the increase would be 1.25-1 = 0.25 = 25%
Answer is C
Triangle MNP is the image of triangle JKL after a 120 degrees counterclockwise rotation about point Q. If the measure of angle L is 47 degrees and the measure of angle N is 57 degrees, determine the measure of angle M. Explain how you arrived at your answer.
The measure of angle M in triangle MNP is 76 degrees. This is determined by utilizing the sum of interior angles property of triangles and understanding the correspondence of angles in rotated or transformed figures.
Explanation:The problem given is associated with the geometry of triangles. From the problem statement, we know that triangle MNP is the image of triangle JKL after 120 degrees counterclockwise rotation. This indicates that the angles of both triangles are the same. Hence, angle M will correspond to angle J of the original triangle.
However, since we are not given the measure of angle J, we need to calculate it using the property of triangles. In triangles, the sum of the interior angles amounts to 180 degrees. Therefore, the measure of angle J can be found by subtracting the measures of the other two angles (angle K and angle L) from 180 degrees.
Given the measure of angle L is 47 degrees and the measure of angle N (which corresponds to angle K in triangle JKL) is 57 degrees, we use the equation:
Angle J = 180 - (angle K + angle L) = 180 - (57+47) = 76 degrees.
Thus, the measure of angle M in triangle MNP, which is corresponding to angle J in triangle JKL, is 76 degrees.
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What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ? Enter your answer in the box. Do not round any side lengths.
Answer:
Area of the rectangle is 24
Step-by-step explanation:
Given the vertices of the rectangle to be (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
Let the the vertices be at point ABCD respectively
so that A(-6, 3) B(-3,6) C(1,2) D(-2 -1)
To find the area, we need to first find the length and height of the rectangle
We let AB to be the length of the rectangle and BC be the height of the triangle. so first, we will find the distance between the two points AB
A(-6, 3) B(-3,6)
Using the distance formula
|AB| = √([tex]x_{2}[/tex] - [tex]x_{1}[/tex])² + ([tex]y_{2}[/tex] - [tex]y_{1}[/tex])²
=√(-3+6)² + (6-3)²
=√(3)² + (3)²
= √(9+9)
=√18
=√(9 ×2)
=√9 × √2
=3√2
|AB| = 3√2
The length of the rectangle is 3√2
We will now proceed to find the height of the rectangle which is the distance between point the two point BC
B(-3,6) C(1,2)
Using the distance formula;
|BC |= √([tex]x_{2}[/tex] - [tex]x_{1}[/tex])² + ([tex]y_{2}[/tex] - [tex]y_{1}[/tex])²
=√(1+3)² + (2-4)²
=√4² + 4²
= √(16 + 16)
=√32
=√(16 × 2)
=√16 × √2
=4√2
|BC| = 4√2
Therefore, the height of the triangle is 4√2
Area of rectangle = l × h
= |AB| . |BC|
= 3√2 × 4√2
=12 (2)
=24
Therefore area of the rectangle is 24
HURRY ASAP NO JOKE 2 MINUTES PLZ HURRY ASAP PLZZZZZ HELP
find the greatest common factor.
4x^3a^2+4x^2a^3
the temperature was -3 degrees last night. it is now -4 degrees . what was the change in the temperature
The length of a rectangle is 10 m less than three times the width, and the area of the rectangle is 77 m2 . find the dimensions of the rectangle
The length and width of the rectangle are 11 m and 7 m respectively.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
Length of the rectangle is 10 m less than three times the width,
And area of rectangle = 77 m²
Let the width of rectangle is x m,
Then length of rectangle = 3x -10 m.
The area of rectangle = 77
length × width = 77
x × (3x - 10) = 77
The value of x = 7 satisfy the equation,
Therefore, the width of rectangle is x = 7 m
And length of the rectangle is 3x - 10 = 21 - 10 = 11 m
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Which is the correct simplified form of the expression x^1/2y^-1/3/x^1/4y^1/2
Answer:
(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
Upon solving the given expression, we get
=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)
=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]
=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
which is the required simplified form of the given equation.
Hence, option A is correct.
Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years? After 65 years?
