General Idea:
Pythagorean theorem states that in a right triangle, if side of triangle is given by ' a ', bottom of the triangle is given by ' b ' and hypotenuse of triangle is given by ' c', then Sum of squares of a and b is equal to the square of hypotenuse.
[tex] a^{2} \; +\; b^{2}\; =\; c^{2} [/tex]
Applying the Concept:
[tex] Given\\Side\;of\;triangle\;(a)\; =\; 8\\ Bottom\;of\;triangle\;(b)=15\\ \\ To\; Find\\Hyptotenuse\;(c)\\ \\ a^{2}+b^{2}=c^{2}\\ 8^2+15^2=c^2\\ \\ 64+225=c^2\\ \\ 289=c^2\\ \\ c^2=289\\ Taking \; Square\;root\;on\;both\;sides\\ \\ \sqrt{c^2}=\sqrt{289} \\ \\ c=17 [/tex]
Conclusion:
The length of the missing side of the right triangle, when side 8 & bottom 15 is 17. The correct answer is option B!!
A builder could get 6 sheets of sheetrock for 3$. If he bought 60 sheets , how much money would he have spent
PLEASE HELP ME! IM GETTING TIMED!!
A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
MAKE SURE TO SHOW YOUR WORK?
1 inch = 2.5 cm.
How many inches are there in 17.4?
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours.
What is the speed of the motorboat?
A) 225 miles per hour
B) 25 miles per hour
C) 75 miles per hour
D) 50 miles per hour
Answer:
Option D.,50 miles per hour
Step-by-step explanation:
The graph shows the distance covered by motor boat at = y, ( in miles )
The certain amount of time on = x ( in hours )
The slope of the given line will represent the speed of the motorboat.
The given line passes through two points ( 0, 25 ) and ( 4, 225 )
Therefore, slope of the line = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{225-25}{4-0}[/tex]
= [tex]\frac{200}{4}[/tex]
= 50
The speed of the motorboat is 50 miles per hour.
A cylinder and a cone have congruent heights and radii. What is the ratio of the volume of the cone to the volume of the cylinder?
Explain how the suffix -less affects the meaning of the spelling words expressionless and fearless. (explain plz) FAST !!!
solve each system by graphing y=2x-4
Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 8 boxes of science textbooks with 16 books per box. He also packed math textbooks with 12 books per box.
If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
A.
y = 128x + 12
B.
y = 12(x - 8) + 128
C.
y = 12x + 128
D.
y = 128(x - 8) + 12
Final answer:
The correct equation to represent the total number of books Jarrod packed is B. y = 12(x - 8) + 128, which acknowledges he packed 8 boxes of science books and the remaining boxes were for math books.
Explanation:
Jarrod packed 8 boxes of science textbooks with 16 books per box, which totals to 8 × 16 = 128 books.
For the math textbooks, if x represents the total number of boxes packed, then Jarrod would have packed (x - 8) boxes of math textbooks since he already packed 8 boxes of science textbooks.
Each math textbook box contains 12 books, so the number of math books packed is 12 × (x - 8). The total number of books that Jarrod packed is the sum of both science and math books, which is given by 128 + 12 × (x - 8).
The correct equation that represents this word problem is B. y = 12(x - 8) + 128, where y is the total number of books packed and x is the total number of boxes packed.
on a city map, the scale is 5 cm = 12 km,if a street is 12.5 cm long on the map what is the actual length of the street?
In decimal form, to the nearest tenth, what is the probability that a randomly selected Riverside High School student is in twelfth grade?
Answer:
The answer is C 0.4
Step-by-step explanation:
Use the elimination method to solve the system of equations.
5x + 2y = 7 −5x + 4y = 5
( 35, 2)
There are an infinite number of solutions.
(2, 1)
There is no solution.
A theater can seat 720 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
Which of the following does not describe slope? A rate of change Rise over run A proportional relationship A line
The curve has an equation containing the variables. The rate of change of any independent variable concerning the dependent variable is entitled as the slope of the tangent to the curve. Thus, the line does not describe the slope.
