The length of every median in an equilateral triangle whose side length is 5 is; 4.33
What is the length of the triangle median?In geometry, a median of a triangle is defined as a line segment joining a vertex to the midpoint of the opposite side which therefore bisects that side.
This tells us that every single triangle has exactly three medians, with one from each vertex, and as a result they all intersect each other at the centroid of the triangle.
The median joins a vertex and the opposite side's midpoint. Thus;
side = 5
half side = 5/2 = 2.5
Using Pythagoras theorem;
a² + b² = c²
Thus;
2.5² + b² = 5²
b² = 18.75
b = √18.75
b ≈ 4.33
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Find the equation for the plane through P0 (−1,−7,2) perpendicular to the following line. x= −1+t , y= −7−5t , z= −2t , −[infinity]
The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30
The plane is passing through point P₀(-1, -7, 2)
And the parametric equation of the line is:
x = -1+t , y= -7-5t , z= -2t
L: (-1, -7, -2) + t(1, -5, -2)
The required plane passes through P₀ and perpendicular to line L.
The direction vector of L is V = <1, -5, -2>.
The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is
1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0
The equation of plane P passing through point P₀ (-1, -7, 2) is:
1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0
(x + 1) - 5(y + 7) - 2(z - 2) = 0
x - 5y-2z + 1 - 35 + 4 = 0
x - 5y - 2z = 30 is the required equation of the plane
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The complete question is:
Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t
1) The end behavior of a rational function is equal to
A) Holes
B) Horizontal Asymptote
C) Vertical Asymptote
D) Domain
Answer:
B) Horizontal Asymptote
A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.
Help me please help thank you and have a great day
Hey Mate,
Answer is (4,3),
Thank you .
The table shows conversions of common units of length.
Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers
1 yard = 3 feet
1 yard = 36 inches
Which shows the best path to find the number of centimeters in 1 yard?
The number of centimetres in the 1 yard will be 9.144 cm.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that:-
Metric System Units
1 inch = 2.54 centimetres
1 foot = 0.3048 meters
1 mile = 1.61 kilometres
1 yard = 3 feet
1 yard = 36 inches
First, we will calculate 1 yard to feet.
1 yard = 3 feet
1 feet = 0.3048 meters
1 feet = 3.048 centimeters
1 yard = 3 x 3.048 centimeters
1 yard = 9.144 centimeters
Hence, the length of 1 yard in cm is 9.144 cm.
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Taylan i elling platic and wooden frame. He old 7 total frame. The number of platic frame Taylan old wa 5 le than twice the number of wooden frame. How many of each type of frame did Taylan ell?
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames
Let x = number of wooden frames
Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:
x + (x * 2) < 7
2x < 7
x < 7/2
x = 3
Therefore, Taylan sold 3 wooden frames and 5 plastic frames.
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
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Gabe purchased a razor for $13.99, a refill pack of razor blades for $5.75, shaving cream for $3.29 and lotion for $7.35. He has a $.65 coupon for the shaving cream and a $3.00 rebate for the razor.
Answer:
13.99 + 5.75 + 3.29 + 7.35 = 30.38
30.38 - .65 - 3.00 = 26.73
Step-by-step explanation:
Hope this helps! =D
Answer:
$26.73
Step-by-step explanation:
razor = $13.99 - $3.00(rebate) = $10.99
refill pack of razor blades = $5.75
shaving cream = $3.29 - $0.65(coupon) = $2.64
lotion = $7.35
Triangle ABC is similar to triangle FGH.
What is the value of x in centimeters?
Triangle ABC is similar to triangle FGH.
And the value of the x is 22.5 centimeters.
What are similar triangles?Those triangles that looks the same but different in sizes.
And in the similar triangle,
the corresponding sides in proportion to each other and corresponding angles are equal to each other.
Given:
Triangle ABC is similar to triangle FGH.
That means, the corresponding sides of the triangles are in proportion to each other.
That means,
13.5/9 = 18/12 = x/15
Now,
18/12 = x/15
x = 270/12
x =22.5 centimeters
Therefore, the value of the x is 22.5 centimeters.
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A recipe for homemade modeling clay includes 1/3 cup of salt for every cup of water. If there are 6 cups of salt, how many gallons of water are needed? Identify the constant of proportionality.
