The linear equation for the moose population p as a function of t the years since 1986 is P(t) = 380t + 2920.
What are linear equations in two variables?The equations with two variables where each variable has the largest exponent order of 1 having one, zero, or an infinite number of solutions, and are referred to as linear equations in two variables. A linear equation with two variables has the conventional form ax + by + c = 0, where x and y are the variables. Additionally, the answers can be expressed as ordered pairs, like (x, y).
What are forms of linear equations?Linear equations have three main forms which are as follows:
Y=mx+b, where m is the line's slope and b is the y-intercept, is the formula for slope-intercept form.Ax+By=C is how standard form is expressed, with A, B, and C all being constants.(Y-Y1)=m(X-X1), where m is the slope and (X1, Y1) is a known point on the line, is how the point-slope form is expressed.We will consider x on the graph to be years since 1986 and y on the graph to be the number of Moose.
We have two points on the graph: (6, 5200) and (11, 7100)
Using the slope formula m = (y2 - y1)/(x2 - x1), we can find the slope of this line:
m = (y2 - y1)/(x2 - x1)
m = (7100 - 5200)/(11 - 6)
m = 1900/5
m = 380
Now, that we have the slope of the line, we can use the point-slope formula (y - y1) = m(x - x1) to find the equation for the line. Here, we're using the first point, but either point will produce the same answer.
(y - y1) = m(x - x1)
y - 5200 = 380(x - 6)
y - 5200 = 380x - 2280
y - 5200 + 5200 = 380x - 2280 + 5200
y = 380x + 2920
Since the equation that is being sought is supposed to be in terms of P and t, We will replace y with P and x with t.
Hence, the equation will be P(t) = 380t + 2920.
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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while.
How many gallons are left in the tank when the car has traveled the following distances on the highway?
90 miles
Answer:
13 gallons
Set It UpIf the car is able to travel 30 miles per gallon and has a 16-gallon fuel tank, its total fuel efficiency is found by evaluating the product of the two factors.
Therefore, we can multiply 30 by 16 and find the total mileage that the car is equipped to travel:
[tex]30\times16=480[/tex]
SolveNow, assuming that the car has a full tank of gas, it travels 90 miles on the highway. We can find out the remaining fuel efficiency by subtracting 90 miles from the maximum fuel efficiency:
[tex]480-90=390[/tex]
Then, since the car can travel 30 miles per gallon, divide this fuel efficiency by 30 miles to find the remaining gallons in the tank:
[tex]\displaystyle \frac{390}{30} = 13[/tex]
Final Answer[tex]\boxed{\bold{13 \ gallons}}[/tex]
pls help will mark as brainliest
Answer:
12.
Step-by-step explanation:
I attached my answerrrrr
Can that be simplified???
Write a simplified equation for the set of points that are equally far from $(12,0)$ as they are from $(3,0)$.
12,0$+3,0$=15,0$ its korrect now
Help me for this ASAP
Pls now
Answer:
9×9=81
4×4×4×4×4= 1024
4×4×4×4×4×4×4=65536
7×7×7=343
9³=729
10∧5=100000
If satisfied please give a like
Help pls. Fill in the blanks that are circled. I'll mark as brainlist!!
Answer:
Top boxes are 18 and bottom boxes are 9
Step-by-step explanation:
Left side
Frist answer
2x3 =6, so 6 x3 = 18. 18 Goes into the top box on the left.
2 x [tex]\frac{3}{2}[/tex] = 3, so 6 x[tex]\frac{3}{2}[/tex] = 9 9 goes in the bottom box on the left.
Top right: 6 x 3 = 18. 18 goes in the top right
bottom right 3x3 = 9 9 Goes in the bottom right.
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If a circle with a radius 3x is inscribed in a square, then the difference between the area of the square and the area of the circle is [tex]9x^{2} (4-\pi )[/tex]
Given,
The radius of the circle = 3x
The area of the circle = [tex]\pi r^{2}[/tex]
Where r is the radius of the circle
Substitute the values in the equation
Area of the circle = [tex]\pi (3x)^{2}[/tex]
=[tex]9x^{2} \pi[/tex]
We know when a circle is inscribed in a square the diameter of the circle is equal to the side of the square
Diameter of the circle = 2× radius
=2×3x
=6x
The area of the square = [tex]a^{2}[/tex]
Where a is the side of the square
Area of the square = [tex](6x)^{2}[/tex]
=[tex]36x^{2}[/tex]
The difference between the area of the square and the area of the circle= Area of the square - Area of the circle
[tex]=36x^{2} -9x^{2} \pi \\=9x^{2} (4-\pi )[/tex]
Hence, if a circle with a radius 3x is inscribed in a square, then the difference between the area of the square and the area of the circle is [tex]9x^{2} (4-\pi )[/tex]
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write equivalent expression without negative exponents of 9^-2
An equivalent expression without negative exponents of 9^-2 is 1/9²
In this question, we have been given an expression 9^-2
We need to write equivalent expression without negative exponents of 9^-2.