Slope can be defined as the ratio of the change in the value of the dependent variable to the change in the value of an independent variable.
Let us consider the equation of a line that is y=mx+c.
Here, m is the slope of the line and the value of m is y/x.
Following are the points that may describe the slope.
Rate of change.Rise over.Proportional relationship.A line can never be a slope because the slope is always a numeric value and a line can always be an equation that contains variables.
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Write the equation of a line that is perpendicular to y=-0.3x+6 and that passes through the point (3,-8)
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1\\m2=-1/m1[/tex]
in this problem the slope of the given line is
[tex]m1=-0.3=-\frac{3}{10}[/tex]
the value of m2 is
[tex]m2=-1/(-3/10)=\frac{10}{3}[/tex]
with the point [tex](3,-8)[/tex] and the slope m2 find the equation of the line
the equation of the line in the form point-slope is
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y+8=\frac{10}{3}*(x-3)[/tex]
[tex]y=\frac{10}{3}x-10-8[/tex]
[tex]y=\frac{10}{3}x-18[/tex]
therefore
the answer is
[tex]y=\frac{10}{3}x-18[/tex]
Express the whole number 4 as a fraction. And express the whole number 1 on a number line as a fraction.
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. What is the theoretical probability of randomly drawing a red marble?
At the local butcher, 9 pounds of a special sausage costs $51.21. How much does one pound of sausage cost? What concept would you use to solve this problem?
Final answer:
The cost of one pound of sausage is $5.69 per pound.
Explanation:
To solve the problem of finding the cost of one pound of sausage when 9 pounds cost $51.21, we use the concept of unit price. The unit price is the cost for one unit of an item when given the total cost for multiple units.
To find the unit price of the sausage, you divide the total cost by the number of pounds.
This gives you the cost per one pound of sausage, which is what we are looking for.
Here is the step by step calculation:
First, write down the total cost for 9 pounds of sausage: $51.21.Next, write down the total number of pounds: 9 pounds.Divide the total cost by the total number of pounds to get the unit price (cost per pound): $51.21 / 9 pounds = $5.69 per pound.Therefore, one pound of the special sausage costs $5.69.
What do you need to add 13/4 to make 4
To make 13/4 to 4 you must have to add 3/4 in the given equation.
What is arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
Let the number is x.
So,
13/4 - x = 4
x = 13/4 - 4
x = (13 - 16)/4
x = -3/4
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What is 312.501 rounded to the nearest whole number? A. 310 B. 311 C. 312 D. 313
In mathematics, the principle of rounding instructs us to look at the decimal part . If it's .5 or higher, we round up; if it's less than .5, we round down. Hence, 312.501 rounded to the nearest whole number is 313.
Explanation:The question pertains to the concept of rounding numbers. In mathematics, rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. To round 312.501 to the nearest whole number, we look at the decimal part of the number. If the decimal is .5 or greater, we round up; if it's less than .5, we round down. In this case, the decimal part is .501, so we round up to the next whole number.
So, 312.501 rounded to the nearest whole number is D. 313.
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you are going to purchase a corvette for 60,000, the interest rate is 8% and you will be paying off the loan in 5 years what will be your monthly payment
Learn how to calculate the monthly payment for a car loan based on the principal amount, interest rate, and loan term.
Explanation:Monthly payment calculation:
Identify the variables provided: principal amount ($60,000), interest rate (8%), loan term (5 years).Use the formula for calculating monthly payments: E = P*r*(1+r)^n / ((1+r)^n - 1), where E is the monthly payment, P is the principal amount, r is the monthly interest rate, and n is the number of payments.Calculate the monthly payment using the given values: E = $60,000 * 0.08/12 * (1+0.08/12)^(5*12) / ((1+0.08/12)^(5*12) - 1).2(-20)+3[5/4(20)]+4(50)
Ivan has 4 hours of Music on his MP3 player jazz makes up 1/6 of the total time how many hours of jazz are on Ivan's MP3 player show your work
The answer for this problem is 2/3
The hours of jazz are on Ivan's MP3 player, if Ivan has 4 hours of Music on his MP3 player is 2/3 or 0.7 hours.
