Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
__
SquaringThe usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.
[tex]\sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}[/tex]
The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
__
SubstitutionAnother way to solve this is using substitution for one of the radicals. We choose ...
[tex]u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}[/tex]
Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
_____
Additional comment
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
176.98 round to the nearest cent
Answer:
See answer(s) below
Step-by-step explanation:
$ 176.98 to nearest cent is $ 176.98
176.98 cents rounded to the nearest cent is 177 cents
Describe the the cross section
A.Square
B.Pentagon
C.Trapezoid
D.Cube
Answer:
A. Square
Step-by-step explanation:
Hmm yes looks very much like a square if you ask me. This is right!!
The first image for the question and the other image for the example please I want the correct answer.
it is 2
Step-by-step explanation:
Answer:
the most appropriate answer will Be 2
Step-by-step explanation:
be happy
Sarah can make 5 tables in 3 days, how many can she make in 21 days?
Answer
the answer is 105
Step-by-step explanation:
multiply 5 and 21
answer is 105
Step-by-step explanation:
multiply 5x21
What is the surface area of a rectangular prism with a height of 5 cm, length of 5.4 cm, and width of
2.4 cm?
The surface area is
3х + 4y = 5
6х + 8y = 10
3/4 fraction plus 7/12 fraction - (-4)
I WILL GIVE U 40 POINTS
answer:
[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)
A piece of machinery depreciates $7000 the first year,
$6800 the second year, and $6600 the third year. If the
rate of depreciation is constant, what is the amount of
depreciation of the piece of machinery in the sixth year?
Answer:
6000 in the 6th year 39000 total
Step-by-step explanation:
depreciates 200 per year
7000 6800 6600 6400 6200 6000
Movies at the rental store are $3.75 each. Snacks and drinks are $1.89 each. Round each amount to the nearest dollar to estimate the cost to rent 3 movies and buy popcorn, a soda, and a candy bar.
Answer:
$14.00
Step-by-step explanation:
First you round 3.75 to 4.00 because 7 is greater than 5 so it would turn the 3 to 4 than add the zeros it's 4.00. Second You multiply by three so 4.00 × 3 you will get 12.00. Than you round 1.89 to 2.00 because 8 is greater than 5 so it would turn to the 1 to the 2 than add the zeros it's 2.00. Finally you add them together and get $14.00
There are three different size bags of the same dog food shown below with the price for each bag. Based on the price per ounce, order the bags from
least expensive to most expensive.
= 32oz for $7 37
= 48oz for $9.50
= T2oz for $17.99
Answer:addaddition
Step-by-step explanation:
just adddd all
Choose the correct simplification of (3xy6)2(y3)3. 9x2y21 6x2y21 9x2y14 6x2y14
Answer:14
Step-by-step explanation: i did the math probly wrong but i made an educated guess
A square plot is 64 m^2 ..find its length..
Answer:
Length: 8 m
Explanation:
square area: length²
Here:area: 64So find Length:length² = 64length = ±√64length = ±8As length is positive, length = +8
Isabel works for a company that makes toys. She is trying to figure out what types of toys kids enjoy
playing with most. She started with a survey that asks about whether kids liked dolls or trains. She
surveyed 80 kids. Of the kids who don't like dolls, 30% more kids like trains than don't like trains.
out the rest of his table.
The type of toy the kids enjoyed the most is the doll.
Evaluation of toys enjoyed mostThe total number of kids evaluated = 80
The percentage of kids that like train = 30%
The percentage of kids that like doll = 70%
30% of 80 = 30/100×80
= 2400/100
= 24
70% of 80 = 70/100×80
= 5600/100
= 56
Therefore, the type of toy the kids enjoyed the most is the doll.
Learn more about percentage here:
https://brainly.com/question/24304697
#SPJ1
Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,0) of this point in which:
(a) r> 0, 2x <0 < 4x.
(b) r<0,0<0<2R.
(c) r> 0, -2x <0<0.
(10,pi/3)
Step 1: Plotting the Point
Make a polar coordinate system.
It looks like this ( look at the first photo)
Step 2: Graph the polar function
r=10.
Here since our first coordinate is 10, our radius of our point will be 10.
This basically means we will have a circle with a radius of 10. ( look at the second photo).
Step 3: Look for the angle pi/3,
So that how u graph polar coordinates.
Next, a polar form can have multiple representations.
a. Here we want a radius of to be positve, so our r will stay 10.
We want our angle to lie between 2 pi and 4 pi.
So we just add 2 pi to pi/3.
[tex] \frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3} [/tex]
So another angle is
[tex](10, \frac{7\pi}{3} )[/tex]
B. We want r to be negative so
[tex]10( - 1) = - 10[/tex]
And we want our angle to be in between 0 and 2 pi. so we add pi to our angle.
