Answer:
[tex]x=10[/tex]
Step-by-step explanation:
We can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
The two legs are x and (x + 14) and the hypotenuse is (x + 16). Therefore:
[tex](x)^2+(x+14)^2=(x+16)^2[/tex]
Expand:
[tex]\displaystyle x^2+(x^2+28x+196)=x^2+32x+256[/tex]
Combine like terms:
[tex]2x^2+28x+196=x^2+32x+256[/tex]
Subtract the right from the left:
[tex](2x^2+28x+196)-(x^2+32x+256)=0[/tex]
Subtract:
[tex]x^2-4x-60=0[/tex]
Factor:
[tex](x-10)(x+4)=0[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+4=0[/tex]
Solve:
[tex]\displaystyle x = 10 \text{ or } x = -4[/tex]
The x cannot be negative since a side cannot measure -4. So, our only answer is:
[tex]x=10[/tex]
So, the legs are 10 and 24 with the hypotenuse being 26.
The value of a boat is depreciating at a rate of 7% per year. In 2006, the boat was worth $17,300. Find the value of the boat in 2011. Enter the exponential decay function for this situation.
The exponential decay function is y = .
In 2011 the boat will be worth $ .
Answer:
Step-by-step explanation:
[tex]V=Ar^t\\ \\ V=17300((100-7)/100)^t\\ V=17300(0.93)^{(y-2006)}\\ V(2011)=17300(0.93)^{(2012-2006)}=\$ 11192.29[/tex]
subtract 10x^2-10x+2 from -8x^2+7x-7
Answer:
-18x^2+17x-9
Step-by-step explanation:
please help giving lot of points
Answer:
They would need to sell 32 calendars to EXCEED their goal.
Explanation:
8 x 32= 256, which is more than the $250 needed!
Step-by-step explanation:
Who needs help in edge classes? $50 a class
Answer:
Step-by-step explanation:
I don’t understand so sorry I can’t help
Answer:
me plz
Step-by-step explanation:
It’s due late tonight can some pls help me pass
Answer:
Table A
Step-by-step explanation:
plugging the x values into the rule f(x)=-2x gets you
f(-3)= 6
f(-1)= 2
f(1)= -2
f(3)= -6
Can you look at the photo and help please.?
Answer:
sorry it aint werking for meeee
Step-by-step explanation:
4x+3(2x-1)-4x i need help
Answer:
x=0.5
Step-by-step explanation:
Simplifying
4x + -3(2x + -1) + -4x = 0
Reorder the terms:
4x + -3(-1 + 2x) + -4x = 0
4x + (-1 * -3 + 2x * -3) + -4x = 0
4x + (3 + -6x) + -4x = 0
Reorder the terms:
3 + 4x + -6x + -4x = 0
Combine like terms: 4x + -6x = -2x
3 + -2x + -4x = 0
Combine like terms: -2x + -4x = -6x
3 + -6x = 0
Solving
3 + -6x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -6x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -6x = 0 + -3
-6x = 0 + -3
Combine like terms: 0 + -3 = -3
-6x = -3
Divide each side by '-6'.
x = 0.5
Simplifying
x = 0.5
Jonny had ? cakes. He eats 1/2 of
his total amount of cakes. How much
cake does he have left?
Answer:
1/2 * (?)
Step-by-step explanation:
Divide (?) Cakes in half
Answer:
How many cakess did he have? impossible to answer otherwise
Step-by-step explanation:
Change x+2y=-6 into y=mx+b form
Answer:
y = -3 - x/2
Step-by-step explanation:
x + 2y = -6
You have to isolate y by minusing x on both sides
2y = -6 - x
Then you will isolate y by dividing both sides by 2
y = -3 - x/2
A group decides to go white-water rafting on a river. The map they have of the river has the scale 3 inches:7 miles. On the map, the distance between the start point and the end point of their trip is 15 inches. What is the actual distance?
Sully has completed 3/10 of a book. He has read 45 pages so far. How many pages are in the whole book?
Answer:
150 pages
Step-by-step explanation:
3/10 is equal to 0.3, or 30% of the book. We can set up an equation to find the total number of pages in the book, with x representing the number of pages.
0.3x=45
0.3x/0.3=45/0.3
x=150
A vase in the shape of a cube measures 8 inches on each side. The vase is half full of water. How many cubic inches of water are in the vase?
Answer:
64in cubes
Step-by-step explanation:
Because if the vase is half full, half of 8 is 4. To find the volume of a cube is l x W x H. So 4 x 4 x 4= 64.
