(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]
Step-by-step explanation:
The form of the recursive rule of an arithmetic sequence sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where
[tex]a_{1}[/tex] is the first term in the sequence[tex]a_{n}[/tex] the nth term in the sequence [tex]a_{n-1}[/tex] the term before the nth term n is the term numberd is the common difference between each two consecutive termsThe form of the explicit rule of nth term of an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first termd is the common difference between each two consecutive terms∵ The sequence is 5, 20, 35, 50, ….......
∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15
∴ The sequence is an arithmetic sequence with a common
difference 15
∵ The form of the recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]
∵ First term = 5
∵ d = 15
∴ [tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
∵ The form of the explicit rule of nth term of an arithmetic
sequence is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 5 and d = 15
- Substitute these values in the rule
∴ [tex]a_{n}=5+(n-1)15[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=5+15n-15[/tex]
- Add like terms
∴ [tex]a_{n}=15n-10[/tex]
(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]
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Solve using a suitable inverse operation:
A) a/5= -2
I just want to know what this means and how to do it.
Answer:
a = - 10
Step-by-step explanation:
Given
[tex]\frac{a}{5}[/tex] = - 2
a is divided by 2. The inverse operation to division is multiplication, thus
Multiply both sides by 5 to clear the fraction
a = 5 × - 2 = - 10
7.66 × 0.55 i need 20 charters to ask this
Answer:
4.213
Step-by-step explanation:
Brenda recorded a temperature of 19°C, and Cooper recorded a temperature 17°C higher. What temperature did Cooper record?
Answer:
Cooper recorded a temperature of 36° C.Step-by-step explanation: If you add 19 and 17 together you get 36.
Hope this helps! :)
Distribute the expression.
5(2s2−3s+4)
Answer:
10s^2-15s+20
Step-by-step explanation:
because 5(2s^2)=10s^2, 5(-3s)=-15s, and 5(4)=20
hope it helps:)
Answer:102−15+20
Step-by-step explanation:that’s that answer because I just did the question on imagine math
10. Estimate by rounding -5 2/5+9 8/11-3 5/6
Answer:
0.5
Step-by-step explanation:
-5 2/5=-27/5
9 8/11=107/11
-3 5/6=-23/6
--------------------
-27/5+107/11-23/6
-27/5-23/6+107/11
-162/30-115/30+107/11
-277/30+107/11
-3047/330+3210/330=163/330=0.493=0.5
what is the answer because am stuck
Answer:
30 Oranges!
Step-by-step explanation:
Given that for every 2 apples there are 3 oranges.
How many oranges would be there in a basket of 20 apples?
Since for every couple of apples we have 3 oranges we will calculate how many couples of apples are there in the basket.
Given there are 20 apples. This means that there are [tex]$ \frac{20}{2} $[/tex] = 10 pairs of apples.
Since for one pair we have three oranges, for 10 pairs we would have 3 X 10 = 30 oranges.
Therefore, we can conclude that the number of oranges in the bigger basket would be 30.
Which of the following is true of vertex-edge graphs?
(1)They can model real-world problems.
(2)They can all be solved.
(3)Euler paths are the same as Hamilton paths.
(4)All vertices must be used once in Hamilton circuits.
What slope passes through -3,7 and is parallel to 4x-1?
Answer:
y = 4x + 19Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\ k:y=4x-1\to m_1=4.\\\\\text{Therefore}\ m_2=4.\\\\l:y=4x+b\\\\\text{Put the coordinates of the point (-3, 7) to the equation of a line:}\\\\7=4(-3)+b\\7=-12+b\qquad\text{add 12 to both sides}\\19=b\to b=19\\\\\text{Finally:}\\\\y=4x+19[/tex]
7 pencils for 16 dollars
Answer:44 cents
Step-by-step explanation:
7/16 = .4375
Answer:
Step-by-step explanation: To find the unit price you could divide 7 by 16
-10x+9x=12 solve for x equation
Answer:
x = -12
Step-by-step explanation:
Remember that ax + bx = (a+b)x
-10x + 9x = 12
Add -10x and 9x together
(-10 + 9)x = 12
-x = 12 (-1x is written as -x, just as 1x is written as x)
÷ -1 both sides
x = -12
I hope this helps. Happy studying. :)
-10x+9x= -1x
-1x=12 -1 divided by 12 equals -12 Therefore x = -12
12x + 3y = 15 for x = -1,0,1
Three points of a function are graphed.
A coordinate plane with 3 points plotted at (10, 18), (14, 24), and (18, 30).
Which statement describes the function through the points?
