The legs of a right triangle are 12 centimetres and 16 centimeters. What is the length of the hypotenuse?
15 centimeters
17 centimeters
20 centimeters
28 centimeters
The length of the hypotenuse is 20 centimeters.
In order to solve this question, we'll use the Pythagoras formula which will be:
a² + b² = c²
where,
First leg = a = 12 centimeters
Second leg = b = 16 centimeters
Hypothenuse = c = Unknown
It should be noted that the hypothenuse is the longest side and therefore the formula will be:
a² + b² = c²
12² + 16² = c²
144 + 256 = c²
400 = c²
Therefore, c = ✓400
c = 20
Therefore, the length of the hypotenuse is 20 centimeters.
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Is this right? It's geometry
What is the value of the expression, 3 1/4 - 1 7/8 in simplest form? Someone please help!
Problem page the ratio of men to women working for a company is 5 to 8 . if there are 169 employees total, how many women work for the company?
44cm is rounded to the nearest whole cm. Write down the maximum possible length it could have been.
The maximum possible length it could have been 44.49cm.
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
44cm is rounded to the nearest whole cm.
as, it is rounded to the nearest whole cm.
so, we get,
The maximum possible length it could have been 44.49cm.
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The temperature dropped 3 °C every hour for 5 hours.
Write an integer that represents the change in temperature.
What are the quotient and remainder when 6x3 + 13x2 + x − 2 is divided by x − 1?
Final answer:
The quotient when dividing 6x³ + 13x² + x - 2 by x - 1 is 6x² + 19x + 20, and the remainder is 18. This solution can be found using synthetic division.
Explanation:
The question asks to find the quotient and remainder when the polynomial 6x³ + 13x² + x - 2 is divided by x - 1. To solve this, we can use polynomial long division or synthetic division. As the divisor is in the form of x - a, where a is 1, synthetic division is a streamlined approach.
We set up our synthetic division with 1 as our key number outside the division symbol and the coefficients of our polynomial (6, 13, 1, -2) inside:
Bring down the 6.
Multiply 1 by 6 to get 6, add this to the next coefficient 13 to get 19.
Continue the process: Multiply 1 by 19 to get 19, add this to 1 to get 20.
Repeat: Multiply 1 by 20 to get 20, add this to -2 to get 18.
The numbers now inside the division symbol represent the coefficients of the quotient polynomial, giving us 6x² + 19x + 20 with a remainder of 18. Therefore, the quotient is 6x² + 19x + 20, and the remainder is 18.
Compound interest question :
Elle invests some money into a bank which pays 5% compound interest per year. She wants it to be worth £8000 at the end of 3 years. What is the smallest amount, to the nearest £, that she can invest?
How many significant digits are in 4.0×10^4
what transformations change the graph of f(x) to the graph of g(x)?
f(x)=x^2
g(x)=(x+3)^2-7
Answer:
B. The graph of g is the graph of f translated to the left 3 units and down 7 units.
Step-by-step explanation:
f(x) = x² to g(x) = (x + 3)² - 7
Notice the difference:
from 'x' to 'x + 3'
and then from 'x²' to '(x+3)² - 7'
The transformation that changes 'x' to 'x + 3' is the translation across the x-axis, three units to the left. The transformation that changes 'x²' to (x + 3)² - 7' is the translation across the y-axis, seven unit down. Refer to the graph attached below to visualize the transformation. Take the vertex of f(x) = x² and translate it three unit left and seven unit down to get g(x).
If Joan read 75 pages in 4 hours how long will it take her to read 250 pages
A student has some $1 and $5 bills in his wallet. he has a total of 1919 bills that are worth $5959. how many of each type of bill does he hav
A data set includes the entries 2, 5, 7, 9, 9, and 12. complete the data set with an entry between 1 and 12 so that the median and mode of the set are equal.
The complete data set will be 2, 5, 7, 9, 9, 9, 12. When the number 9 is added to the collection, the median and mode are both 9.
What is the median of data?The median is defined as the value range. To get it, arrange the numbers in ascending order from smallest to largest, then hide one number on either end until you reach the center.
The median of a set is the middle number when the numbers are arranged in numerical order.
The mode of a set is the number that appears most frequently.
To find an entry that will make the median and mode equal, we first need to arrange the given numbers in numerical order: 2, 5, 7, 9, 9, 12.
The median of this set is the middle number, which is 9.