[tex] \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} [/tex]
So our new representation is
[tex]( - 10, \frac{4\pi}{3} )[/tex]
C. Finally, we want our r to be positvr and our angle to be negative and in between -2pi and 0.
So we just subtract 2 pi.
[tex] \frac{\pi}{3} - 2\pi = \frac{\pi}{3} - \frac{6\pi}{3} = - \frac{5\pi}{3} [/tex]
So our new representation is
[tex](10, - \frac{5\pi}{3}) [/tex]
A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different type from the rest. How many different bags of 3 can you make
Answer:
[tex]165[/tex].
Step-by-step explanation:
Since repetition isn't allowed, there would be [tex]11[/tex] choices for the first donut, [tex](11 - 1) = 10[/tex] choices for the second donut, and [tex](11 - 2) = 9[/tex] choices for the third donut. If the order in which donuts are placed in the bag matters, there would be [tex]11 \times 10 \times 9[/tex] unique ways to choose a bag of these donuts.
In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type [tex]3 \times 2 \times 1 = 6[/tex] times.
For example, if a bag includes donut of type [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex], the count [tex]11 \times 10 \times 9[/tex] would include the following [tex]3 \times 2 \times 1[/tex] arrangements:
[tex]xyz[/tex].[tex]xzy[/tex].[tex]yxz[/tex].[tex]yzx[/tex].[tex]zxy[/tex].[tex]zyx[/tex].Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count [tex]11 \times 10 \times 9[/tex] by [tex]3 \times 2 \times 1 = 6[/tex] to find the actual number of donut combinations:
[tex]\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].
Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of [tex]3[/tex] objects from a set of [tex]11[/tex] distinct objects:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].
Tom and his sister both decided to get part-time jobs afterschool at competing clothing stores. Tom makes $15 an hour and recieves $3 in
commission for every item he sells. His sister makes $7 an hour and recieves $5 in commission for every item she sells. How many items
would each of them have to sell to make the same amount of money in an hour?
Answer:
Each of them would sell four items.
Step-by-step explanation:
Tom - 15+3+3+3+3= $27
His sister - 7+5+5+5+5= $27
How many distinguishable permutations are there of the letters in BUBBLE?
There are 6 letters, hence 6! = 720 total permutations of BUBBLE. But there are 3 indistinguishable copies of B, so we divide by the number of ways we can rearrange them, 3! = 6. Then there are
6!/3! = 720/6 = 120
distinguishable permutations of BUBBLE.
A. Transform F using the rule (x, y) → (-x, y)
B. Describe the transformation precisely.
C. Does the transformation result in a a congruent figure?
Answer:
A: Use these points to plot the shapes reflection (-3,4) (-3,6) (-5,6) (-7,4)
B: The transformation would be described as a reflection over the y axis
C: The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width
Step-by-step explanation:
So our plots from the figure are: (3,4) (3,6) (5,6) (7,4)
This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.
So using the rule (x, y) → (-x, y) are new points would be:
(-3,4)
(-3,6)
(-5,6)
(-7,4)
Solve the inequality 2c/3 + 1 > 7
Answer:
c > 9
Step by Step explanation
What is the domain of the relation below?
Domain are the x values
{-4,-2,0,2}
Answer:
{-4, -2, 0, 2]
Step-by-step explanation:
THIS IS THE SET OF X-VALUES:
Domain is {-4, -2, 0, 2]
1. If a triangle of area 95 square units has a height of length 19 units, calculate
the base of the triangle.
True or False: A scalene obtuse triangle has sides of all different lengths, and it
contains one obtuse angle.
a. True
b. False
Answer:
All three sides and angles are different in measurement.
Step-by-step explanation:
A litter of puppies has some male and
some female puppies. This can be
described with the following equation.
L = m + f
Solve the equation for the number of
female puppies, f.
Enter the variable that belongs in the green box.
f = [?] - [
Which scenario shows an example of conditional probability?
a
The probability of getting heads when flipping a coin five times
b
The probability of winning a raffle
c
The probability of pulling a red marble out of a bag that contains one red marble and nine blue marbles
d
The probability of it raining when it is cloudy
Answer:
Id say D but im noot 100% positive so im sorry if its wrong
Step-by-step explanation:
Hi pls guys uf you know pls help me this is my last chance ok this theta pls guys help me
The table shows the colors of the cars sold from a dealership over the last month
Based on this information, which prediction about next month's car sales is
most reasonable?
Answer:
The anser is B
Step-by-step explanation:
There are twice as many silver cars as blue cars
12 x 2 = 24 24 / 12 = 2
Fu Da spent a whole day traveling. 5/8 of the journey was spent by the airplane and 1/4 of the remainder was by the train. He spent 6 3/4 h on the bus journey.
a) How long did Fu Da spend on the train journey?
b) How much longer did Fu Da spend on the airplane than on the bus?
