The value of x is [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
Given:
[tex] \sqrt{x} + \sqrt{x + 2} = 2[/tex]
Rearranging the radical on left side,
[tex]\sqrt{x + 2} = 2 - \sqrt{x}[/tex]
Power on both sides,
[tex](\sqrt{x + 2})^{2} = (2 - \sqrt{x})^{2} [/tex]
Simplifying the left,
[tex]x + 2 = (2 - \sqrt{x} )^{2}[/tex]
For the RHS equation, use the property of (a-b)² = (a²-2ab+b²),
[tex] = > x + 2 = {2}^{2} - (2 \times 2 \sqrt{x}) + ( \sqrt{x})^{2} [/tex]
Now calculating its powers,
[tex] = > x + 2 = 4 - 4\sqrt{x} + x[/tex]
Now sending -4√x to the LHS (left side), its sign becomes plus (+),
[tex] = > 4 \sqrt{x} = 4 + x - x - 2[/tex]
Now the +x and -x will be cancelled,
[tex] = > 4 \sqrt{x} = 4 - 2[/tex]
[tex] = > 4 \sqrt{x} = 2[/tex]
Bringing 4 to the right side, it becomes the denominator,
[tex] = > \sqrt{x} = \frac{2}{4} [/tex]
[tex] = > \sqrt{x} = \frac{1}{4} [/tex]
Now powering both sides,
[tex] = > ( \sqrt{x})^{2} = ( \frac{1}{2})^{2}[/tex]
[tex] = > x = \frac{1}{4} [/tex]
please I need help!!!!
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Slope: m
(-3,1) and (3,3)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{3-(-3)} =\frac{2}{6}=\frac{1}{3}[/tex]
Hope this helps!
8 A circle passes through the points (0, 2) and (0,8) and its centre lies on the line
x=4.
Draw a sketch and find the equation of the circle.
Step-by-step explanation:
A circle that passes through point 0,2 and (0,8) and has a center that lies on x=4 is what given.
So we know is center (4,p) for some number p,
Since the points on circumference of the circle have the same x value, then we know that the y coordinate of the center must be the midpoint of the circumferences' y coordinates.
Why?
A circle is not a function since it doesn't pass the vertical line test. And the standard form of a circle is
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
With center (0,0).
Consider the equation
[tex] {x}^{2} + {y}^{2} = 9[/tex]
The radius is 3 so two points with x coordinate 0 is
(0,3) and (0,-3). And the midpoint of them is (0,0) which is the center. Which is the defining trait of all circles.
Now, back on hand, our the midpoint of 2 and 8 is 5 so our center is
(4,5).
Now, we must find the radius. We use distance formula.
For (4,5) and (0,8).
[tex]d = \sqrt{(8 - 5) {}^{2} + ({0 - 4) {}^{2} } } [/tex]
[tex]d = \sqrt{3 {}^{2} + {4}^{2} } [/tex]
[tex]d = \sqrt{25} [/tex]
[tex]d = 5[/tex]
So our radius is 5.
So now we use the equation of center h,k.
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
H is 4
K is 5
[tex](x - 4) {}^{2} + (y - 5) {}^{2} = 25[/tex]
Above is sketch of graph.
pls help i forgot how to do this
Find the area of the parallelogram.
Answer:
3484 [tex]ft^{2}[/tex]Step-by-step explanation:
Given,
The figure is of a parallelogram
Height (h) of the parallelogram = 52 ft.
Since,
In a parallelogram opposite sides are equal so,
Corresponding base to the height of the parallelogram is = 67 ft.
Therefore,
Area of the given parallelogram
= base × height
[On substituting their values]= 67 ft. × 52 ft.
[On multiplying]= 3484 [tex]ft^{2}[/tex]
Hence,
The required area of the parallelogram is 3484 [tex]ft^{2}[/tex] (Ans)
a boy standing on a vertical cliff, 50m high is looking down an angle of depression of 20° at a car. How far is the car from the base from the cliff?
