The recursive formula if the sequence is 4,7,10,13 is aₙ = 3n - 2.
What is a Sequence?This is referred to as the list of the things or items in mathematics in which repetitions are allowed and a certain order is followed and an example of a sequence is 1,3,5,7...etc.
The formula for arithmetic sequence is aₙ = a₁ + d ( n -1) in which a is the first term while d is the common difference. a₁ is referred to as the first term while d is the common difference which is 7 - 5 = 2 or 5 - 3 = 2.
aₙ = a₁ + d ( n -1)
= 4 + 3 ( n - 1) --- expand the bracket
= 4 + 3n - 3 = 4 -3 + 3n
aₙ = 3n + 1
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Systems of equations converting words to equations math word promblems into systems of equationsThere were 166 paid admissions to a game. The price was $2.10 each for adults and $0.75 each for children. The amount taken in was $293.25 How many adults and how many children attended?Problem#2 on a table are 20 coins, quarters and dimes. Their value is $3.05 how many of each kind of coin are there?
Problem #1:
x = adults
y = children
x + y = 166
2.10x + 0.75y = 293.25
x = 166 - y
Now we substitute the x value on the second equation:
2.10(166 - y) + 0.75y = 293.25
And we solve for y:
y = 41.
Now we substitute the y value on the first equation:
x = 166 - 41
x = 125
There are 125 adults and 41 children
Determine whether the given function is even, odd, or neither f(x)=2x+x^3
Explanation:
A function is even if f(x) = f(-x), so in this case, f(x) and f(-x) are equal to:
[tex]f(x)=2x+x^3[/tex][tex]\begin{gathered} f(-x)=2(-x)+(-x)^3 \\ f(-x)=-2x-x^3 \end{gathered}[/tex]Consider the following pair of points.
(-3, -3) and (2, 9)
Step 1 of 2: determine the distance between the two points.
Step 2 of 2: determine the midpoint of the line segment joining the pair of points.
The distance between (-3 , -3) and (2 , 9) is 13cm The midpoint of the line segment joining (-3 , -3 )and (2 , 9) is
(-1/2 , 3)
Explanation:Given two points, (-3 , -3) and (2 , 9).
to find the distance between two points,
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
by substituting the values,
d = [tex]\sqrt{(2 - (-3))^{2} + (9-(-3))^{2} }[/tex]
d = [tex]\sqrt{5^{2} + 12^{2} }[/tex]
d = [tex]\sqrt{25 + 144}[/tex]
= [tex]\sqrt{169}[/tex]
= 13 cm
distance between (-3,-3) and (2,9) = 13 cm
to find the midpoint,
midpoint = (x₁ + x₂)/2, (y₁ + y₂)/2
= ((-3 + 2)/2 , (-3 + 9)/2 )
= ((-1 /2) , (6/2))
= (-1/2 , 3)
so the midpoint between (-3 , -3) and (2 , 9) is (-1/2 , 3).
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e for y. 2r + 14y < 21
conquestnick48, this is the solution:
2r + 14y < 21
14y < 21 - 2r
Dividing by 14 at both sides:
14y/14 < (21 - 2r)/14
y < (21 - 2r)/14
What is the solution interval(s) for (3x + 21 - 2 > 3?-2.3 >x> 1x < -2.3 or x > 1x < 1X> 2.3
Given,
[tex]\lvert3x+2\rvert-2>3[/tex]Now, solving the above equation ,
[tex]\begin{gathered} \lvert3x+2\rvert-2>3 \\ \pm(3x-2)-2>3 \\ 3x-2-2>3 \\ 3x>3+4 \\ 3x>7 \\ x>2.3 \\ -(3x-2)-2>3 \\ -3x+2-2>3 \\ -3x>3 \\ -x>1 \\ x<-1 \end{gathered}[/tex]So, the solution is,
[tex]\begin{gathered} 2.31} \end{gathered}[/tex]So, the correct option is option B.
How do you know a relationship in Linear? Describe how you know based on thegraph, based on the table and based on if you have an equation.
The linear relationship must follow the general rule:
[tex]y=m\cdot x+b[/tex]where m is the slope of the linear relationship and b is called the y-intercept
if b = 0, so, it will be a proportional relationship
So, if we have a graph, the graph will be a line
The slope of the line will be = rise/run
Where rise = the difference between y-coordinates
And the run will be = the difference between x-coordinates
If we have a table, we will find the slope using two points from the table with the ordered pair (x1, y1) and ( x2, y2 ) as follows:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]The ratio must be constant between any two points from the table
Finally, if we have an equation, it must be like the general form or can be converted to the general form
In general, the linear equation has a degree of 1
find the product 16 × 60
Answer: 960
Step by step explanation:
We can start by multiplying in this way:
After multiplying 16 by 6, we add the 0.
