The expression for modelling the pattern is n² + 2
Charlie can observe 38 guppy fish in month 6.
Given,
Number of guppy fish in Charlie's fish tank for the first time = 3
Number of guppy fish after one month = 6
Number of guppy fish in the following month = 11
The increasing pattern of guppy fish in the tank:
First month = 6 - 3 = 3
Second month = 11 - 6 = 5
So, we get that the number of guppy fish is increasing by odd numbers.
That is, 3, 6, 11, ........
Now, we have to find an expression for this pattern.
First term is 3.
That is, first term² + 2 = 1² + 2 = 3
Let n be the number of term.
n = 3
So, third term be:
3² + 2 = 9 + 2 = 11
So the expression for modelling the pattern is n² + 2
Now, we have to find the number of guppy fish in month 6.
That is,
n = 6
So,
n² + 2
6² + 2 = 36 + 2 = 38
That is, Charlie can observe 38 guppy fish in month 6.
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Pre-calculus: Write the quadratic function in standard form.
The quadratic function h(x) = x^2 - 12x + 36 is a quadratic function in standard form
How to write the quadratic function in standard form?The quadratic function is given as:
h(x) = x^2 - 12x + 36
Quadratic functions in standard form are represented as
h(x) = ax^2 + bx + c
Where the value of a is not 0
This means that we can conclude that h(x) = x^2 - 12x + 36 is a quadratic function in standard form
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If 5/9 of the vegetable medley is green beans and there is a total of 5 pounds of
vegetable medley, how many pounds of green beans do they have? Leave your
answer as an improper fraction, if applicable.
The pounds of green beans in the vegetable medley is 2.78 pounds
FractionTotal pounds of vegetable medley = 5 poundsFraction of green beans in vegetable medley = 5/9Pounds of green beans in the vegetable medley = Fraction of green beans in vegetable medley × Total pounds of vegetable medley
= 5/9 × 5
= (5 × 5) / 9
= 25 / 9
= 2.777777777777777 pounds
Approximately,.
Pounds of green beans in the vegetable medley = 2.78 pounds
Therefore, the pounds of green beans in the vegetable medley is 2.78 pounds
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Solve for d.
-6 + d = 7 + 3d + 3
d = [
Submit
Answer:
so if add everything and subtract them for d you get 7
Find the quadratic function with vertex (1,-2.9) and no intercepts.
Please help me I really just don't understand how to get the answer y+2.9 = -12(x-1)^2 as I need to mathematically prove this equation works.
Answer:
[tex]y+2.9=-12(x-1)^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.a is some constant.Given vertex: (1, -2.9)
Therefore:
h = 1k = -2.9Substitute the values of h and k into the formula:
[tex]\implies y=a(x-1)^2-2.9[/tex]
As the function has no x-intercepts, and the vertex is in Quadrant IV, the parabola will open downwards. Therefore, "a" will be negative. Without any further information, any number can be substituted for "a". Therefore, according to the given answer, let a = -12:
[tex]\implies y=-12(x-1)^2-2.9[/tex]
Note: If "a" was positive, the parabola would open upwards, which means there would be two x-intercepts (two points at which the curve intercepts the x-axis).
Finally, add 2.9 to both sides of the equation so that the equation is in the format of the given answer:
[tex]\implies y+2.9=-12(x-1)^2-2.9+2.9[/tex]
[tex]\implies y+2.9=-12(x-1)^2[/tex]
in jeff’s sample, the number of siblings each person has is as follows: one, two, three, four, and ten. what is the median number of siblings in his sample?
If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
Given,
The number of siblings each person has = 1,2,3,4 and 10
Arrange them in ascending order =1,2,3,4 and 10
We know the median is the middle term of the ordered pair
The number of terms n= 5
Middle term is = [tex]\frac{n+1}{2}[/tex]
=[tex]\frac{5+1}{2}[/tex]
=3
The 3rd term is 3.
