Answers
The perimeter of polygon ABC = 67.4
The perimeter of polygon PQRS = 78.8
What is the Perimeter of a Polygon?The perimeter of a polygon is calculated by adding the lengths of all sides of the polygon together.
What is the Two-tangents Theorem?The Two-Tangent Theorem states that if two tangents are drawn to a circle from the same external point, then the tangents are congruent (have the same length).
Perimeter of polygon ABC = AB + BC + AC
AB = 10.5 + (23.2 - 11.2) = 22.5 [based on the Two-Tangent Theorem]
BC = 23.2
AC = 10.5 + 11.2 = 21.7
Perimeter of polygon ABC = 22.5 + 23.2 + 21.7 = 67.4
Perimeter of polygon PQRS = PQ + QR + RS + PS
PQ = 25
PS = 21.8
QR = 13 + 4.6 = 17.6
RS = 4.6 + 9.8 = 14.4
Perimeter of polygon PQRS = 25 + 21.8 + 17.6 + 14.4 = 78.8
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Related Questions
Calculate midpoint 6 for f(x)= 6 * ln(x^2) over [1,2]
Answers
The midpoint of f(x) over the interval [1, 2] is 4.8655
What is the midpoint of an interval?Generally, The point that represents the precise midway point between an interval's beginning and ending points is known as the midpoint of the interval. It may be determined by calculating the average of the two values that serve as endpoints.
For instance, the value 5 would represent the point that is exactly in the middle of the interval [3,7].
The midpoint of the interval [1, 2] is
(1 + 2) / 2
= 1.5.
To calculate the value of f(x) at x = 1.5, we need to substitute 1.5 for x in the function:
f(1.5) = 6 * ln(1.5^2)
= 6 * ln(2.25)
= 6 * 0.83
= 4.8655
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During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function
Answers
The daily cost to heat a building at 10 degrees celsius is $82.72
How to interpret the function valuesFrom the question, we have the following parameters that can be used in our computation:
f(x)=6(1.3)^-x
Then, we have
x = 10
This implies that
f(-10) = 6(1.3)^-(-10)
Evaluate the expression
f(-10) = 82.72
This means that the cost to heat is $82.72
Also, the domain is all set of real numbers and the range is y > 0
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Complete question
During the winter if the low temperature outside is x Celsius,the daily cost to heat a building can be determined using the function f(x)=6(1.3)^-x.find and interpret the given function values and determine an appropriate domain for the function
f(10)
A teacher gave his students the four graphs below. Which graph represents a geometric sequence?
Answers
The graph that represents a geometric sequence is Graph A.
What is a geometric sequence ?A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding one by a fixed, non-zero number called the common ratio.
Examples of geometric sequences include:
2, 4, 8, 16, 32, ... (common ratio of 2)
1/3, 2/3, 4/3, 8/3, ... (common ratio of 2/3)
5, -25, 125, -625, ... (common ratio of -5)
Geometric sequences have the property that the ratio of any two consecutive terms is always the same, and the quotient of any two consecutive terms is the common ratio.
This is shown only in the first graph so Graph A shows the geometric sequence.
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A large western state consists of 2051 million acres of land
Approximately 56% of this land is federally owned. Find the
number of acres that are not federally owned
million acres
Answers
To find the number of acres that are not federally owned, we can use the following formula:
(percent not federally owned/100) x total acres = non-federally owned acres
(44/100) x 2051 = 908.44 million acres
So, approximately 908.44 million acres of land in the state are not federally owned.
Find the sum of the following geometric series:
8 + 1.6 + 0.32 + 0.064 + ...
Answers
Answer:
10
Step-by-step explanation:
The given series is a geometric series with the first term a = 8, and the common ratio r = 1/5. To find the sum of the series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
So, in this case, the sum of the series is:
S = 8 / (1 - 1/5) = 8 / (4/5) = 8 * (5/4) = 40/4 = 10.
Therefore, the sum of the series is 10.
Answer:
10
Step-by-step explanation:
A geometric series is the sum of the terms of a geometric sequence.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric series:
8 + 1.6 + 0.32 + 0.064 + ...The ellipsis means to "continue in this pattern". Therefore, find the sum to infinity of the given geometric series.
From inspection of the sequence, the first term is 8:
[tex]\implies a=8[/tex]
To find the common ratio, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{1.6}{8}=0.2[/tex]
Substitute the found values of a and r into the geometric series formula:
[tex]\implies S_{\infty}=\dfrac{8}{1-0.2}=\dfrac{8}{0.8}=10[/tex]
Therefore, the sum of the given geometric series is 10.
work this out for points and brainliest !
