The distance between PQ : 7
Given points P: (1,6)
Q : (7,2)
distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2
(x1,y1)= (1,6)
(x2,y2) = (7,2)
therefore
= √(7-1)^2 +(2-6)^2
= √36+16
= √52
= 7.211
find tan theta where theta is the angle shown.
Here we would like to find out the value of given trigonometric ratio . A right angled triangle is given to us with perpendicular= 8 and hypotenuse= 11 . Firstly let's calculate the base using Pythagoras theorem as ,
[tex]\longrightarrow h^2=p^2+b^2\\[/tex]
[tex]\longrightarrow 11^2 = 8^2+b^2\\ [/tex]
[tex]\longrightarrow 121 = 64 + b^2\\ [/tex]
[tex]\longrightarrow b^2=121-64=57\\ [/tex]
[tex]\longrightarrow b =\sqrt{57}=7.54 \\ [/tex]
Now we know that,
[tex]\longrightarrow \tan\theta =\dfrac{p}{b}\\ [/tex]
so substitute the respective values,
[tex]\longrightarrow \tan\theta =\dfrac{8}{7.54}\\ [/tex]
[tex]\longrightarrow\underline{\underline{ \tan\theta = 1.06 \approx \boxed{1}}} [/tex]
and we are done!
In a survey of 120 people who visited a lake, 20% went fishing. Of those who went fishing, 75% also went swimming. Of those who did not go fishing, 50% went swimming.
The two-way frequency table to display the data will be:
Fishing Not Fishing Total
Swimming 15 30 45
Not Swimming 5 45 50
Total 20 75 95
What is the frequency table about?20% of 120 people is 24 people, but since 20% of the people went fishing, we know that 24 people went fishing.
75% of 24 people who went fishing is 18 people.
50% of 96 people who did not go fishing is 48 people.
Total number of people who went swimming is 45 (15+30)
Total number of people who did not go swimming is 50 (5+45)
Total number of people in the survey is 95 (24+71)
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In a survey of 120 people who visited the a lake, 20% went fishing.of those who went fishing,75% also went swimming. Of those who did not go fishing ,50% went swimming. Construct a two-way frequency table to display the data.
The points on this graph represent a relationship between x
- and y
-values. Which statement about the relationship is true?
Since the points on this graph represent a relationship between x- and y-values, a statement about the relationship which is true is that: A. it cannot be proportional because a straight line through the point does not go through the origin.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
In conclusion, the relationship between the x-value and y-value isn't proportional because the straight line does not pass through the origin (0, 0).
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Jasmine's average speed was 33 3/4 miles per hour.
How far did she travel if it took her 3½ hours?
jel
A. 79 1/2 miles
B. 89 1/2miles
C. 98 miles
D. 108 miles
Answer:
Step-by-step explanation:
114 purple pins 361 yellow pins, what percent of the pins where purple?
Answer: About 31%
Step-by-step explanation:
1. Divide 114 to 361
Simplify (s-5)³. Write your answer using only positive exponents.
The solution is…
Answer:
s³ - 15s² + 50s - 125
Step-by-step explanation:
yes
Translate the phrase into a variable expression. Use the letter g to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.
The total number of seagulls standing on the pier and the 51 gulls in the air
The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:
g/51.
How to obtain the ratio?The ratio between two amounts a and b is found applying a proportion, which is the division between them.
The amounts for this problem are given as follows:
g is the number of seagulls standing on the pier.51 is the number in the air.Hence the ratio is given as follows:
g/51.
Missing InformationThe problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.
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25% of 72 is what value? 21 18 12 7
Answer:
18
Step-by-step explanation:
To find a percent of a number, change the percent to a decimal by dividing the percent by 100 and multiply by the number.
25% of 72 =
= 25/100 × 72
= 0.25 × 72
= 18
Answer: it would be 18
Step-by-step explanation:
Analysis A question on a test asks students to find the speed at which a car
travels. The graph shows a proportional relationship between the distance traveled
in miles and time in hours. Anna incorrectly says that the speed of the car is 59
mile per hour. What is the speed of the car? What error might Anna have made?
The speed of the car is 59 miles per hour. Anna might have made an error by using change in y-coordinates/change in x-coordinates to find a unit rate, instead of change in x-coordinates/change in y-coordinates.
