Answers
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
Pythagorean Theorem: If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse. Alternatively, x^2 + y^2 = r^2.
The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order. Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).
Performing the indicated operations, we get:
4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1. Simplify this first by combining like terms:
20x^2 - 16x = 16x^2, or
4x^2 - 16x = 0, or
4x(x - 4) = 0. Thus, x = 0 (which makes no sense here) or x = 4.
The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1. Substituting 4 for x, we get
P = 8 + 16 - 1 + 16 + 1, or 40.
The perimeter of the triangle is 40.
Related Questions
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answers
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
PLEASE HELP Polynomial Graph Studies Polynomials are great functions to use for modeling real-world scenarios where different intervals of increase and decrease happen. But polynomial equations and graphs can be trickier to work with than other function types. In mathematical modeling, we often create an equation to summarize data and make predictions for information not shown on the original display. In this activity, you’ll create an equation to fit this graph of a polynomial function. Part A Describe the type of function shown in the graph. Part B What are the standard form and the factored form of the function? Part C What are the zeros of the function? Part D Use the zeros to find all of the linear factors of the polynomial function. Part E Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form. Part F Use the y-intercept of the graph and your equation from part E to calculate the value of a. Part G Given what you found in all of the previous parts, write the equation for the function shown in the graph.
Answers
Answer:
Here's what I get
Step-by-step explanation:
Part A
The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.
Part B
The standard form of a cubic equation is
y = ax³ + bx² + cx + d
The factored form of a cubic equation is
y = a(x - b₁)(x² + b₂x + b₃)
If you can factor the quadratic, the factored form becomes
y = a(x - c₁)(x - c₂)(x - c₃)
Part C
The zeros of the function are at x = -25, x = - 15, and x = 15.
Part D
The linear factors of the function are x + 25, x + 15, and x - 15.
Part E
y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)
y = a(x³ + 25x² - 225x - 5625)
Part F
When x = 0, y = 1.
1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a
a = -1/5625
Part G
[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]
Answer
Actually, the answer should be -0.0007(x+20)(x+5)(x-15)
Step-by-step explanation:
This is continuing off of the previous answer
PART C
The zeros should be (15,0), (-5,0), and (-20,0)
PART D
x - 15, x + 5, and x + 20
PART E
a(x - 15)(x + 5)(x + 20)
Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]
PART F
The y-intercept is at (0,1), so we replace the x's with 0:
1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500
Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007
a= -0.0007
PART G
Just place the numbers where they should go and your answer is
y =-0.0007(x + 20)(x + 5)(x - 15)
the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007
Could someone clarrify this for me Factor completely 3x^2 + 2x − 1. (3x + 1)(x − 1) (3x + 1)(x + 1) (3x − 1)(x + 1) (3x − 1)(x − 1)
Answers
Answer:
(3x-1) (x+1)
Step-by-step explanation:
3x^2 + 2x − 1
3x^2 factors into 3x and x
-1 factors into -1 and 1
We want a postive 2x
(3x-1) (x+1)
Answer:
(3x-1)(x+1)
Step-by-step explanation:
3x² + 2x − 1
when factorizing , first look at the constant number( in this case it is 1 prime number), then find the GCF if found.
(3x )(x ) first step : 3x*x=3x^2
(3x- ) (x+ ) the sign for the constant is minus so the factoring has to be minus and plus on each side
(3x-1)(x+1) look at the 2x it has positive sign, means the sign is plus:
3x-1
x+1
regular standard multiplication
3x(x)-1(x)+1(3x)-1
3x²+2x-1
Kapil deposited Rs. 1600 in a bank on 1st January 2005. Find the amount in his bank account on 1st January 2006, if the bank pays interest at 8% per annum and the interest is calculated every year on 30th June and 31st December.
Answers
Answer:
SI=PRT/100
=10000*5*42/12*100
=1750
SI=1750
TOTAL AMOUNT=PRINCIPLE+SI
=10000+1750
=101750
PLEASE help me solve this question! No nonsense answers please!
Answers
Answer:
[tex]\boxed{\sf Option \ 1}[/tex]
Step-by-step explanation:
The profit is revenue (R ) - costs (C ).
Subtract the expression of costs (C ) from revenue (R ).
[tex]10x-0.01x^2-(2x+100)[/tex]
Distribute negative sign.
[tex]10x-0.01x^2-2x-100[/tex]
Combine like terms.
[tex]8x-0.01x^2-100[/tex]
The first option has a positive 100, which is wrong.
The rest options are right, when we expand brackets the result is same.
