Since this is a right triangle, we know we have to use the Pythagorean Theorem: A² + B² = C² , where A and B = the legs of the triangle (which are shorter than the hypotenuse) and C = the hypotenuse.
In this isosceles triangle, A = B (because the legs are the same size) and C is 10cm longer than A and B.
Thus we get the following,
A = x
B = x
C = x + 10
We simply plug in these variables into the equation and solve for x:
x² + x² = (x+10)²
2x² = x² + 20x + 100
x² - 20x - 100 = 0
We solve for x by completing the square:
(x² - 20x + 100) - 100 = 100
(x-10)² -100 = 100
(x-10)² = 200
x - 10 = √(200)
x - 10 = 10 √2
x = 10 + 10√2 = 24
Finally,
A ≈ 24 (or 10 + 10√2)
B ≈ 24 (or 10 + 10√2)
C ≈ 24 + 10 ≈ 34 (or 10 + 10√2 + 10 = 20 + 10√2)
Mrs. Smith is shopping for a toy chest to go in her kids' playroom. She looks at the options shown.
Image_7181
If Mrs. Smith needs a toy chest that has at least 35 ft3 of storage space, which chest should she purchase
The volume of a cuboid toy chest is equal to their product of the length,
width, and height.
The correct option for the toy chest she should purchase is; Only toy chest A will provide the necessary storage space.Reasons:
The dimensions of the toy chest are;
Toy chest A;
Length = 5 feet
Width = 4 feet
Height = 2 feet
Toy chest B;
Length = 4 feet
Width = 2 feet
Height = 4 feet
Volume of Toy chest A = 5 ft. × 4 ft. × 2 ft. = 40 ft.³
Volume of Toy chest B = 4 ft. × 2 ft. × 4 ft. = 32 ft.³
The volume of the toy chest Mrs. Smith needs = 35 ft.³
The toy chest Mrs. Smith should purchase is Toy chest A, that has a volume of 40 ft.³, which can store items that with a volume of 35 ft.³
The correct option is; Only toy chest A will provide the necessary storage space
Possible question options obtained from a similar question found online are;
Either toy chest have the storage space needed
Neither has the storage space needed
Only toy chest A
Only toy chest B
Learn more about calculating volumes of various shapes here:
https://brainly.com/question/3789826
1. 543.5 = _______ ft _________ in
Answer:
uważam że nie wiem ale bym wiedział tylko muszę wiedzieć
What is 11% of 96 students
Answer:
8.7
Step-by-step explanation:
8.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.7
7 1/2 sticks of butter are needed to make 5 cakes. How much butter is needed to make one cake?
Answer:
1 1/2
Step-by-step explanation:
because when you divide 7.5 by 5 you get 1.5
Select the best answer.
sin(3pi/3 + x) =
• sinx
• -sinx
• -cosx
• cosx
Answer:
-sin x
Step-by-step explanation:
sin(3π/3+x)=sin (π+x)=-sin x
or
sin (π+x)=sin πcos x+cos π sin x=(0)cos x+(-1)sin x=0-sin x=-sin x
Please help. NEED THE ANSWER SOON AS POSSIBLE.
Answer:
y=4x-17
Step-by-step explanation: Distribute the 4(x-5)
4x-20
Then add three to both sides
y=4x-17
.45 is 1/10 of what?
Answer:
The answer is 4.5
One year, professional sports players salaries averaged $1.6 million with a standard deviation of $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players exceeded $1.1 million.
Answer:
1
Step-by-step explanation:
One year, the distribution of salaries for professional sports players had mean $1.6 million and standard deviation $0.8 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players that year exceeded $1.1 million.
z = (x-μ)/σ/√n
where
x is the raw score
μ is the population mean
σ is the population standard deviation
n = random number of samples
Mean $1.6 million and Standard deviation $0.8 million.
z = (1100000- 1600000)/800000/√400
z = -500000/800000/20
z = -500000/40000
z = -12.5
Probability value from z score table is :
P(x ≤ Z) = P(x = 1100000) = P(z = 12.5)
= 0
P(x>Z) = 1 - P(x < Z)
= 1 - 0
= 1
The approximate probability that the average salary of the 400 players that year exceeded $1.1 million is 1
In a class of 33 pupils, there were 3 girls who were in the school quiz team and 14 boys who were not in the school quiz team. (a) How many boys were there in the school quiz team if there were 17 girls in the class?
33 pupils - 17 girls = 16 total boys in the class
16 boys - 14 boys not on the team = 2 boys on the team.
Answer: 2
Solve for x.
−2x−1+3x=7
x=−2
x=−1
x = 6
x = 8
Answer:
x=8 is the answer. x-1=7 => x=7+1= 8
Whats the area and the perimeter of this shape. show calculations
Answer:
The answer is 15 cm
Step-by-step explanation:
as one square is 1 cm and there are 15 squares used for this shape then it is 15 cm
How do the expressions 5h2−3g and 3(g+h)h compare when g = 10 and h = 3?
Drag a symbol into the box to correctly complete the statement.
5h2−3g Response area 3(g+h)h when g = 10 and h = 3.
Answer:
the answer is >
Step-by-step explanation:
I took the test
If here are approximately 15000 red cabs in Hong Kong. This represents approximately 80% of the total taxis. Find the total number of taxis in Hong Kong.
