Answers
∠GML ≅ ∠HMJ by the Vertical Angles Congruence Theorem.
∠GMH ≅ ∠LMJ by the Vertical Angles Congruence Theorem.
∠GMK ≅ ∠JMK by the Right Angles Congruence Theorem. They form a linear pair which means they are supplementary by the Linear pair Postulate and because one is a right angle so is the other by the Subtraction Property of Equality.
What is the Vertical Angles Congruence Theorem?According to the congruence theorem of vertical angles or angles that are vertically opposing, two opposing vertical angles that are created when two lines intersect one other are always equal.
So from the figure, we can determine the vertically opposite angles,
∠GML ≅ ∠HMJ
Similarly, ∠GMH ≅ ∠LMJ
The angles ∠GMK and ∠JMK form a linear pair and are supplementary by the linear pair postulate which states that the two angles in the linear pair add up to 180°.
We know that all right angles are congruent from the Right Angle Congruence Theorem.
Hence,∠GMK ≅ ∠JMK
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Related Questions
Find the exact value of y
Answers
In the right triangle, the value of y is 3√2
How to determine the value of y?The right triangle represents the given parameter
On the right angle, the value of y can be calculated using the following sine rule
This is represented as
sin(angle) = Opposite/Hypotenuse
So, we have
sin(45) = y/6
Make y the subject
y = 6 * sin(45)
Evaluate
y = 3√2
Hence, the value of y in the right triangle is 3√2
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Walt is mixing fruit punch for a party. He combines 1 gallon 2 quarts 3 pints of orange juice, 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. What's the total liquid measure of the punch? New answers Rating 3 emdjay23 1 gallon = 8 pints. 1 quart = 2 pints.
Answers
When Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.
As given in the question,
Conversion factor as follows:
1 gallon = 8 pints.
1 quart = 2 pints.
Walt is mixing fruit punch for a party
Convert all the units to pints we get,
Walt combines 1 gallon 2 quarts 3 pints of orange juice, which is equivalent to 15 pints
He also combines 1 gallon 3 quarts 7 pints of pineapple juice, which is equivalent to 21 pints
He then combines 1 gallon 3 quarts 3 pints of ginger ale, which is equivalent to 17 pints.
Total measure of the punch = 15 + 21 + 17 = 53 pints.
Therefore, when Walt mixes fruit punch for a party, the total liquid measure of the punch is 53 pints.
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What equation is graphed in this figure?
A y+2=−32(x−2)
B y−4=−23(x+2)
C y+1=−23(x−3)
D y−3=32(x+1)
Answers
The equation of the line that passes through the graph is y + 2 = -3/2(x - 2)
How to determine the equation of the line?The graph represents the given parameter
From the graph, the points are given as
(0, 1) and (2, -2)
Calculate the slope of the points using
Slope = (y₂ - y₁)/(x₂ - x₁)
Rewrite as
m = (y₂ - y₁)/(x₂ - x₁)
This means that
Slope = m
So, we have the following representation
m = (-2 - 1)/(2 - 0)
Evaluate
m = -3/2
The equation of the line is then calculated as
y = m(x - x₁) + y₁
Where
(x₁, y₁) = (2, -2)
m = -3/2
So, we have
y = -3/2(x - 2) - 2
Add 2 to both sides
y + 2 = -3/2(x - 2)
Hence, the equation of the line is y + 2 = -3/2(x - 2)
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Given g(x) = 4x - 7, find g(-9)
Answers
Answer:
g(- 9) = - 43
Step-by-step explanation:
substitute x = - 9 into g(x) , that is
g(- 9) = 4(- 9) - 7 = - 36 - 7 = - 43
Domain and range, HELP!
Answers
The function is decreasing because it is going down.
The domain is the set of x-values, which is [tex]x \leq 4[/tex] or [tex](-\infty, 4][/tex].
The range is the set of y-values, which is [tex]-6 \leq y < -1[/tex] or [tex][-6, -1)[/tex].
HELP FAST! Write an inequality for each of the phrases or word problems. Solve for the missing variable and
graph the solution set on the number line.
a. The value of number plus 17 is less than 12.
b. A number times negative three is at least 12.
c. The difference between a number and three is more than 10.
d. There were at most b bananas on your banana bunch. You have eaten at least one and have 8
left. How many were on the bunch?
e. Susanna purchased a shirt for $5, pants for $10, and a jacket for $25. She wants to buy at least
one purse for the outfit, but she wants to have something left of her original $65. How much
money might she spend on the purse?
f. An lift holds no more than 1200 pounds. If you are rolling a cart that weighs 760 pounds, how
much more can the elevator hold?