The median = 3
Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
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Use version 2 of the arc length formula to find the length of the curve defined by 16xy^2 - y^6 = 9 from (9/16,1) to (9/8,2)
The arc length of the curve is 1.3125
What do you understand by length of the curve?The length of an arc is the separation of two locations along a segment of a curve.
A defined integral between the two points is used to calculate the area under a curve between two points. Integrate y = f(x) between a and b's limits to find the area under the curve y = f(x) between x = a & x = b. Integration within the defined bounds can be used to calculate this area.
the arc length formula
[tex]$$L=\int_C d s=\int_a^b \sqrt{1+\left(\frac{d x}{d y}\right)^2} d y$$[/tex]
now
[tex]$$\begin{aligned}16 x y^2-y^6 &=8 \\y^2\left(16 x-y^4\right) &=8 \\16 x-y^4 &=8 y^{-2} \\16 x &=8 y^{-2}+y^4 \\x &=\frac{1}{2} y^{-2}+\frac{1}{16} y^4\end{aligned}$$[/tex]
[tex]\frac{d x}{d y}=-y^{-3}+\frac{1}{4} y^3[/tex]
now differential line element is
[tex]$$\begin{aligned}d s &=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y \\&=\sqrt{1+\left(-y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\sqrt{1+y^{-6}-\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{y^{-6}+\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{\left(y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\left(y^{-3}+\frac{1}{4} y^3\right) d y\end{aligned}$$[/tex]
now arc length of the curve in the given interval
[tex]$$\begin{aligned}L &=\int_C d s \\&=\int_1^2\left(y^{-3}+\frac{1}{4} y^3\right) d y \\&=\left[-\frac{1}{2} y^{-2}+\frac{1}{16} y^4\right]_1^2 \\&=-\frac{1}{2}\left(\frac{1}{2^2}-\frac{1}{1^2}\right)+\frac{1}{16}\left(2^4-1^4\right) \\&=\frac{\mathbf{2 1}}{\mathbf{1 6}} \approx \mathbf{1 . 3 1 2 5}\end{aligned}$$[/tex]
this is the arc length of the curve
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The perimeter of a geometric figure is the distance around the outside of the figure. The perimeter of a rectangle is 44 feet. The length of the rectangle is 6 feet more than the width. What is the measure of the width?
Write the equation for find the perimeter of the rectangle. (Use the variable w)
How fast is the second car traveling>
The width of the rectangle is 8 feet.
What is the Area of Rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.
Perimeter = 44
Length = width + 6
perimeter formula of rectangle = 2(L +W)
44 = 2(W+6 +W)
22 = 2W +6
11 = W + 3
W = 8
therefore , the width of the rectangle is 8 feet
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What is the domain of the relation {(-3, 3), (–1, 0), (6, 3), (9, -2)}?
(3, 6, 9)
(-3,-2, -1)
(-2, 0, 3)
(-3,-1, 6, 9)
Answer:
Domain { -3,-1,6,9}
Step-by-step explanation:
The domain is the input values
Domain { -3,-1,6,9}
Convert five hours into minutes
Answer:
300 minutes
Step-by-step explanation:
1 hour = 60 Minutes
60x5=300
Pls help me with this
Answer:
ans) 4G and 6/x+y
Step-by-step explanation:
10) it says the product of both so when both multiply each other , we get the product
A 4-pound box of blackberries costs $16.64. What is the price per ounce?
Cost of 4 pound box of blackberries = $16.64
Cost of 1 pound box of blackberry = [tex]\bf\frac{\cancel{16.64}}{\cancel{4}}4.16[/tex]
Hence, the cost of 1 pound of blackberry is $4.16.
Para encriptar un
mensaje secreto se
va a utilizar una
clave privada que
es el producto de
dos números
primos. ¿Cuál de
los números NO
puede usarse para
la clave privada?
A.105
B.133
c.143
D.221
Answer:
c.143
Step-by-step explanation:
No estoy seguro de que esté Mal o mal
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-2, 5) \text{ and } (-8, -3)
(−2,5) and (−8,−3)
The distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.
