Answer:
Below
Step-by-step explanation:
(2x+15) / ( 3x+15) = 11/14 cross multiply to get
28x + 210 = 33x + 165
45 = 5x
x = 9 so the larger number is 3 X 9 = 27
(smaller number is 2 x 9 = 18)
One number is 7 more than another number. The sum of these two numbers is 101. What are the numbers?
Answer:
54 and 47
Step-by-step explanation:
Lets first number be "x" and second number be "y"
x = y + 7
x + y = 101
(y + 7) + y = 101
2y + 7 = 101
2y = 94
y = 47
x = 47 + 7
x = 54
In the figure below angle A and angle B make a right angle.
Suppose A = 2x - 8
and L B = 3x + 5.
Given this information the measure of B would be
degrees
The measure of ∠B of the right angle is 152°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the measure of ∠A = 2x - 8
The measure of ∠B = 3x + 5
And , angle A and angle B make a right angle
On simplifying the equation , we get
2x - 8 = 90
Adding 8 on both sides of the equation , we get
2x = 98
Divide by 2 on both sides of the equation , we get
x = 49
Substitute the value of x in equation , we get
∠B = 3 ( 49 ) + 5
The measure of ∠B = 152°
Hence , the angle is ∠B = 152°
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How do I solve this problem using the Rational Zeroes Theorem?
1) Find the real number solutions of the following polynomial equation:
f(x) = 4x^5 - 40x^3 + 36x
Answer:
Step-by-step explanation:
The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).
Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.
Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.
Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.
Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.
Someone help me with this quadratic functions
The graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.
What is a quadratic equation?
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x). Where it equals zero is where the quadratic equation finds its solutions. They are also known as the equation's roots.
Assuming the question is to graph the quadratic function y = 6x².
The x-intercept can be found by substituting y = 0
0 = 6x²
x = 0
x-intercept = (0,0)
y-intercept can be found by substituting x=0
y = 6 * 0
y = 0
y-intercept = (0,0)
The given quadratic equation is the equation of an upward parabola with the vertex as (0,0).
The axis of symmetry is x = 0 i.e y-axis.
Hence the graph of the quadratic equation y = 6x² is an upward parabola with vertex (0,0) and axis of symmetry as y-axis.
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Anota una magnitud vectorial y explica tu respuesta
A physical quantity with both magnitude and direction is called a vector quantity.
A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.
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Complete Question
Write down a vector quantity and explain your response.
i just really need a help guys thank u mwa
Answer:
See below
Step-by-step explanation:
My man, how did you even get these numbers??? no whole number multiplied by 6.65 even equals 22??? Regardless, here's what I did.
a) r = 40/2 = 20
A = πr^2 = (3.14)(20)^2 = 1256
b) 1256/50 = 25.12 basically, 26
c) 26 x 6.65 = 172.9
Thoughts and prayers my guy. Keep trying
Answer:
A. 1256[tex]ft^{2}[/tex] B. 26 pounds C. $172.90
Step-by-step explanation:
PART A
1st find the radius of the area
radius = diameter / 2
r = 40/2
radius = 20ft
Area of circle = radius^2* pi
Area = 400 * 3.14
Area = 1256 [tex]ft.^{2}[/tex]
PART B
1256 / 50 = 25.12
Because we can only buy full pounds and we need the whole area to be reseeded, we round 25.12 to 26.
26 pounds of seeds will be needed to reseed the whole area.
PART C
Multiply the number of pounds of seeds needed to be bought by 6.65
26 x 6.65
$172.90 for the total cost of grass seeds
Identify the percent of change as an increase or a decrease.
9 points to 4 points
o increase
decrease
Find the percent of change. Round to the nearest tenth of a percent if necessary.
The percent of change is
%.
The percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
What is the Percent of change?
The percent of change is a measure that compares the difference between two values to the original, or initial, value. It is usually expressed as a percentage and indicates how much a value has increased or decreased from its initial value.
To find the percent of change from 9 points to 4 points, we need to first calculate the amount of change, which is the difference between the final value (4 points) and the initial value (9 points):
Amount of change = Final value - Initial value = 4 - 9 = -5
The negative sign indicates a decrease in value.