Answers
b. -3n ≥ 12
c. n - 3 > 10
d. b ≥ 8
e. p ≤ 60
f. 1200 - 760 = 440
David is a nurse, he wants to buy an apartment near his sister. Apartments in her neighborhood cost around $120,000. The bank has approved him for a loan with an interest rate of 3.95%. David is a recent graduate and needs his monthly payment to be low, he can afford to pay about $550 a month. David plans to sell the apartment or refinance the loan within five years when he knows he will be earning more money. PLEASE HELP
Answers
Answer:
Describe how anthropology challenges more commonly held notions of progress
Step-by-step explanation:
A trapezium of area 140cm square has parallel sides 10cm apart and one of these 16m long. Find the length of the other parallel side
Answers
The length of the other parallel side = 7.5 cm
what is trapezium?
Trapezium is the quadrilateral whose only one pair of side is parallel.
as we know ;
AREA OF TRAPEZIUM=1/2*(sum of parallel side)*(height)
given:- one parallel side = 10 cm
height = 16 cm
Area= 140 cm
Assume:-
other parallel side =x cm
so,
140=1/2*(10+x)*16
140*2/16=10+x
280/16=10+x
35/2=10+x
17.5-10=x
x= 7.5cm
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If Calvin gets paid on the 15th and last day of the month, how many paychecks will he receive in
one year?
Will he receive the same number of paychecks if gets a paycheck
very two weeks? Y/N explain.
Answers
Answer:
24
Step-by-step explanation:
12 months in a year and Calvin gets 2 paychecks in one month
so 2 times 12 = 24 paycheck
No, because if he gets a paycheck every 2 weeks that would be about 4 paychecks in one month
so that would be about 48 paychecks in a year.
Suppose that 14 inches of wire costs 56 cents.
At the same rate, how many inches of wire can be bought for 44 cents?
Answers
by using the unitary method, 11 inches of wire can be bought for 44 cents.
We are given that:
14 inches of wire costs 56 cents.
14 inches = 56 cents
Now, by using the unitary method, we get that:
1 cent = 14 / 56 inches.
1 cent = 1 / 4 inches.
Now, for 44 cents, by using the multiplication, we get that:
44 cents = 1 / 4 inches × 44
44 cents = 11 inches.
Therefore, we get that, by using the unitary method, 11 inches of wire can be bought for 44 cents.
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What is the product of 8300 and 7.7x 10^2 expressed in scientific notation
Answers
Answer: 6391000 or 6.391 x 10^6
Step-by-step explanation:
**First, convert 7.7 x 10^2 to a number**
770
**Then multiply 8300 and 770**
6391000
**Convert to scientific notation**
6.391 x 10^6
Hope this helps <3
A 429 g piece of cheese costs $9.50. What will be the cost for 1.42 kg of this cheese?
Answers
The cost for 1.42 kg of this cheese will be $ 31.44 .
The process of translating measurements of a given quantity between different units, frequently using multiplicative conversion factors that change the value of the measured quantity without changing its effects, is known as unit conversion. The specific circumstances and the desired result dictate the conversion process. This may be governed by a regulation, contract, set of technical requirements, or other publicly available standards.
Why is the unitary technique used? What is it?In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.
How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units. This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.
Given that 0.429 kg of cheese cost $9.50
As a result, the price of 1 kg of cheese is $9.50/0.429, which is $ 22.14.
As a result, 1.42 kg of cheese will cost you $22.14 * 1.42 = $31.44.
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considerthetypeofclothesdryer(gasorelectric) purchased by each of five different customers at a certain store. a. if the probability that at most one of these customers purchases an electric dryer is .428, what is the probability that at least two pur- chase an electric dryer? b. if p(all five purchase gas) 1⁄4 .116 and p(all five purchase electric) 1⁄4 .005, what is the probability that at least one of each type is purchased?
Answers
The probability of at least two purchasing an electric dryer is 0.572 and the probability of at least one type of purchase is 0.879.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability.For instance, the theoretical chance of receiving a head while tossing a coin is 12.a dryer
1 - 0.428 = 0.572
P(all 5 for purchasing gas) = 0.116
P(all 5 electrical purchases) = 0.005
P(at least 1 of each type purchased) = 1 -(P(only 1 type is purchased))
= 1 - [ P(all 5 for purchasing gas) + P(all 5 electrical purchases)
= 1 - 0.116 - 0.005
= 1 - 0.121
= 0.879
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Question 7A: Keisha has $585.43 in her checking account. She must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today. Write an inequality, using x for the variable, that would be used for the least amount of money she needs to deposit to avoid a fee.