A: $80,000; $100,000
B: $160,000; $320,000
C: $520,000; $650,000
Answer:
Step-by-step explanation:
The answer is actually B. $160,000; $320,000
The reason for this is because -
$10,000 is the constant, so let a= 10,000.
The investment doubles every 13 years, so let b=2.
Let x= the number of 13-year periods.
The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.
Explanation:To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).
The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).
After 52 years, the investment's worth would be calculated as follows:
$10,000 × (2^4) = $10,000 × 16 = $160,000
After 65 years, the investment's worth would be:
$10,000 × (2^5) = $10,000 × 32 = $320,000
Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.
Help me please thanks
The volume of a rectangular prism can be computed using the formula V = lwh. What is the height of a prism that has a volume of 2376 cubic centimeters, a length of 18 centimeters, and a width of 11 centimeters?
A. 24 cm
B. 726 cm
C. 16 cm
D. 12 cm
Answer:
The Correct Answer is D
Step-by-step explanation:
Joan has a credit card that uses the previous balance method. The opening balance of one of her 30-day billing cycles was $6390, but that was her balance for only the first 3 days of the billing cycle, because she then paid off her entire balance and didn't make any new purchases. If her credit card's APR is 17%, which of these expressions could be used to calculate the amount Joan was charged in interest for the billing cycle?
Answer:
Step-by-step explanation:
(0.17/365 x30)(6390)
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To calculate the amount Joan was charged in interest for the billing cycle using the previous balance method, we need to find the average daily balance for the billing cycle, which is calculated as the sum of the daily balances divided by the number of days in the billing cycle.
The daily balance is the balance at the end of each day, and it is calculated by adding new purchases and subtracting payments and credits from the previous day's balance.
In this case,
Joan had a balance of $6390 for the first 3 days of the billing cycle, so her average daily balance for the billing cycle can be calculated as:
((3 x 6390) + (27 x 0)) / 30
= 1917
This means that her average daily balance for the billing cycle was $1917.
To calculate the amount of interest Joan was charged for the billing cycle, we can use the following expression:
Interest = Average Daily Balance x Daily Interest Rate x Number of Days in Billing Cycle
The daily interest rate is calculated as the APR divided by 365 since there are 365 days in a year. In this case, the daily interest rate is:
0.17 / 365
= 0.000465753
So, the expression that can be used to calculate the amount of interest Joan was charged for the billing cycle is:
Interest = 1917 x 0.000465753 x 30
= $26.84 (rounded to the nearest cent)
Therefore,
The expression that represents the amount Joan was charged in interest for the billing cycle is $26.84.
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What happens to a line when the y-intercept is changed ?
Write the parametric equations x = 4 \sin^2 \theta , \quad y = 3 \cos^2 \theta in the given cartesian form.
The Cartesian form of equation is,
3x + 4y = 12
We have to given that,
The parametric equations are,
x = 4 sin² θ
y = 3 cos² θ
Now, Change the parametric equations into cartesian form as,
x = 4 sin² θ
sin² θ = x/4 .. (i)
y = 3 cos² θ
cos² θ = y/3 (ii)
Add equation (i) and (ii),
sin² θ + cos² θ = x/4 + y/3
1 = x/4 + y/3
1 = (3x + 4y)/12
12 = 3x + 4y
3x + 4y = 12
Therefore, The Cartesian form of equation is,
3x + 4y = 12
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The perimeter of a pool table is 30 ft. The table is twice as long as it is wide. What is the length of the pool table
This isosceles triangle has two sides of equal length , a, that are longer than the length of the base , b. The perimeter of the triangle is 15.7 cm. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 cm, which equation can be used to find the length of the base ?
Apply THe ORder of operations to simplify the expression
90/ [10+(3² - 4)]
most with best answer gets brainliest please help.
The simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
As we know, the expression can be defined as the combination of constants and variables with mathematical operators.
To begin, either multiply or divide the value in parentheses (32-4), which equals 5.
Add the number in the parentheses once more: 90/[10+5 (always do the parenthesis first) [10+5]= 15.