What is defined as speed?Speed is a measure of how quickly something is moving, or how quickly something can be done. It is usually measured in terms of distance traveled per unit of time, such as miles per hour or kilometers per hour. The unit of speed is Miles per hour (mph).Speed can also be measured in terms of the rate of change of a certain quantity. For example, speed can be used to measure acceleration, which is the rate of change in velocity. Speed can also be used to describe the rate of flow of a certain quantity, such as the rate of water flow in a river. Speed is also used to measure the rate at which a certain process is taking place, such as the rate at which a person is typing words. In many cases, speed is used to describe how quickly something is happening relative to something else, such as the speed of light relative to the speed of sound. Speed is an important concept in many fields, including physics, engineering, and sports.To learn more about speed refer to:
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How to solve 3x+30+x=10+2x+5x+2
After simplification, the value of x is 6.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 3x + 30 + x = 10 + 2x + 5x + 2
Now, We can solve as;
⇒ 3x + 30 + x = 10 + 2x + 5x + 2
Combine like terms;
⇒ 4x + 30 = 12 + 7x
Subtract 4x both side,
⇒ 4x + 30 - 4x = 12 + 7x - 4x
⇒ 30 = 12 + 3x
Subtract 12 both side,
⇒ 30 - 12 = 3x
⇒ 18 = 3x
⇒ 3x = 18
Divide by 3;
⇒ x = 6
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if the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2) Find the vaue of x and y
If the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2), then the values of x = -12 and y = 3.
What is mean by translated by vector?Vector translation is a mathematical concept that describes how an object is moved in space. It involves the use of a vector, which is a quantity that has both magnitude and direction. A vector can represent a displacement, a velocity, an acceleration, or any other physical quantity that has both magnitude and direction.
When an object is translated by a vector, it moves a certain distance in a specific direction. This is usually done by adding the vector to the current position of the object. The magnitude of the vector determines the distance of the translation, while the direction of the vector determines the direction of the translation.
Additionally, the vector can be used to rotate the object. This is done by multiplying the vector by the object’s rotation matrix. The result is the object's new orientation in space, which can be used to orient the object in a different direction.
Vector translation is used in a variety of applications, including computer graphics, robotics, and navigation systems. It i also used in mathematics and physics to represent physical phenomena, such as forces, velocities, or accelerations.
Let the point P(x,5) be translated by the vector t(6,-2).
The image of point P is (x',y') = (x+6,5-2) = (-6,y)
Therefore, x+6 = -6
=> x = -6-6 = -12
Similarly, 5-2 = y
=> y = 5-2 = 3
So the value of x is -12 and y is 3.
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g soccer fields vary in size. a large soccer field is 108 meters long and 56 meters wide. what are its dimensions in feet? length ft width ft what are its dimensions in inches? length in width in
The dimension of soccer field is 4252.176 in long and 2204.832 in wide.
The power to which the fundamental quantities are elevated in order to express a physical quantity is known as its dimension.
The dimension of soccer field is 108 meters long and 56 meters wide.
The dimension of soccer field in ft is 354.348 ft long and 183.736 ft in width.
As it is given that 1 m =3.28 ft
Therefore the length of the soccer field in ft is
108*3.281 = 354.348 ft
And width of the field is
56*3.281 = 183.736 ft
We know that 1 ft =12 in
Therefore, the length of the soccer field in inches is
354.348 × 12 = 4252.176 in
And width of the field is
183.736 *12 = 2204.832 in
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The mean per capita income is 21,604 dollars per annum with a standard deviation of 727 dollars per annum.
What is the probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected? Round your answer to four decimal places
The probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected is 65.53%.
This can be calculated using the normal distribution. The mean of the normal distribution is the population means, which in this case is 21,604 dollars per annum. The standard deviation is 727 dollars per annum. Using this information, we can calculate the z-score of 21635 dollars per annum by subtracting the population mean from it and dividing it by the standard deviation. This gives us a z-score of 0.42.
21635-21329/727=0.42
Using a z-table, we can calculate the probability of the sample means being less than 21635 dollars to be 0.6553.
This can also be written as 65.53%. This means that there is a 65.53% probability that the sample mean of 193 persons randomly selected would be less than 21635 dollars per annum.
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a big cruise ship dropped anchor off the caribbean island of antigua. the heavy anchor dropped into the water at a rate of 2.5 2.52, point, 5 meters per second. after 45 4545 seconds, the anchor was 40 4040 meters below the water's surface. from what height (above the water's surface) was the anchor released?