[tex]16\times6=96[/tex][tex]16\times60=960[/tex]Given rectangle ABCD with vertices A(5,-4), B(5,4), C(-5,4) and D(-5,-4), what is the length ofthe diagonal of ABCDA 12.81B 13.54C 12.57D 25.62E11.81
The rectangle ABCD has coordinates given.
The diagonal is either of AC or BD, and the lengths are the same.
The distance between point A and point C (length of the diagonal) is calculated with the formula below;
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{The coordinates are;} \\ (x_1,y_1)=(5,-4) \\ (x_{2,}y_2)=(-5,4) \\ d=\sqrt[]{(-5-5)^2+(4-\lbrack-4\rbrack)^2} \\ d=\sqrt[]{(-10)^2+(4+4)^2} \\ d=\sqrt[]{100+(8)^2} \\ d=\sqrt[]{100+64} \\ d=\sqrt[]{164} \\ d=12.8062\ldots \\ d\approx12.81 \end{gathered}[/tex]The correct answer is option A
. A theater is being designed to hold 945 people. There are 15 seats per row in the main section and 6 seats per row in each wing. I Diagram Wing (6 seats) XXXXXX XXXXXX Main Section(15 seats) XXXXX ХХХХХХХ XXXXXXXXXXXXXXX Wing (6 seats) XXXXXX XXXXXX a. How many rows will they need to seat 945?
Let there are 'x' rows of 15 seater and 'y' rows of 6 seater.
Given that the total number of people to be seated is 945, so the number of seats required will also be 945.
[tex]15x+6y=945[/tex]Find the perimeter of ATUV. Round your answer to the nearest tenth if necessary.Figures are not necessarily drawn to scale.
Explanation
To solve the question, we will first apply a similar triangle theorem
Similar triangles are triangles that have the same shape, but their sizes may vary.
so, we can compare similar sides to get x before we get the perimeter
Thus
[tex]\frac{SR}{VU}=\frac{QR}{TU}[/tex]Hence
[tex]\frac{23}{x}=\frac{20}{24}[/tex]Solving for x
[tex]\begin{gathered} x=\frac{23\times24}{20} \\ x=27.6 \end{gathered}[/tex]Thus, we will have
Then the perimeter will be:
[tex]VT+VU+TU=36+24+27.6=87.6[/tex]Therefore, the perimeter of the triangle TUV is 87.6
evaluate a-b if a =-2.5 and b = [tex]\frac{2}{5}[/tex]
The expression has a value of -2.9, when evaluated
How to evaluate the expression?The expression is given as
a - b
The values of the variable are given as
a = -2.5
Also, we have the values of the another variable to be given as
b = 2/5
Substitute a = -2.5 and b = 2/5 in the expression a - b
So, we have
a - b = -2.5 - 2/5
Express the fraction as decimal
a - b = -2.5 - 0.4
Evaluate the difference
a - b = -2.9
Hence, the value of the expression is -2.9
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For the function f(x) = -2(x + 3)2 - 1, identify the vertex, domain, and range. (2 points)
We have Function f(x) = -2(x + 3)2 - 1
We know that ,
y = a(x - h)² + k where h and k are vertex
The parabola opens upward if a > 0 (vertex is a minimum)
The parabola opens downward if a < 0 (vertex is a maximum)
The point ( -3 , -1 ) serves as the vertex in this problem.
So the parabola opens downward when -2 > 0 (vertex is a maximum)
The interval (-∞,∞) is the domain.
that implies only actual numbers.
The range is the interval (-∞, -1]
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Identify the zeros and state their multiplicities describe the effect on the graph #7
Answer:
Explanation:
Here, we want to get the zeros, multiplicity, and effect of the zeros of the polynomial
To get this, we can set the function to zero and factorize it
Mathematically, we have that as:
[tex]x^2(x^2-2x-8)\text{ = 0}[/tex]We can further have the equation broken down as follows:
[tex]\begin{gathered} x^2((x+2)(x-4))=\text{ 0} \\ x^2=0 \\ x+2\text{ = 0} \\ x-4=0 \\ x\text{ = 0 twice, -2 , 4} \end{gathered}[/tex]Now, let us get the effect of these zeros on the graph
As we can see, only x = 0 has an even multiplicity (2), x = -2, and 4 have an odd multiplicity
When there is an even multiplicity, the zero will touch the the graph, but when there is an odd multiplicity, the graph will cut through the x-axis at that point
Thus, we can conclude that:
At x = 0, the curve or graph will touch the x-axis and bounce off
At x = -2, the graph will cut through the point x = -2
At x = 4 , the graph will cut through the point x = 4
Why do farmers add fertilizer to the soil where their plants grow?