Answer:
A) 13.5 Hours
B) 27 Hours
Step-by-step explanation:
So the total journey was 54 hours.
5/8 of that would be 33 and 3/4 hours or how long the airplane journey was.
1/4 would be 13 and a half hours or how long the train journey was
And the remaing amount was the 6 3/4 hours which was the bus journey
So the answers are Fu Da spent 13 and a half hours on the train journey and he spent 27 more hours on the plane than the bus
Someone please help me!!
98
41
A. Isosceles
B. Scalene
C. Acute
D. Right
E. Obtuse
F. Equilateral
A) Isosceles
E) Obtuse
Step-by-step explanation:Ways to Define a Triangle
Triangles can be defined in two ways: by angles and by sides. Equilateral, isosceles, and scalene are based on side length. Acute, right, and obtuse are based on angle measurements. Triangle may only fall under one category for side length and one for angle measure (2 categories total).
Side Length
First, let's define equilateral, isosceles, and scalene.
Equilateral - All 3 sides of the triangle are congruent (equilateral are always acute angles).Isosceles - 2 of the sides are congruent.Scalene - There are no congruent sides; each side has a different length.The triangle above has 2 congruent sides as shown by the tick marks on the left and right sides. This means the triangle is isosceles.
Angle Measurements
Now, let's define acute, right, and obtuse.
Acute - All 3 angles are less than 90 degrees; all angles are acute.Right - 1 of the angles is exactly 90 degrees; it has a right angle.Obtuse - 1 of the angles is greater than 90 degrees; there is an obtuse angle.The largest angle in the triangle is 98 degrees, which is obtuse. This means that the triangle is obtuse.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.
[tex]\large\bold{{Question :}}[/tex]
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.
[tex]\large\bold\red{\underline{Solution :-}}[/tex]
Here, O is the center of the circle.
⟼ Given :
OQ = 25 cmPQ = 24 cm⟼ To Find : We have to find the radius OP.
Since QP is tangent, OP perpendicular to QP.
(Since, Tangent is Perpendicular to Radius ⠀⠀⠀⠀⠀⠀⠀at the point of contact)
So, ∠OPQ=90°
⟼ By Applying Pythagoras Theorem :
OP² + RQ² = OQ²
OP² + (24)² = (25)²
OP² = 625 - 576
OP² = 49
OP = √49
OP = 7 cm
Hence, The Radius is 7 cm
⠀⠀
⠀
-MissAbhiHere after drawing the diagram for the question we came to knew that the length of line OQ is 25 cm and length of line PQ is 24 cm.
(Angle OP is of 90°)So line OQ is hypotenuse , line OP is perpendicular , line PQ is base.
Let us simply apply the concept of Pythagoras theorem to find out the length of line OP.
Base (PQ) = 24 cm Hypotenuse (OQ) = 25 cm Perpendicular (OP) = ?[tex]: \: \implies \: \sf{(Hypotenuse) {}^{2} \: = \: (Base) {}^{2} \: + \: (Perpendicular) {}^{2} } \\ \\ : \: \implies \: \sf{(OQ) {}^{2} \: = \: (OP) {}^{2} \: + \: (PQ) {}^{2} } \\ \\ : \: \implies \: \sf{(25) {}^{2} \: = \: (OP) {}^{2} \: + \: (24) {}^{2} } \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25) {}^{2} - \: (24) {}^{2}} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25 \times 25) - \: (24 \times 24)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (625) - \: (576)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 625 - \: 576} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 49} \\ \\ : \: \implies \: \sf{OP \: = \: \sqrt{49} } \\ \\ : \: \implies \: \red{\bf{OP \: = \: 7}}[/tex]
★ Therefore,
Radius of the circle is of 7 cm.A bag contains 5 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be blue?
Answer:
4.4%
Step-by-step explanation:
The overall probability is the product of the individual probabilities.
Total number of marbles: 15
Original number of blue marbles: 6
First drawing (6 blue and 15 total):
p(blue) = 6/15 = 2/5
Second drawing (5 blue and 14 total):
p(blue) = 5/14
Third drawing (4 blue and 13 total):
p(blue) = 4/13
p(blue followed by blue followed by blue) = 2/5 × 5/14 × 4/13 = 40/910 = 4/91
p(blue followed by blue followed by blue) = 4/91 = 0.043956... = 4.4%
Find the shaded area. Choose the letter for the best answer.
I’m checking if I’m correct
Answer:
H. 36 sq inches
Step-by-step explanation:
area of rectangle
= 4 x 6
= 24
area of triangle
= 1/2 x (10-6) x (4+2)
= 12
total shaded area
= 24 + 12
= 36 sq inches
so answer is H
hope this helps!