Next, we can calculate the percent of change using the formula:
Percent change = (Amount of change / Initial value) x 100%
Substituting the values we get:
Percent change = (-5 / 9) x 100% ≈ -55.6%
Hence, the percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
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What is the value of x? enter your answer in the box. X = cm a bow tie shape polygon made of two bow ties that share a vertex. The shape is created by two segments intersecting forming two triangles with vertical angles. An alternate interior angle of the triangles are marked congruent to each other. The larger triangle is on the left and the smaller triangle is on the right. In the larger triangle, the left side of the triangle is 32 centimeters. The south side of the triangle is 40 centimeters. On the smaller triangle, the right side of the triangle is 4 centimeters. The north side of the triangle is labeled x.
By proving the two triangles as similar triangles , the value of x in the triangles is x = 5 cm .
By using the proportions, for the two triangles which are similar because they contain three equal angles ;
The One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and
the third angle one has to be same because of the sum of the three internal angles of a triangle must equal 180 degrees.
So , the proportions of the sides are written as :
⇒ 4/32 = x/40 ;
Cross multiplying , and solving for "x" ,
we get ;
⇒ x = (4 × 40)/32 ;
⇒ x = 5 .
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The given question is incomplete , the complete question is
What is the value of x in the polygon given below ?
Financial planning case 2-2
Victor Hernandez Considers a Career Change
Victor is somewhat satisfied with his sales career and has always wondered about a career as a teacher in a public school. He would have to take a year off work to go back to college to obtain his teaching certificate, and that would mean giving up his $40,000 salary for a year. Victor expects that he could earn about the same income as a teacher. Round your answers to the nearest dollar.
What would his annual income be after 12 years as a teacher if he received an average 4 percent raise every year? Round Future Value of a Single Amount in intermediate calculations to four decimal places. (Hint: Use Appendix A-1.)
$
Victor also could earn $3,000 each year teaching during the summers. What is the accumulated future value of earning those annual amounts over 12 years assuming a 5 percent raise every year? Round Future Value of a Series of Equal Amounts in intermediate calculations to four decimal places. (Hint: Use Appendix A-3.)
$
Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
Step-by-step explanation:
To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.
Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:
FV = $40,000 * (1 + 0.04)^12 = $47,564
So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.
To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n - 1 / r), where A is the annual payment and r is the interest rate.
Plugging in the values, we get:
FV = $3,000 * (1 + 0.05)^12 - 1 / 0.05 = $41,592
So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.
In ADEF, J is the intersection of the three medians. If EI = 33, find JI.
D
Q
H
F
The value of JI in the given triangle is 11.
What is a triangle?A triangle is a polygon with three sides, vertices and angles.
Given that, in a triangle DEF, J is the intersection of the three medians.
EI = 33, we are asked to find the value of JI,
Since, all the median is intersecting at J, therefore, J is the centroid.
We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.
Therefore,
Let, EI = 3x,
JI = x,
Therefore, JI = 11
Hence, the value of JI in the given triangle is 11.
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The complete question is :
In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.
Figure is attached
Write the set using set-builder notation
(9, 18, 27, 36, ...}
How do i do this
The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the set be represented as A
Now , the value of A is
A = { 9 , 18 , 27 , 36 , ... }
The set A contains all the positive multiples of 9
So , let x be the set of natural numbers and the value of A is
A = { 9x | x ∈ N } , and
A = set of all x’s containing multiples of 9
Hence , the set builder notation is { 9x | x ∈ N }
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where are the vertical asymptotes for y = 6 tan(0.2x)
The vertical asymptotes of y = 6tan(0.2x) is [tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]
How to determine the vertical asymptotesFrom the question, we have the following parameters that can be used in our computation:
y = 6tan(0.2x)
The equation is a trigonometry function
The best way to determine the vertical asymptotes is with the use of a graphing tool
Using the above as a guide, we have the following:
From the graphing tool, we have
[tex]\:x=\frac{5\pi }{2}+\frac{\pi }{0.2}n[/tex]
This gives
[tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]
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Algebra 1, slope of coordinate plane on table
The y-intercept of the line passing through the given points is -26 and the slope is -13/17
What is y-intercept?The y-intercept is the point where the graph intersects the y-axis.
Given that, the pair of coordinates of some points, we need to find the y-intercept,
To find the same, we will firstly find the equation of the line passing through these points,
We know that, the equation of a line passing through two points is given by,
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Considering the points, (34, -52) and (51, -65)
The equation will be,
y+52 = -65+52 / 51-34 (x-34)
y+52 = -13/17(x-34)
y+52 = -13x/17+26
y = -13x/17-26
Hence, the y-intercept of the line passing through the given points is -26.