Answer:
18 cups but each gallon = 16 cups. so 1.125 gallons
Step-by-step explanation:
ratio = 1/3 salt :1 water = 1 salt : 3 water
so 6 salt :18 water
Dana sees a street sign and a pine tree. The street sign is 8 feet tall and casts a shadow that is 15 feet long. What is the height of the pine tree if the pine tree's shadow is 30 feet long?
In 1957 an earthquake in Alaska
measured about 9.0 on the Richter
scale. An earthquake with magnitude 6.0 occurred in Japan in early 2007. How many times more intense was the earthquake in Alaska than the one in Japan?
The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.
How much more intense the earthquake in Alaska and find ratio of amplitude?To determine how much more intense the earthquake in Alaska was than the one in Japan, we can use the formula:(magnitude of Alaska earthquake / magnitude of Japan earthquake) = (9.0 / 6.0) = 1.5This means that the earthquake in Alaska was 1.5 times more intense than the one in Japan.Alternatively, we can use the logarithmic relationship of the Richter scale to calculate the ratio of amplitude.(10^(magnitude of Alaska earthquake)/10^(magnitude of Japan earthquake)) = (10^9.0/10^6.0) = (1000000000/1000000) = 1000This means that the amplitude of the earthquake in Alaska was 1000 times greater than the one in Japan.So the answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.To learn more about ratio of amplitude refer:
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A jewelry designer is making beaded jewelry with the 999 beads she currently has in stock. Bracelets use 10 beads and necklaces use 57 beads.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
The inequality in standard form that describes this situation is 10x + 57y < 999.
What is inequality ?This refers to the relationship between two values that are not of the same value.
Solving the inequality, we have:
Let x be the number of b=racelets that can be made and y be the number of necklaces that can be made. The inequality in standard form that describes the situation is:
x = the number of bracelets
y = the number of necklaces
Number of beads / bracelets =10
Number of necklaces = 57
10x + 57y < 999.
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What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, f ( x ) decreases in value. As x increases in value, f ( x ) decreases in value. B. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) increases in value. C. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) decreases in value. D. As x decreases in value, f ( x ) decreases in value. As x increases in value, f ( x ) increases in value.
The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) decreases in value.
What is a radical function on graph?A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.
The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.
Therefore, the correct answer is as given above
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if x=4, whats the value of x^2+2x
(^2 = ‘to the power of two’ - the mini two)
if x=4, the value of the expression x^2+2x is 24
What is an algebraic expression?An algebraic expression can be described as a mathematical expression comprising of variables, terms, coefficients, factors and constants.
Algebraic expressions are also known to comprise of some mathematical or arithmetic operations, such as;
SubtractionAdditionFloor divisionBracketMultiplicationParenthesesDivisionFrom the information given, we have the expression as;
x² + 2x
For the value of x = 4, substitute the value of x as 4 in the expression, we get;
(4)² + 2(4)
find the square, we have
16 + 2(4)
expand the bracket
16 + 8
add the values
24
Thus, the value is 24
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there are 24 psychiatrists and 30 psychologists attending a certain conference. three of these 54 people are randomly chosen to take part in a panel discussion. what is the probability that at least one psychologist is chosen?
Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.
To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:
54 choose 3 = 54! / (3! * 51!) = 19,958
Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:
24 choose 3 = 24! / (3! * 21!) = 1,344
Now, we can use these values to calculate the probability of no psychologists being chosen:
P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%
Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:
P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%
So the probability that at least one psychologist is chosen from the conference is 93%
Step-by-step explanation:
Hi, I am trying to solve a the sin graph y=1-3sin(3/2)Theta. can someone explain to me how to get the y-values for each x value?
The graph of the function is added as an attachment and the function values are y = 4 for all x values
How to detemrine the function valuesFrom the question, we have the following parameters that can be used in our computation:
y=1-3sin(3/2)Theta
Express properly
So, we have the following representation
y = 1 - 3sin(3/2π)
Next, we create a plot of the graph (see attachment)
From the graph, we can see that the function is a horizontal line at y = 4
This means that for all x values, the y value is constant at 4
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Hotel P offer two type of room for it cutomer: a Deluxe room and a Suite room. The price per night for the uite room for check-in on Sunday until Thurday i 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday i 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thurday. If the hotel management want to maintain the price difference between the two type of pace, and the price per night for a Suite room for check-in on Sunday until Thurday i $223, what hould be the price per night for a Suite room for check-in on Friday and Saturday?