At a distance of 72.5 meters above the water's surface, the anchor was let go.
It takes 29 seconds to reach the water's surface.
The anchor dropped for 45 seconds at a speed of 2.5 m/s.
112.5 metres are equal to (2.5 m/s) x (45 s).
It must have dropped if it ended up only 40 meters under the water.
(112.5 m - 40 m) equals 72.5 m
Before it ever got to the water, it was in storage on the large cruise ship.
It took longer because it was descending at a speed of 2.5 m/s.
29 seconds are equal to 72.5 m / (2.5 m/s)
it began to drop, to get down to the water's surface.
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4/9 x 7/8 =7/18 what is 7/8x4/9 how do u know without multiplying?
Answer:
7/18.
Step-by-step explanation:
We know that the result is the same because multiplication is Commutative.
The order of the operation does not matter.
An automatic filling machine is used to file 1-liter bottles of cola. The machine's output is approximately normal with a mean of 1. 0 liter and a standard deviation of 0. 01 liter. Output is monitored using means of sample of 25 observations. What is the z-value we should use if the control limits will include roughly 97% of the sample means
The UCL and LCL are 1.00434 and 0.99566. The process is not in control and the z-value is 2.17.
We already know that the mean, x = 1.0, and the standard deviation of the process, σ = 0.01.
We already know that according to the central limit theorem, the standard deviation of sample means is equal to the standard deviation of the population divided by the square root of the sample size.
So, it is equal to = 0.01 / √25 ⇒ 0.002
For a sample size of 25. The z value, or the z-score, is about 2.17 for a confidence level of 97 percent.
So, UCL = 1.0 + 2.17 * 0.002 = 1.00434
LCL = 1.0 - 2.17 * 0.002 = 0.99566
Lastly, the process is not in control because the sample means 1.005 and 0.995 are outside the control range.
The complete question that you must be looking for is given below.
An automatic filling machine is used to fill 1-liter bottles of cola. The machine output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.
a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.
b. Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control.
c. What is the z-value we should use if the control limits will include roughly 97% of the sample means?
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Pop's Cycle Shop sells bicycles and tricycles. The
number of bicycles is 1 less than 4 times the number
of tricycles. All the bicycles and tricycles together have
a total of 174 wheels. How many bicycles are there?
The number of bicycles there is given as follows:
63.
How to obtain the number of bicycles?The number of bicycles and tricycles is obtained using a system of equations, for which the variables are given as follows:
Variable x: number of bicycles.Variable y: number of tricycles.The number of bicycles is 1 less than 4 times the number of tricycles, hence:
x = 4y - 1.
There is a total of 174 wheels, hence:
2x + 3y = 174.
The number of tricycles is obtained as follows:
2(4y - 1) + 3y = 174
11y = 176
y = 176/11
y = 16.
Hence the number of bicycles is of:
x = 4(16) - 1
x = 63.
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Two triangular sculptures are similar. The leg of the first sculpture is 4.5 feet and the base is 7.2 feet. The leg of the second sculpture is 6 feet. What is the length of the base for the second sculpture? Show your work.
For two similar triangular sculptures having leg l1 = 4.5 ft, l2 = 6 ft, and base b1 = 7.2 ft, the measurement of b2 is 9.6 ft.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
Two triangles are similar.
Let the two similar triangles sculptures be ΔABC and ΔDEF.
The length of the leg ΔABC, AB = 4.5 feet
The length of the base of ΔABC, BC = 7.2 feet
The length of the leg ΔDEF, DE = 6 feet
The length of the base of ΔDEF, EF = x feet
To find the measure of base of ΔDEF, use the formula for indirect measurement.
According to indirect measurement the formula will be -
AB/DE = BC/EF
Substitute the values in the equation -
4.5/6 = 7.2/x
4.5 × x = 7.2 × 6
4.5x = 43.2
x = 43.2/4.5
x = 9.6
Therefore, the value for x is obtained as 9.6 feet.
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Conider the line .3x-6y=-8
Find the equation of the line that i parallel to thi line and pae through the point .4,2
Find the equation of the line that i perpendicular to thi line and pae through the point . (4,2)
The equation of the straight line perpendicular to the line 3x - 6y = - 8 is y-2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y=0.