585.43x - 302.05 ≥ 300
585.43 - 302.05 + x ≥ 300
585.43 - 302.05 + x ≤ 300
585.43x - 302.05 ≤ 300
Answers
The inequality that shows the least amount of money she needs to deposit to avoid a fee is 585.43 - 302.05 + x ≥ 300
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Let x represent the least amount of money Keisha needs to deposit to avoid a fee. Keisha has $585.43 in her checking account and must maintain a balance of $300 to avoid a fee. She wrote a check for $302.05 today, Hence:
585.43 - 302.05 + x ≥ 300
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In a randomly generated list of numbers from 0 to 6, what is the chance that
each number will occur?
OA. 1/6
B. 1/8
C. 1/6
O D. 1/9
Answers
The chance that each number will occur when a randomly generated list of numbers, generates the number from 0 to 6 is 1/7.
What is probability?Probability is a field of mathematics that focuses on determining the possibility that an event will occur. The proportion of favorable outcomes to all other outcomes determines an event's chances or probability.
Given:
A randomly generated list of numbers from 0 to 6.The total number are 7 (0,1,2,3,4,5,6).
The chance that each number will occur is,
P = 1/7
Therefore, the chance that each number will occur when a randomly generated list of numbers, generates the number from 0 to 6 is 1/7.
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Please help me on this. I really need this done.
Answers
The area hexagon using Lin's and Andre's method is:
By Lin's method = 93.48inch^2
By Andre's method = 93.53 inch^2
What is Mensuration ?
The field of mathematics known as mensuration explores how to measure geometric objects and their attributes, such as length, volume, shape, surface area, lateral surface area, etc.
By Lin's method
He parted the hexagon into six equilateral triangle
So, area of equilateral triangle = √3/4 × (side)^2
Since the given side = 6inch
Therefore,
area of equilateral triangle = √3/4 × (6)^2
=√3/4 × 36
= √3 x 9
= 1.732 x 9
= 15.58inch^2
The area of hexagon will be = 15.58 x 6
= 93.48inch^2
Now, By Andre's method
he parted two triangle and one rectangle
The triangle has two equal side that means its an isosceles triangle
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
given,
base = 10.4 inch
side = 6 inch
Area of isosceles triangle using only sides = ½[√(a^2 - b^2/4) × b]
= ½[√(6^2 - 10.4^2/4) × 10.4]
= ½[√(36 - 108.16 /4) ×10.4]
= ½[√(36 - 27.04) × 10.4]
= ½[√(8.96) × 10.4]
= ½[2.99 × 10.4]
= 15.56inch^2
for two triangles the area will be = 15.56 x 2
= 31.13 inch^2
Now, area of rectangle = length x width
where,
Length = 10.4 inch
Width = 6 inch
So,
area of rectangle = 10.4 x 6
= 62.4 inch^2
Then, The area of hexagon will be = area of rectangle + area of two triangle
= 62.4 inch^2 + 31.13 inch^2
= 93.53 inch^2
Hence, by both methods the area from Lin's method = 93.49 inch^2
and by Andre's method = 93.53 inch^2
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Which is a counterexample of: The difference of two numbers is less than the greater
number.
(5)-(2) = 3
(-5)-(4) = -9
(3)-(3)=0
(2)-0 =2
Answers
The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"
How to determine the counterexample?"The difference of two numbers less than the greater number," is how the claim is expressed.
Give us x and y, where x is greater than y.
Thus, the statement can be interpreted as follows:
x - y < x
To both sides, add x.
-y < 2x
Replace with: y > -2x
This indicates that only when the smaller number is higher than twice the additive inverse of the larger number is the assertion true.
The smaller number must be bigger than twice the additive inverse of the larger number in order for the statement "the difference of two numbers is greater than the greater number" to be false.
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The part of marketing copy that asks the audience to do something with the information you've just provided is known as what? Question 20 options: A. Return on investment B. call to action C. vernacular D. emotional language HELPPPPLSSSSSSSSSSSSSSSSS
Answers
The part of marketing copy that asks the audience to do something with the information you've just provided is known as call to action. Option B
What is a marketing copy?Marketing copy can be defined as a content that is written to boost sales or to promote a product or service and also to persuade the readers to take a certain actions.
It is an important tool that is used to educate customers, and it provides the resources and contact details information to help various businesses increase the awareness of their products and services.
What is call-to-action?Call-to-action can be defined as the part of an advertisement or content that encourages the audience to do something.
In marketing, it help in converting a reader or visitor to a lead for the business sales team.
It also drives other marketing actions depending on the content's goal.