Answers
a) The perimeter of a rectangle is the sum of all four sides. So to find the perimeter we can add these two sides together, and then double the result.
The simplified expression for the perimeter of the rectangle would be:
2(2n - 3 + 4)
This can also be written as:
2(2n + 1)
This expression represents the mathematical operation where the sum of 2n - 3 and 4 is calculated, then multiplied by 2 to find the perimeter of the rectangle.
b) If the perimeter of the rectangle is 26, we can use the expression for the perimeter that we found earlier to solve for the value of n.
The perimeter of the rectangle is:
2(2n + 1) = 26
So if we divide both sides of the equation by 2, we get:
2n + 1 = 13
then if we subtract 1 from both sides
2n = 12
then if we divide by 2
n = 6
So the value of n is 6.
I hope this helps :)
Answer:
a. [tex]P = 4n + 2[/tex]
b. [tex]n = 6[/tex]
Step-by-step explanation:
a. The formula for the perimeter of a rectangle was:
[tex]P = 2L + 2W[/tex]
Given that the length was 2n-3 and the width was 4, substitute the values its formula:
[tex]P = 2L + 2W\\P = 2(2n-3) + 2(4)\\P = 4n - 6 + 8\\P = 4n + 2[/tex]
b. Since the perimeter of the rectangle was already indicated, we will just sunstitute it to the expression that we get from a.
[tex]P = 4n + 2\\26 = 4n + 2\\26 - 2 = 4n\\24 = 4n\\6 = n[/tex]
fill in the blank: the________ creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find.
Answers
The geom_ jitter () method creates a scatter plot and then it adds a small amount of random noise to every point in the plot to make the points easier to find.
geom is the method that draws a point which are defined by x and y coordinate in the scatterplot.The jitter geom is convenient short cut geom _ point here position is equal to jitter.It helps to add random amount of variation in the location of each point defined on the plot.One of the useful way to handle overplotting by small data base.geom_jitter ( mapping = NULL, data = NULL, stat = "identity"position = "jitter", ..., width = NULL, height = NULL, na.rm = FALSE, show.legend = NA, inherit.aes = TRUE)stat : defined statistical transformation , position : position adjustment, width : vertical and horizontal adjustment.Therefore, the geom_jitter is shortcut that creates a scatterplot and add random variation in each point.
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The product of 46 and a number added to the reciprocal of a number squared.
Answers
The expression for the given word phrase is
46M + M² + 2 + 1/M²
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,
Number = M
Reciprocal of M = 1/M
Now,
46 x (M + 1/M)²
Step 1:
46M + M² + 2 + 1/M²
Thus,
The expression is 46M + M² + 2 + 1/M²
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In the following descriptions of a study, confounding in present. Describe the explanatory and confounding variable in the study and how the confounding may invalidate the conclusions of the study. Furthermore, suggest how you would change the study to eliminate the effect of the confounding variable.
(a)A hospital introduces a new blood clot medication that can be given to the patients suffering from a stroke during the crucial period of 12 hours after stroke begins. The new medication appears to be very successful because in the first year of its implementation there is a higher rate of total recovery by the patients in comparison to the rate in the previous year for patients admitted to the hospital.
(b) A high school mathematics teacher is convinced that a new software program will improve math scores for students take the SAT. As a method of evaluating her theory, she offers the students opportunity to use the soft-ware on the school’s computers during a 1-hour period after school. The teacher concludes the software is effective because the students using the software has significantly higher scores on the SAT than did the students who did not use the software.
Answers
a. The explanatory variable is the new blood clot medication, and the confounding variable is the time period of 12 hours after the stroke begins.
b. The explanatory variable is the new software program, and the confounding variable is the 1-hour period after school
What are the variables?The confounding variable may invalidate the conclusions of the study because it is possible that the higher rate of total recovery is not due to the new medication, but rather due to the fact that the patients are being treated within the crucial 12-hour period after the stroke begins. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where patients are randomly assigned to receive either the new medication or a placebo, and both groups are treated within the 12-hour period after the stroke begins.
In (b) the explanatory variable is the new software program, and the confounding variable is the 1-hour period after school. The confounding variable may invalidate the conclusions of the study because it is possible that the higher scores are not due to the software, but rather due to the fact that the students using the software were given more time to study and practice. To eliminate the effect of the confounding variable, the study could be conducted as a randomized controlled trial, where students are randomly assigned to use the software or not, and both groups are given the same amount of time to study and practice.
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Idil has a points card for a movie theater.
She receives 85 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 155 points for a free movie ticket.