The mode is 9, since it appears twice while the other numbers appear only once.
To make the median and mode equal, we need to find a number that is between 1 and 12 and that is equal to 9. The only such number is 9.
Therefore, if we add the number 9 to the set, the median and mode will both be 9. The complete data set will be 2, 5, 7, 9, 9, 9, 12.
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As a group, are sellers better or worse off with the price ceiling compared to trade in a market with no price controls? That is, do they capture more or less gain with the ceiling?
Find the measures of two complementary angles if the difference in the measures of the two angles is 14
-3x+2y=25
19x+3y=-33
If you know that a line has a slope of 2/3 and a y-intercept of 7, what is the equation for that line in slope-intercept form?
the equation for a line is y = mx+b
m = slope
b = y intercept
you know the slope is 2/3 and the y intercept is 7 so just replace them in the equation:
y =2/3x +7
If the maximum acceleration that is tolerable for passengers in a subway train is 1.74 m/s2 and subway stations are located 930 m apart, what is the maximum speed a subway train can attain between stations?
To calculate the maximum speed a subway train can reach between stations, given the maximum tolerable acceleration, we use the equation Vmax = sqrt(2 × a × d), resulting in a maximum velocity of approximately 40.21 m/s.
To find the maximum speed a subway train can attain between stations, given a maximum tolerable acceleration for passengers, we need to use the equations for uniformly accelerated motion. Since the train starts and ends at rest at the stations and because the stations are 930 meters apart, we can think of the train's trip as two identical parts: an acceleration phase and a deceleration phase.
Let's denote the maximum speed as Vmax, the acceleration as a, and the distance for each phase as d (half the distance between stations). We have:
Acceleration: a = 1.74 m/s2Total distance to the halfway point: d = 930 m / 2 = 465 mUsing the equation Vmax2 = 2ad, we can solve for the maximum speed (Vmax) as follows:
Vmax = sqrt(2 × a × d)
Substituting the values, we get:
Vmax = sqrt(2 × 1.74 m/s2 × 465 m)
Vmax ≈ sqrt(1617) m2/s2 ≈ 40.21 m/s
Therefore, the maximum speed the subway train can attain between stations is approximately 40.21 m/s.
Is -5 an irrational number?
A restaurant compiled the following information regarding 40 of its employees. Of these employees, 9 cooked food, 14 washed dishes, 22 operated the cash register, 4 cooked food and washed dishes, 2 cooked food and operated the cash register, 7 washed dishes and operated the cash register, and 1 did all three jobs. Complete parts a) through e) below.
a) How many of the employees only cooked food?
Answer: 2
Step-by-step explanation:
Let Set A represents the number of employees cooked food.
Set B represents the number of employees washed dishes.
Set C represents the number of employees operated the cash register .
Given : n(A)=9 ; n(B)=14 ; n(C)=22
n(A∩B)=4 ; n(A∩C) = 2 ; n(B∩C)=7 ; n(A∩B∩C)=1
Using the given information, we have made a Venn diagram below.
Using Venn diagram , we have
n(only A)= n(A)-(n(A∩B)+n(A∩C)+n(A∩B∩C))
⇒n(only A)=9-(4+2+1)=9-7=2
Hence, 2 employees only cooked food.
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $39 . The total cost to rent 9 chairs and 7 tables is $63 . What is the cost to rent each chair and each table?
Which choice shows a true conditional with a correctly identified hypothesis and conclusion?
A. If next month is January, then this month is the last of the year. Hypothesis: This month is the last of the year. Conclusion: Next month is January.
B. Next month is February, so this month is the last month of the year. Hypothesis: Next month is February. Conclusion: This month is the last of the year.
C. Next month is February, so this month is the last month of the year. Hypothesis: This month is the last of the year. Conclusion: Next month is February.
D. If next month is January, then this month is the last of the year. Hypothesis: Next month is January. Conclusion: This month is the last of the year.
The correct choice is D, where 'If next month is January' is the hypothesis, and 'then this month is the last of the year' is the conclusion, demonstrating the proper format and identification of a true conditional statement.
The question is concerning a true conditional statement and the identification of its hypothesis and conclusion. To form a proper conditional, we use the format 'If... then...' where the 'if' part represents the hypothesis and the 'then' part represents the conclusion. The hypothesis is the supposed condition, while the conclusion is the result or outcome that follows from the hypothesis.