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-10 -8 -6 -4 -2 0 2 4 6 8 10
Plot the integer -7 on the number line.
The distance between 0 and -7 is
The absolute value of -7 is
The magnitude of -7 is
Step-by-step explanation:
To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:
-10 -8 -7 -6 -4 -2 0 2 4 6 8 10
The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.
The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.
The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.
Solve it but using the SQUARE ROOT PROPERTY
please help need ASAP!
The solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
What is quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic equation is:
ax^2 + bx + c = 0
where x is the variable, and a, b, and c are constants, with a not equal to 0. The quadratic equation can have two solutions, one solution, or no real solutions, depending on the values of a, b, and c.
Starting with the given equation:
25 = (x + 9)²
We can start by taking the square root of both sides of the equation, which gives us:
±5 = x + 9
Next, we can isolate x by subtracting 9 from both sides of the equation:
x = -9 ± 5
This gives us two solutions:
x = -9 + 5 = -4
or
x = -9 - 5 = -14
Therefore, the solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
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Help!!
Write an equation to show the total cost, y, for x months.
YOU WIL GET BRAINLIEST!!
The equation to represent the total cost, y, for x months is y = 12x + 30.
From the given table, we can observe that the total cost increases by $12 for each additional month of usage.
This means that the rate of change, or the slope of the equation, is $12 per month.
We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.
Putting it all together, the equation to represent the total cost, y, for x months is:
y = 12x + 30
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What is the average of the points A, B, and C with weights 1, 3, and 4 respectively? A (-8, 5) B (8, 2) C (5, 4)
The average of the three weighted points, A, B, and C, is (-1, 2.875).
In mathematics, what does average weight mean?A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.
weighted average = (w1 × x1 + w2 × x2 + w3 × x3) / (w1 + w2 + w3),
where wi is the weight of the ith point, and xi is the coordinate of the ith point.
Substituting the given values, we get:
weighted average = (1 × (-8, 5) + 3 × (8, 2) + 4 × (5, 4)) / (1 + 3 + 4)
= (-8, 5 + 3 × 2 + 4 × 4) / 8
= (-8, 23) / 8
= (-1, 2.875)
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A hole in a steel plate has a diameter of 1.166 cm
at 23.00 ∘C
At what temperature is the diameter of the hole equal to 1.164 cm
?
will give brainliest
So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.
A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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WILL GIVE 200 POINTS !!!!> find the x intercept and the y intercept. write each intercept as an ordered pair. y=5x-10
Answer:x intercept (2,0)
Yintercept (0,-10)
Step-by-step explanation:
y=mx+b b= y intercept
To find x you just solve
Y=5x-10
10=5x
2=x
Astronomers believe that the radius of a variable star increases and decreases with the brightness of the star. Suppose a variable star has an average radius of 20 million miles and changes by a maximum of 1.6 million miles from this average during a single pulsation, and that the time between periods of maximum brightness is 5.2 days. Find an equation that describes the radius of this star as a function of time. (Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing.) R(t) =
Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then R(t) = 20 + 1.6sin(2πt/5.2).
The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.
In this case, the amplitude is 1.6.
Since the radius changes by a maximum of 1.6 million miles.
The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)
The phase shift is 0, since when t = 0 the radius is increasing.
The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)
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The store you are buying the item down offers you an installment plan.
The terms of the contract for the plan are:
• $50 down
• 12 payments
• Finance charge of $100
Interest = Finance Charge = ________________
Total Payment = Cost of item + Finance charge = _____________
Monthly Payment = (Total Payment – Down payment / 12 = __________
1) Based on the percentage of the downpayment, the total payment made for the store item is $1,100, which includes a finance charge or interest of $100.
2) The monthly payment for 12 installments is $87.50.
How the total payment is computed:The total cost of the item is based on the downpayment's equivalent percentage (proportion).
A proportion is the equation of two or more ratios.
Finance Charge (Interest) = $100
Downpayment = $50 or 5%
Installment period = 12 months
Cost of item = $1,000 ($50/5%)
Total payment = $1,100 ($1,000 + $100)
Monthly payment = $87.50 ($1,100 - $50)/12
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Question Completion:The downpayment is 5% of the total cost of the item.