Answer: 18,750
Step-by-step explanation: First you divide 80 by 100, getting .80. Then you divide 15,000 by .8, getting 18,750 cars.
Which expression finds the length of side y in this right triangle?
Answer:
y = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]
Step-by-step explanation:
Pythagorean Theorem : a² + b² = c²
19² + 8.2² = c²
c = [tex]\sqrt{19^2 + 8.2^2}[/tex]
c = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]
-Chetan K
Bạn dự định đi học thêm vào mùa hè này. Nếu đi học bạn sẽ không thể đi làm với thu nhập là 5 triệu đồng và không thể ở nhà nghỉ ngơi. Học phí là 2 triệu, tiền mua giáo trình 300 ngàn, sinh hoạt phí là 1.5 triệu. Hãy xác định chi phí cơ hội của việc đi học thêm vào mùa hè này.
Answer:
4 better inbox
Step-by-step explanation:
What is the value of x?
Answer:
41º
Step-by-step explanation:
As this is an isosceles B and D are congruent.
The sum of the angles in a triangle is 180º
Therefor
2x = 180 - 98
2x = 82
x = 41º
Can someone help me with this problem 9(n+3)<10(n+1)
[tex]9(n+3)~<~10(n+1)\implies 9n+27~<~10n+10 \\\\\\ 27~<~n+10 \implies 17 ~<~ n[/tex]
Does anyone know this?
Answer: 8.6?
Step-by-step explanation:
an elevator descends 26 feet in 6s
Answer:
Starting position of mine shaft is = 10m above ground
but,
it moves in opposite direction so it travels the distance (-350 m ) below the ground.
Total distance covered by mine shaft = 10m - (-350m)
= 10 + 350
= 360m
Now, taken to cover a distance of 6m by it = 1 minute
Time taken to cover a distance of 1m by it = \frac{1}{6\ }\min
Therefore, tie taken to a cover a distance of 360m = \frac{1}{6}\times\ 360\ =\ 60\ \min\ \
60 minutes = 1 hour
thus, in one hour the mine shraft reaches = 350 below the ground
Step-by-step explanation:
The scale for a map to actual distance is 2 centimeters to 100 miles. The driving distance on the map between Los Angeles and Las Vegas is 5.4 centimeters. What is the actual distance, in miles, between Los Angeles and Las Vegas?
[tex]\begin{array}{ccll} \stackrel{cm}{map}&\stackrel{mi}{actual}\\ \cline{1-2} 2&100\\ 5.4&x \end{array}\implies \cfrac{2}{5.2}=\cfrac{100}{x}\implies 2x = 520\implies x = \cfrac{520}{2}\implies x = 260[/tex]
Write 2 over 5 as a percent.
Answer:
40%
Step-by-step explanation:
2/5 = 40/100 = 40%
geomtry plzzzzz help. me
Answer:
N=3.5
Step-by-step explanation:
it is 3.5 because it said line p is the perendicular bisector so the triangle has to be equal. so the line ZY=XY
14/4=3.5
Just number three pls give right answer and will give brainless
Answer:
i think 34
Step-by-step explanation:
because thats the answer i got on calculator
Find m<1
(Picture included)
Answer:
m<1 =30
Step-by-step explanation:
[tex] < 1 + 117 + 33 = 180 \\ < 1 + 150 = 180 \\ < 1 = 180 - 150 \\ < 1= 30[/tex]
at the fish market, a whole fish costs $4.20. If the body costs $1 more than the tail, and the body costs $2 more than the head, how much does the head cost?
Answer:
$ 0.4
Step-by-step explanation:
if we assume head costs $ x then,
body will cost $x + 2 (2 more than head)
and tail will cost $x+1
x+x+2+x+1 = $ 4.20
or, 3x = 4.20-3
or, x= 1.20/3
therefore, x=0.4
Answer:
$ 0.4
Step-by-step explanation:
pls say the answer to me
Answer:
Sohan has read more pages and Sonali was more faster
Multiplications that give 48 as a result
Answer:
1 ×48=48
2×24=48
3×16=48
4×12=48
6×8= 48
calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii
Take the Laplace transform of both sides:
L[y'' - 4y' + 8y] = L[δ(t - 1)]
I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :
(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]
s²Y - 4sY + 8Y = exp(-s)
(s² - 4s + 8) Y = exp(-s)
Y = exp(-s) / (s² - 4s + 8)
and complete the square in the denominator,
Y = exp(-s) / ((s - 2)^2 + 4)
Recall that
L⁻¹[F(s - c)] = exp(ct) f(t)
In order to apply this property, we multiply Y by exp(2)/exp(2), so that
Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)
Then taking the inverse transform, we have
L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]
L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]
L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]
Next, we recall another property,
L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)
where F is the Laplace transform of f, and u(t) is the unit step function
[tex]u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}[/tex]
To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is
L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)
Then we find
L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))
and so we end up with
y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)
what is the answer for number 2?
Answer:
7/3
Step-by-step explanation:
integral of equation is x^3/3-6x^2/2+5x/1
the answer will be
7^3/3-3*7^2+5*7-0= 343/3-147+35= 7/3
Select the correct answer.
(-1,1)
(0,-1)
(5,-11)
(10,-21)
What is the domain of the set of ordered pairs above?
A.
{-1, 1}
B.
{-1, 0, 5, 10}
C.
{-1, 10}
D.
{1, -1, -11, -21}