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.
1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:
$223 / 1.70 = $131.18
2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:
$131.18 x 1.25 = $163.98
3. Calculate the price of a Suite room for check-in on Friday and Saturday:
$163.98 x 1.70 = $278.50
The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.
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Select the correct answer.
What is the y-intercept of function f?
(-3x - 2,
-∞ <
-x + 1,
-2 ≤ x ≤ 3
2x + 5,
3 ≤ x < 00
f(x)
=
OA. -1
OB. 5
O C. 1
OD. -2
< -2
The y-intercept of function f is 1.
f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3 = 2x + 5, 3 ≤ x < ∞
For y-intercept, x =0, f(x) = -x + 1 [∵ -2 < 0 < 3]
f(0) = -0 + 1 = 1
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.
This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.
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the following data are for 30 observations involving two categorical variables, x and y. the categories for x are a, b, and c; the categories for y are 1 and 2. observation x y 1 a 1 2 b 1 3 b 1 4 c 2 5 b 1 6 c 2 7 b 1 8 c 2 9 a 1 10 b 1 11 a 1 12 b 1 13 c 2 14 c 2 15 c 2 observation x y 16 b 2 17 c 1 18 b 1 19 c 1 20 b 1 21 c 2 22 b 1 23 c 2 24 a 1 25 b 1 26 c 2 27 c 2 28 a 1 29 b 1 30 b 2 (a) develop a crosstabulation for the data, with x as the row variable and y as the column variable. y total 1 2 x a b c total (b) compute the row percentages. (round your answers to one decimal place.) y total 1 2 x a b c (c) compute the column percentages. (round your answers to one decimal place.) y 1 2 x a b c total (d) what is the relationship, if any, between x and y? category a values for x are ---select--- for y. category b values for x are ---select--- for y. category c values for x are ---select--- for y. need help?
The row percentage of A is 0% , B is 83.3% and of C is 15.4%.
Percentage describes the relative value of a number. Its shows the 100th part of the number with respect to a number whose value is provided in the problem.
Here various data is given about A, B and C in the format of two tables and this shows the relationship between the two.
Now, the row percentage of A is
[tex]\frac{0}{5} * 100=0%[/tex]%
Then, the row percentage of B is
[tex]\frac{10}{12}*100 = 83.3%[/tex]%
Now, we have to find the row percentage of C
[tex]\frac{2}{13}*100 = 15.4%[/tex].%
Hence, The row percentage of A is 0, the row percentage of B is 83.3% and the row percentage of C is 15.5%.
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Find the length of side x to the nearest tenth.
Considering the figure the side length x is solved to be 6.6
How find the value of xInformation given from the question is interpreted as
√11 = adjacent
x = hypotenuse
The side x is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The side x is calculated using cos, CAH
cos 60 = Adjacent / hypotenuse
cos 60 = √11 / x
x = √11 / cos 60
x = 6.633
x = 6.6 to the nearest tenth
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Karen is trying to get to the MRT station, which is 7
10
km away
from where she parked her car. She has already walked for 2
5
km. How much farther does she have to walk to reach the MRT
station?
answer quickly please and please send solution if possible
Answer:
The answer is 685 km hopefully I understood your question and helped you ☻
Step-by-step explanation:
710 km - 25 = 685
(subtitution)Determine each ordered pairs if it is a solution of the system 1.{2x + 5y=20{3x-4y=7 a.(5,0)b.(3,2)c.5,2)
Answer: c. (5,2)
Step-by-step explanation: We have two equations here and need to calculate the value of x and y.