HELP IMMIDIATELY MY TEACHER IS TIMING ME! 30 POINTS
Answer:
27 and 23
Step-by-step explanation:
-6
O A. Q = (1,2); P =(3,4); R = (5,6)
O B. Q = (3,5); P = (7,6); R = (5,2)
O c. Q = ( 6, 10); P = ( 14, 12); R = (10,4)
D. Q = (12, 20); P = ( 28, 24); R = (20,8)
Other
Answer:
IS A guys okay A
Step-by-step explanation:
You Suck So Much ohhhhhhhhhhhhhhhhhhhhhhhh
Solve the inequality 8c + 6 < -6c - 1
Answer:
c < - 0,5
Step-by-step explanation:
8c + 6 < - 6c - 1
// move the terms
8c + 6c < - 1 - 6
// collect the terms
14c < - 7
// divide both sides by 7
2c < -1
// divide both sides by 2
c < - 0,5
Lamar went to a baseball game. The game started at
11;50AM, and it was 3 hours 39minutes long. When did the game end?
Answer:
The game ends at 2:39
Step-by-step explanation:
11:50 + 3 hours (3:00) = 2:00
2:00+ 0:39 = 2:39
Which expression shows another way to write 36+16?
4(9)+4
4(9+4)
6(6+8)
(6+4)(6+4)
Answer:
36+16= 52
4(9)+4= 40, which does not equal 52.
4(9+4) = 52.
6(6+8) = 84, which does not equal 52.
(6+4)(6+4) = 100, which does not equal 52.
So, 4(9+4) is correct.
Let me know if this helps!
what is 240 x 343 x 234 x 123 x 23 - 89
Which is the slowest reading rate?
A. 3 pages in 9 minutes
B. 4 pages in 10 minutes
C. 5 pages in 13 minutes
D. 7 pages in 20 minutes
Answer:
A. 3 pages in 9 minutes
Step-by-step explanation:
3 & 9 are all the lowest out of those options.
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. x2 9y2
This question is incomplete, the complete question is;
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
x² + 9y² = 9
(a) About
y = 3
(b) About
x = 3
Answer:
a) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
Step-by-step explanation:
a) the volume of solid of revolution
about y=3
Using SHELL METHOD;
Volume V = 2π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) (2.3√(1-y²)) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) √(1-y²) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (( 3√(1-y²) - y(√(1-y²)) dy
= 12π[ [tex]\frac{3}{2}[/tex]π - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b)
the volume of solid of revolution
about x=3
Using SHELL METHOD;
Volume V = [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) ([tex]2.\frac{1}{3}[/tex]√(9-x²)) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) √(9-x²) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3√9-x² -x√(9-x²) dx
= [tex]\frac{4}{3}[/tex]π [ [tex]\frac{27}{2} \pi[/tex] - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
5 cm
12 cm
What is the area
of this rectangle?
And why
Answer:
60cm^2
Step-by-step explanation:
5X12=60
1.
Identify the vertex, complete the table, and graph g(x) = (x - 4)2 – 5.
y
g(x)
X
Vertex:
Answer:
g(x) = (x - 4)^2 - 5, and the vertex is (4, -5)
Step-by-step explanation:
Please, use " ^ " to indicate exponentiation: g(x) = (x - 4)^2 – 5. Comparing this to y = a(x - h)^2 + k, we see that h must be 4 and k must be -5. Thus, the vertex is (4, -5).
Make a table showing several x-values and the corresponding y-values:
x g(x) = (x - 4)^2 - 5 (x, y)
0 (-4)^2 - 5 = 11 (0, 11)
4 (4 - 4)^2 - 5 = -5 (4, -5)
work out yhe value of 6.105×10^8/3.7×10^3 give your answer in standard form
it cost 0.60 cents to run a fan for 4 hours how much does it cost to run the fan for 6 hours I need an answer asap
Answer:
$0.90
Step-by-step explanation:
So first you need to find the rate (showing how much money it costs to run for 1 hour) so you get 0.60 and divide it by 4 and its 0.15, then multiply 0.15 by 6 and get 0.90
60÷(63÷7)=
I don't understand plz help
Answer:
answer is simple
first we will solve the bracket
(63÷7)
it is 9
and then 60÷ 9
which gives 6.67
21< -4+5x Hurry I need it
Solve this system by substitution. y = 3x - 12 6x + y = 6 *Remember to write your answer as a coordinate voint (x, y).
Help me pls pls pls
Answer:
1.61
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.61
Find cosX and cosZ. Write each answer as a fraction and as a decimal. Round to four decimals places, if necessary. Fractions to reduce and use /.
Answer/Step-by-step explanation:
Recall the acronym, SOHCAHTOA.
✔️Cos X = adj/hyp (CAH)
Adj = 10
Hyp = 26
Cos X = 10/26
Simplify
Cos X = 5/13 (as a fraction)
Cos X = 0.3846 (as a decimal to 4 d.p)
✔️Cos Z = adj/hyp (CAH)
Adj = 24
Hyp = 26
Cos Z = 24/26
Cos Z = 12/13 (as a fraction)
Cos Z = 0.9231 (as a decimal to 4 d.p)
You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the
(h,k)
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y -k)² = r²
(x+ 3)² + (y + 9)² = 144
(x+ 3)² + (y + 9)² = 12²
h = -3 ; k = -9