Write and solve an inequality which can be used to determine
�
x, the number of visits Idil can make to earn her first free movie ticket.
Answers
Answer:
6
Step-by-step explanation:
85 +12.5*x visits =155
12.5x≥70
x must be greater than 5.6 so she need to go 6 times & then she'll get her free ticket
Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS
SOMEONE HELP! PLEASE!
Answers
The two column proof showing that ΔWXZ ≅ ΔYXZ is as shown below
From the given triangle, we see that;
Given: WX ≅ XY, XZ bisects WXY
Prove: ΔWXZ ≅ ΔYXZ
The two column proof for the above is as follows;
Statement 1; WX ≅ XY, XZ bisects 2
Reason 1; Given
Statement 2: ∠WXZ ≅ YXZ
Reason 2; Angle bisector
Statement 3; XZ ≅ XZ
Reason 3: Reflexive property of congruence
Statement 4: ΔWXZ ≅ ΔYXZ
Reason 4: SAS Congruence Postulate
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You decide to put $5,000 in a savings account to save for a $6,000 down payment on a new car. If the account has an interest rate of 7% per year and is compounded monthly, how long does it take until you have $6,000 without depositing any additional funds?
Answers
The time it takes until the deposit amounts to $6,000 is 2.6 years
Compound interest: Calculating timeFrom the question, we are to calculate how long it takes until the deposit amounts to $6000
From the compound interest formula, we have that
A = P(1 + r/n)^nt
Where A is the amount
P is the principal
r is the interest rate
n is the number of times compounded per year
and t is the time.
From the given information,
P = $5,000
r = 7%= 0.07
n = 12
t = ?
A = $6,000
Putting the parameters into the formula
A = P(1 + r/n)^nt
6000 = 5000(1 + 0.07/12)^(12×t)
6000/5000 = (1 + 0.0058333)^12t
1.2 = (1.0058333)^12t
Take log1.0058333 of both sides
31.346375 = 12t
31.346375/12 = t
t = 2.6 years
Hence, the time it takes is 2.6 years
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Ranhita biked from home to school in 1/5 of and hour . her speed was 10mph what is the distance from her home to school
Answers
Answer:
2 miles
Step-by-step explanation:
Distance = speed x time
= 10mph x 1/5
= 2 miles
Find the measure of the given angle
Answers
Answer:
A= 110 degrees AND B= 140 degrees.
Y= 112 degrees and X= 157 degrees.
Step-by-step explanation:
Triangle XYZ is an isocoles triangle, because it has two congruent sides. 70 degrees is a measurement of an angle opposite of one of those congruent sides, so angle YXZ is also 70 degrees. By the triangle angle sum theorem, we can say that the measurement of angle YZX is 40 degrees. So, for the first triangle, by the linear pairs theorem, we can find the two missing angles.
A= 110 degrees AND B=140 degrees.
For the triangle on the right, we can use the triangle angle sum theorem to say that angle BDC is 68 degrees. Then, we can say that by the by the linear pairs theorem that angle ADE is 112 degrees. From there, we need to look at the 23 degree measurement on the lower right triangle. We can see that the angle steadily rises on that line and then we can take 180-23 by the linear pairs theorem to conclude than angle BEA is 157 degrees. This can be confirmed by looking at the two innermost angles in the top right triangle. If you take 180-23-112, you will get 45. If you add 45 to 112, you will get 157.
Y= 112 degrees and X= 157 degrees.
Round 843,857 nearest hundred thousands
Answers
Answer: 844000
Step-by-step explanation:
843857 = 844000 because you round up
In planning her retirement, Liza deposits some money at
3.5%
interest, with twice as much deposited at
4.5%.
Find the amount deposited at each rate if the total annual interest income is
$1875.
Answers
Answer:
$15000 at 3.5%$30000 at 4.5%Step-by-step explanation:
You want to know the amounts invested at each rate if twice as much is invested at 4.5% as at 3.5%, and the total earnings are $1875.
Interest earnedLet x represent the amount invested at 3.5%. Then 2x is the amount invested at 4.5%, and the total earnings are ...
0.035x +0.045(2x) = 1875
0.125x = 1875 . . . . . . . . . collect terms
x = 15000 . . . . . . . . . divide by 0.125
2x = 30000 . . . . . . . find the other value invested
The amount deposited at 3.5% is $15,000; the amount deposited at 4.5% is $30,000.
1. Raymond is ordering these expressions, so he would first like to find the expressions with the greatest value. Which is the greatest value? a. √25 b. √5 c. √8 d. √10
Answers
√25 is the greatest value of the expressions .
What is an expression in maths ?
