In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $18.$ What is the length of the hypotenuse of the triangle?
The length of the hypotenuse of the triangle is; AB = 2√106 ≈ 20.591
How to use the Pythagorean theorem?The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs. Thus;
For median AM, we have;
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have;
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations gives us;
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
Thus, we conclude that the length of the hypotenuse of triangle ABC is;
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
Read more about Pythagorean theorem at; https://brainly.com/question/343682
#SPJ1
the volume of the atlantic ocean is about 3.1 \cdot 10^{17}3.1⋅10 17 3, point, 1, dot, 10, start superscript, 17, end superscript cubic meters. the mississippi river has an annual flow of 6.3 \cdot 10^{11}6.3⋅10 11 6, point, 3, dot, 10, start superscript, 11, end superscript cubic meters. how many times would the annual flow of the mississippi river fit in the atlantic ocean?
4.92*10^5 times the annual flow of the Mississippi River fit in the Atlantic Ocean
Given that,
Volume of the Atlantic Ocean = 3.1*10^17cubicmetres
Annual flow of the Mississippi River = 6.3*10^11cubicmeters
Now, we have to find how many times the annual flow of the Mississippi River fit in the Atlantic Ocean
So,
= Volume of the Atlantic Ocean / Annual flow of the Mississippi River
= 3.1*10^17 / 6.3*10^11
= 0.4921*10^6 (Approximately)
=4.92*10^5
Therefore,
It takes 4.92*10^5 times for the Mississippi River to fit into the Atlantic Ocean.
To know more about “The Mississippi River”
Refer this link:
https://brainly.com/question/7999616
#SPJ4
I need help and I’m not sure how to solve this. we’re supposed to copy the answers from our workbooks but I haven’t got mine :(
Step-by-step explanation:
here you go i don't know if this will be helpful or not
6.) The quotient of Jorge's age and 3 minus 2 is 30. How old is Jorge?
Answer:
96 years
Step-by-step explanation:
let Jorge's age be x
then the quotient of his age and 3 is x divided by 3 , so
[tex]\frac{x}{3}[/tex] - 2 = 30 ( add 2 to both sides )
[tex]\frac{x}{3}[/tex] = 32 ( multiply both sides by 3 to clear the fraction )
x = 3 × 32 =96
Jorge is 96 years old
What is the equation of a line that contains the points (5, 0) and (5, −2)?
a) x = 5
b) x = 0
c) y = 0
d) y = 5
Thank you!
The equation of the line is x = 5
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope and y-intercept
(5, 0)(5, - 2)
m = -2 - 0 / 5 - 5
m = -2 / 0
m = infinity
Hence, It is a vertical line, since the x is the same for both of them, and it is equal to both times.
Therefore, the equation of the line is x = 5
learn more on equation here: https://brainly.com/question/12885324
#SPJ1
25 point to who gets these problems plus thank
Cameron's current service charge of $0.95 per song, and the new service charge of $0.89 per song and $12 fee for joining, gives;
Formula for finding the number of songs that makes the cost of both services the same is; 0.95•s = 12 + 0.89•sComputing the value of s that satisfies the above equation gives the number of songs at which the cost of both service is the same as 200 songs The interpretation is the the cost of either service is the same when 200 songs are downloadedHow can the equation that gives the required number of songs be found?To Formulate
The charges for songs on the current music service is, C1 = 0.95•s
The charges for the new download service is, C2 = 12 + 0.89•s
Where the $12 is the joining fee
When the cost is the same for both service, we have;
C1 = C2
Which gives;
0.95•s = 12 + 0.89•sThe equation to represent when the cost for both service is the same is therefore;
0.95•s = 12 + 0.89•s
Computing;
The number of songs that gives the same costs is therefore;
0.95•s = 12 + 0.89•s
12 = 0.95•s - 0.89•s = 0.06•s
s = 12 ÷ 0.06 = 200
The number of songs at which the cost of each option will be the same is s = 200 songsInterpreting the solution;
The interpretation is, the cost of songs downloaded on both service will be the same, when 200 songs are downloaded.