Hence, the marketing copy is call-to-action
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Answer:
Step-by-step explanation: B
HELP PLEASE!!
Use the point and the slope to graph each line. Write the equation of the line
Answers
Answer:
y = x in the slope intercept form
y - 2 = 1(x -2) in the point-slope form of a line
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals of each other. So the perpendicular slope would be 1.
We could write this in the point slope form of a line and the answer would be:
y - 2 = 1(x -2) This would be the point slope form of a line.
If you want your answer in the slope intercept form
y -2 = 1(x-2)
y - 2 = x - 2 Add two to both sides
y = x
WHAT DO WE KNOW ABOUT PERPENDICULAR LINES ?
IS THAT WHEN THEIR GRADIENTS ARE MULTIPLIED THEY GIVE A PRODUCT OF -1.
TO FIND THE GRADIENT OF THE LINE PERPENDICULAR TO THE LINE WITH SLOPE/GRADIENT -1 WE CAN SAY
[tex]m1 \times m2 = - 1 \\ - 1 \times m2 = - 1 \\ m2 = 1[/tex]
THIS MEANS THAT THE GRADIENT OF THE NEW LINE IS 1
the general equation of the straight line is y=mx+c
[tex] - 2 = 1(2) + c \\ - 2 = 2 + c \\ c = - 2 - 2 \\ c = - 4[/tex]
This means that
[tex]y = 1x - 4 \\ simply \\ y = x - 4[/tex]
An object in real life is 55 feet long. How many inches long should it be in the scale drawing?
Answers
Based on the length of the object in real life, and the scale factor used, the length of the object on the scale drawing in inches can be found to be 9.17 inches
How to find the length?The scale factor tells us how the measurement of an object on a drawing relates the measurement of the same object in reality.
For a scale factor of 1 inch to 6 feet, it means that every inch of an object on a drawing, would be 6 feet of the same object in real life.
For this object that is in a drawing with a scale factor of 1 inch to 6 feet, the length in real life of 55 feet tells us that the length in the drawing is:
= Number of feet in real life / Number of feet in scale factor per drawing
= 55 / 6
= 9.17 inches
Full question is:
A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?
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What’s the answer to this question
Answers
The recursive formula of the arithmetic sequence is:
xₙ = n*4 + 13
With that we can see that x₁₁ = 57
How to write the arithmetic sequence?Here we know that the first elements of the sequence are:
17, 21, 25, 29, ...
To find the common difference, d, we take the difference between any two consecutive elements, so we have:
c = 21 - 17 = 4
Then the recursive formula for the n-th term is:
xₙ = n*4 + d
The first element x₁ is 17, so we will have:
17 = 1*4 + d
17 - 4 = d = 13
The recursive formula is:
xₙ = n*4 + 13
b) the eleventh term of the sequence is given by replacing n in the above formula by 11.
x₁₁ = 4*11 + 13 = 44 + 13 = 57
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please answer number 5 by finding the length indicated
Answers
You take 180 and subtract by all given angles and whatever’s left is x
What is the expression in radical form?
(5ab) =
○ √√25a²b²
O√√5a²b²
O √5a³b3
O √125a³b3
Answers
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
What does radical form mean?Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.
What in mathematics is radical form?The sign used to represent the square root or nth root. Square-root-containing expressions are known as radical expressions.
According to the given data:Radical equation = b[tex]\frac{m}{n}[/tex]
= [tex]\sqrt[n]{b^m}[/tex]
So,
(5ab)[tex]^\frac{3}{2}[/tex] = [tex]\sqrt[2]{5^3}[/tex]
[tex]\sqrt[2]{5^3}[/tex] a³ b³
5³ = 125
√(125 a³b³)
The radical form of the expression (5ab)[tex]^\frac{3}{2}[/tex] is √(125 a³b³).
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Expand and simplify (y + 3)(y + 7)
Answers
⇒[tex]=(y+3)(y+7)\\=y(y+7)+3(y+7)\\=y^{2} +7y+3y+21\\=y^{2} +10y+21[/tex]
Attached is the solution in detail
44 less than the product of 1 and x
Answers
Answer: -44
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Use the given information to prove that DE=FD
Answers
The condition for the figure to be similar is that; DE = FD
What are similar figures?Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
In the problem, the ratio should be CD/DE = GD/DF
We can also write the ratios of the corresponding sides as:
CD/DE = GD/DF
Therefore, CE and GF are similar
Thus, the condition for the figure to be similar is that;
DE = FD
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is w a subspace of v? if not, state why. assume that v has the standard operations. (select all that apply.) w is the set of all 2 × 2 matrices of the form 0 v u 0 v = m2,2
Answers
A) W is a sub space of V
given that V =R^4 and W= [(x1, x2, x3, 0)|x1 ,x2, x3 E..R]
W is a subspace of V because of the following.