What’s the correct answer answer asap for brainlist
Answer:
Farmers add fertilizers to the soil because this maintains the soil fertility, so the farmer can continue to grow nutritious crops and healthy crops. Farmers turn to fertilizers because these substances contain plant nutrients such as nitrogen, phosphorus, and potassium.
Graph this point on the coordinate plane: (5, -21/2)
To answer this question, we have that the point is:
[tex](5,-2\frac{1}{2})[/tex]We can see that the value for x = 5, and the value for y is a mixed fraction, and this fraction is equivalent to:
[tex]-2\frac{1}{2}=-(2+\frac{1}{2})=-(\frac{4}{2}+\frac{1}{2})=-(\frac{5}{2})=-\frac{5}{2}=-2.5[/tex]Therefore, we can rewrite the coordinates as (5, -2.5).
Now, to graph this point, we need to find in the coordinate plane, x = 5, and y = -2.5 as follows:
A table of values of a linear function is shown below
The equation of the linear function in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the table,
when x1 = - 2, y1 = 0
when x2 = - 1, y2 = 3
m = (3 - 0)/(- 1 - - 2) = 3/(- 1 + 2) = 3/1
m = 3
Slope = 3
The y intercept is the value of y when x = 0. Thus,
y intercept = 6
By substituting m = 3 and c = 6 into the slope intercept equation, the equation for the function is
y = 3x + 6
In order to find the average rate (speed) of a car travelling on a highway, the distance traveled is divided by the time: R=. If the distance is D= 25 miles and the time is T 5a²+10 ²+7+10 hours, find a simplified expression for the average rate of the car.
Step 1
Given;
[tex]undefined[/tex]The product of two numbers is 10,000. If neither number contains a zero digit, what are the two numbers?
The two numbers are 16 and 625.
What is multiplication?
Multiplication is a basic arithmetic process in which we add a number, particular number of times.
We are given a number is 10000.
The factor of 10000 are [tex]2,2,2,2,5,5,5,5,[/tex]
Now we multiply all the 2 and all the 5 separately
Hence the factor becomes, [tex]2^{4}[/tex]·[tex]5^{4}[/tex]
i.e [tex]16[/tex]·[tex]625[/tex]
as 16 and 625 neither contains any zero and there product is 10000
Hence the two numbers are 16 and 625
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write the formula used to find the area of the trapezoid
The area is given by
[tex]\begin{gathered} A=\frac{1}{2}(A+B)H,\text{ when c is the length of the hypotenuse.} \\ A=\frac{1}{2}(A+(\sqrt[]{C^2-H^2}+A)H \end{gathered}[/tex]Where,
[tex]A=\text{ 6m, B=}\sqrt[]{10^2-8^2}+6=12m,and\text{ H =}8m[/tex]Factor to find the zeros of the function y = 2x^2 -3x + 1.
The zeros of the function are x = 1/2, 1
Explanation:The given function is:
[tex]y=2x^2-3x+1[/tex]This can be factorized as shown below
[tex]\begin{gathered} y=2x^2-2x-x-1 \\ \\ y=2x(x-1)-1(x-1) \\ \\ y=(2x-1)(x-1) \end{gathered}[/tex]To find the zeros of the function, let y = 0
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \\ \\ \\ x-1=0 \\ x=1 \end{gathered}[/tex]The zeros of the function are x = 1/2, 1
As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 50 milligrams of Medication A with 40 milligrams of Medication B. However this week, the doctor said to only use 16 milligrams of Medication B. How many milligrams of Medication A should be mixed this week? Answer: milligrams Question Help: D Video Read Submit Question
If by last week, your patient's doctor indicated that you should mix 50 milligrams of Medication A with 40 milligrams of Medication B, then;
A:B = 50:40
Using equality postulate, we can say;
50mg of A = 40mg of B
however if this week, the doctor said to only use 16 milligrams of Medication B, in order for us to get the amount of equivalent milligram for medication A, we will also usse the equality postulate say:
x mg of A = 16mg of B (I had to use x since we do not know the dosage of medication A)
Solving both expression to get x:
50mg of A = 40mg of B
x mg of A = 16mg of B
Simply cross multiply since both medications are always mixed in the same proportion:
40 * x = 50 * 16
40x = 800
Divide both sides by 40
40x/40 = 800/40
x = 20
Therefore 20miligram of medication A should be mixed this week
super easy one to one function!!! 50 POINTS HELP!!
The correct value of the given function is (E) g⁻¹(-3) = 3.
What are functions?A mathematical expression, rule, or law establishes the relationship between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
So, g⁻¹(-3):
x = -1g(x) = -3Then, g(x)·x = (-1)(-3) = 3
Then, g⁻¹(-3) = 3.Therefore, the correct value of the given function is (E) g⁻¹(-3) = 3.