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 7000 equation 1
0.1a + 0.11b = 730 equation 2
Where:
a = amount invested in the account that earns 10% interest
b = amount invested in the account that earns 11% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.1
0.1a + 0.1b = 700 equation 3
Subtract equation 3 from equation 2
0.01b = 30
Divide both sides of the equation by 0.01
b = 30 / 0.01
b = 3000
Substitute for b in equation 1:
a + 3000 = 7000
a = 7,000 - 3000
a = 4000
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Hannah is helping her younger brother learn to count money. She gave her brother a total of 20 coins nickels and pennies. Hannah’s brother said he counted $0.68. How can Hannah solve a system of equations to tell whether he counted the money correctly?
Hannah’s brother counted correctly it Hannah gave him & 8 pennies and 12 nickels.
What does a math equation mean?The concept of an equation in algebra is a mathematical declaration that demonstrates the equality of two mathematical expressions. Declaration of equivalence between two expressions made up of numbers or variables
Finding the counted the money correctly , we obtain:
x= number of pennies
y = number of nickels.
x + y =20
so , x = 20-y
x+5y = 68
20-y +5y = 68
4y= 48 so y = 12 and x = 8.
8 pennies and 12 nickels
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If the radius of one of the semicircles is 7 meters, what is the circumference of one of the semicircle? asap 70 Ponits!!!!!!!!!!
10.99 m
21.98 m
87.92 m
43.96 m
Answer:
The circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Step-by-step explanation:
The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius of the circle.
For a semicircle with a radius of 7 meters, the circumference can be calculated as follows: Because the semicircle is a half circle, then:
C = (2πr)/2= 3.14 × 7 = 21.98 meters
So, the circumference of one of the semicircles with a radius of 7 meters would be approximately 21.98 meters.
Answer:
The circumference of one of the semicircles is 21.98 m.
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
A semicircle is half a circle, therefore the length of the curved part of the circumference of a semicircle is half the circumference of a circle: πr.
Given the radius of one of the semicircles is 7 m and π ≈ 3.14, the circumference of the semicircle is:
⇒ C = 3.14 · 7
⇒ C = 21.98 m
13) A theater has 38 rows of seats. The first row has 25 seats, the second
row has 29 seats, the third row has 33 seats, and so on.
What is the total number of seats in the theater?
O3,762
O3,838
O 7,524
O 7,676
Answer:
Step-by-step explanation:
To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:
S = n/2 * (a_1 + a_n)
where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.
In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:
n = 38 (the number of rows)
a_1 = 25
a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173
Now, we can substitute these values into the formula:
S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762
So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.
find the sum of the series. make sure you use the formula and show your work for credit.
please help me I didn't get this at all!
Answer:
The sum of the series is 260.
------------------------
Each term of given series is expressed as:
tₙ = 3n - 1This is an arithmetic progression with 13 terms and the first and last terms are:
t₁ = 3*1 - 1 = 2t₁₃ = 3*13 - 1 = 38Use the sum of the first terms of AP formula:
Sₙ = (t₁ + tₙ)*n/2S₁₃ = (2 + 38)*13/2 = 40*13/2 = 20*13 = 260Answer:
The sum of the series is 260.
Step-by-step explanation:
[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]
The given sigma notation means:
Sum of the series with nth term (3n - 1), starting with n = 1 and ending with n = 13.As (3n - 1) is linear, the series is arithmetic.
The first term (n = 1) is:
a₁ = 3(1) - 1 = 2The second term (n = 2) is:
a₂ = 3(2) - 1 = 5The third term (n = 3) is:
a₃ = 3(3) - 1 = 8… and the last term (n = 13) is:
a₁₃ = 3(13) - 1 = 38Therefore, we need to find 2 + 5 + 8 + ... + 38.
Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.
[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]
Therefore, the sum of the series is 260.
Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.8° is added to the data, how does the range change?
The range decreases to 44°.
The range increases to 52°.
The range stays 46°.
The range stays 48°.
Answer: the enswer is c the range is 46
Step-by-step explanation:
The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
1. what are the three equations that are used.
2. what are the lengths of the sides?
(the shortest side, the longest side, and the third side.
The equations used are:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.
What are the length of the sides?The perimeter of a triangle is the sum of the length of the three sides of the triangle.
Let the following expressions represent the lengths of the sides of the triangle:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
Perimeter = a + 1/2a + a - 1 = 39
a + 1/2a + a = 39 + 1
2a + 1/2a = 40
2 1/2a = 40
5/2a = 40
a = 40 x 2/5
a = 16 inches
Shortest side = 1/2 x 16 = 8 inches
Third side = 16 - 1 = 15 inches
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