Learn more about writing formulas here:
https://brainly.com/question/26666091
#SPJ1
a high school graduating class is made up of 410 students. there are 66 more girls than boys. how many boys are in the class?
Total number of boys in class are 172
A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
We have total number of students in class = 410
We assume that the number of boys in class = X
Number of girls in class is 66 more then boys we assume total number of girls = X+66
If we add number of girls and boys then we found total strength of classX+X+66=4102X+66=4102x=344X=172
Number of boys = 172
Number of girls =238
To learn more about linear equation visit: brainly.com/question/11897796
SPJ4
evaluate 7x2x7x5 using property of numbers name the property in each step
7x2x7x5:
7x7x2x5
(7x7)x(2x5)
49x10= 410
By the commutative property, the value of the expression 7 x 2 x 7 x 5 is 490
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression using mathematical properties?The expression is given as
7 x 2 x 7 x 5
The above expressions are grouped by the product sign
This means that the factors of the expressions can be rearranged by the commutative property
So, we have
7 x 7 x 2 x 5
Group the factors
So, we have
(7 x 7) x (2 x 5)
Evaluate the products
So, we have
49 x 10
Evaluate the products
So, we have
490
Hence, the value of the expression 7 x 2 x 7 x 5 is 490
Read more about expressions at
https://brainly.com/question/723406
#SPJ1
6.
(11x-47)
(6x-2)
m
1
Solve for missing variable l and m are parallel
The solved polynomial is 66x² -304x+94.
We are given a problem related to the polynomial function, where Polynomial functions are expressions that will contain factors of changing degrees, coefficients, positive types, and constants.
Since the given equation (11x-47)(6x-2), both the term are in the form of multiplication, so here we use the distribute rule,
we multiply the 6x-2 individually with the 11x and 47
11x(6x-2) -47(6x-2 )= 66x² -22x -282x + 94
Now, we have two common variables of coefficients -22 and -282, after adding both of them, the final outcome we get is
= 66x²-304x +94
The solved function for the given equations is 66x2 -304x+94,
To know more about linear equations refer to the link https://brainly.com/question/12976257?referrer=searchResults.
#SPJ9
the model represents a polynomial of the form ax2 bx c. an algebra tile configuration. 4 tiles are in the factor 1 spot: 3 x , 1 negative. 2 tiles are in the factor 2 spot: 1 x, negative. 8 tiles are in the product spot in 4 columns with 2 rows. first row: 3 x squared, 1 negative x. second row: 3 negative x, 1 . which equation is represented by the model? 3x2 – 4x – 1
The Quadratic equation modeled is [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex].
Quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are numbers and a cannot be 0.
the given equation Much easier to understand with the symbol [tex]3x^{2} -4x+1=(3x-1) (3x-1)[/tex]
[tex]3x^{2} -4x+1= 9x^{2} -6x+1\\6x^{2} -2x=0[/tex]
That is how I interpreted the "tile" set up.
Now count up the factors:
These are (4 -x) and ( x +1) factor of Quadratic equation.
learn more about Quadratic equation .brainly.com/question/17177510
#SPJ4
find an equation for a line:
a. with slope 6 passing through (-1, 4)
b. that passes through (-5, 0) and (5, 6)
Answer:
y=6x-1
y=3/5x+5
Step-by-step explanation:
6-0= 6= 3/5
5+5 =10
Ramon has $4896 in his bank account. he has been depositing the same amount of money monthly for 2 years. how much money did ramon deposit monthly?
Answer:
Ramon deposited $204 monthly
Step-by-step explanation:
Step 1: Firstly convert 2 years to month
1 year = 12 month
∴ 2 years = 24 month
Step 2: Divide $4896 by 24
➟ 4896 ÷ 24
➟ 204
he first step in simplifying the expression: (1.8 x 10^5) - (2.6 x 10^3)
a
Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).
b
Addition and subtraction do not require any changes, so you would just subtract (2.6 - 1.8) and (10^(5-3))
c
Addition and subtraction do not require any changes, so you would just subtract (1.8 - 2.6) and (10^(5-3))
d
Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (2600 x 10^5).