We know that for any number x, the multiplicative inverse of x is represented as x^-1 which is equal to 1/x
We can write 9^-2 as,
9^-2
= 9^(2 × -1)
= (9²)^-1
= 1/9²
Therefore, an equivalent expression without negative exponents of 9^-2 is 1/9²
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I need help asap!!!!!!
Answer:
Second choice: Student failed to square the x part
Step-by-step explanation:
x - 2y = 6 - 2.3 = 0 so that is the only plausible explanation
Answer: The student failed to square the x² part. This led to calculating x² as six instead 36
NEED HELP ASAP TODAY IF Can. I have no idea how solve these....
Answer:
62º
Step-by-step explanation:
So this is supplementary angles. Supplementary angles are two or more angles that add up to 180º. This is also vertical angles. Vertical angles are angles across from one another that are congruent(such as the 180º angle and the one up and to the right of it). So if vertical angles are congruent that means that the angle to the right of x is also 118º. And since it is a supplementary angle this is now simple subtraction.
180-118=62.
Hope I could help!
Answer:
62.Step-by-step explanation:
Find the value of x:
118 + x = 180180 - 118 = x180 - 118 = 6262 = xValue x equals 62.Pls help me PLSPLS #ineedhelp #helpme #isuckatmath
Answer:
300 ones
Step-by-step explanation:
300 one = 300 of 1 = 300
The other answers are wrong
30 ones = 30 of 1 = 30
3 tens = 3 of 10 = 30
300 tens = 300 of 10 = 3000
Find the value of x when 6-2x=5x-9x+12 .
Answer:
x=3
Step-by-step explanation:
Factor the expression.
4xy + 18ry²
Answer:
2y ( 2x + 9ry)
Step-by-step explanation:
A.) Find the greatest common factor and factor out:
(2y x 2x) + (2y x 9ry) = 2y ( 2x + 9ry )
or
B.) Expand each expression:
4xy = ( 2 x 2 x X x y )
18ry^2 = ( 2 x 3 x 3 x r x y x y )
( 2 x 2 x X x y ) + ( 2 x 3 x 3 x r x y x y )
Then, take out like terms and put the expanded factors back together:
2y ( 2 x X + 3 x 3 x r x y ) = 2y ( 2x + 9ry )
Hope this helps!
A mother is choosing which baby foods to serve her infant. A jar of meat has 2g of protein and 34 calories. A jar of vegetables has 1g of protein and 17 calories. How much of each will she need to serve to get 5g of protein and 120 calories?
A mother will need 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.
Given that, a mother is choosing which baby foods to serve her infant. A jar of meat has 2g of protein and 34 calories. A jar of vegetables has 1g of protein and 17 calories. Now , we have to calculate how much she will be needed if she wants to serve 5g of protein and 120 calories respectively.
So, let's proceed to solve this question.
For 5g of protein she will be needed 2 jars of meat having 2g protein and 1 jar of vegetables which has 1g protein, then total protein will be equals to 5g.
5g of protein = 2 x A jar of meat + 1 x A jar of vegetables
For 120 calories, she will be needed 3 jars of meat and 1 jar of vegetable then it comes out to be 119 calories approximately equals to 120 calories.
So, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories.
Therefore, 2 jars of meat and 1 jar of vegetable for 5g of protein and 3 jars of meat and 1 jar of vegetable for approx 120 calories is the required answer.
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8. You are skiing down a 1,350 meter ski slope at 60 meters per second. Let t
represent your skiing time in seconds and d(t) represent the distance from the
bottom of the ski slope.
The time taken to reach the bottom when the person skies down will be 22.5 seconds.
How to calculate the value?It should be noted that the person is skiing down a 1,350 meter ski slope at 60 meters per second.
There, t represent your skiing time in seconds.
The appropriate expression to illustrate the scenario will be:
1350 - 60t = 0
Therefore, 60t = 1350
t = 1350/60
t = 22.5
The time taken to each the bottom will be 22.5 seconds.