The two equations are:
2x+5y = 20
3x - 4y = 7
Using the Substitution method,
2x=20-5y
x=(20-5y)/2
Now substitute the value of x in equation (2)
3 × [tex]\frac{20-5y}{2} - 4y = 7[/tex]
60-15y-8y = 14
60-23y=14
-23y = -46
y=2
Now put the value of y in any equation.
x = (20-10)/2
x=5
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Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
The value of x and y is -10 and 5 respectively in the given equations.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - x + 3y = 5
The second linear equation is - -3x - 2y = 20
On evaluating individually the equation obtained is -
-3x - 2y + x + 3y = 20 + 5
-2x + y = 25
Multiply equation (1) with 3 -
3(x + 3y) = 5 × 3
3x + 9y = 15.....(3)
Adding equation (3) and (2) -
-3x - 2y + (3x + 9y) = 20 + 15
-3x - 2y + 3x + 9y = 35
-2y + 9y = 35
7y = 35
y = 35/7
y = 5
Substituting the value of y in equation (1) -
x + 3y = 5
x + 3(5) = 5
x + 15 = 5
x = 5 - 15
x = -10
Therefore, the value of x and y is -10 and 5 respectively.
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Dupe's age
and Olu's
age
add
up to 25 years.
Eight years ago, Dupe was twice as old as
Olu. How old are they now?
Dupes's age is 14 year and Olu's age is 11 year now.
What is linear algebraic equations?
Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.
Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.
Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:
x + y = 25
(x - 8) = 2(y - 8)
This system of linear equations can be transformed into the following by using a little algebraic trickery:
x + y = 25
x - 2y = -8
To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.
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The diagram shows several planes, lines, and points.Which statement is true about line h? Line h intersects line f at two points, A and B. Line h is the intersection of planes R and T. Line h intersects plane P at point C. Line h has points on planes R, P, and T.
The expression to determine the distance between the lowest and the highest point is -
{x} = 14505 + |- 282|
What is a plane in geometry?In mathematics, a plane is a Euclidean, two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point, a line and three-dimensional spaceGiven is a diagram that shows several planes, lines, and points.
The correct statement with respect to line {h} is -
Line h has points on planes R, P, and T.
Therefore, line {h} has points on planes {R}, {P} and {T} is the correct alternative.
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Lat year, Kaitlin opened an invetment account with $5200 . At the end of the year, the amount in the account ha decreaed by 7% . How much i thi decreae in dollar? How much money wa in her account at the end of lat year?
The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.
This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.
This can be expressed algebraically as:
Let x = amount in Kaitlin's account at the end of the year
Initial Amount (x) = 5200
Decrease (%) = 0.07
Decrease in Dollars = x * 0.07
Decrease in Dollars = 5200 * 0.07
Decrease in Dollars = 364
Amount in Account at the End of the Year = 5200 - 364
Amount in Account at the End of the Year = 4836
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Can 90 over 60 be simplify
Answer:
30/20 = 6/4 = 2/3 (I hope this makes sense)
Step-by-step explanation:
U are dividing by LCM
The team won the game 114-113. The teams scored only 2s and 3s. The winning team scored 50 baskets and the losing team scored 48 baskets. How many more 3s did the winning team than the losing team?
By using linear equations, The winning team scored 3 less 3s than the losing team.
What are linear equations?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
For winning team
let x=no. of 2s and y=no. of 3s
Therefore, these linear equations will be formed
x+y=50
2x+3y=114
After solving these we get x=36 and y=14
For losing team
let a=no. of 2s and b=no. of 3s
Therefore, these linear equations will be formed
a+b= 48
2a+3b=113
After solving these we get a=31 and b=17
Difference between 3s scored=17-14
Difference between 3s scored=3
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For this polynomial function, state the coordinate points of the zeros
The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).
How determine the zeros of the polynomial?The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.
For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.
Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.
f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
Step 2: Factor the polynomial to solve for x.
[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
x([tex]x^{2}[/tex] - 3x + 4) = 0
Step 3: Factor the quadratic equation.
x(x - 1)(x - 2) = 0
Step 4: Set each factor equal to 0 and solve for x.
x = 0, x = 1, x = 2
Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.
When x = 0, y = 4
When x = 1, y = 0
When x = 2, y = 0
Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).
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(01.02 MC)
Using the Factor Theorem, which polynomial function has the zeros 3 and 4 - 5i?
The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)
How to determine the polynomialFrom the question, we have the following parameters that can be used in our computation:
zeros 3 and 4 - 5i
The polynomial is represented as
P(x) = (x - zeros)
So, we have
P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))
Expand
So, we have
P(x) = (x - 3)((x - 4)^2 + 25)
Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)
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Brian invests £7900 into his bank account.
He receives 2. 3% per year compound interest.
How much will Brian have after 5 years?
Give your answer to the nearest penny where appropriate
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]