The pythagorean theorem says a^2 + b^2 = c^2 when a and b are the sides of the right triangle and c is the hypotenuse (longest side, opposite the 90 degree angle).
so if 8^2 + 6^2 = 10^2, then it's a right triangle.
8^2 + 6^2 = 64 + 36 = 100 = 10^2, so yes, this is a right triangle.
Suppose you want to buy a $160,000 home. You found a bank that offers a 30-year loan at 3.3% APR.
What will be your monthly payment? (Round to the nearest cent.)
$
How much would you end up paying the bank for the home after 30 years? (Round to the nearest cent.)
$
Suppose you wanted to reduce the time of your loan to 25 years. What would be your new monthly payment? (Round to the nearest cent.)
$
How much would you end up paying the bank for the home after 25 years? (Round to the nearest cent.)
$
How much did you save by reducing the time of your mortgage loan? (Round to the nearest cent.)
$
The required solution with the concern of mortgage has been shown below.
$695.67, $250,441.20, $783.93, $235179, and $15262.2.
Using the formula for the monthly payment of a mortgage:
[tex]P = L[c(1 + c)^n]/[(1 + c)^n - 1][/tex]
Here P is the monthly payment, L is the loan amount, c is the monthly interest rate, and n is the total number of payments (in this case, 30 years = 360 months).
Plugging in the values given:
L = 160000
c = 0.033/12 (monthly interest rate)
n = 360
P = 695.67
So the monthly payment is $695.67.
To find out how much will be paid in total over 30 years, we can multiply the monthly payment by the total number of payments:
Total payments = P * n = $695.67 * 360 = $250,441.20
So the total amount paid to the bank for the home over 30 years is $250,441.20.
To calculate the new monthly payment for a 25-year loan, we can use the same formula but with n = 25*12 = 300 months:
P = 160000[(0.033/12)(1 + (0.033/12))^300]/[(1 + (0.033/12))^300 - 1]
P = $783.93
So the new monthly payment for a 25-year loan is $783.93.
The total amount paid over 25 years would be:
Total payments = P * n = $783.93 * 300 = $235179
So the total amount paid to the bank for the home over 25 years is $235179.
The amount saved by reducing the time of the mortgage loan is the difference between the total amount paid for the 30-year loan and the total amount paid for the 25-year loan:
Savings = $250,441.20 - $235179 = $15262.2
So the amount saved by reducing the time of the mortgage loan is $15262.2.
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Describe in words each of the transformations
represented by the rules below:
a. (x,y) → (x-5, y + 6)
b. (x,y) → (y, -x)
c. (x, y) (1.2x, 1.2y)
d. (x,y) → (x, y)
Write "forty-two thousand, fifteen" as a whole number using digits.
The whole number for "forty-two thousand, fifteen" is 42,015.
We have, "forty-two thousand, fifteen".
To write a sentence as a whole number using digits, you would typically replace the words with their numerical representations. Here's an example:
Sentence: "I have three apples and four bananas."
Whole number: "I have 3 apples and 4 bananas."
Here the numeric terms are forty- thousand and fifteen then the numerical digit will be
= 42, 015.
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Given △HJK ~ △RST, what is cos T?
Answer:
cos T = 5/9-------------------
As per definition, the cosine function is:
cosine = adjacent / hypotenuseSince triangles are similar, the ratio of corresponding sides is same:
cos T = ST / RTcos T = cos K = JK / HK = 5/9Determine if it’s a 1 proportion z interval, 1 proportion z test, 1 sample T interval or 1 sample T test
The type of test used in this problem is given as follows:
1 proportion z test.
How to test the hypothesis?At the null hypothesis, we consider if there is not enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_0: p = 0.55[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_a: p \neq 0.55[/tex]
We are testing a proportion, hence the z-distribution is used, thus the correct option is given as follows:
1 proportion z test.
(in the case of a proportion, a z test is used, for sample means that we can use either z test or t test depending on the problem).