The general equation of a straight line is -
y=mx+c
where -
m is slope of line which tells the unit rate of change of y with respect to x.
c is the y - intercept i.e., the point where the graph cuts the y axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
[tex]y=\frac{-A}{B} x-\frac{C}{B}[/tex]
Given that: -
[tex]3x-6y=8\\\\6y=3x-8\\\\y=\frac{1}{2}x-\frac{4}{3}[/tex]
then,
[tex]m=\frac{1}{2}\\\\c=\frac{4}{3}[/tex]
For a parallel line,
[tex]m=\frac{1}{2}\\and,(4,2)[/tex]
[tex]y-y_{1}=m(x-x_{1})\\\\y-2=\frac{1}{2}(x-4)\\\\2y-4=x-4\\\\y=\frac{x}{2}[/tex]
The equation of parallel line is y=0.5x
For a perpendicular line
[tex]m=2\\\\y-2=2(x-4)\\\\y-2=2x-8\\y-2x=-6\\y-2x+6=0\\[/tex]
Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y -2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y = 0.5x.
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Jolly Roger Peanut Butter cost $3. 59 for a small jar last year. This year the jar costs $4. 19. What is the inflation rate, to the nearest tenth percent?
The inflation rate is 16.71 %
As we know the inflation rate is given by the percentage error.
We know that the formula for the percentage error:
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
Let us assume that A represents the inflation rate of percentage error.
Here, the cost of the Jolly Peanut butter is = $ 3.59
So , the original cost = $ 3.59
The increased cost of Jolly Peanut butter is = $ 4.19
So , the new rate = $ 4.19
Now , the inflation rate is given by the formula of percentage error,
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
A = [ ( 4.19 - 3.59 ) / 3.59 ] x 100
A = ( 0.6 / 3.59 ) x 100
A = 0.16713 x 100
A = 16.71 %
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Solve for c
a(c + b)=d
Answer:
[tex]c = \frac{d}{a} - b[/tex]
Step-by-step explanation:
Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, divide a from both sides of the equation:
[tex]a(c + b) = d\\\frac{a(c + b)}{a} = \frac{d}{a} \\c + b = \frac{d}{a}[/tex]
Next, isolate the variable, c, by subtracting b from both sides of the equation:
[tex]c + b = \frac{d}{a} \\c + b (-b) = \frac{d}{a} (-b)\\c = \frac{d}{a} - b[/tex]
[tex]c = \frac{d}{a} - b[/tex] is your answer.
~
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Answer:
c = (d/a) - b
Step-by-step explanation:
Now we have to,
→ Find the required value of c.
The equation is,
→ a(c + b) = d
This can be distributed as,
→ a(c + b) = d
→ a(b) + a(c) = d
→ ab + ac = d
Then the value of c will be,
→ a(c + b) = d
→ a × (c + b) = d
→ c + b = d/a
→ c = -b + (d/a)
→ [ c = (d/a) - b ]
Hence, value of c is (d/a) - b.
U.S. inflation is intentionally kept at a steady 5%, for a variety of economic reasons. Because of this, the cost
of most things is expected to increase by 5% per year, with few exceptions.
In 2009, minimum wage was set to 7.25, and has not changed since. If it had risen to meet the intended
inflation, what would minimum wage be now in 2023?
A$21.16
B $14.35
C$15.05
D$2,116,.49
Philip wants to run a total of 3 miles each day. Monday morning, he ran 1 7/8 miles. How many more miles does he still need to run?
On Monday, for completing the daily target Philip needs to travel 9/8 more miles.
As per the question,
As Philip wants to run a total of 3 miles each day.
As on Monday morning, he ran only 1(7/8) miles.
First, we will convert the given mixed fraction in form of improper fractions.
So, converting 1(7/8),
It will become equal to (8*1+7)/8 = 15/8
From above,
We can say, out of the 3 miles he only travel 15/8 miles on Monday.
So, for calculating the required distance we need to subtract the given value 15/8 from 3
Thus we will get it as:
3-15/8 = (24-15)/8 = 9/8 miles.
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Valerie created a table of a proportional relationship that contains the point (3, - 18). which of the tables below could be Valerie’s?
Valerie's table is the table for which the y-value is given by the multiplication of the x-value by -6.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
The constant for the relationship in this problem is given as follows:
k = -18/3
k = -6.
Hence the relationship is given as follows:
y = -6x.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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00:00
A parking garage has 612 parking spaces on 4 levels. Each level has about the same number
of parking spaces. Select all of the statements that are reasonable estimates for the number
of parking spaces on each level
There are 153 parking spaces on each level of the parking garage.
