First make note of the domain of the left hand side.
• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1.
• √(2 + √(x + 1)) is defined for 2 + √(x + 1) ≥ 0. If x ≥ -1, then this condition is satisfied.
• √(7 + √(2 + √(x + 1))) is defined for 7 + √(2 + √(x + 1)) ≥ 0. This condition is also satisified automatically if x ≥ -1.
Now solve the equation. Taking the square of both sides of
√(7 + √(2 + √(x + 1))) = 3
yields
7 + √(2 + √(x + 1)) = 3² = 9
√(2 + √(x + 1)) = 2
Squaring both sides again gives
2 + √(x + 1) = 2² = 4
√(x + 1) = 2
And once more,
x + 1 = 2² = 4 ⇒ x = 3
convert f(x) = 5x(x – 6) to standard form
Answer:
[tex]5x^{2} - 30x[/tex]
Step-by-step explanation:
Find the amount and the compound interest on rupees 5000 for 2 years at 6% per annum, Interest payable yearly. Answer with full steps and formula NO BAD ANSWERS REQUIRED :D
Answer:
I. Amount = 5618 Rupees
II. Compound interest = 618 Rupees
Step-by-step explanation:
Given the following data;Principal = 5000 RupeesTime = 2 yearsInterest rate = 6%To find the compound interest;
Mathematically, compound interest is calculated using the formula;
A = P(1 + r)^t
Where;
A is the future value.P is the principal or starting amount.r is annual interest rate.t is the number of years for the compound interest.Substituting into the formula, we have;
A = 5000(1 + 0.06)^2
A = 5000(1.06)^2
A = 5000 * 1.1236
A = 5618 Rupees
Next, we would determine the compound interest using the formula;
C.I = A - P
C.I = 5618 - 5000
Compound interest (C.I) = 618 Rupees
[tex]\sqrt{\frac{x-4\sqrt{x}+4 }{x+4\sqrt{x} +4} }[/tex]
Answer:
\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}
\begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)=1\:\\ \:\mathrm{Interval\:Notation:}&\:f\left(x\right)=1\end{bmatrix}
Step-by-step explanation:
asap help -------------------
Answer:
C. Complex
Step-by-step explanation:
A complex number consists of a real part (-4.8) and an imaginary part (56i)
How can you use what you know about 5(2) to find 5(-2)?
Please help
Answer:
-10
Step-by-step explanation:
5(2) or fives times two is positive ten. The rule about multiplying with negatives is a negative times a positive is a negative. We take the multiplication answer from 5(2)=10 and apple the nagative from 5(-2). Hope this helps:)
Davina uses a diagram to demonstrate the Pythagorean Theorem.
3
hypotenuse
How are the squares related to the sides of the triangle?
The area of each square is equal to the square of the length of the side to which it is adjacent.
The area of each square is equal to the length of the side to which it is adjacent.
The sum of the areas of the squares is equal to the square of the perimeter of the triangle.
The perimeter of each square is twice the length of the side of the triangle squared.
Answer:
the first option : The area of each square is equal to the square of the length of the side to which it is adjacent.
A student recorded the weight of potatoes she used for a science fair project. Read
the data. For each potato, draw an X above the line plot to show its weight.
B
E
1
Weight in
읍 유 2 / 4 1 2 3 4 2
A
Potato
С
3
D
F
G
H
2
4
pounds
Кеу
1 potato = x
4.
4
O
2
4.
4
What is the total weight of all the potatoes? Give your answer in simplest form.
3
What is the difference in weight between potatoes that weigh 4 pound and those that
weigh pound? Give your answer in simplest form.
what?
Step-by-step explanation:
I dont understand
Will give brainliest to the first person
Step-by-step explanation:
Area=b×h
= (x+5)×(x+6)
=x^2+6x+5x+30
=x^2+11x+30
If u simplify u will get (x+5)(x+6) as answer.
Keep smiling and hope u are satisfied with my answer.Have a good day :)
please answer this!!!!!
Answer: Choice A. 338 meters
Step-by-step explanation:
tan(31°)=203/x
Answer: 338 m
Step-by-step explanation:
Tan 59 = x/203
(1.66)(203)=338m
A hot air balloon is flying at an altitude of 2926 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 25°
25
°
, how far is the house from the pilot? Round to the nearest tenth.(1 point)
Choices:
The house is 1236.6 feet from the pilot.
The house is 6274.8 feet from the pilot.
The house is 3228.5 feet from the pilot.
The house is 6923.5 feet from the pilot.
Answer:
The house is 6274.8 feet from the pilot.
Step-by-step explanation:
Explain why cos(-3π/4)=cos(5π/4).