Using scientific notation, the first step in simplifying the expression is given by:
a. Addition and subtraction requires the terms to be "like terms" with the same power of the base 10, so you would need to change the second number to (0.026 x 10^5).
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For two numbers in scientific notation to be added or subtracted, they need to have the same exponent, which removes options b and c.
Moving the second number for 10^3 to 10^5 would be equivalent to a multiplication by 100, hence we have to divide by 100 at the base, that is:
2.6 x 10^3 = (2.6/100) x 10^5 = 0.026 x 10^5.
Hence option a is correct.
More can be learned about scientific notation at https://brainly.com/question/16394306
#SPJ1
Malcolm answered 12 questions correctly on his social studies assignment and scored 75%. how many questions were on the assignment
If Malcolm answered 12 questions correctly on his social studies assignment and scored 75%, then the total number of questions on the assignment were 16.
The number of questions on the assignment can be determined by converting the given percentage.
A percentage is a numeral expressed as a fraction of 100
75% = 75 / 100 = 0.75
The equation can be formed as,
75 % of x = 12
Here x is equal to the total number of questions on the assignment
As 75% = 75 / 100 = 0.75
0.75 x = 12
x = 12 ÷ 0.75
x = 16
As x represented the total number of questions, hence the total number of questions on the assignment were calculated to be 16.
To learn more about percentages, click here:
https://brainly.com/question/24877689
#SPJ4
what is the value of (x+y)^2 when x=2 and y= -4?
Answer: 20
Step-by-step explanation:
Everything within the parenthesis gets an exponent of two, so you should have (x^2+y^2).
After this, you plug in the 'x' and 'y' given, so the next part should look like (2^2+(-4)^2)
After step 2, do 2*2 and -4*-4 (exponents ask you to multiply numbers by a specific amount. In this case, both numbers are multiplied by themselves 2 times).
A negative times a negative is a positive, so -4^2 or -4*-4 is 16. 2^2 or 2*2 is simply 4.
Add 4 and 16 together to get your final answer of 20.
Hope this helps!
i need help with this please
Answer:
x = 67.5
Step-by-step explanation:
90 + x + 3x = 360
90 + 4x = 360
4x = 360 - 90
4x = 270
x = 270 / 4
x = 67.5
Hope it helps!!!
7x - 2y = 1
3x + 4y = 15
Substitution method Linear Equations
The value of 'x' and 'y' is '1' and '3' , respectively.
Substitution method :The substitution method is the algebraic method to solve simultaneous linear equations.
The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.
Lets solve the given linear equations:
7x − 2y = 1 ... eq. (1)
3x + 4y = 15 ... eq. (2)
By equation 1 we got,
x = (1 + 2y)/7
Now, we will put x = (1 + 2y)/7 in equation 2,
3x + 4y = 15
3 [(1 + 2y)/7] + 4y = 15
3/7 × (1 + 2y) = 15 - 4y
3(1 + 2y) = 7(15 - 4y)
3 + 6y = 105 - 28y
6y + 28y = 105 - 3
34y = 102
y = 102/34
y = 3
Now, put the value y =3 in equation 1,
7x - 2y = 1
7x - (2×3) = 1
7x - 6 = 1
7x = 1 + 6 = 7
7x = 7/7
x = 1
Hence, the value of x is 1 and y is 3.
To learn more about Substitution Method visit :
https://brainly.com/question/14619835
#SPJ9
Solve the following integers
Step-by-step explanation:
here is the answer of each question respectively
82 78 80 72 85 80 calculate the mean and standard deviation of service speed using the formula for each. Show work.
The mean is 79.5.
