides. This is given bellow:
surface area = 2*(base area) + (side area)
base area = pi*r²
base area = pi*(4)²
base area = pi*16 = 16*pi
side area = 2*pi*r*h
side area = 2*pi*4*7
side area = 8*7*pi
side area = 56*pi
surface area = 2*(16*pi) + 56*pi
surface area = 32*pi + 56*pi
surface area = 88*pi
The surface area is 88*pi square units.
Answer:
112π cubic units
Step-by-step explanation:
The volume of a cylinder is the area of the base × height.
The area of a circle is πr to the 2nd power
So the area of the base is π × 4 to the second power = 16π
The height of the cylinder is 7, so the volume is 16π × 7 = 112π cubic units
If a given line has a slope of 2/7, what is the slope of a parallel line?
Answers
Answer:
2/7
Step-by-step explanation:
Parallel lines have the same slopes but different y-intercepts. That way they go infinity without touching so are perfectly parallel
National League Hockey play-off games go into overtime if the score is tied at the end of a game. Overtime lasts until one of the teams scores a goal. From years of experience we know that the distribution of the lengths of the overtime periods is right skewed with a mean of 9.8 minutes and a standard deviation of 12 minutes. What is the (approximate) probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes? Give your answer to 3 decimal places, e.g, 0.123.
Answers
Answer:
0.07215 = 0.072 to 3 d.p.
Step-by-step explanation:
Central limit theorem explains that the sampling distribution obtained from this distribution will be approximately a normal distribution with
Mean = population mean
μₓ = μ = 9.8 minutes
Standard deviation of the distribution of sample means = σₓ = (σ/√n)
σ = 12 minutes
n = sample size = 30
σₓ = (12/√30) = 2.191
Probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes
Required probability = P(x > 13)
Since we've established that this distribution of sample means approximates a normal distribution
We first standardize 13 minutes.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (13 - 9.8)/2.191 = 1.46
Required probability
P(x > 13) = P(z > 1.46)
We'll use data from the normal probability table for these probabilities
P(x > 13) = P(z > 1.46) = 1 - P(z ≤ 1.46)
= 1 - 0.92785 = 0.07215
Hope this Helps!!!
What is the slope of the line that passes through the points (5,-2) and (1, 10)
Answers
Answer:
-3
Step-by-step explanation:
10 - -2 = 12
1 - 5 = -4
12 / -4 = -3
Answer:
m = -3
Step-by-step explanation:
slope formula [tex]\frac{10-(-2)}{1-5} = -\frac{12}{4}[/tex] = -3
A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.
Answers
Answer:
1
Step-by-step explanation:
Volume of Cube = a³
a is the length of one side of cube
Volume = a³ = 1³ =1x1x1 = 1
find perimeter and area pleasee
Answers
Answer:
Perimeter: 36 m
Area: 60 m squared
Step-by-step explanation:
The perimeter is the sum of the exterior side lengths of the shape. Here, we see that there are two side lengths given, but we need to find the third one.
Notice that the triangle is split up into two right triangles, which means that we can use the Pythagorean Theorem to solve for half of the remaining side. The right triangles have hypotenuses of 13 and one leg of 12. That means the second leg will be [tex]\sqrt{13^2-12^2} =\sqrt{169-144} =\sqrt{25} =5[/tex].
So, the third side is made up of the two legs with length 5. This makes the length of the remaining side: 5 + 5 = 10.
Now, we can calculate the perimeter: P = 10 + 13 + 13 = 36 meters.
The area is calculated by the formula: [tex]A=\frac{1}{2} bh[/tex] , where b is the base and h is the height. Here, the base is what we found above, 10, and the height is the length that makes a perpendicular with the base, which is 12. So, the area is: [tex]A=(1/2)*10*12=(1/2)*120=60[/tex]. So, the area is 60 square meters.
Hope this helps!
Answer:
36m
60m²
Step-by-step explanation:
Base of 1 right angle triangle:
sqrt(13² - 12²)
5
Base of the bigger triangle:
5 + 5 = 10
Perimeter = 13 + 13 + 10
36 m
Area = ½ × 10 × 12
60 m²