Can someone please help me, it's due in 30 mins
Answer:
explanation is in the diagram
As part of a community service project at your highshcool you are organizing a fund raiser at the neighborhood movie theater money raised will benefit a summer camp for children with special needs the admission charge is 10.00 per person, 5.50 of which is used to pay the movie theaters rental fee, the remainder is donated to the summer camp fund what are the two variables involved in this problem
Answer:
Yes it is a function. It passes the vertical line test. In other words, it is impossible to draw a single vertical line through more than one point on the V shaped graph. Any input leads to exactly one output.
The domain is the set of all real numbers. This is because we can plug in any x value leading to some specific y value. There are no holes or gaps or jumps to indicate we must restrict any given x value. The domain would not be the set of whole numbers only because values between the whole numbers (eg: decimal values like x = 2.75) work just fine.
The range is the set of y values such that y is either 0 or larger than 0. In short, the range is . Notice how any point on the V shaped graph has a y coordinate that is either 0 or larger than 0. It is impossible to get a y value that is negative.
Step-by-step explanation:
Which number is closest to 63(square root)?
A. 8.4
B. 7.2
C. 7.9
D. 6.7
Answer:
C-7.9
Step-by-step explanation:
Because the square root is actually 7.93
Answer:
C. 7.9
Step-by-step explanation:
Do the square root of 63.
[tex]\sqrt{63} = 7.93725[/tex]
Your answer isn't perfect, but it's asking for which number is the closest to the [tex]\sqrt{63}[/tex].
[tex]\sqrt{63}[/tex] ≈ [tex]7.9[/tex]
How many solutions does the system have? x y = 5 x y = 6 none one two infinite.
Answer:
none
Step-by-step explanation:
{ x=5-y
{ x=y=6
substitute the given value of x into the equation x+y=6
5-y+y=6
the equation for y
y∈⊘
The angle of elevation of the sun is 39° from the ground. A business building downtown casts a shadow that is 89 m long. How tall is the building?
[tex]\tan 39 \textdegree = \displaystyle \frac{h}{89}\\\\89\tan 39 \textdegree = h\\\\h = 72[/tex]Answer:
72 m
Step-by-step explanation:
Hi there!
Using the given information, we can construct a diagram. Please see the attached image.
We need to solve for the height of the building, or the length of the side opposite the angle that measures 39°. Given the only other piece of information is the length of its adjacent side, which is 89 m, we can use the tangent ratio to solve for the height:
[tex]\tan \theta = \displaystyle \frac{opposite}{adjacent}[/tex]
Plug in the given values:
tan 39° = h/89
89 tan 39° = h
h = 72
Therefore, the height of the building is 72 m.
I hope this helps!
Six times a number increased by 4 is no less than 50
Answer:
Number>2
Step-by-step explanation:
If number is 1 then 6×1=6
6×4=24
which is less than 50
If number is 2 then 6×2=12
12×4=48
which is less than 50
Pleaseee help me solve this and show work
Answer:
x
Step-by-step explanation:
The greatest common factor is x. This is the biggest term that each term can be divided by.
Which 2 numbers have a mean of 10 and a range of 4?
Answer:
12 and 8
Step-by-step explanation:
basic knowledge of math i guess
hope that helps love
Help on Math I need answers As soon as possible if you can :) I will add you to brainlist thingy
Answer:
[tex]-5°F, 0°F, 2°F , 5°F , \\ 13°F, 20°F[/tex]
Hope it helps you<3Simplify 5^2 • 5^4
O A. 5^8
O B. 5^6
O C. 5•8
O D. 5^2
Please help me I'm really stuck and I can't get a red if I get this wrong I will
Answer:
-0.75
Step-by-step explanation:
(0 , 22) (12, 13)
=13 - 22/12 - 0
=-9/12
=-0.75
Someone, please help
and instead of 10yd its 30yd
and instead of 20yd its 60yd
John is planning for retirement and wants to have an interest income of $3000 a year. How much Must he invest for one year at 8% interest
Answer:
240
Step-by-step explanation:
All of the following are equivalent, except _____.
2 x + x
x(2 + 1)
3 x
2 x²
Please help matimatik 10 points
Answer:
0.03
Step-by-step explanation:
Hope I helped
-Hunter Cross
Please mark Brainliest if Correct
Which function is linear?