The standard deviation is 3.99
What is the mean and standard deviation?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
(82 + 78 + 80 + 72 + 85 + 80) / 6 = 477 / 6 = 79.5
Standard deviation is used to determine how the values in a group differs from the mean of the values in the group.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation:79.50
Determine the difference between each value and the mean and then square the result: (82 - 79.5)² + (78 - 79.5)² + (80- 79.5)² + (72- 79.5) ²+ (85- 79.5)² + (80- 79.5)² = 6.25 + 2.25 + 0.25 + 56.25 + 30.25 + 0.25 = 95.5
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√95.5 / 6 = 3.99
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
If a train is going 3 miles in a hour how much will it go into 2 3/4 a hour
Answer: 8.25 miles in 2 3/4 hours
Step-by-step explanation:
As a fundraiser for the Lax Team, they plans to sell tees with the school logo. The company ducing the fees charges $125 for the design and set up plus $5 per tee. The lax members will sell tees for $10 each. How many do they need to sell to break even? PLEASE HELP
The company must produce 25 t-shirts to break even.
Here, we are given that a company producing t-shirts charges $125 for the design and set up plus $5 per tee.
This means-
fixed cost of producing the t-shirts = $125
Variable cost of producing a t-shirt = $5
Let x be the number of t-shirts produced
Thus, the total cost of producing t-shirts will be-
Total cost = 125 + 5x
Further, the selling price of 1 t-shirt = $10
Thus, selling price of x t-shirts = $10x
Now, at the break even point, the profit is 0, this implies-
Selling price = cost price
⇒ 10x = 125 + 5x
10x - 5x = 125
5x = 125
x = 125/5
x = 25
Thus, the company must produce 25 t-shirts to break even.
Learn more about break even here-
https://brainly.com/question/21137380
#SPJ9
Find the equation of the line that passes through the points (1,2) and 3, 10).
Answer:
y=4x-2
Step-by-step explanation:
m=[tex]\frac{8}{2}[/tex]=4
2=4(1)+b 2=4+b -2=b
two sides of a triangle have the same length. the third side measures 6 m less than twice the common length. the perimeter of the triangle is 10 m. what are the lengths of the three sides?
As for the answer, the length of the three sides was x=4.
Let [tex]x[/tex] be the length of the two sides that are the same.
Then the third side would be 2x-3
The perimeter of the triangle will come from adding all of the sides together and setting it equal to the value given, 13.
That is,
x + x + (2x-3)=13
4x-3=13
4x=13+3
4x=16
x=4
The length of each of the common sides is 4, making the third side 5, to get a total perimeter of 13.
What are two sides of a triangle?The hypotenuse of a right-angled triangle is its longest side, the base is its lower side, and the perpendicular, which stands next to the right angle, is its standing line.
You may determine the sides of a right-angled triangle using a number of techniques, such as the Pythagoras theorem or the triangle's perimeter.
To learn more about sides of a triangle visit:
https://brainly.com/question/16986516
#SPJ4
Determine whether the equation 32 +15= 3(x+5) has one solution, no solution, or infinitely many solutions.
one solution
infinitely many solutions.
O no solution
1
2
POSSIBLE PO
3 4
U
In ΔOPQ, o = 1.2 inches, p = 3.2 inches and ∠Q=37°. Find the area of ΔOPQ, to the nearest 10th of a square inch.
I need assistance with this problem.
Answer: it is upside down
Step-by-step explanation:
cant see the problem
Consider the polynomials:
A(x) = (3-x)2² - (x-3) (7x+4)-18+2x²
B(x) = (3x + 2)² - (x - 1)²
1) Develop and reduce A (x).
2) Factorize A (x) and B (x).
3) Solve the equation A (x)= B(x)
4) Prove that B (X) -3 = 2x(4x+7) , then solve the equation B(x) =3
Answer:
1) -5x² + 13x + 6
2) B(x) =(4x + 1 )(2x + 3)
A(x) = (5x +2)(3-x)
Step-by-step explanation:
1) Expand the equation by using distributive property. Then simplify by combining the like terms.