PLEASE HELP! 20 POINTS 1) A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the function H(t)=−4.9t2+25t+2. What is the height of the ball at each second from 0 to 5? (I'll put a picture of the graph.) 2) Which expression could represent the height of a soccer ball as it is in the air after being kicked? (This is part 2 to question 1) A. −16t+9 B. −16t2+4t3 C. 9t2+25t D. −16t2+25t+1
Answers
Answer:
a or b
Step-by-step explanation:
it just looks like b or a
H(t) = -4.9t^2 + 25t + 2
Height is a function of time
plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.
at t = 0
H(0) = -4.9(0)^2+25(0) + 2 = 2 meters
Repeat for T=1,2,3,4 and 5
Notice the ball peaks around t = 3 seconds and starts to descend.
H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters
H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters
H(3) = 32.9 meters
H(4) = 23.6 meters
H(5) = 4.5 meters
How many solutions does the nonlinear system of equations graphed below
have?
y
10+
-10
10
-10
A. One
B. Two
0
O
C. Four
O
D. Zero
Answers
Answer:
D. zero
Step-by-step explanation:
Since the graphs do not intersect, there are zero solutions.
The number of solutions on the graph is zero
How to determine the number of solutions?The graph shows a linear equation (the straight line) and a non linear equation (the curve)
From the graph, we can see that the straight line and the curve do not intersect
This means that the graph do not have any solution
Hence, the number of solutions on the graph is zero
Read more about non-linear graphs at:
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The projected worth (in millions of dollars) of a large company is modeled by the equation w = 206(1.1) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 10%; $534.31 million B. 11%; $646.52 million C. 10%; $587.74 million D. 11%; $226.60 million
Answers
Answer:
Hey There!! The Correct answer is: The equation is w = 241(1.06)t
And here variable t represents the number of years since 2000.
In 2001 means t=2001 -2000 = 1
So we plug 1 for t in the given expression , that is w = 241(1.06)1 = 241 * 1.06 = 255.46
Therefore in 2001, it should be worth to 255.46.
And in the given expression 1.06=1 +0.06, where 0.06 is the annual percent of growth that is 6 % .
Hope It Helped!~ ♡
ItsNobody~ ☆
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions. Then the correct option is C.
What is an exponent?Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %.
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %.
The projected worth (in millions of dollars) of a large company is modeled by the equation is given as,
[tex]\rm w = 206\times (1.10)^t\\\\w = 206\times (1+0.10)^t[/tex]
Then the projected annual percent of growth is 10%.
The variable t represents the number of years since 2000.
Then the company worth in 2011 will be
w = 206 × 1.1¹¹
w = $587.74 millions
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions.
Then the correct option is C.
More about the exponent link is given below.
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Which type(s) of symmetry does the following object have?
Select all that apply.
Answers
Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.
We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.
We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.
Answer:
Theres more than one answer so b and a
Step-by-step explanation:
(a²b²-c²)(a²b²+c²)
simplify
Answers
Answer:
a⁴b⁴ - c⁴
Step-by-step explanation:
The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.
Answer:
a^4b^4 - c^4.
Step-by-step explanation:
(a²b²-c²)(a²b²+c²)
Difference of 2 squares:
= (a²b²)^2 - (c²)^2
= a^4b^4 - c^4.
Let f (x) = |2). Write a function g whose graph is a vertical shrink by a factor of
followed by a translation 2 units up of the graph of f.
Answers
Answer:
This is poorly written, so i will answer it as it was:
"Let f (x) = |2). Write a function g(x) whose graph is a vertical shrink by a factor of A, followed by a translation 2 units up of the graph of f."
I don't really know what you do mean by I2), so i will answer it in a general way.
First, we do a vertical shrink of factor A.
A must be a number smaller than one and larger than zero., then if g(x) is a vertical shrink of factor A of the graph of f(x), we have that:
g(x) = A*f(x)
As 0 < A < 1
We will have that the graph of g(x) is a vertical compression of the graph of f(x)
Now we do a vertical shift of 2 units up.
A general vertical shift of N units up is written as:
g(x) = f(x) + N
Where N is a positive number.
So in our case, we have:
g(x) = A*f(x) + 2.
Where you will need to replace the values of A and f(x) depending on what the actual question says,
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answers
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
Answers
7/20+3/5+21/100
The missing probability P(A∪B) will be 37/50.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given information;
P(A)= 7/20,
P(B)=3/5,
P(A∩B) =21/100 ,
We need to find the missing probability P(A∪B).
We know that
P(A∪B)= P(A) + P(B) + P(A∩B)
P(A∪B) = 7/20 + 3/5 + 21/100
P (A U B) = 37/50
Therefore, the missing probability P(A∪B) will be 37/50.
Learn more about probability here;
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The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
Answers
Answer:
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Step-by-step explanation:
[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]
Factorizing the expressions we have
[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]
[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]
[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]
Cancelling out the like factors, (x -1) and (x - 2), we have
[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]
= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
20 POINTS! ***CORRECT*** ANSWER GETS BRAINLIEST!!!!
The fraction model below shows the steps that a student performed to find a quotient.