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I ne table below represents the function r, and the tonowing grapn represents the function g.
0 1
-6 -5 -4 -3 -2 -1
-10 -8
-2
22
X
f(x) 8-2-8
Complete the following statements.
The functions / and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -3), the average rate of change of fis
9
-4 -2
6
4
the average rate of change of g.
Since the average rates of change of f and g cannot be determined from the given information provided.
We can find the average rate of change of function f over the interval [-6, -3) as:
The average rate of change of f;
= (f (6) - f (3)) / (6 - 3)
= (71 - 59) / 2 = 6
We have the two given points to set up equations:
-53 = a(3)^b - 41
-53 = a(5)^b - 41
0 = a(3^b - 5^b)
Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.
Therefore,
We can conclude, that the average rates of change of f and g cannot be determined.
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if y varies inversely as the same of x, and =7/4 whenx = 1, find y when x=3
if y varies inversely as the same of x, and y=7/4 when x = 1 then value of y is 7/12 when x=3
If y varies inversely as the same of x, we can write the equation:
y = k / x
where k is the constant of proportionality.
Let us find the value of constant of proportionality k:
y = 7/4 when x = 1
7/4 = k / 1
Apply cross multiplication we get:
7/4 = k
k=7/4
Now plug in the value of k to find y when x = 3:
y = k /x
y = (7/4) / 3
When a fraction is divided by the whole number then fraction is multiplied with reciprocal of the whole number.
y=7/4×1/3
Multiply the numerators and denominators.
y=7×1/4×3
We know that 7×1 is 7 and 4×3 is 12.
y=7/12
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Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x+2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x-7.
Calculate the limit as 1.
The correct statement is:
"Divide out a common factor of x - 7." The limit of the given expression is 1/6.
Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):
This statement is not correct.
We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.
Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.
Divide out a common factor of x - 7:
This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Calculate the limit as 1/6:
This statement is not correct. We need to perform further simplification to determine the limit.
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.
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i need help graphing y=-4/3+2
Find the area of a rectangle with a base of 9 feet and a height of 7 feet
Answer:
63
Step-by-step explanation:
b x h = A
9 x 7 = 63
What are the exact values of a and b?
0 a =7/2,
The required exact values of a and b are 7 / 2 and 7√3/2 respectively. Option A is correct.
A triangle ABC is given with measures,
AB = 7, BC = a, and AC = b. Also, angle A is 30°.
To find out the missing measures, we need to apply the trigonometric ratio.
sinA = BC/AB
sin30 = a/7
1/2=a/7
a = 7 / 2
Similarly,
cosB = AC/AB
cos30 = b/7
√3/2 = b/7
b = 7√3/2
Thus, the required exact value of a and b are 7 / 2 and 7√3/2 respectively. Option A is correct.
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In the figure, angle ESY is vertical to angle TSL. Find the value of x given that M angle ESF=125 degrees. Then find m Angle ESY, m Angle TSL, m Angle EST, m Angle YSF, and m Angle FSL.
Find the value of X
The measure of Angle YEA is 70 degrees in the given parallelogram
Given Parallelogram EASY with diagonal ES
∠AES = 40
∠Y = 110
∠ESY = 40 by Z theorem of a parallelogram
∠A = ∠Y by property of parallelogram
∠A = <110 as ∠Y=110
∠YES = 180 - ∠Y
∠YES = 180 - 110 - 40
∠YES = 30
∠YEA = ∠YES + ∠AES
∠YEA = 30 + 40
∠YEA = 70
Hence, the measure of Angle YEA is 70 degrees
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The table below shows the demand for a new bath soap in a shop for each of the last 7 months.
Month 1 2 3 4 5 6 7 8
Demand 23 29 33 40 41 43 49 52
Calculate a 3-month moving average for months two to nine.
A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.
How much taller is the large prism than the small prism?