A number, a variable, or a mix of both plus certain operation symbols make up an expression. Two expressions are combined to form an equation, which is joined by the equal sign.
The combination of 8 and 3 is an example of a word. Example sentence: The result of adding 8 and 3 is 11. An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.
√25 = 5
√5 = 2.2360
√8 = 2.8284
√10 = 3.1622
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calculate the first derivative of the following function
g(x) = In(3x^3 + 12x)
Answers
Answer:
Step-by-step explanation:
Love these kinda problems.
Alr,
d/dx of lnx = 1/x
let 3x³ + 12x = t
dt/dx = 9x² + 12 ( d/dx of xⁿ = n[tex]x^{n-1}[/tex])
then, d/dx of ln t= 1/t x dt/dx = 1/(3x³+12x) x (9x² + 12) = (3x² + 4)/(x³ + 4x)
Pls mark as brainliest if possible. Cheers
Round to nearest tenth show all work
Answers
Side AC in the triangle is 3.6 and side BC in the triangle is 1.7
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
To find side AC :
4/sin90 = AC / sin64.3
AC × sin90 = sin 64.3 × 4
AC = 0.9 ×4
AC = 3.6 ( nearest tenth)
To find side BC:
using Pythagoras theorem
4² = 3.6² + (BC)²
16 = 12.96 +(BC)²
(BC)² = 16 - 12.96
(BC)² = 3.04
BC = √ 3.04
BC = 1.7( nearest tenth)
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Which angle corresponds to <8?
Answers
Answer:
>4
Step-by-step explanation:
the answer of the question is >4
Draw the polygon with the given vertices in a coordinate plane.
22).(-5,5),(-4,1) pls help
Answers
Plot the given coordinates of the polygon in the coordinate plane and connect it with a smooth curve.
What are polygons?A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end.
What is a coordinate plane?A coordinate plane is a two-dimensional plane created by the intersection of two number lines. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two of these number lines.
Plot the points on the graph according to the given coordinates. Connect all the points. The polygon is triangle.
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HELP PLSS
Find the difference: √20-√80
O -12,5
O-2√5
O2√5
O-2√15
DONE✔
Answers
Answer:
[tex] - 2 \sqrt{5} [/tex]
Step-by-step explanation:
[tex] \sqrt{20} - \sqrt{80} [/tex]
[tex]2 \sqrt{5} - 4 \sqrt{5} [/tex]
[tex](2 - 4) \sqrt{5} [/tex]
[tex] - 2 \sqrt{5} [/tex]
Michael is going to buy a car,
The car costs £2400,
He pays a deposit of 20%,
He pays the rest of the money over 20 monthly payments,
Work out the cost of each monthly payment.
Answers
Answer: 96 Euros each month
Step-by-step explanation: 2400 * 0.2 = 480 -> 2400-480 = 1920(this is the amount of money needed to pay each month) 1920 / 20 = 96
Solve the word problem completely. Determine also the kind of proportion used
Answers
The values are;
1. 35/3 days - Direct proportion
2. 4254 - Direct proportion
3. 120 teachers - Indirect proportion
What is proportion?Proportion can be described as an equation that has two ratios set equal to each other.
It is also seen as a mathematical comparison of numbers, terms, or variables.
The different types of proportion are;
Direct ProportionInverse ProportionCompound ProportionContinued ProportionFrom the information given, we have;
1. If 3 men completes the project in 7 days
Then 5 men would finish it in x days
cross multiply
x = 5(7)/3
x = 35/3 days
2. If 25kg of rice cost 1130
Then 100kg would cost x
cross mutiply
x = 1130(100)/25
x = 4,254
3. If there are 90 teachers = 1500 students
Then x teachers = 2000 students
x = 2000(90)/1500
x = 120 teachers
Hence, the values are 35/3 days, 4, 254 and 120 teachers.
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Problem in the attached image! Pls help only 10 and 11
Answers
The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.
What is alternate interior angles?Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.
Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.
In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.
At the point of intersection of transversal and two lines we have:
∠3 + ∠4 = 180 .........(1)
∠6 + ∠8 = 180 ...........(2)
We know that angle 4 and angle 8 are equal:
Thus, using 1 and 2 we have:
∠3 = ∠6
Hence, ∠3 and ∠6 are congruent.
Now, using the alternate interior angle we know that:
∠3 = ∠6
Also, we have:
∠5 + ∠6 = 180 (Straight line)
Substituting the value of ∠6 = ∠3 we have:
∠5 + ∠3 = 180
Thus, the two angles are supplementary.