let (x1, x2, x3, 0), (y1, y2, y3, 0) ∈ W and a, b ∈ V
now
a(x1, x2, x3, 0)+b (y1, y2, y3, 0)= (a x1, a x2, a x3, 0)+(b y1, b y2,b y3, 0)
= (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)=
(a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ,0+0)
LHS =RHS
∈W
since (a x1+ b y1 , a x2+ b y2 , a x3+ b y3 ) are all elements of R
W is closed under vector addition and scalar multiplication.
Hence W is a sub space of V.
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Jasim works in a restaurant.
The table shown gives his rates of pay.
Day
Mon to Fri
Weekend
Jasim worked for a total of 30 hours last week.
He worked 12 of these hours at the weekend.
Work out Jasim's pay for last week.
Rate of pay
£8.70 per hour
£10.80 per hour
Answers
Answer:
Step-by-step explanation:
The option that is most suitable for tabular data will be provided by-
Jasim's last week's total pay was £286.2.
Describe tabular data.Tabular data is data presented in the form of rows and columns.
Here,
Total time for which Jasim works last week = 30 hours
Time for which Jasim works at the weekend = 12 hours
Time for which Jasim works at the weekdays = (30 - 12) hours
= 18 hours
Jasim's pay during weekdays = £8.70
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £8.70 [tex]\times[/tex] 18
= £156.6
Jasim's pay during weekends = £10.80
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £10.80 [tex]\times[/tex] 12
= £129.6
Total pay of Jasim for last week = £(156.6 + 129.6)
= £286.2
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A landscape architect accrued $7,834.54 in credit card debt. If the architect makes a monthly payment of $500 (and makes no additional charges on the account), how many months will it take to repay the debt if the annual interest rate on the credit card is 18.6%? (Round your answer up to the nearest month.)
Answers
The $7,834.54 borrowed at 18.6% annual interest rate with the landscape architect's monthly payment of $500, gives the number of months it will take to repay the debt as approximately 19 months
What is a monthly payment?Monthly payment on a loan, is the amount the person who takes the loan, pays each month in order to settle the loan in a given time period.
The monthly payment formula is presented as follows;
[tex] \displaystyle{M = \frac{P \cdot \left( \frac{r}{12} \right) \cdot \left( 1 + \frac{r}{12} \right)^{n} }{\left( 1 + \frac{r}{12} \right)^{n} - 1} }[/tex]
Where;
M = The amount the landscape architect paid monthly = $500
P = The amount loaned or borrowed = $7,834.54
r = The interest per annum = 18.6%
n = The number of monthly payment made
Therefore;
[tex] \displaystyle{500 = \frac{7834.54 \cdot \left( \frac{0.186}{12} \right) \cdot \left( 1 + \frac{0.186}{12} \right)^{n} }{\left( 1 + \frac{0.186}{12} \right)^{n} - 1} }[/tex]
Evaluating the above equation gives;
[tex] \displaystyle{500 = \frac{121.43537.1 \cdot 1.0155^{n} }{1.0155^{n} - 1} }[/tex]
[tex] \displaystyle{500 \times (1.0155^{n} - 1) = 121.43537.1 \cdot 1.0155^{n} }[/tex]
[tex] \displaystyle{500 \times 1.0155^{n} - 121.43537.1 \cdot 1.0155^{n} ) = 500 }[/tex]
Which by taking natural logarithms of both sides gives;
n•ln(1.0155) = ln(1.32077843609)
n = ln(1.32077843609) ÷ ln(1.0155) ≈ 18.09
Rounding up to the nearest month gives;
The number of months it will take the architect to pay the debt is approximately 19 months
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write the equation of the line that is parallel to the given line and goes through the point (-8 2)
Answers
The equation for the line that is parallel to the given line and goes through the point (-8 2), is y = 3x + 26. See the explanation below.
What is the explanation for the above?Recall that the equation for the line is always given as:
y = mx + b
Where m is the slope.
Assuming that you have a line y = 3x + 2
The line parallel to this line but intersecting the point (-8,2) is found by using y = mx + b and solving for b
m = 3; x = -8; and y = 2
b = y - mx
b = (2) - (3) (-8)
b = 26
Hence the equation for the line that is parallel to the given line going through point (-8, 2) is
y = 3x + 26
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Full Question:
Find the equation in slope-intercept form of the line y= 3x + 2 that passes through the point (-8,2) and is parallel to the line.