The function is a direct variation function with a constant of variation of 1.5.
The function is a direct variation function with a constant of variation of 1.8.
The function is linear but is not a direct variation function.
The function is not a linear function.
The function through the points (10, 18), (14, 24), and (18, 30) is a direct variation function with a constant of variation of 1.8.
Explanation:In this case, we have a linear function. We can determine this by checking if the changes between the x-values and the y-values are consistent. For the change in x-values: (14-10 is 4) and (18-14 is also 4), the change is constant. Similarly, check the change in y-values: (24-18 is 6) and (30-24 is also 6), thus the change is constant. Hence, the function is linear.
More so, this function is a direct variation function because it passes through the origin. In direct variation functions, the ratio of y to x remains constant. In this case, the y divided by x at each point [(18/10=1.8), (24/14=1.71), (30/18=1.67)] is approximately 1.8, which is almost constant.
So, the best description of this function is: 'The function is a direct variation function with a constant of variation of 1.8'.
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Answer:
The function is linear but not a direct variation function.
Step-by-step explanation:
There are 450 students, 20 teachers and 5 teacher's aides at Canyon Hills Middle School. What is the ratio of students to teachers and their aides?
A
9:2
B
90:1
C
1:18
D
18:1
Answer:
D. 18 : 1
Step-by-step explanation:
Students : teachers and aides
450 : 25
Treat it like a fraction. 450 over 25 simplifies to 18 over 1 because 450/25=18 and 25/25=1.
Therefore, the ratio is 18 : 1
Answer: 18:1
Step-by-step explanation:
450 students : 25 teachers
18 students : 1 teachers
450/25= 18
consider the parabola with a focus at the point (0,-3) and directrix y=2 . which two equations can be used to correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola ?
The two equations that can be used to relate the distance from the focus and the directrix to any point on the parabola are x² = 4py and y = (x-k)² + h.
Explanation:To correctly relate the distance from the focus and the directrix to any point (x,y) on the parabola, we can use the following two equations:
x² = 4pyy = (x-k)² + hWhere p is the distance from the focus to the directrix, (h,k) is the vertex of the parabola, and the equation x² = 4py represents a parabola with its axis parallel to the y-axis, and y = (x-k)² + h represents a parabola with its axis parallel to the x-axis.
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Urgent!!! Triangle ABC has angles the following angle measures. m<A=2x+7 , m<B=10x+10 and m<C=8x+23. what is the value of x and what is the measure of each angle?
x=
m<A=
m<B=
m<C=
Answer:
The Value of x= 7.
m∠A= 21°
m∠B= 80°
m∠C= 79°
Step-by-step explanation:
Given:
m∠A = 2x+7
m∠B = 10x+10
m∠C = 8x+23
We need to find the value of x and measures of each angle.
Now by angle sum property which states that sum of all angles of a triangle are 180°.
Hence from above statement we can say in ΔABC;
m∠A+m∠B+m∠C=180
Now substituting the given values in above equation we get;
[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]
Hence value of x is 7.
Substituting the value of x in all angles we get;
m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]
m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]
m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]
Final answer:
To find the value of x and the measure of each angle in triangle ABC, set up an equation using the given angle measures. Solve for x and substitute it back in to find the measures of each angle. Then : m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
Explanation:
To find the value of x and the measure of each angle in triangle ABC, we need to set up an equation using the given angle measures. Since the sum of the angles in a triangle is 180 degrees, we can write the equation as:
m<A + m<B + m<C = 180
Substituting the given angle measures, we have:
(2x + 7) + (10x + 10) + (8x + 23) = 180
Simplifying the equation:
20x + 40 = 180
Subtracting 40 from both sides:
20x = 140
Dividing both sides by 20:
x = 7
Now that we know the value of x, we can find the measure of each angle by substituting x into the respective expressions:
m<A = 2(7) + 7 = 21 degrees
m<B = 10(7) + 10 = 80 degrees
m<C = 8(7) + 23 = 79 degrees
When the solution of x2 + 9x − 9 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r? x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
A: 117
B: 54
C:45
D: 9
Answer:
The answer is option A. 117
Step-by-step explanation:
The general solution of the quadratic equation is:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
The given equation is x2 + 9x − 9 is expressed as minus 9 plus or minus the square root of r, all over 2
Comparing to the general solution
∴ r = determinant = b² - 4 a c
From the given equation: a = 1 , b = 9 and c = -9
∴ r = 9² - 4 * 1 * (-9) = 81 + 36 = 117
The answer is option A. 117
Answer:
117
Step-by-step explanation:
A 14 pound bag of dog food cost $16.24 and a 30 pound bag of dog food cost $33.30 which statement is true and can be used to determine the better buy?