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Question 15<>Last year, Pinwheel Industries introduced a new toy. It cost $2600 to develop the toy and $5 tomanufacture each toy. Fill in the blanks below as appropriate.A.) Give a linear equation in the fohon C(x) = mx + b that gives the total cost, C, to produce ofthese toys:C(x) =B.) The total cost to produce 2 = 2400 toys is $Question Help: Video Message instructorSubmit QuestionJump to Answer
The linear function of the cost needs to be determined.
Using the given cost function,
C(x) = mx + b, where m = cost of each toy; x = number of toys produced; b = innitial cost of manufacturing:
C(x) = 5x + 2600
To answer the second part of the question: cost of producing 2 toys, we have:
C(x) = 5(2) + 26000
C(x) = 10 + 2600
C(x) = $2610
A recipe called for the ratio of sugar to flour to be 7 : 3. If you used 63 ounces of sugar, how many ounces of flour would you need to use? Solve by using equivalent fractions.
Answer:
The correct answer is 27 ounces of flour.
Step-by-step explanation:
I did it on Edge and got it correct so I'm 100% sure it's 27.
Sum of the arithmetic sequences Find each sum. 1+3+5+...+59
Manny, this is the solution to the arithmetic sequence:
Sum = 1 + 3 + 5 + 7 + 9........+ 59
d = 2 (Common difference)
An = 2n - 1
A1 = 1
n = 59 + 1 /2 (Last number of the sequence plus 1 and the result divided by 2)
n = 30
Therefore, we use the arithmetic sequence sum formula:
n (A1 + d (n - 1)/2)
Replacing by the values we know:
30 (1 + 2 (30 - 1)/2)
30 * 30
900
The sum of this arithmetic sequence is 900
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The function f(-5) has a value of -6
How to evaluate the function?The given parameters are the graphs in the figure
From the question, we have the function definition to be f(-5)
Next, we analyze the functions of the graphs
The function on the first graph is a function of f(x), while the second graph is a function of g(x)
This means that we use the first graph to calculate the value of the function f(-5)
The function f(-5) means the value of x is -5
On the first graph, we have
f(x) = -6 when x = -5
So, we have
f(-5) = -6
Hence, the value of the function is -6
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Where can I Get L1 and L4 from a missing vertical angles?
Vertical Angles, are angles that are opposite to each other that shares the same vertex. The vertex in the image is where the two lines cross.
[tex]\begin{gathered} \angle2\text{ and }\angle4\text{ are vertical angles} \\ \angle1\text{ and }\angle3\text{ are vertical angles} \end{gathered}[/tex]Vertical Angles have a property where they are congruent. So whatever is the measurement of one angle, it would be the same to its vertical angle pair.
[tex]\begin{gathered} m\angle1=m\angle3 \\ m\angle1=86.7\degree \\ \text{and} \\ m\angle2=m\angle4 \\ m\angle2=93.3\degree \end{gathered}[/tex]Solve the tringle round your answers to the nearest tenth
ANSWER:
Angles:
41°
49°
90°
Sides:
a = 13.6
b= 11.8
c = hypotenuse = 18
STEP-BY-STEP EXPLANATION:
We can calculate the sides a and b, with the use of trigonometric ratios, like this:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{ replacing} \\ \sin 41=\frac{b}{18} \\ b=\sin 41\cdot18 \\ b=11.8 \\ \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \text{ replacing} \\ \cos 41=\frac{a}{18} \\ a=18\cdot41 \\ a=13.6 \\ \\ \alpha=180-90-41 \\ \alpha=49\text{\degree} \end{gathered}[/tex]I know how to find answers I get them mixed up every time
We are to evaluate for
[tex]\begin{gathered} f(2)=? \\ f(x)=-1,x=? \end{gathered}[/tex]Let us upload the image and evaluate for f(2)
From the image, we can observe that
[tex]f(2)=1[/tex]Let us upload the second image and evaluate for x, when f(x)=-1
From the image above, the value of x for which f(x)=-1 is
[tex]x=0[/tex]Final answers
[tex]\begin{gathered} a)\text{ 1} \\ b)\text{ 0} \end{gathered}[/tex]Factor the expression 36a-16 to write an equivalent expression in which all coefficients and constants are integer values.
The expression 36a - 16 to write an equivalent expression in which all coefficients and constants are integer values is; 4(9a - 4)
How to factor Algebraic expressions?We are given the expression as; 36a - 16
Now, we want to write an equivalent expression of 36a - 16.
However, according to question, 36 and 16 are both divisible by 4. Thus, we will divide both sides by 4 to get;
36/4 = 9 and 16/4 = 4
Now, factorize the given expression 36a - 16.
Taking 4 as a common factor, we get,
36a - 16 = 4(9a - 4)
Therefore, 4(9a - 4) is the factor to write an equivalent expression 36a - 16.
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