Answer:
Step-by-step explanation:
[tex]4\sqrt{3-\frac{1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\4\sqrt{\frac{3x-1}{x} } -\sqrt{\frac{x}{3x-1} } =3\\\\put ~\sqrt{\frac{3x-1}{x}} =a\\4a-\frac{1}{a} =3\\4a^2-1-3a=0\\4a^2-4a+1a-1=0\\4a(a-1)+1(a-1)=0\\(a-1)(4a+1)=0\\a=1,-\frac{1}{4}\\[/tex]
[tex]\sqrt{\frac{3x-1}{x} } =1\\3x-1=x\\3x-x=1\\2x=1\\x=\frac{1}{2}[/tex]
when a=-1/4
[tex]\sqrt{\frac{3x-1}{x} } =-\frac{1}{4} \\[/tex]
[tex]\frac{3x-1}{x} =\frac{1}{16} \\48x-16=x\\47x=16\\x=\frac{16}{47}[/tex]
[tex]\frac{(1-2x)^2 \times (x^2-9)}{-x^2-x+6} \geq 0,\\both ~numerator ~and~denominator ~are~of~same~sign.\\\frac{(1-2x)^2(x^2-9)}{-x^2-3x+2x+6} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{-x(x+3)+2(x+3)} \geq 0\\\frac{(1-2x)^2(x+3)(x-3)}{(x+3)(-x+2)} \geq 0\\(1-2x)^2\geq 0~(always)\\x\neq -3\\case.~1.\\both~numerator~and~denominator >0\\\frac{x-3}{-x+2} \geq 0\\x-3\geq 0\\x\geq 3\\-x+2> 0\\-x>-2\\x<2\\so~ solution~ is~ (-\infty,-3)U(-3,2)U[3,\infty)[/tex]
case 2.
both numerator and denominator are negative.
[tex]x-3\leq 0\\x\leq 3\\-x+2\leq 0\\-x\leq -2\\x\geq 2\\solution~is~(-\infty,-3)U(-3,3]U[2,\infty)[/tex]
Find the quotient of
x3−4x2−4x+16x−2
Answer:
x^2 - 2x - 8.
Step-by-step explanation:
Using long division:
x - 2)x^3 - 4x^2 - 4x + 16( x^2 - 2x - 8 <------ Quotient
x^3 - 2x^2
-2x^2 - 4x
-2x^2 + 4x
- 8x + 16
-8x + 16
............
Helppp quick! That’s the question^ please help guysss
Answer:
The slope represents the cost per gallon for heating oil while the y-intercept represents the fee for heating oil.
Which is a quadratic function?
A y = X-9
B y = x² +9
C y = x + 2x -9
Answer:
B y = x² +9
Step-by-step explanation:
A quadratic function must have the highest power of x being x^2 and must have an x^2 term
A y = X-9 - linear
B y = x² +9 quadratic
C y = x + 2x -9 - linear
which tessellation uses more than one type of regular polygon?
Answer:
semi-regular tessellations
Step-by-step explanation:
Last question of the day :)
Answer:
yehshjdjejrdjjej3u Rudd ixjje
Find the measure of angle A
Answer:
This is an isosceles triangle, meaning it has 2 congruent angles and one other angle.
Looking at this triangle, we know that ∠B = ∠C.
∠B = 57 degrees
All the angles in a triangle add up to 180, so you need to subtract the two values from 180 to get ∠A.
∠A = 180 - 57 - 57
= 66 degrees
Hope this helps!
Find the equation of the line with a slope of 2 and a point of (5,11)
PLEASE HELP !!!! THANKS !!!
Answer:
y=2x+1
Step-by-step explanation:
Hi there!
We are given the slope (m), which is 2, as well as the point (5,11).
We need to find the equation of the line.
There are 3 ways to write the equation of the line, but the most common type is slope-intercept form, or y=mx+b, where m is the slope and b is the y intercept
We're already given the slope (2), so we can substitute it into the equation right away
here's the equation so far:
y=2x+b
now we need to find b.
We can do this by plugging (5,11) into the equation, as the line passes through that point.
Substitute x as 5 and 11 as y
11=2(5)+b
multiply
11=10+b
subtract 10 from both sides
1=b
substitute 1 as b into the equation
y=2x+1
Hope this helps! :)
Henry is buying orange juice to make punch for a party. He can buy the juice in 32-oz cartons for $2.56 each or 48-oz cartons for $3.36 each. Which is the better value? Use the drop-down menus to explain your answer.
Answer:
the 48
Step-by-step explanation:
fairly obvious
Jonathan George and his friend spend a total of $100 at the school's fair. They spend $25 on parking, $50 for lunch, and the rest on two admission tickets? How much does each admission ticket cost, in dollars?