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Maggie is making trail mix. She makes 4 batches of the recipe shown. She divides it into 3 equal-sized bags. How many ounces are in each bag?
Answer:
There are several steps to this problem, but they are easy steps . First, determine how many ounces are in one recipe by adding all the ounces of the ingredients together: 8 + 5 + 2 + 3 = 18.
Now multiply that amount by 4, because she made 4 batches:
18 x 4 = 72
Finally, divide the total amount by 3, because she put it in three bags. 72/3 = 24
10 points for this math question
Answer:
a = x -4b = y +3Step-by-step explanation:
You want the transformation rule that describes the translation from R(5, 0) to R'(1, 3).
TranslationThe difference between R' and R is ...
R' -R = (1, 3) -(5, 0) = (1-5, 3-0) = (-4, 3)
The difference between the point (x, y) and the translated point (a, b) is ...
(a, b) -(x, y) = (a -x, b -y)
These differences are equal, so we have ...
a -x = -4 ⇒ a = x -4b -y = 3 ⇒ b = y +3<95141404393>
which functions are even? check all of the boxes that apply. f (x) = x superscript 4 baseline minus x squared f (x) = x squared minus 3 x + 2 f (x) =
Function (D) f(x) = |x| is even.
What are functions?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.To find which functions are even:
We are aware that a function is even when f(x) = f(-x).
(A)
[tex]$$\begin{aligned}&\text f(x)=x^{4-x^2} \\&f(-x)=(-x)^{4-x^2} \\&f(x) \neq f(-x)\end{aligned}$$[/tex]
So, the function is not even.
(B)
[tex]$$\begin{aligned}& f(x)=x^2-3 x+2 \\&f(-x)=x^2+3 x+2 \\&f(x) \neq f(-x)\end{aligned}$$[/tex]
So, the function is not even.
(C)
[tex]$$\begin{aligned}&\text f(x)=\sqrt{x-2} \\&f(-x)=\sqrt{-x-2} \\&f(x) \neq f(-x)\end{aligned}$$[/tex]
So, the function is not even.
(D)
[tex]f(x)=|x|\\f(-x)=|-x|=|x|=f(x)[/tex]
So, the function is even.
Therefore, function (D) f(x) = |x| is even.
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The complete question is given below:
Which functions are even? Check all of the boxes that apply.
a. F (x) = x Superscript 4 Baseline minus x squared
b. f (x) = x squared minus 3 x + 2
c. f (x) = StartRoot (x minus 2) EndRoot
d. f(x) = |x|
Mrs Smith packed 7,866 grams of mixed nuts into 25 big and small packets. There were 13 big packets of 462 grams of mixed nuts. What was the mass of each small packet of mixed nuts?
A, B & C form the vertices of a triangle, where ∠CAB = 90°.
AB = 10.2 m and AC = 5.6 m.
Evaluate ∠CBA, giving your answer rounded to 3 SF.
The unknown angle of the right triangle is as follows:
∠CBA = 28.8°
How to find the angle of a right triangle?The triangle is a right triangle because one of its angle is equals to 90 degrees.
The angle ∠CBA, can be found using trigonometric rations,
hence,
tan ∅ = opposite / adjacent
where
∅ = ∠CBA
Therefore,
tan ∠CBA = opposite / adjacent
opposite side = 5.6 m
adjacent side = 10.2 m
Hence,
tan ∠CBA = 5.6 / 10.2
tan ∠CBA = 0.54901960784
tan ∠CBA = 0.54901960784
∠CBA = tan⁻¹ 0.54901960784
∠CBA = 28.7676493388
∠CBA = 28.8°
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Given the set of information, find a linear equation satisfying the conditions.
X-intercept at (x,y)=(7,0) and y-intercept at (x,y)=(0,2)
Answer:
y = -2/7x + 2
Step-by-step explanation:
y=mx + b is the slope intercept form of a line. The b is the y-intercept. We are given that. The point (0,2) tells us that the line crosses the y intercept at 2.
Now we have to find the slope. The slope is the change in y over the change in y. Given the points (7,0) and (0,2) The y's are 2 and 0 and the x's are 0 and 7. Subtract the y's and subtract the x's.
[tex]\frac{2 - 0}{0 - 7}[/tex] = [tex]\frac{-2}{7}[/tex]
Now we can put in the slope and the y-ntercept
y = mx + b
y = [tex]\frac{-2}{7}[/tex]x + 2
Which is an x-intercept of the continuous function in the table? (0, –6) (3, 0) (–6, 0) (0, 3)
(3, 0) is the x-intercept
The x-intercept is the value of x when the value of the function is equal to zero.