Answer:
Step-by-step explanation:
Because the cosine is a positive function from which we can deduce [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{Rule : cos(-\alpha)=cos\alpha } \\\\\\ \cos\bigg(\frac{-3\pi }{4} \bigg)=cos135=-sin45=-\frac{\sqrt{2} }{2} \\\\\\cos\bigg(\frac{5\pi }{4} \bigg)=cos225=-sin45=-\frac{\sqrt{2} }{2}[/tex] Therefore, they are equal
Rose has $83. She is saving up for a new bike. If she saves $15 per week, how much money will she have after 8 weeks?
How much money does Rose have after 8 weeks? Solve on paper, then enter your answer on Zearn.
Rose has $
after 8 weeks.
Answer:
$203
Step-by-step explanation:
15x8=$120
120+83=$203
A basketball team won 8 games and lost 7 games. Based on these results what is the probability of winning a game
the probability is made of the desired outcome divided by the total outcome.
desired = wins = 8
total = wins and losses = 15
8/15 is the probability (approx. 53%)
hope it helps :)
wo large tanks A and B are each partially filled with 100 gallons of salt water. Initially,80 pounds of salt is dissolved in the solution in tank A, and 30pounds of salt is dissolvedin the solution in tank B. The system is closed so that the wellstirred saline solution ispumped only between tanks A and B. The saline solution in tankA travels to tank Balong a pipe at the rate of 3 gallons per minute, and the salinesolution in B travels totank A at the rate of 2 gallons per minute. Write a system of IVPs that will describe theamount of salt,x1, in tank A at timetand the amount of salt,x2in tank B at timet.
At the start, it's given that x₁ (0) = 80 lb and x₂ (0) = 30 lb.
The amounts of salt in either tank change according to
dx₁/dt = (2 gal/min) (x₂/(100 - t ) lb/gal) - (3 gal/min) (x₁/(100 + t ) lb/gal)
dx₂/dt = (3 gal/min) (x₁/(100 + t ) lb/gal) - (2 gal/min) (x₂/(100 - t ) lb/gal)
To break this down a bit, consider tank A, for instance:
• solution flows in from B at a rate of 2 gal/min
• the volume of liquid in tank B after t minutes is
100 gal + (2 gal/min - 3 gal/min) (t min) = (100 - t ) gal
because the tank starts with 100 gallons of liquid, and 2 gallons are pumped in while 3 gal are pumped out each minute
• at any time t, the solution in B contains x₂ pounds of salt
• the concentration of the solution in A is then x₂/(100 - t ) lb/gal
• multiplying this by the inflow rate tells you how much salt is moving around each minute
(a) Write
[tex] {2}^{5} \div {2}^{5} [/tex]
as a single power if 2.
Answer:
2^0
Step-by-step explanation:
When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.
There are two ways to go about this problem.
The first way, the generic way, is to know that,
[tex]\frac{a^n}{a^m}=a^{n-m},a\neq0[/tex].
So,
[tex]\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}[/tex].
The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,
[tex]\frac{a}{a}=1, a\neq0[/tex]
And 1 equals to any number raised to the power of zero,
[tex]a^0=1,a\neq0[/tex]
So we just have to say that the 1 we got is rewritten as some base to the power of zero.
Since our base needs to be 2, we just simply say,
[tex]2^0[/tex].
Et Viola.
Hope this helps.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Answer:
[tex]6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.
Vertices A, B, and C form a right triangle with legs [tex]AB=3[/tex], [tex]BC=4[/tex], and [tex]AC=5[/tex]. The two legs, 3 and 4, represent the triangle's height and base, respectively.
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. Therefore, the area of this right triangle is:
[tex]A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}[/tex]
The other triangle is a bit trickier. Triangle [tex]\triangle ADC[/tex] is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are three sides of the triangle and [tex]s[/tex] is the semi-perimeter ([tex]s=\frac{a+b+c}{2}[/tex]).
The semi-perimeter, [tex]s[/tex], is:
[tex]s=\frac{5+5+4}{2}=\frac{14}{2}=7[/tex]
Therefore, the area of the isosceles triangle is:
[tex]A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}[/tex]
Thus, the area of the quadrilateral is:
[tex]6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}[/tex]
If a cylindrical vessel is 12 cm long and its surface area is 540 cm2, set up an
equation to find its radius.
Answer:
Option (1)
Step-by-step explanation:
Surface area of a cylindrical vessel is given by the expression,
Surface area = [tex]2\pi r^{2}+2\pi rh[/tex]
= [tex]2\pi r(r+h)[/tex]
Here, r = Radius of the vessel
h = Length of the vessel
By substituting the values of 'h' and surface area in the expression,
2πr(12 + h) = 540
Therefore, Option (1) will be the correct option.
Three dressers are placed side by side. One dresser is 5 feet 5 inches wide, another is 5 feet 10 inches wide, and the third is 3 feet 11 inches wide. How wide are they combined?
Answer:
15 feets 2 inches
Step-by-step explanation:
Given the widths :
1st dresser = 5 feets 5 inches
2nd dresser = 5 feets 10 inches
3rd dresser = 3 feets 11 inches
Their combined width is :
5ft + 5ft + 3 ft + 5in + 10in + 11in
13 feets 26 inches
Recall :
1 foot = 12 inches
26 inches = 26/12 feets = 2 feets 2 inches
Hence,
13 feets + 2feets 2 inches
Combined width = 15 feets 2 inches
Mary wants to buy a mobile phone; the least expensive one she's spotted so far is $15. Mary has $4.25 saved for a mobile phone. If Mary works at a rate of $2.15 per hour, how many hours (H) will she have to work in order to afford a mobile phone?
Answer:
Mary would have to work 5 hours to afford a mobile phone.
Step-by-step explanation:
$15-$4.25= $10.75 that Mary would need to save.
2.15 x 5= 10.75
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$.
If the numbers on your ticket match the three white balls and the red SuperBall, then you win the jackpot. (You don't need to match the white balls in order). What is the probability that you win the jackpot?
This question is solved using probability concepts.
A probability is given by the number of desired outcomes divided by the number of total outcomes.The order in which the balls are chosen don't matter, which means that the combinations formula is used to find the number of outcomes.Doing this, we get that:
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
------------------------------------------
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
----------------------------------------------------
Total outcomes:
3 white from a set of 10(numbered from $1 to $10).1 red from a set of 10(numbered from $11 to $20).Thus:
[tex]T = C_{10,3}C_{10,1} = \frac{10!}{7!3!} \times \frac{10!}{1!9!} = 120 \times 10 = 1200[/tex]
Desired outcomes:
The correct balls, order does not matter, so only one outcome, that is, [tex]D = 1[/tex]
What is the probability that you win the jackpot?
[tex]p = \frac{D}{T} = \frac{1}{1200}[/tex]
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
A similar question is given at https://brainly.com/question/23966554
Answer:
6/7200=1/1200
Step-by-step explanation:
[3! ways to arrange the three white balls] over [10x9x8 ways to pick three white balls and 10 ways to pick a red] =3x2x1/10x9x8x10=6/72x100=6/7200=1/1200
<(-_-)>__ConNelL__>(-_-)<
someone help me with this please!!!!
Answer:
0*i+5j
Step-by-step explanation:
The vector is given by 0*i+5j
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{4}{16}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{4}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{sin30}{2}[/tex]
[tex]\\ \sf\longmapsto sin\theta=sin15[/tex]
[tex]\\ \sf\longmapsto \theta=15°[/tex]
HELPPPP
You invest $2700 in an account at 1.5% per year simple interest. The equation
that represents this scenario is:
A(n) = 2700 + (n - 1)(0.015. 2700)
How much will you have in the account in year 5? Round your answer to the
nearest dollar.
What is the solution to the inequality x2 < 16 – 6x?
Question 7 options:
A)
x < –8 or x > 2
B)
x < –8 and x > 2
C)
–8 ≤ x ≤ 2
D)
–8 < x < 2
Answer:
D
Step-by-step explanation:
2x < 16 - 6x
Bring the variables to one side
2x < 16 - 6x
+6x +6x
8x < 16
Divide both sides by the coefficient
8x/8 < 16?8
x < 2
everything I do is not right help please
49 - 2/3 x = 32 - 1/6 x
Move the constant terms to one side and the terms containing x to the other:
49 - 32 = 2/3 x - 1/6 x
Simplify the left side, and pull out the common factor of x on the right side:
17 = (2/3 - 1/6) x
Write the fractions in terms of a common denominator. In this case, you would take
2/3 = 4/6
so that
(2/3 - 1/6) x = (4/6 - 1/6) x = 3/6 x = 1/2 x
Then the equation is
17 = 1/2 x
Multiply both sides by 2:
2 × 17 = 2 × 1/2 x
34 = x
can someone pls help me
On the last option, since you can substitute y=3x+1 into the other equations to solve for x.
tìm 2 phân số có tử số bằng 1 mẫu số là 2 số tự nhiên liên tiếp sao cho 7/59 ở giữa 2 phân số
Answer:
Bajaj Pulsar of a great time in the 7th century there where you will have the gall the subcontinent the
What is the y-intercept of the line whose equation is y=−3x ?
Answer:
y=mx+b
b is the y intercept
b=0, so 0 is the y intercept
Step-by-step explanation:
please tell me the angle of elevation
Answer:
32°
Step-by-step explanation:
The model forms a triangle. The sum of the angles of a triangle is 180°. Solve with the following equation:
? + 90 + 58 = 180
? + 148 = 180
? = 32
Therefore, the angle of elevation is 32°.