Let's analyze the choices:
Choice A has the conclusion and hypothesis reversed.
Choice B is an incorrect format for a conditional because it uses 'so' instead of 'if... then...'.
Choice C has the same issue as choice B.
Choice D is in the correct format and has the hypothesis and conclusion properly identified. If next month is January is the hypothesis, and then this month is the last of the year is the conclusion.
Therefore, the answer is Choice D.
What is m∠PTS??????????
11(y-10) = 4y-5
11y-110 = 4y-5
7y -110 = -5
7y =105
y = 105/7 = 15
PTS = 11(15-10) = 11*5 = 55 degrees
Answer:
55
Step-by-step explanation:
We are given with two lines that intersects each other .
the vertical opposite angles are same.
So we equate the angles and solve for y
[tex]11(y-10)= 4y-5[/tex]
[tex]11y-110=4y-5[/tex]
Subtract 4y from both sides
[tex]7y-110=-5[/tex]
Now we add 110 on both sides
[tex]7y=105[/tex]
Now we divide by 7 on both sides
y=15
now we find m∠PTS
m∠PTS=[tex]11(y-10)[/tex]
Plug in 15 for y
m∠PTS=[tex]11(15-10)=55[/tex]
The difference of two positive numbers is 5 and the sum of their squares is 125. find the numbers.
The two positive numbers are 10 and 5.
Given that,
The difference between two positive numbers is 5.
And the sum of their squares is 125.
Let us assume that,
The numbers are x and y.
Here, the difference between two positive numbers is 5.
x - y = 5
x = 5 + y .. (i)
And, the sum of their squares is 125.
That is,
x² + y² = 125
Substitute the value of x from (i);
(5 + y)² + y² = 125
25 + y² + 10y + y² = 125
2y² + 10y + 25 = 125
2y² + 10y - 100 = 0
2 (y² + 5y - 50) = 0
y² + 5y - 50 = 0
y² + (10 - 5)y - 50 = 0
y² + 10y - 5y - 50 = 0
y (y + 10) - 5 (y + 10) = 0
(y - 5) (y + 10) = 0
This gives,
y = 5
y = - 10
Since the numbers are positive.
Hence, y = - 10 is not possible.
From (i);
x = 5 + y
Put y = 5;
x = 5 + 5
x = 10
Hence,
The two positive numbers are 10 and 5.
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Kai calculates that he spends 75 minutes of a school day in science class. if he spends 500 minutes in school, what percent of his school day does kai spend it science class
what is the answer for 13=4x-9
The solution of the given equation is 5.5.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The given equation is 13=4x-9.
The collection of values used to replace the unknowns in an equation to make it true is known as the solution.
Here, add 9 on both the sides of an equation.
That is, 13+9=4x-9+9
4x=22
Divide 4 on both the sides of an equation.
4x/4 =22/4
x=5.5
Therefore, the value of x is 5.5.
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I need to find the equation for this.. I keep getting confused please explain
Define a variable and write an equation for each situation. Solve each equation to answer the question.
A plumber finished three jobs on Tuesday. The first two only cost the owner $45 trip fee because they took very little time to complete. For the third job, the plumber charged the trip fee plus 6 times his hourly rate. If the plumber received a total of $303 for the day, what is the hourly rate?
H = Hourly Rate
for my Equation I made,
5(45)+6h=303
but cant figure out how to solve it
(9th Grade ALG 1)
Plz work out the problem, thnx :-)
|5v-10|=0 solve for v
The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t)
PART A:
The function in vertex form by completing the square is:
[tex]f(t)=(t+3)^2-29[/tex]
PART B:
The vertex is located at (-3,-29)
and the vertex is the minimum point of the graph.
PART C:
The axis of symmetry of f(t) is:
t= -3
Step-by-step explanation:The function f(t) is given by:
[tex]f(t)=t^2+6t-20[/tex]
We know that the vertex form of a equation is given by:
[tex]f(t)=a(t-h)^2+k[/tex]
where a,h and k are real numbers.
and the vertex is located at (h,k)
The function is given by:
[tex]f(t)=(t+3)^2-29[/tex]
Hence, the vertex is given by:
(-3,-29)
Also, as the leading coefficient is positive.
Hence, the parabola is upward open parabola.
Hence, the vertex will be the minimum point of the graph.
Also, the axis of symmetry of a graph is given by:
t=h
Hence, here the axis of symmetry is: t= -3