A.The unit rate per pound of a 14 pound bag $0.05 less than the unit rate of a 30 pound bag.
B.The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
C.The unit rate per pound of a 14 pound bag is $0.50 less than the unit rate of a 30 pound bag.
D.The unit rate per pound of a 14 pound bag is $0.50 more than the unit rate of a 30 pound bag.
Answer:
B)
Step-by-step explanation:
16.24/14=1.16
33.3/30=1.11
1.16-1.11=0.05
The correct statement is The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
What is unitary method?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:
14 pound bag cost = 16.24
cost of 1 pound bag = 16.24/14
= $1.16
and,
another bag which is of 30 pound costs = 33.30
= 33.30 / 30
= $1.11
Hence, The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.
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Please help. I dont know what Im doing!
The Fendley family is planning a vacation, and they are trying to choose which resort they will stay in. Mrs. Fendley has created the table below showing their four options. They want to spend no more than $250 per night for the resort. Which resorts will fit into their budget? Select two that apply.
Resort Amount Charged
A $550 for 2 nights
B $694 for 3 nights
C $1028 for 4 nights
D $1153 for 5 nights
A no
Resort A $275 per night
B maybe
Resort B $231.33 per night
C no
Resort C $257 per night
D maybe
Resort D $230.60 per night
the answer is b or d you choose which one you would like to choose
The lengths of the sides of a triangle are6, 8, 10. Can the triangle be a right triangle?
Answer:
Yes
Step-by-step explanation:
Another way of stating the question: Does the Pythagorean Theorem apply here? Does 6^2 + 8^2 = 10^2?
Does 36 + 64 = 100? YES
Yes, this is a right triangle.
Answer: Yes. That is because it fits the requirements of the Pythagoream Therom:
6^2+8^2 10^2
36+64 100
100 = 100 :)
3. In a single growing season at the Smith Family Orchard, the average yield per apple
tree is 150 apples when the number of trees per acre is 100. For each additional tree
over 100, the average yield per tree decreases by 1.
a. What would be the average yield per tree if the number of trees per acre was
doubled? What would be the total yield in that case?
b. How many trees should be planted per acre to maximize the total yield?
Answer:
a. Average yield per tree will be 50 apples. Total yield in that case will be 10,000 apples per acre.
b. 25 more trees are to be planted per acre to maximize the total yield.
Step-by-step explanation:
If the no. of trees per acre is doubled then it will be equal to,
[tex]100 \times 2[/tex]
= 200
So, the no. of trees per acre is increased by (200 - 100) = 100
hence, the average yield per tree will be,
(150 - 100) = 50 in that case.
Hence, the total yield will be,
[tex]50 \times 200[/tex]
= 10,000 apples per acre
Now , if x trees are planted, the total no. of apples produced per acre will be,
[tex](150 - x) \times (100 + x)[/tex]
= [tex]15000 + 50x - x^{2}[/tex]
= f(x) [say]
So. [tex]\dfrac {df(x)}{dx}[/tex] = f'(x)
= 50 - 2x---(1)
taking f'(x) = 0 , we get,
50 - 2x = 0
⇒ x = 25 --------------(2)
Again,
[tex]\dfrac {d^{2}f(x)}{dx^{2}}[/tex] at x = 25
= -2 (<0)
So, f(x) attains it's maximum value at x = 25
Hence,
25 more trees are to be planted per acre to maximize the total yield.
Please help :DDDDDD
question is in the pic!
Equivalent expressions to given expression are:
A : -8+19-3x
C : -11x+19
Step-by-step explanation:
Given
[tex]-5+4(-2x+6)-3x[/tex]
We will simplify the given expression to find the equivalent expressions
[tex]-5+4(-2x+6)-3x\\= -5-8x+24-3x\\= -8x+19-3x\\=-11x+19[/tex]
by observing the simplification we can see that the equivalent expressions are:
A : -8+19-3x
C : -11x+19
Keywords: Polynomials, Expressions
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Find the volume of a sphere with a radius of 100yd . Express your answer in terms of pi.
Answer:
4/3*100^3*π
Step-by-step explanation:
V = 4/3*π*r^3
= 4/3*π*100^3
≈ 4.18879*10^6
You can rent time on computers at the local copy center for a a $ 7 setup charge and an additional $ 3.50 for every 10 minutes. How much time can be rented for $ 22?