Equation
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that a parking garage has 612 parking spaces on 4 levels, and each level has about the same number of parking spaces, to determine the number of parking spaces on each level the following calculation must be performed: -
so the equation is ,
612/4 = X
153 = X
X = 153.
Thus, there are 153 parking spaces on each level of the parking garage.
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aldo's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs $4.10 aldo per pound, and type b coffee costs $5.45 per pound. this month's blend used twice as many pounds of type b coffee as type a, for a total cost of $465. how many pounds of type a coffee were used?
The amount of type A used is A=31 lbs.
Assign variables for unknowns.
Let A be the number of pounds of Type A coffee.
Let B be the number of pounds of Type B coffee.
If one pound of Type A costs $4.10 then A pound costs 4.10A
If one pound of Type B costs $5.45 then B pounds cost 5.45B
At this point, you have two equations with A and B as variables. You can use the substitution or elimination method to solve for A.
Equations:
B = 2A----(1)
4.10A + 5.45B = 465.00
4.10A + 5.45(2A) = 465.0
4.10A + 10.9A = 465.00
15A = 465.00
A = 31 lbs (amt. of type A coffee used)
To know the amount of type B coffee used just plug the A value in equation(1) we get:
B=2(31)
B=62.
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For which values of x does the expression √x+11 make sense?
The value of x that best represent this expression √x = 11 is 121.
What is square and square roots?The square root of a number is the part of the number that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents. The portion of a number that yields the original number when multiplied by itself is known as the square root of the number.
Examples of special exponents include squares and square roots. Think about the number 9. Nine is the result of multiplying 3 by itself. This can be expressed as either or 3*3. We refer to this as a square since it has a 2 exponent. When the exponent is now 1/2, the integer's square root is being discussed.
An integer or number (not a fraction) multiplied by itself produces a "Square Number," which is the result. For instance, 3 x 3 = or 3 squared is the result of 3 times 3.
Given:
√x+11 = 0
√x = -11
can be written as
x = -11²
x = 121
The value of x that best represent the expression √x+11 = 0 is 121.
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Correct question:
For which values of x does the expression √x + 11 = 0 make sense?
three people ann, bob and colin have a total of $1.80 between them, each having a different amount. does ann have the most money? (1) ann has $0.6 (2) bob has $0.5
Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.
In the given question, we have to find Ann have the most money or not.
Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.
Ann has $0.6 amount and Bob has $0.5 amount.
Ann + Bob + Colin = 1.80
0.6 + 0.5 + Colin = 1.80
1.1 + Colin = 1.80
Subtract 1.1 on both side, we get
Colin = 0.70
So Colin has $0.70.
So, Colin has more amount than Ann and Bob. So Ann does not have most money.
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need explanation and steps
The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
AB = 6
BC = 6
CG = 6
Then the length of diagonal AC is given as,
AC² = AB² + BC²
AC² = 6² + 6²
AC = 6√2
Then the length of diagonal AG is given as,
AG² = AC² + CG²
AG² = (6√2)² + 6²
AG = 6√3
The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.
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Sandra Williams bought a home with a 10. 25% adjustable rate mortgage for 25 years. She paid $9. 27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then interest rates have increased to 12. 75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11. 10 monthly per thousand on her loan. You can ignore the small amount of principal paid during the 3 years. What was the old monthly payment? $ a0 What is the new monthly payment? $ a1 What is the percent increase in her monthly payment (to the nearest tenth)? a2 %
a) The old monthly payment was = 9.27 × 50 = 463.5
b) The new monthly payment is = 11.10 × 50 = 555
c) The percent increase in his monthly payment is 1.947 %
With a 25-year, 10.25% adjustable rate mortgage, Sandra Williams purchased a property. She made monthly payments of $9.27 per thousand on his initial debt.
According to the question,
The per thousand value of $65000 is, 50000/1000 = 50
Now, the old monthly payment was = 9.27 × 50 = 463.5
She makes the decision to renew and will now make monthly loan payments of $11.10 per thousand.
So, the new monthly payment is = 11.10 × 50 = 555
The percent increase in his monthly payment is = 11.10 /9.27 - 1 × 100
⇒ 19.7411 %
And to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 × 50 = 463.5
The new monthly payment is = 11.10 × 50 = 555
Thus, the percent increase in his monthly payment is 1.947%.
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