Answer:
$12.50
Step-by-step explanation:
$100-$25-$50=$25
$25 / 2 = $12.50
Answer:
$12.50
the answer is b the second one
What value of x will make the triangles similar by the
SSS similarity theorem?
Answer:
x=28
Step-by-step explanation:
Hi there!
SSS similarity theorem is a theorem that can determine similar triangles; the criteria for SSS~ is that the corresponding sides of the triangles create proportions which is the same as the ratio of similitude (k)
First, we need to find the ratio of similitude.
We need to assume that the triangles are similar.
15 corresponds with 20 (if you turn both triangles until they're titled the same way, you will see that 15 and 20 are the measures of the same sides on the triangles)
so that means 15/20 must make the ratio of similitude
15/20 is equal to 3/4
therefore k=3/4
as the triangle is already assumed similar, that means that 21/x will also give us a ratio that is equal to 3/4 (ratio of similitude)
therefore, 21/x=k
Since both ratios are equal to k, set 3/4 and 21/x equal to each other. This is possible via a property called transitivity (if a=b and b=c, then a=c)
3/4=21/x
cross multiply
3x=84
divide both sides by 3
x=28
So that means that 28 will make the triangles similar by SSS similarity
*you double check by doing 21/28 and see that it's also equal to 3/4
Hope this helps!
x2 - 2x + 1
show the method
Answer:
x2 - 2x +1
x2 - 1x -1x +1
(x2 - 1x) - (1x+1)
x(x-1) -1 ( x - 1)
(x - 1) (x - 1)
Which of the following equations correctly represents the distance between points (1, -1) and (-2, 2)?
Answer:
3√2
Step-by-step explanation:
d = √(x2 - x1)² + (y2 - y1)²
√(-2 - 1)² + [2 - (-1)]
√(-3)² + (3)²
√9 + 9
√18
= 3√2
George rolls a six sided die. What is the possibility that he rolls a 1 or a prime Number.
Answer:
1: 16.7%
prime number: 50%
Step-by-step explanation:
divide the numbers
Answer:
2/3
Step-by-step explanation:
There are 6 possible numbers
all of the prime numbers from 1 to 6 are
2, 3, 5 ( plus 1 because this problem is counting 1 along with the prime numbers)
That is 4 numbers
4 out of 6 numbers
so there is a 4/6 or 2/3 chance that George will roll a 1 or a prme number
4 out of every 12 children in a school are girls. What is the ratio of boys to girls in the school?
Answer:
1:3. That's the answer to this question.
5 to the power -2 * 5x is equal to 1 solve for x
5^-2 * 5x = 1
Simplify:
5^-2 = 1/25
Now you have 1/25 * 5x = 1
1/25 x 5 = 1/5
1/5x = 1
Divide both sides by 1/5 ( when dividing by a fraction, flip the fraction over an multiply)
x - 1 x 5/1 = 5
X = 5
Answer:
x = 5
Step-by-step explanation:
This statement translates into 5^(-2)*5x = 1, which by rules of exponents simplifies to:
5x x
--------- = 1, or ----- = 1
5^2 5
Cross-multiplying, we get x = 5
what is the a value of the vertex form...
y = (x - 3 )^2 - 36
Answer: I'm not smart or nun but u tryna find the graph? It's (3, -36)
Step-by-step explanation:
Kinda did it-
Activity 1 : Complete Me Directions write the statement or a reason and two column proof used two different definitions postulates theorems in geometry to support the given statement.
Paki ANSWER naman
[tex]-a-\frac{7}{8} a[/tex]
paso a paso
Step-by-step explanation:
-a-7a/8
-8a-7a/8
-15a/8
Hope it helps you
Answer:
Step-by-step explanation:
WE have to find the least common denominator and it is 8
[tex]-a =\frac{-a*8}{1*8}=\frac{-8a}{8}\\\\-a -\frac{7}{8}a=-\frac{8}{8}a-\frac{7}{8}a\\\\=\frac{-8a-7a}{8}\\\\=\frac{-15a}{8}\\\\[/tex]
If Jorge arrives and carries a stuffed animal what fraction of the children at the Larry now have stuffed animals
Answer:
erm....
Step-by-step explanation:
you are gonna have to give us a little bit more of the background info here!
am I not smart or does this make no sense
Help me with this I will give you brainlist
Answer:
3/20
Step-by-step explanation:
Of means multiply. When it says 3/10 of 4/8, it just means 3/10*4/8 which when multiplied across gives you 12/80. Which can be simplified to 3/20.
Hope this helps.
Which parallelograms have perpendicular diagonals
Answer: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. To prove a square, you must prove it is both a rectangle and a rhombus.