Answer:
A,B,and D is a linear equation
Answer:
B. 4x - y + 2.5 = 0
Step-by-step explanation:
Its linear as it doesn't have any square or division.
ignore - ², division, xy being together. if so option D, C, A cancels out.
Write an equation in slope-intercept form for the line with slope -6 and y-intercept 7. Then graph the line.
Answer:
y = -6x + 7
Step-by-step explanation:
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Given: a line with a slope of -6, and y-intercept of 7
Equation: y = -6x + 7
y-intercept: (0, 7)Randomly select x-values that will help you graph the equation:
when x = -2:
y = -6(-2) + 7 [multiply]
y = 12 + 7 [add]
y = 19
coordinate: (-2, 19)
when x = 1:
y = -6(1) + 7 [multiply]
y = -6 + 7 [add]
y = 1
coordinate: (1, 1)
when x = 2:
y = -6(2) + 7 [multiply]
y = -12 + 7 [add]
y = -5
coordinate: (2, -5)
These coordinates fall on the line for the linear equation. Graph them on a coordinate plane, and they should give you the line for the equation.
Ross says a $125.95 skateboard at 40% off is cheaper than a $169.95 skateboard at 60% off. Is he correct?
Answer:
Ross isn't right.
Step-by-step explanation:
Skateboard $125.95 at 40% off is $75.57
How I got the number:
125.95/100 = 1.2595
1.2595 x 40 = 50.38
125.95 - 50.38 = 75.57
Skateboard $169.95 at 60% off is $67.98
169.95/100 = 1.6995
1.6995 x 60 = 101.97
169.95 - 101.97 = 67.98
Therefore the skateboard that is 60% off is cheaper.
.PLEASE HELP!!
Paul opens a savings account with $350. He saves $150 per month. Assume that he does not withdraw
money or make any additional deposits.
a. Write a linear model that represents the total amount of money Paul deposits into his account after m months.
b. After how many months will Paul have $2,000?
Answer:
350+150m=total money
11 months
Step-by-step explanation:
you just put in the number of months that have passed in for m and solve for total money.
After how many months will Paul have $2,000?
350+150m=2000
350-350+150m=2000-350
150m=1650
150m/150=1650/150
m=11
What is the solution to the system of equations below?
Answer:
(9,3)
Step-by-step explanation:
Answer:
x=9,y=3
Step-by-step explanation:
Simplify to a single power of 6:
Answer:
6^2
Step-by-step explanation:
When they are divided, just subtract the exponents. 5 - 3 = 2
please help with a full explanation at the bottom i’ll mark brainliest
Answer:
240 employees or A
Step-by-step explanation:
12 employees : 2 instructors
or 6:1
so there are 40 instructor
so 6*40 equals 240 employees
what does the maximum point represent in the function?
a. Y-Int
b. x=0
c. height
d.vertex
From the observation deck of a skyscraper, Bashir measures a 45^{\circ} the angle of depression to a ship in the harbor below. If the observation deck is 1057 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
2 2/3 lbs of rice cost $5.52. What is the cost of 1lb
Answer: I'm not fully sure but I think its 2.07
Answer:
$2.07 per pound
Step-by-step explanation:
we can rewrite 2 2/3 as 8/3
now we can create a proportion from cost to pounds of rice
5.52 is to 8/3 pounds as 'c' is to 1:
(5.52 ÷ 8/3) = c/1
cross-multiply to get:
8/3c = 5.52
multiply each side by 3/8 to get:
c = 5.52(3/8)
c = 2.07
I will give brainliest
Answer:
2,-5,-12,-19,-26
Step-by-step explanation:
-7n +9
-7(1) +9 = 2
-7(2)+ 9= -5
-7(3)+9 = -12
-7(4)+9 = -19
-7(5)+9 = -26
=
Гу
Which function represents g(x), a reflection of f(x) = {
(3) across the y-axis?
90
f
4
2
1
O g(x) = 2(3)
O g(x) = -2(3x
o g(x) = {(3*
O g(x) = 2(3)*
-2
-3
Next
Submit
Mark this and return
Answer:
4th answer I believe
hope this helps