Answer:
The answer should round up to 40 minutes. Do it to make sure the answer is 4 which in this case = 40
Step-by-step explanation:
[tex]22 - 7 \div 3.50[/tex]
Answer:
Computer can be rented for 42.85 minutes using $22
Step-by-step explanation:
Given:
Setup charge = $ 7
Additional charge for every 10 minutes = $ 3.50
To find:
The time for which the computer can be rented for $ 22
Solution:
Let the additional time be x
for additional charge for 10 minutes =3.50
for 1 minute , additional charge = [tex]\frac{3.50}{10}[/tex]= $0.35
According to the question
setup cahrge + additional charge= $22
[tex]7+(0.35\times x)=22[/tex]
[tex](0.35\times x)=22-7[/tex]
[tex](0.35\times x)=15[/tex]
[tex]x=\frac{15}{035}[/tex]
x=42.85
how do i solve this
Answer:
y = -2x + 3
Step-by-step explanation:
Slope-intercept equation of a line is:
y = mx + b
where m is the slope and b is the y intercept.
Here, m = -2 and b = 3.
y = -2x + 3
Which absolute value function, when graphed, represents
the parent function, f(x) = |xl, reflected over the x-axis and
translated 1 unit to the right?
5 -4 -3 -2 -1
1
2
3
4
5
f(x) = -1 | + 1
f(x) = -x-11
f(x) = |-*1 + 1
f(x) = |-* - 11
anche
Save and Exit
Answer:
f(x) = -|x| + 1
Step-by-step explanation:
f(x) = |xl when reflected over the x-axis is f(x) = -|x|.
When reflected over x-axis a graph becomes negative in y value.
f(x) = -|x| then translate 1 unit to the right is f(x) = -|x| + 1. Adding 1 translates the graph towards the right because the positive x-axis is on the right.
Is the sequence -3, 1, 5, 9,... An arithmetic sequence
Answer:
Yes, it's an arithmetic sequence.
Step-by-step explanation:
Each term in this sequence is 4 more than the previous term. Therefore we have an arithmetic sequence.
What is the equation of the line that is perpendicular to the y-axis and contains the point (-2,7)
A: y=-x+5
B: x=-2
C: y=x+9
D: y=7
Answer:
y = 7
Step-by-step explanation:
The straight line which is perpendicular to the y-axis will be either x-axis or parallel to the x-axis.
Now, the general equation for all straight line which is either x-axis or parallel to x-axis are given by y = c ........... (1), where c is any constant.
For c = 0 the line will be x -axis. therefore, y = 0, is the equation of x-axis.
Now, if the line (1) passes through the point (-2, 7), then the equation will be y = 7. (Answer)
{Since, the point (-2,7) will satisfy the equation (1) and then c will be equal to 7.}
Which postulate proves these two triangles are congruent ?
Answer:
HL
Step-by-step explanation:
HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
Here, we have,
A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles.
Two angles are said to be complementary if their sum is 90 degrees.
Two triangles are said to be congruent if all their corresponding sides and angles are congruent.
This means that the triangles have equal angles and equal sides.
here, we have,
HL is used for right triangles that are congruent.
These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.
The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.
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y is inversely proportional to the square of x.
A table of values for x and y is shown.
a) Express y in terms of x.
b) Work out the positive value of x when y = 25
Answer:
a) [tex]y=\frac{K}{x^{2} }[/tex]b) [tex]x=\frac{2}{5}[/tex]Step-by-step explanation:
If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like
[tex]y=\frac{K}{x^{2} }[/tex]
Where [tex]K[/tex] is the constant of propotionality.
Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]
[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]
Replacing this constant, the expression between variables is
[tex]y=\frac{4}{x^{2} }[/tex]
Which is the answer to a).
Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be
[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]
Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]
In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.
Explanation:In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.
To express y in terms of x, we can rearrange the equation as y = k/(x^2).
To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).
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Jimmy measured four pieces of wood. their measures are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft. what's the length of the shortest piece
After converting all measurements to the same format (decimals), we can see that the shortest piece of wood Jimmy measured is 4.02 ft.
To find the shortest piece of wood, we first need to convert all the lengths to the same format, preferably in decimals for easier comparison. The lengths of the wood pieces given are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft.
Let's break it down:
4.2ft remains as it is. 9/2ft equals 4.5ft when converted to a decimal. 4.02ft remains as it is. 4 2/9ft equals approximately 4.22ft when the fraction is converted to a decimal.
So, we have pieces of wood that are 4.2 ft, 4.5 ft, 4.02 ft, and 4.22ft. Looking at these numbers, it is clear that the piece of wood that measures 4.02 ft is the shortest.
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