What is fraction?Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions are first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.
Given:
Ivan has 4 hours of Music on his MP3 player,
jazz makes up 1/6 of the total time,
Calculate the hours of jazz on Ivan's MP3 player as shown below,
The hours of jazz are on Ivan's MP3 player = 1 / 6 of the total time
The hours of jazz are on Ivan's MP3 player = 1 / 6 × 4 hours
The hours of jazz are on Ivan's MP3 player = 4 / 6
The hours of jazz are on Ivan's MP3 player = 2 / 3
Thus, the time of jazz is 2 / 3 or 0.7 hours.
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what is the supplementary angle of 32
The following table represents the sample space of rolling two number cubes.
1 2 3 4 5 6
1 1-1 1-2 1-3 1-4 1-5 1-6
2 2-1 2-2 2-3 2-4 2-5 2-6
3 3-1 3-2 3-3 3-4 3-5 3-6
4 4-1 4-2 4-3 4-4 4-5 4-6
5 5-1 5-2 5-3 5-4 5-5 5-6
6 6-1 6-2 6-3 6-4 6-5 6-6
How many favorable outcomes are there for the event "rolling exactly one even number"?
Please help on 9. Begging
find the length of the side not given hypotenuse =14, leg =13
[tex]\boxed{x=3\sqrt{3}}[/tex]
Step-by-step explanation:A right triangle is the one that has a 90° degree side. The hypotenuse is the largest side while the legs are the other two sides. The sketch for this problem is shown in the Figure below. To compute the other side, that is x, we must use the Pythagorean Theorem as follows:
[tex]H=\sqrt{Leg_{1}^2+Leg_{2}^2} \\ \\ \therefore H^2=Leg_{1}^2+Leg_{2}^2 \\ \\ Leg_{2}=\sqrt{H^2-Leg_{1}^2} \\ \\ x=\sqrt{14^2-13^2} \\ \\ \therefore \boxed{x=3\sqrt{3}}[/tex]
A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700. Before receiving this statement, John saw he was charged a total of $48.10. Write and solve an equation to determine how many minutes he must have used during the month. Write an equation without decimals.
There are 18 minutes John must have used during the month.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700.
Before receiving this statement, John saw he was charged a total of $48.10.
Let the time he must have used during the month = x
So, We can formulate the equation as;
⇒ $48.10 = $40 + $0.45 x
Solve for x as;
⇒ 48.10 - 40 = 0.45x
⇒ 8.10 = 0.45x
⇒ x = 8.10 / 0.45
⇒ x = 18
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Irene thinks she has space for a 45-inch wide bookcase.it turns out that she only has space for a 40 inch wide bookcase.what is the present error in Irene’s measurement
The problem statement is about the estimation of error in computation, here we will be presented with two values, the actual and the estimated value.
The present error in Irene’s measurement is 11.1%
Given data
Actual value = 40 inch
Estimate value = 45 inch
The formula for calculating the percent error is given as
Percent error = (Actual - Estimated/Estimated) *100
Percent error = (40 - 45/45) *100
Percent error = (-5/45) *100
Percent error = (-0.111) *100
Percent error = 11.1 %
Hence the percent error is 11.1%
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Which algebraic expressions are polynomials? Check all that apply. PLEASE HELP
Answer:
b,c,e,f just did it trust me
Step-by-step explanation:
Based on the information provided in the net worth statement, what is the net worth of this person?
A) $265,000.00
B) $307,000.00
C) $445,500.00
D) $752,500.00
To find this person's net worth, you will add the assets together to get a total value of what they are worth. Then you will need to subtract the amount of liability (amount owed).
( $487,500 + $265000) - $445500
$307000
This person's net worth is $307000.