What is the length of the side opposite D?
units=
sin(D) =
Applying the Sine Ratio Warm up
Edge 2021
Answer:
5 units
sin(D)= 5/13
Step-by-step explanation:
i just did the question
find the value of x,y,z
Answer:
x y z are all equal to 60 because it on a line
Answer:
Step-by-step explanation:
40 + x + 80 = 180 degree (being linear pair)
120 + x = 180
x = 180 - 120
x = 60 degree
y + 120 = 180 degree (being linear pair)
y = 180 - 120
y = 60 degree
70 + 50 + z = 180 degree (being linear pair)
120 + z = 180
z = 180 - 120
z = 60 degree
x + y + z = 180 degree (being linear pair)
Note : A linear pair is a pair of adjacent angles formed when two lines intersect.
Triangle X W Y is shown. The length of side X W is 5. The length of side W Y is 11. The length of Y X is 7. What is the order of the angles from largest to smallest? Angle W, Angle X, Angle Y Angle X, Angle W, Angle Y Angle X, Angle Y, Angle W Angle Y, Angle W, Angle X
Answer:
Step-by-step explanation:
The angle opposite to longest side is the largest angle.
WY is the longest side. ∠x is the greatest
Arrange sides from largest to smallest
WY > YX > XW
∠X > ∠W > ∠Y
Answer:
angle X, angle W, and angle Y
Step-by-step explanation:
got it right on edge
19. Which of the following are examples of segments
from the figure?
BCD
D
CA
BAD
DA
AB
BD
Answer:
BCD
Step-by-step explanation:
You can easily find out by the points at the end of line. These points indicate that this is line segment.
PLEASE HELP HURYYYYYYYYY
Answer:
273 - 153.94 = 119.1 [tex]in^{2}[/tex]
Step-by-step explanation:
area of a trapezoid - area of a circle = shaded area
8. A warehouse 25 feet tall casts a shadow that is 15 feet long. At the same time of day, how
long is the shadow cast by an apartment building that is 90 feet?
Answer:
D
Step-by-step explanation:
Which of the following states the conditions that the graph meets?
Answer:
x ≤ 3
Step-by-step explanation:
The vertical line at x = 3 is solid and shaded to the left
Therefor
x ≤ 3
Answer:
x≤3
Step-by-step explanation:
There is a solid line at x =3
The graph is shaded to the left and includes the solid line
x≤3
i need help with #2 and #6 pleaseeeeee
Answer:
Area of the rectangle = x² - 3x - 10
2019
Step-by-step explanation:
Length of the rectangle = x + 2
Width of the rectangle = x - 5
Area of the rectangle = length × width
= (x + 2) (x - 5)
= x² + 2x - 5x - 10
= x² - 3x - 10
Area of the rectangle = x² - 3x - 10
C = 20t² + 135t + 3050
Where
C = the number of new cars
t = year the number of new cars was purchased
t = 0 corresponds to 1998
Find the when c = 15,000
C = 20t² + 135t + 3050
15,000 = 20t² + 135t + 3050
20t² + 135t + 3050 - 15,000 = 0
20t² + 135t - 11,950 = 0
4t² + 27t - 2390 = 0
Solve using quadratic equation
t = -b ± √b² - 4ac / 2a
= -27 ± √27² - 4(4)(-2390) / 2(4)
= -27 ± √729 -(-38240) / 8
= -27 ± √729 + 38240 / 8
= -27 ± √38969 / 8
= -27/8 + √38969/8 or 27/8 - √38969/8
= -3.375 + 197.41/8 or -3.375 - 197.41/8
= -3.375 + 24.67625 or -3.375 - 24.67625
t = 21.30125 or - 28.05125
t cannot be negative
Therefore,
t = 21.30125
To the nearest whole number
t = 21
Recall,
t = 0 corresponds to 1998
Therefore
1998 + 21 = 2019
c = 15,000 in the year 2019
Find the measure of C to the nearest degree.
Let the ∠C be : θ
From the figure, We can see that the Side which is opposite to angle θ is measuring 7 units
Also, We can notice that Hypotenuse is 11 units
As we are dealing with opposite and hypotenuse, we can clearly use Sinθ to find out the angle θ
We know that :
[tex]\bigstar \ \ \boxed{\sf{Sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}[/tex]
[tex]\implies \sf{Sin\theta = \dfrac{7}{11}}[/tex]
[tex]\implies \sf{\theta = Sin^{-1}\bigg(\dfrac{7}{11}\bigg)}[/tex]
[tex]\implies \sf{\theta = 39.52^{\circ}}[/tex]
Answer : The measure of ∠C to the nearest degree is 38°