A(x) = (3 -x)2² - (x -3)(7x+ 4) - 18 + 2x²
= (3 - x)4 - [x*7x + x*4 - 3*7x - 3*4] - 18 + 2x²
= 3*4 - x*4 - [7x² + 4x - 21x - 12] - 18 + 2x²
= 12 - 4x - 7x² - 4x + 21x + 12 - 18 + 2x²
= 2x² - 7x² -4x - 4x + 21x + 12 + 12 - 18
= -5x² + 13x + 6
B(x) = (3x + 2)² - (x - 1)²
Identities:
(a + b)² = a² + 2ab + b² ; Here a =3x & b = 2
(m -n)² = m² - 2mn + n² ; Here m = x & n = 1
2) B(x) = (3x)² + 2*3x*2 + 2² - [x² - 2*x*1 + 1]
= 9x² + 12x + 4 - [x² - 2x + 1]
= 9x² + 12x + 4 - x²+ 2x - 1
= 9x² - x² + 12x + 2x + 4 - 1
= 8x² + 14x +3
Product = 8*3 = 24
Sum = 14
Factors = 2 , 12 {2*12 = 24 & 2 +12= 14}
= 8x² + 2x + 12x + 3 {Rewrite the middle term}
= 2x(4x + 1) + 3(4x + 1)
= (4x + 1 )(2x + 3)
A(x) = - 5x² + 13x + 6
= -5x² + 15x -2x + 6
= 5x(-x +3) +2 (-x + 3)
= (5x +2)(3-x)
4) B(x) - 3 = 8x² + 14x + 3 - 3
= 8x² + 14x
= 2x *4x + 2x *7
=2x(4x + 7)
Hence proved.
B(x) = 3
8x² + 14x + 3 = 3
8x² + 14x + 3 - 3 = 0
8x² + 14x = 0
2x(4x + 7) = 0
2x = 0 or 4x + 7 = 0
x = 0 or 4x = -7
[tex]\sf x = \dfrac{-7}{4}[/tex]
x = 0 or [tex]\sf \dfrac{-7}{4}[/tex]
Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute. Then she stopped and went into the store for 4 minutes. From there, she drove in the same direction at a speed of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store. She stopped at the bank for 3 minutes. Then she drove home at a speed of 3 blocks every minute. Make a graph of showing the number of blocks away from home that Scarlett is xx minutes after she leaves her house, until she gets back home.
Click twice to plot a segment.
Click a segment to delete it.
0
Time Elapsed (Minutes)
Distance (Blocks from Home)
x
y
The required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.
As given in the question Scarlett left her house at time zero and drove to the store, which is 3 blocks away, at a speed of 1 block per minute.
Then she stopped and went into the store for 4 minutes.
she drove in the identical at a rate of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store.
Here,
1 Approach, Scarlett moves with the speed of a block per minute
Total distance travel = 3 block
Approach 2 Scarlett moves with the speed of 5 blocks per minute for 3 minutes
Total distance travel = 15 block
Approach 3 Scarlett moves with the speed of 3 blocks per minute for 1 minute
Total block traveled = 3 + 15 = 18
Now, Approach 3 is to retrace the path at the rate of 3 blocks per minute,
All these calculations is been shown in the block diagram.
Thus, the required block diagram that shows how much distance Scarlett is away from the home is shown in the image attached.
Learn more about distance here:
brainly.com/question/15172156
#SPJ1
is i get one point each 5 minutes how long until i get 50 points?
Answer:
250 minutes.
Step-by-step explanation:
1/5=50/x
cross product
5*50=1*x
250=x
At the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning
The total change in the stock market from the beginning based on the information will be 171 1/4 points.
How to illustrate the information?It should be noted at the beginning of the day the stock market goes down 50 1/2 points and stays at this level for most of the day and at the end of the day the stock market goes up 120 3/4 points from the low at the beginning of the day.
Therefore, the total change in the stock market from the beginning will be the difference between the fractions that are given. This will be:
= 120 3/4 - (- 50 1/2)
= 120 3/4 + 50 1/2
= 171 1/4
Therefore, the total change in the stock market from the beginning based on the information will be 171 1/4 points.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1