Which statement best interprets the quotient?
A. There are 5 1/6 three-fourths in 4 1/8
B. There are 5 1/6 three and one-eights in 3/4
C. There are 5 1/2 three and one-eights in 3/4
D. There are 5 1/2 three-fourths in 4 1/8
Answers
Answer:
(D) There are [tex]5 \frac{1}{2}[/tex] three-fourths in [tex]4 \frac{1}{8}[/tex]
Step-by-step explanation:
We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.
So this becomes the division statement:
[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].
We can convert [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.
[tex]\frac{33}{8} \div \frac{3}{4}[/tex].
Multiply by the reciprocal:
[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]
Which simplifies down to
[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.
Hope this helped!
Answer:
D
Step-by-step explanation:
What is the main difference between simplifying and solving? Which one gives you a value for a variable? How do you know the difference?
Answers
Answer:
when you simplify you continue until you get to the simplest form but when you solve you continue until you get an answer. Solving gives you a value for a variable. You mean simplify and get 2x - 10 but when you solve you continue until you get x as 5
Step-by-step explanation:
Answer: ok, so simplifying is when you make something less complex or complicated. Solving means an expression can be used for representating the solutions. for Example, say if you have the equation x+y=2x-1 is solved for the unknown x by the expression x=y+1. solving gives you the value for the variable. you know the difference by when you are simplifying you are trying to make the problem less complicated or less complex. and when you are solving you are trying to find the answer to the problem..
Step-by-step explanation:
Need help on the third question. how do i generalise the number of ways to win.(check the attatchment)
Answers
Answer:
2n+2 ways to win
Step-by-step explanation:
You generalize by observing patterns in the way you solve the smaller problems.
The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.
For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.
Please Help me with this math question
Answers
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
A.
385.33 cubic units
B.
4,913 cubic units
C.
6,550.67 cubic units
D.
3,275.34 cubic units
Answers
Answer:
20582.195 unitsStep-by-step explanation:
This problem is on the mensuration of solids.
A sphere is a solid shape.
Given data
radius of sphere = 17 units
The volume of a sphere can be expressed as below
[tex]volume = \frac{4}{3}\pi r^3[/tex]
Substituting our data into the expression we have
[tex]volume = \frac{4}{3}*3.142*17^3[/tex]
[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]
The volume of the sphere is given as
20582.195 units
what is mean absolute deviation (MAD) and how do I find it?
Answers
Steps to find MAD:
Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] , where x denotes data points and n is the number of data points.
Step 2. Calculate distance of each data point from mean :
Distance = [tex]|x-\overline{x}|[/tex]
Step 3. Divide distance of each data point from mean by n:
MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.
A students wants to report on the number of movies her friends watch each week. The collected date are below:
0, 0, 1, 1, 2, 2, 2, 14
which measure of center is most appropriate for this situation and what's its value?
A.) Median; 1.5
B.) Median; 3
C.) Mean; 1.5
D.) Mean; 3
Answers
Answer:
A.) median; 1.5
Step-by-step explanation:
Hello!
The median is the number that is in the middle when the numbers are listed from least to greatest
0, 0, 1, 1, 2, 2, 2, 14
We can take one from both sides till there are one or two numbers left
0, 1, 1, 2, 2, 2
1, 1, 2, 2
1, 2
If there are two numbers left we add them then divide by 2 to get the median
1 + 2 = 3
3 / 2 = 1.5
The answer is A.) median; 1.5
Hope this helps!
how do you find the length of the hypotenuse when you have only the length of the altitude of the hypotensuse and a length of a leg?
Answers
Answer:
By using The Pythagorean Theorem:
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex]
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
Step-by-step explanation:
The Pythagorean theorem states that: Given a Right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides ( Here, being the length of the altitude and length of leg). That is,
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \[/tex] and hence,
/Hypotenuse/ = [tex]\sqrt\ /Length of altitude/^{2} + /Length of leg/^{2} \}[/tex]
For example, If the length of the altitude is 4m and the length of leg is 3m. Using The Pythagorean theorem, the length of the hypotenuse will be
[tex]/Hypotenuse/^{2} = /Length of altitude/^{2} + /Length of leg/^{2} \\\/Hypotenuse/ = \sqrt{/Length of altitude/^{2} + /Length of leg/^{2}} \\/Hypotenuse/ = \sqrt{4^{2} + 3^{2} }[/tex]
[tex]/Hypotenuse/ = \sqrt{16+9} \\/Hypotenuse/ = \sqrt{25} \\/Hypotenuse/ = 5m[/tex]
The length of the hypotenuse for the given example will be 5m.
This is how to find the length of an hypotenuse.