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Tamara has $30,000, part or all of which she wants to invest into a combination of corporate bonds and municipal bonds. She wants to invest no less than $8,000 into corporate bonds, and at least three times as much into corporate bonds than into municipal bonds.
Let x be the amount invested in corporate bonds, and let y be the amount invested in municipal bonds.
Which system of inequalities describes Tamara’s investment options?
x + y ≤ 30,000
x ≤ 8,000
x ≥ 3y
x + y ≤ 30,000
x ≥ 8,000
x ≥ 3y
x + y ≤ 30,000
x ≥ 8,000
x ≤ 3y
x + y ≤ 30,000
x ≤ 8,000
x ≤ 3y
Answers
Answer:
B) x + y ≤ 30,000
x ≥ 8,000
x ≥ 3y
Step-by-step explanation:
Definition of the variables:
Let x be the amount invested in corporate bonds,Let y be the amount invested in municipal bonds.If Tamara has $30,000 and part or all of which she wants to invest into a combination of corporate bonds and municipal bonds, then the sum of the investments in the two bonds will be less than or equal to $30,000:
x + y ≤ 30,000If Tamara wants to invest no less than $8,000 into corporate bonds, then the amount invested in corporate bonds (x) will be greater than or equal to $8,000:
x ≥ 8,000If Tamara wants to invest at least three times as much into corporate bonds than into municipal bonds, then the amount invested in corporate bonds (x) will be greater than or equal to 3 times the amount invested in municipal bonds (y):
x ≥ 3yI have 18 students that took a test. 4 of the students passed. What is the percentage of the students that passed and the students that didn't pass?
Answers
Step-by-step explanation:
as always with % calculations :
first find what is 100% or 1%. everything else can be calculated from that.
in our case, we got 100% = 18.
therefore, 1% = 100%/100 = 18/100 = 0.18
how many % are 4 students ?
as many as the times 1% (0.18) fits into 4 :
4 / 0.18 = 22.22222222... %
so,
22.22222222... %
of the students passed.
therefore,
100 - 22.22222222... = 77.77777777... %
of the students did not pass.
NO LINKS!!
Part 2: Graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the preimage and image using the correct notation.
4. A(2, 1), B(3, -1), C(4, 2), D(3, 3)
Reflection : in the line x = -1
5. A(2, 3), B(1, 4), C(3, 4)
Rotation: 180° about the origin
6. A(5, -2), B(5, 2), C(3, 1), D(2, -1)
Rotation: 270° about the origin
Answers
Answer:
Question 4:
A' (-4, 1)B' (-4, -1)C' (-6, 2)D' (-5, 3)Question 5:
A' (-2, -3)B' (-1, -4)C' (-3, -4)Question 6:
A' (-2, -5)B' (2, -5)C' (1, -3)D' (-1, -2)Step-by-step explanation:
Question 4Given vertices of the pre-image:
A = (2, 1)B = (2, -1)C = (4, 2)D = (3, 3)If the pre-image is reflected in the line x = -1, the transformation rule is:
[tex](x, y) \rightarrow (x-2(x+1), y)[/tex]Therefore the vertices of the image are:
A' = (2 - 2(2 + 1), 1) = (-4, 1)B' = (2 - 2(2 + 1), -1) = (-4, -1)C' = (4 - 2(2 + 1), 2) = (-6, 2)D' = (3 - 2(2 + 1), 3) = (-5, 3)Question 5Given vertices of the pre-image:
A = (2, 3)B = (1, 4)C = (3, 4)If the pre-image is rotated 180° about the origin, the transformation rule is:
[tex](x, y) \rightarrow (-x,-y)[/tex]Therefore the vertices of the image are:
A' = (-2, -3)B' = (-1, -4)C' = (-3, -4)Question 6Given vertices of the pre-image:
A = (5, -2)B = (5, 2)C = (3, 1)D = (2, -1)If the pre-image is rotated 270° about the origin, the transformation rule is:
[tex](x, y) \rightarrow (y,-x)[/tex]If the direction of a rotation is not specified, then it is counterclockwise.
Therefore the vertices of the image are:
A' = (-2, -5)B' = (2, -5)C' = (1, -3)D' = (-1, -2)PLEASE HELP ASAP
what are the possible values for 1/4 + S = 18/20
Answers
Answer:
0.65 and 13/20
Step-by-step explanation:
University Bank pays 5% interest compounded quarterly on regular savings accounts and Rosemont
Savings Bank
pays 5.5% compounded semiannually. Vasily and Oxana Cherchenko had $4,000 to invest
for 4 years. Based on the interest to be earned, which bank offers the better investment?
Answers
well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years
[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\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 &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\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 &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]