That is the function is equal to 0.
When x = 3
f(x) = 0
Therefore the x-intercept is the point (3,0)
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helppppppppppppppppppppp
here's your answer check if it's right or not
identify the type of angle formed between the hands of each clock
Answer:
5) acute
6)acute
7)reflex
8)reflex
Step-by-step explanation:
No 6&5 are acute because they are each less than 90 degrees while no7&8 are reflex because they exceed 180 degrees.
m²=68 what is m? help,please
The answer to the expression is 8.246
How to calculate the square root ?A square root can be described as a factor of a number that when multiplied twice gives the original number.
The first step is to write out the expression
m² = 68
Take the square root of both sides
√m² = √68
m= 8.246
Hence the value of m in the expression is 8.246
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A walking map of a city has a scale of 1 inch to 2,000 feet. Another map of the same city has a scale of 1 inch to 1,500 feet Which map is smaller? Explain how you know.
by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller than the map of scale of 1 inch to 1,500 feet as it includes more area in a single inch.
We are given that:
A map of the city has a scale of 1 inch to 2,000 feet.
This means that 1 inch of the map represents the 2,000 feet of the actual area of the city.
Now, we are given another map which has a scale of 1 inch to 1,500 feet.
This means that 1 inch of the map represents the 1,500 feet of the actual area of the city.
So, by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller as it includes more area in a single inch.
Therefore. by comparing the two maps, we get that, the map with the scale of 1 inch to 2,000 feet is smaller than the map of scale of 1 inch to 1,500 feet as it includes more area in a single inch.
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Write an inequality for the graph
The absolute value inequality graphed is:
y ≥ |x - 5| + 1
How to write the graphed inequality?
We can see that we have an absolute value equation, and the region above the graph is shaded, so we have:
y ≥ absolute value equation
We can see that the slope of the absolute value equation is 1, and the vertex is (5, 1), then the equation is:
|x - 5| + 1
Replacing that in the inequality we will get:
y ≥ |x - 5| + 1
That is the graphed inequality.
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the table shows statistics for a basketball player. use rates to compare the player's performance between the two seasons
Using proportions, it is found that the height of the object is of 12 m, hence you can use a ladder that reaches height of up to 13 m to climb the object.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For similar triangles, equivalent side lengths are proportional, hence, in this problem, we have that:
h/1.5 = 8.8/1.1
h/1.5 = 8
h = 8 x 1.5
h = 12m.
The height of the object is of 12 m, hence you can use a ladder that reaches height of up to 13 m to climb the object.
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landon elliot fumigates rooms and charges $21.95 per room. on monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third.
The total charge for the rooms will be $197.55.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
The charge for one room = $21.95
Total number of rooms = 3+2+4=9 rooms
Total charges for the room= Charge for one room × total number of room
Substitute the values:-
The total charge for the room = 21.95 × 9 = 197.55
Hence, the total charge for the room is 197.55
The complete question is given below:-
Landon Elliot fumigates rooms and charges $21.95 per room. on Monday, he fumigated 3 rooms in one house, 2 in another, and 4 in a third. find his total charges.
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HELP 100 POINTS
A group of friends wants to go to the amusement park. They have $247.50 to spend on parking and admission. Parking is $12, and tickets cost $39.25 per person, including tax. Writer and solve an equation which can be used to determine p, the number of people who can go to the amusement park.
Equation:
Answer: p =
Answer:
p = 6
Step-by-step explanation:
Define the variable
Let p be the number of people who go to the amusement park.
Given information:
Maximum amount available to spend = $247.50Cost of parking = $12Cost of ticket (per person) = $39.25Therefore, the equation that represents the given information and the defined variable is:
[tex]39.25p + 12 \leq 247.50[/tex]
(We have used the inequality sign since the question states the maximum amount of money the group of friends have to spend).
To solve, subtract 12 from both sides:
[tex]\implies 39.25p + 12 - 12 \leq 247.50 - 12[/tex]
[tex]\implies 39.25p \leq 235.50[/tex]
Divide both sides by 39.25:
[tex]\implies \dfrac{39.25p}{39.25} \leq \dfrac{235.50}{39.25}[/tex]
[tex]\implies p\leq 6[/tex]
Therefore, the maximum number of people that can go to the amusement park is 6.