We are given the two points:
( − 2 , 5 ) and ( − 8 , − 3 )
We need to find the distance between the two points.
The formula for distance is given as:
Distance = √ (x₂ - x₁)² + (y₂ - y₁)²
Substituting the values, we get that:
Distance = √ ( - 8 + 2 )² + (- 3 - 5)²
Distance = √ ( - 6 )² + ( - 8 )²
Distance = √ 36 + 64
Distance = √ 100 .
Distance = 10 units.
Therefore, we get that, the distance between the two points ( − 2 , 5 ) and ( − 8 , − 3 ) is 10 units.
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Jorge works as a car salesman. He gets a commission of 3.5% on used cars and 191
5.4% on new cars. What was his commission for a month when he sold used cars
for a total of $16,583 and new cars for a total of $34,792?
The total commission of Jorge was $2459.173.
What is the percentage?Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) besides a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. To calculate a percentage, divide the value by the total value and multiply the result by 100. (value/total value)100% is the formula for calculating the percentage.So,
3.5% commission of used cars.5.4% commission on new cars.Now,
3.5% of $16,583
16,583/100 × 3.5 = $580.4055.4% of $34,792
34,792/100 × 5.4 = $1,878.768Total commission: $580.405 + $1,878.768 = $2459.173
Therefore, total commission of Jorge was $2459.173.
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PLEASE HELP NO TIME :(
Using proportions, we have that:
A. 0.05x + 0.4(10 - x) = 0.2(10).
B. You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. 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.
In item A, we have that the total amount that she has is 20% acid of 10 liters, hence:
0.2(10).
She wants to split it into a 5% solution and a 40% solution, a total of 10 liters, hence the amounts to each solution are x and 10 - x, as follows:
0.05x + 0.4(10 - x).
Hence the equation is:
0.05x + 0.4(10 - x) = 0.2(10).
The solution for x is found as follows:
0.05x + 4 - 0.4x = 2.
0.35x = 2
x = 2/0.35
x = 5.7.
Hence, for item b:
You need 5.7 liters of the 5% solution and 4.3% liters of the 40% solution.
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Number 8 only is algebra
The coordinates of the endpoints of
DE
are D(–13,–10) and E(3,14). Point F is on
DE
and divides it such that DF:EF is 5:3.
What are the coordinates of F?
Write your answers as integers or decimals.
Using proportions, the coordinates of F are given as follows: F(-3,5).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. 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.
Point F divides the segment such that DF:EF is 5:3, hence the point F is 5/8 of the way, that is:
F - D = 5/8(E - D).
The x-coordinate of F is given by:
x + 13 = 5/8(3 + 13)
x + 13 = 10
x = -3.
The y-coordinate of F is given by:
y + 10 = 5/8(14 + 10)
y + 10 = 15
y = 5.
The coordinates of F are given as follows: F(-3,5).
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Simplify the expression
Answer:
A
Step-by-step explanation:
Answer:
your answer will be A the first one
Step-by-step explanation:
ten students are taking both algebra and drafting. there are $24$ students taking algebra. there are $11$ students who are taking drafting only. how many students are taking algebra or drafting but not both?
25 students are taking algebra and drafting but not both.
How to find how many students are taking algebra or drafting but not both?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values.
given that
10 students are taking both algebra and drafting.
24 students taking algebra.
11 students who are taking drafting only.
now, find how many students are taking algebra or drafting but not both?
from the question
10 students are taking both algebra and drafting.
24 students taking algebra.
so, subtract 10 in 24
24 - 10 = 14
so, 14 students are taking algebra only.
now, add the both students who are taking algebra and drafting.
11 + 14 = 25.
Hene, 25 students are taking algebra or drafting but not both.
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Find the distance between each pair of points.
(21,5) and (28,-1)
Answer:
9.22 units (3 s.f.)
Step-by-step explanation:
The distance between a pair of points can be found using the distance formula shown below, where [tex](x_1, y_1)[/tex] is the 1st coordinate and [tex](x_2,y_2)[/tex] is the 2nd coordinate.