Finally, divide 90/15 by 6, always keeping that in mind (PEMDAS)
Thus, the simplification form of the expression 90/ [10+(3² - 4)] is 6 the answer is 6.
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The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 10 + 15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
We are given a function H(t) that represents the height of a cannon ball after t seconds as:
[tex]H(t)=-16t^2+48t+12[/tex]
and a second cannon ball is represented by the function g(t) as:
[tex]g(t)=10+15.2t[/tex]
PART A:
t 0 1 2 3
H(t) 12 44 44 12
g(t) 15.2 25.2 40.4 55.6
Hence, between t= 2 seconds and t=3 seconds the ball will meet
such that H(t)=g(t)
Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.
and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.
Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.
and the time at which they meet is calculated by solving:
[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]
As t can't be negative.
Hence, we get:
t=2.109 seconds
PART B:
The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.
The volume of a rectangular prism can be computed using the formula v = lwh. what is the length of a prism that has a volume of 1344 cubic centimeters, a width of 8 centimeters, and a height of 12 centimeters?
a. 111 cm
b. 18 cm
c. 896 cm
d. 14 cm
We are given the formula:
V = l w h
and the following values:
l = ?
V = 1344 cm^3
w = 8 cm
h = 12 cm
SO rewriting the formula in terms of l:
l = V / w h
l = 1344 cm^3 / (8 cm * 12 cm)
l = 14 cm
Answer:
d
The answer would be 14
Find the z-score such that the area under the standard normal curve to the right is 0.370.37. loading... click the icon to view a table of areas under the normal curve. the approximate z-score that corresponds to a right tail area of 0.370.37
Using the standard normal table, it is found that the z-score is z = 0.33.
-------------------------
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the standard normal table and find the p-value associated with this z-score, which is the percentile of X. This p-value is the left-tailed area.The right-tailed area is 1 subtracted by the p-value.In this problem:
Right-tailed area of 0.37, thus the p-value is of 1 - 0.37 = 0.63.Looking at the standard normal table, the z-score is z = 0.33.A similar problem is given at https://brainly.com/question/7001627
Find the greatest common factor of 75, 8, and 21
What is the equation of the axis of symmetry for the function shown below? y-2=-(x+5)^2?
Answer:
-5
Step-by-step explanation:
Multiply 5x2(2x2 + 13x − 5). 10x4 + 65x3 − 25x2 10x2 + 65x − 25 7x2 + 18x − 10 7x4 + 18x3 − 10x2
Answer:
[tex]10x^4+65x^3-25x^2[/tex]
Step-by-step explanation:
Multiply 5x^2(2x^2 + 13x − 5)
[tex]5x^2(2x^2 + 13x - 5)[/tex]
Multiply 5x^2 inside the parenthesis
[tex]5x^2 * 2x^2 = 10x^4[/tex]
[tex]5x^2 * 13x = 65x^3[/tex]
[tex]5x^2 * (-5) = -25x^2[/tex]
Collect all the terms together
[tex]10x^4+65x^3-25x^2[/tex]
3469131824 what would be the next number
it cost $526.30 to repaire Carol's car. rounded to the nearest ten dollars, how much did carol pay?
A. $500
B. $520
C. $530
D. $550
What is the square root of the fraction 25/100?
Constance invested $4500 for 3 years in a savings account paying simple interest with a yearly interest rate of 3.5%. How much simple interest did she earn?
Answer:
$420
Step-by-step explanation:
Yeet! I need some help! 16 points to whoever answers!
How to solve this P-1=5p+3p-8
Eddie is reading a novel for English class he has read 173 out of 480 pages about what percent of the book has he read
Answer: The percent of the book has he read is 36.04 %.
Step-by-step explanation:
Given: The number of pages read by Eddie= 173
The total number of pages = 480
The percent of the book has he read is given by:_
[tex]P=\frac{\text{number of pages read}}{\text{total pages}}\times100\\\\\Rightarrow\ P=\frac{173}{480}\\\\\Rightarrow\ P=0.36041\times100\\\\\Rightarrow\ P=36.04\%[/tex]
Hence, the percent of the book has he read is 36.04 %.
Factor the expression 20k + 50