Write your answer as a whole number or decimal. Do not round.
the volume of a prism is
length × width × height
so, for the small prism we have
5 × 4 × height = 100 in
height = 100/20 = 5 i
for the large prism we have
5 × 4 × height = 200 in³
height = 200/20 = 10 in
the larger prism is 10/5=2 times taller than the small prism.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
To represent a circle with a diameter of 12 units and a center that lies on the y-axis, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
If the center of the circle lies on the y-axis, then the x-coordinate of the center is 0. Also, since the diameter is 12 units, the radius is 6 units.
Using these values, we can eliminate the equations that do not meet these conditions:
- x2 + (y – 3)2 = 36: This circle has a center at (0, 3), which is not on the y-axis.
- x2 + (y – 5)2 = 6: This circle has a center at (0, 5), which is not on the y-axis.
- (x – 4)² + y² = 36: This circle has a center at (4, 0), which is not on the y-axis.
- (x + 6)² + y² = 144: This circle has a center at (-6, 0), which is not on the y-axis.
- x2 + (y + 8)2 = 36: This circle has a center at (0, -8), which is on the y-axis.
Therefore, the two equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
- x2 + (y + 8)2 = 36
- x2 + (y - 8)2 = 36
Note that the second equation is also valid, since the center of the circle can also be located at (0, -8).
Find the slope and y intercept of the line 5x-9y=45
Answer:
slope = [tex]\frac{5}{9}[/tex] , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
5x - 9y = 45 ( subtract 5x from both sides )
- 9y = - 5x + 45 ( divide through by - 9 )
y = [tex]\frac{-5}{-9}[/tex] x + [tex]\frac{45}{-9}[/tex] , that is
y = [tex]\frac{5}{9}[/tex] x - 5 ← in slope- intercept form
with slope m = [tex]\frac{5}{9}[/tex] and y- intercept c = - 5
A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
The maximum distance of the fire engine from the school is D = 4.5 miles
Given data ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P = P ( -4 , -3 )
Let the second point be Q = Q ( -7 , -3 )
First distance D₁ = √ ( -4 + 7 )² + ( -3 + 3 )
D₁ = √9
D₁ = 3 units
Now , each unit on the grid represents 1/2 mile
And , the distance from P to school is S ( -4 , 3 )
D₂ = √ ( -4 + 4 )² + ( -3 - 3 )²
D₂ = √36
D₂ = 6 units
So , the total distance D = 3 + 6 = 9 units
And , the distance in miles = 9/2 = 4.5 miles
Hence , the distance is 4.5 miles
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The complete question is attached below :
A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
What is the solution to |x-2| + 3 > 17?
Ox<-12 or x > 16
Ox<-14 or x>7
O-12
O-14
Answer:
x<-12 or x>16
Step-by-step explanation:
Answer:
|x - 2| + 3 > 17
|x - 2| > 14
x - 2 < -14 or x - 2 > 14
x < -12 or x > 16
What is 5x6 + (5x5-5)
Answer:50
Step-by-step explanation:
A solid has as its base the region bounded by the curves y = –2x^2 + 2 and y =-x^2+ 1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the length of the lower base, and height equal to 2 times the length of the lower base.
If it rains tomorrow, the probability is 0.7 that John will practice his cello. If it does not rain tomorrow, there is only a 0.6 chance that John will practice.
Suppose the chance of rain tomorrow is 60%.
What is the probability that John will practice his cello?
P(John will practice) =
(Type an integer or a decimal.)
Answer:
0.66
Step-by-step explanation:
please read attachments
La señora Luisa pide un presupuesto para reparar ocho joyas. El encargado de la joyería le dice que cobrará $6 por la primera joya, y por cada pieza sucesiva lo triple que la anterior. ¿Cuánto le cobrará el joyero a la señora Luisa?