[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
Substituting the coordinates into the formula:
Distance between (21, 5) and (28, -1)
= [tex]\sqrt{(-1-5)^{2} + (28-21)^{2} } }}[/tex]
= [tex]\sqrt{(-6)^2+7^2}[/tex]
= [tex]\sqrt{85}[/tex]
= 9.22 units (3 s.f.)
Additional:
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What is the median of 35, 2, 7, 33, 25, 70, 75, 40, 42, 12,
15, 7, 44, 20, 25, 3, 65, 62
Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similar, then choose NOT.
B = E
B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.
What do we mean by the congruency of triangles?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.The triangle congruence criteria are as follows:
SSS (Side-Side-Side)SAS (Side-Angle-Side)ASA (Angle-Side-Angle)AAS (Angle-Angle-Side)RHS (Hypotenuse-Leg, right angle)For the given figure it is said that B=E and it is solely not possible to prove that △ABC≅△DEF with any congruency condition.
Therefore, B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.
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The correct question is given below:
Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similarly, then choose NOT.
B = E
Options:
(A) AA
(B) SAS
(C) SSS
(D) NOT
which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) lance gains 1 level each time he plays his favorite video game. he started at level 10. (2 points) f(x) g(x) h(x) the functions all have the same slope
According to the question, the points are [tex](-3,-10)[/tex] and [tex](-1,-7)[/tex] for the function [tex]f(x).[/tex]
The calculated slope for these values are as follows:
[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(-7-(-10))}{(-1-(-3))} = \frac{3}{2} = 1.5[/tex]
The slope for the function [tex]f(x)[/tex] is: [tex]m=1.5[/tex]
Now, the function [tex]g(x)=\frac{1}{2} x+3[/tex]
Using the standard formula that is [tex]y = mx+c[/tex] to calculate the slope for the function [tex]g(x).[/tex]
Slope(m) for [tex]g(x) = \frac{1}{2} = 0.5[/tex]
As per the question, lance gains [tex]1[/tex] level each time he plays the video game.
Therefore, [tex]slope = \frac{1}{1} =1[/tex]
Hence, the slope for the function [tex]h(x)[/tex] is [tex]1[/tex].
Therefore, the function [tex]f(x)[/tex] has the largest slope and it is [tex]1.5.[/tex]
What is the equation of the line?
To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.
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Charlie drove for 5 hours to get from his house to grandma’s house. He averaged 47 miles per hour on the trip. Write
and solve an expression that represents the approximate distance from Charlie’s house to grandma’s house.
Answer:
Answer:
420 miles
Step-by-step explanation:
Distance traveled per hour = 55 miles
Distance traveled in 6 hours = 55 * 6 = 330 miles
Distance of the trip = 330 + 90 = 420 miles
Step-by-step explanation:
Evaluate (f+2)(g+8) , when f=4 and g=2.
Answer:
60
Explanation below
elowHope this helps :)
Step-by-step explanation:
1. Substitute the variables with the given numbers.
(4 + 2) (2 + 8)
2. Add the numbers to get the sum.
(6) (10)
3. Since they are in parenthesis multiply the two numbers.
(6) (10) = 60
3
5
Dan reads chapters in
56
hours.
What is the unit rate in chapters per hour?
Write your answer in simplest form.
Answer:
How many chapters does Dan read in 56 hours?
Step-by-step explanation:
What is the equation of the slant asymptote of the rational function f(x) = 4x^2+6x-1 / x+2?
Answer:
Hello,
y=4x-2
Step-by-step explanation:
1: slope.
[tex]\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\[/tex]
2:
[tex]\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\[/tex]
Slant asymptote is y=4x-2
Can someone help me plss
Complete the table
kilometers
1
5
20
0.3
meters
1,000
5 kilometers equals how many meters?
Please hurry , Will give brainliest to anybody . Very simple question !!!
Answer:
Step-by-step explanation:
The left option
(4,3), (1,3), (0,5), (1,8)