On Wednesday at camp, Samuel went for a hike at 6:30 A.M. The hike took 2 hours and 15 minutes. As soon as he got back from the hike, Samuel played volleyball for 1 hour. What time did Samuel finish playing volleyball?
Answers
Answer:
9:45 A.M.
Step-by-step explanation:
First, add the time that took him to hike:
6:30 + 2 hours and 15 minutes = 8:45 A.M.
Next, add the 1 hour that he played volleyball for:
8:45 + 1 hour = 9:45 A.M.
So, he finished playing volleyball at 9:45 A.M.
Answer:
9:45 am
Step-by-step explanation:
He went at 6:30 am to a hike.
It took him 2 hours 15 minutes
=> 6 : 30
+ 2 15
=> 8 : 45
He came back from the Hike at 8:45 am
He played volleyball for 1 hour.
=> 8 : 45
+ 1
=> 9 : 45
He finished playing volleyball at 9:45 am
what is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?
Answers
Answer:
-16, 0 real solutions. (Complex Roots)
Step-by-step explanation:
[tex]5x^2-2x=-1\\5x^2-2x+1\\A=5\\B=-2\\C=1\\(-b±√(b^2-4ac))/2a\\=\\=-2^2-4(5)(1)\\=4-20\\=-16[/tex]
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 6 doses, and each measles vaccination consists of 3 doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total of 225 doses. How many more measles vaccines did Mr. Potter give than polio? Show All Work !!
Answers
Answer:
The number of measles vaccines that Dr. Potter give than polio vaccines is 30
Step-by-step explanation:
The parameters given are;
The number of doses given in a polio vaccine = 6 doses
The number of doses given in a measles vaccine = 3 doses
The number of vaccinations given by Dr. Potter last year = 60 vaccinations
The number of doses given in the 60 vaccinations = 225 doses
Let the number of polio vaccine given last year by Dr. Potter = x
Let the number of measles vaccine given last year by Dr. Potter = y
Therefore, we have;
6 × x + 3 × y = 225.......................(1)
x + y = 60.......................................(2)
From equation (2), we have;
x = 60 - y
Substituting the derived value for x in equation (1), we get;
6 × x + 3 × y = 225
6 × (60 - y) + 3 × y = 225
360 - 6·y + 3·y = 225
360 - 225 = 6·y - 3·y
135 = 3·y
y = 45
x = 60 - y = 60 - 45 = 15
Therefore;
The number of polio vaccine given last year by Dr. Potter = 15
The number of measles vaccine given last year by Dr. Potter = 45
The number of measles vaccines that Dr. Potter give than polio vaccines = 45 - 15 = 30 vaccines.
The number of measles vaccines that Dr. Potter give than polio vaccines = 30 vaccines.
Use distributive property to evaluate the expression 5(4/1/5)
Answers
Answer:
21
Step-by-step explanation:
4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]
5 × [tex]\frac{21}{5}[/tex] = (5×21)/5
[tex]\frac{105}{5}[/tex] = 21
make u the subject of the formula
u-x/v-x=u/v²
Answers
Answer:
See below.
Step-by-step explanation:
[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]
Cross multiply and distribute.
[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]
Move all the u to the left side:
[tex]uv-ux-uv^2=-xv^2[/tex]
Factor out a u:
[tex]u(v-x-v^2)=-xv^2[/tex]
Divide:
[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]
(I factored out a negative in the second term.)
If f(x) = 4x + 15, then f(-3) = ?
Answers
Answer:
[tex]\Huge \boxed{3}[/tex]
Step-by-step explanation:
The function is given :
f(x) = 4x + 15
For f(-3), the input for the function f(x) is -3.
Replace the x variable with -3.
f(-3) = 4(-3) + 15
Evaluate.
f(-3) = -12 + 15
f(-3) = 3
The output for f(-3) is 3.
Answer: f(-3) = 3
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(-3).
We find f(-3) by plugging -3 in for x,
everywhere that x appears in the function.
So we have 4(-3) + 15.
4(-3) is -12 so we have -12 + 15 which is 3.
So f(-3) is 3.
Please answer this question now
Answers
Answer:
156.6 square yards
Step-by-step explanation:
To find the surface area of the pyramid, find the area of each surface and add them together.
formula for area of a triangle = 1/2(b·h)
1. There are three triangles with a base of 9 and a height of 9
1/2(9·9) = 40.5
Multiply by the three triangles
40.5 · 3 = 121.5
2. There is one triangle with a base of 9 and a height of 7.8
1/2(9·7.8) = 35.1
3. Add the areas of all surfaces
121.5 + 35.1 = 156.6
How many triangles exist with the given side lengths? 2mm,6mm,10mm
Answers
Answer:
Zero
Step-by-step explanation:
2+6=8 which means it can't be. It has to be a length higher than 10