The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680
How to find the total cost ?The charge for repairing the jewelry pieces is calculated in a geometric progression:
= 6, 63, 63 ², 63 ³, ..., 63 ⁷
The sum of the first n terms in such a progression is:
S = a x (r ⁿ - 1) / ( r - 1 )
Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:
S = 6 x ( 3 ⁸ - 1) / ( 3 - 1 )
S = 6 x ( 6561 - 1 ) / 2
S = 6 x 6560 / 2
S = 3 x 6560
S = $ 19, 680
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MULTIPLE CHOICE QUESTION:
The table shows the amount of time different students studied for an exam and the scores they received. Draw a line that best represents the data, which equation in slope-intercept form best represents the line of best fit?
OPTION 1: y=1/3x +75
OPTION 2: y=3x + 67
OPTION 3: y=1/3x + 67
OPTION 4: y= 3x +75
Answer:
Option 3: y = 1/3x +67
Step-by-step explanation:
You want the equation of the best-fit line in slope-intercept form for the data given.
Best fitThe attached calculator display shows the best-fit line for the data, where x is in minutes, is approximately ...
y = 0.41x + 64
The closest answer choice is ...
Option 3: y = 1/3x +67
__
Additional comment
The second attachment shows a plot of the data (study minutes, test score) with the best-fit line in red, and the Option 3 line in blue.
<95141404393>
Question 5 of 25 The Wildcats and the Leopards are evenly matched football teams. When they play, there is a 0.5 probability that the Wildcats will win. If they play 9 times, what is the probability that the Wildcats will win 4 of the games? Round your answer to the nearest tenth of a percent. O A. 7.0% OB. 24.6% OC. 0.2% O D. 16.4% SUBMITTE
Answer:
24.6%
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
n = 9, r = 4, p = 0.5
P = ₉C₄ (0.5)⁴ (1−0.5)⁹⁻⁴
P = 126 (0.5)⁴ (0.5)⁵
P ≈ 0.246
A path is made of white tiles and grey tiles.
There is a total of 56 tiles.
Work out the number of grey tiles.
The number of tiles that would be grey tiles out of the total tiles given would be = 28 tiles.
How to calculate the number of grey tiles?To calculate the number of grey tiles, the total number of tiles given should be divided into two since the path is made up of only white and grey tiles.
The total number of tiles = 56 tiles.
Therefore the grey and the white tiles have the same number of tiles = 56/2 = 28 grey tiles
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An earthquake in Gansu, China, on December 16, 1920, measured 8.6 on the Richter scale and killed 100 000 people. An earthquake that usually causes no damage measures 4 on the Richter scale. Compare the intensities of the two earthquakes. (THE ANSWER IS 40000).
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
Let's compare the intensities of the two earthquakes using the Richter scale.
Step 1: Understand that the Richter scale is logarithmic, which means each whole number increase represents a tenfold increase in intensity.
Step 2: Determine the difference between the magnitudes of the two earthquakes. The Gansu earthquake measured 8.6, and the earthquake causing no damage measured 4.
8.6 - 4 = 4.6
Step 3: Calculate the intensity ratio between the two earthquakes using the difference in magnitudes. Since each whole number increase represents a tenfold increase in intensity, we need to raise 10 to the power of the difference.
10^4.6 ≈ 39,810.71705535
Step 4: Round the result to a whole number.
39,810.71705535 ≈ 39,811
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
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Find the derivative of the function
thank you guys sm
The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = log₂ ( 3x + 4 )³
On simplifying , we get
On taking the derivative of the function , we get
f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )
d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]
On applying chain rule , we get
f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )
So , cancelling out the similar terms , we get
f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
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write equivalent fraction for 1 1/5 and 1 1/3
Answer:
1 1/5 = 6/5
1 1/3 = 4/3
Step-by-step explanation:
hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you
Sarah spends 30 minutes reading,20 minutes writing,and 20 minutes doing her math. How many minutes does she spends on school work in all
Answer:
She spends 70 minutes in total or 1h 10min
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Stuck on question number 3
Answer:90
Step-by-step explanation:
