Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{x}+1 }{x-\sqrt{x}+1 }=\frac{\sqrt{x}+1}{(x+1)-\sqrt{x}}\\\\=\frac{(\sqrt{x}+1)([x+1]+\sqrt{x})}{([x+1]-\sqrt{x})+([x+1)+\sqrt{x}])}\\\\=\frac{\sqrt{x}*x+\sqrt{x}*1+\sqrt{x}*\sqrt{x}+1*x+1*1+1*\sqrt{x}}{(x+1)^{2}-(\sqrt{x})^{2}}\\\\\\=\frac{x\sqrt{x}+\sqrt{x}+x+1+x+\sqrt{x}}{x^{2}+2x+1-x}\\\\=\frac{x\sqrt{x}+2\sqrt{x}+2x+1}{x^{2}+x+1}\\\\[/tex]
A father is 51 years old and his son is 19. How many years ago was the father 5 times his son's age?
Answer:
x=11
Step-by-step explanation:
51-x-5*19= -5x
51-5*19= -4x
4x=5*19-51
4x=95-51
4x=44
x=11
Step-by-step explanation:
let x year ago son age was 5 time his father age.
age of son before x year = 19-x
age of father before x year = 51-x
NOW
according to the question
5(19-x) =51-x
95-5x =51-x
95-51 = -X-5x
44 = 4x
x=11
so your ans is 11years ago
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
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°.
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]
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 :)
can someone explain step by step how to get the answer?
Answer: x³+8x²+11x-20
Step-by-step explanation:
To find which polynomial has the roots of -5, -4, and 1, we want to first put them into an equation.
-5 is the same as x+5=0
-4 is the same as x+4=0
1 is the same as x-1=0
Now that we have the factors, we can multiply them together.
(x+5)(x+4)(x-1) [FOIL]
(x²+4x+5x+20)(x-1) [combine like terms]
(x²+9x+20)(x-1) [FOIL]
x³-x²+9x²-9x+20x-20 [combine like terms]
x³+8x²+11x-20
Therefore, x³+8x²+11x-20 is the correct polynomial with those roots.
can someone pls help me
On the last option, since you can substitute y=3x+1 into the other equations to solve for x.
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
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The diagram above shows the quadrant OPQ centred at O.
ORST is a square.
Given OP = 10 cm and OR = 7 cm.
Calculate the area of the shaded region, in cm². State the answer in pi.
Answer:
the square is 49cm^2
A=pi(r)^2/4
A=pi(10)^2/4
A=100pi/4
A=25pi
25pi -49
29.5398
Step-by-step explanation:
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.
Solve 2x−10y=18 for x.
Answer:
x = 5y + 9
Step-by-step explanation:
2x - 10y = 18
(2x - 10y) + 10y = 18 + 10y
2x - 10y + 10y = 10y + 18
2x = 10y + 18
x = 5y + 9
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
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:
Use the grouping method to factor this polynomial.
x2 + 2x2 + 12x + 24
O A. (x2 +12)(x+2)
O B. (x2 +6)(x+2)
C. (x² + 2)(x+6)
O D. (x2 + 2)(x+12)
Answer:
A. (x² + 12)·(x + 2)
Step-by-step explanation:
Question; Factor x³ + 2·x² + 12·x + 24, using the grouping method
The given polynomial is presented as follows;
x³ + 2·x² + 12·x + 24
Using the grouping method, we have;
(x³ + 2·x²)( + 12·x + 24)
Which gives;
x²·(x + 2) + 12·(x + 2)
Therefore, we get;
(x² + 12)·(x + 2)
The correct option is A. (x² + 12)·(x + 2).
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
[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:
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
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Answer:
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TIME REMAINING
43:02
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Mark this an
the answer of this question is (-2,2)
Write an equation in slope-intercept form for the line with slope -4 and y-intercept - 1. Then graph the line.
Answer:
I posted the steps in my photos for an answer.
Show that (x+1)(x+3)(x+5) can be written in the form ax3+bx2+cx+d where a b c and d are all positive intergers
Answer:
Step-by-step explanation:
(x+1)(x+3)(x+5), multiply first two parenthesis
(x² +3x +x +3)(x+5), combine like terms
(x² +4x +3) (x+5), multiply the parenthesis
(x³ +5x² +4x² +20x +3x +15), combine like terms
x³ +9x² +23x +15 is in the form ax³ +bx² +cx +d
a=1, b=9, c=23, d=15 are all positive integers
NEEDED ASAP will MARK THE CORRECT ONE
Answer:
→ m∠ABE + m∠EBC =180°
→ m∠ABF + m∠FED + ∠DBC =180°
→ ∠ABF ≅ ∠EBC
→ ∠ABE ≅ FBC
~OAmalOHopeO
convert f(x) = 5x(x – 6) to standard form
Answer:
[tex]5x^{2} - 30x[/tex]
Step-by-step explanation:
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
Instructions: Find the missing side. Round your answer to the nearest
tenth.
22
х
50°
X =
Answer:
x = 16.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 50 = x/22
22 sin 50 =x
x=16.85297
To the nearest tenth
x = 16.9
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.
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]
it's emergency pls.
Answer:
see above there is the answer sorry for rough
Please answer this!!
Answer:
BC = 6.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta =opp /adj
tan C = AB / BC
tan 45 = 6.8/ BC
BC = 6.8 / tan 45
BC = 6.8 / 1
BC = 6.8
Answer: Choice D. 6.8
Step-by-step explanation:
45,45,90 triangles, memorize that the short sides are equal to each other in length and are [tex]\frac{1}{\sqrt{2} }[/tex] the length of the long side.
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.
