Answers
Answer:
Step-by-step explanation:
[tex]\displaystyle\ \lim_{n \to a} \dfrac{\sqrt{2x}-\sqrt{3x-a} }{\sqrt{x}-\sqrt{a}} =\frac{0}{0} \\\\we\ can \ use\ Hospital's\ Rule\\\\\\f(x)=\sqrt{2x}-\sqrt{3x-a} \qquad f'(x)=\dfrac{2}{2*\sqrt{2x}} -\dfrac{3}{2*\sqrt{3x-a}} \\\\g(x)=\sqrt{x} -\sqrt{a} \qquad g'(x)=\dfrac{1}{2\sqrt{x}} \\\\\\\displaystyle\ \lim_{n \to a} \dfrac{\sqrt{2x}-\sqrt{3x-a} }{\sqrt{x}-\sqrt{a}} =\lim_{n \to a} \dfrac{\dfrac{2}{2*\sqrt{2x}} -\dfrac{3}{2*\sqrt{3x-a}} }{\dfrac{1}{2\sqrt{x}} }\\\\[/tex]
[tex]\displaystyle \lim_{n \to a} \dfrac{2\sqrt{x} }{\sqrt{2x}} -\dfrac{3*\sqrt{x} }{\sqrt{3x-a}} =\lim_{n \to a} \dfrac{2 }{\sqrt{2}} -\dfrac{3*\sqrt{x} }{\sqrt{3x-a}}\\\\\\=\dfrac{2}{\sqrt{2}} -\dfrac{3*\sqrt{a} }{\sqrt{2a}}\\\\\\=\dfrac{2}{\sqrt{2}} -\dfrac{3}{\sqrt{2}}\\\\\\=-\ \dfrac{1}{\sqrt{2}}\\\\[/tex]
Related Questions
11. The news reports that today's high temperature is 16°F colder than
yesterday's high temperature. Yesterday's high temperature was -2°F.
a. Write an expression to represent today's high temperature.
b. Reasoning is today's high temperature positive or negative? Why?
Answers
The expression to represent today's temperature is given by
- 2°F - 16°F = - 18°F and todays high temperature is negative as the
temperature is colder.
Temperature is a numerical expression of how hot a substance or radiation is.
There are three different types of temperature scales: those that are defined by the average translational kinetic energy per freely moving microscopic particle, like an atom, molecule, or electron, in a body, like the SI scale. Those that rely only on macroscopic properties and thermodynamic principles, like Kelvin's original definition of temperature. Those that are not defined by theoretical principles but rather by useful empirical properties of particulate matter.The temperature yesterday was -2°F . The temperature is colder today and by 16°F more cold.
Since colder temperature is denoted by negative sign and hotter temperature by the positive sign then when the temperature is colder today then we have to subtract the values to the given values.
Hence - 2°F - 16°F = - 18°F .
So todays high temperature will be a negative value.
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Suzannes school are painting a rectangular mural outside the buillding that will be 15 feet by 45 feet the students are also going to paint a smaller mural inside the building the scale is 1 unit = 3 feet
Answers
Answer:
THE LENGTH OF THE STUDENTS PAINTING=15/3=5
THE BREADTH OF THE STUDENTS PAINTING=45/3=15
AREA OF THEIR PAINTING=15×5=75
In the proof of the Law of Cosines, the equation [tex]c^2=h^2+(b-x)^2[/tex] was created using the Pythagorean theorem. Which equation is a result of expanding [tex](b-x)^2[/tex]?
A [tex]c^2=h^2+b^2-x^2[/tex]
B [tex]c^2=h^2+b^2-2bx+x^2[/tex]
C [tex]c^2=h^2+b^2+x^2[/tex]
D [tex]c^2=h^2+b^2-2bx-x^2[/tex]
Answers
9514 1404 393
Answer:
B c² = h² + b² -2bx +x²
Step-by-step explanation:
The square of the binomial can be expanded using the distributive property:
c² = h² +(b -x)²
c² = h² +(b -x)(b -x)
c² = h² +b(b -x) -x(b -x)
c² = h² +b² -xb -bx +x²
c² = h² +b² -2bx +x² . . . . . matches choice B
Find the midpoint of the line segment joining the points (-3,-2) and (-7,5)
Answers
Answer:
The midpoint is (-5,1.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -3+-7)/2 = -10/2 = -5
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
( -2+5)/2 = 3/2 = 1.5
The midpoint is (-5,1.5)
Simplify addition radical expression
√36+√64
Answers
Answer:
14
Step-by-step explanation:
√36+√64
√36=6
√64=8
6+8
14
THANK YOU
Can anyone help with this please
Answers
Answer:
None
Step-by-step explanation:
Simply, the absence of s^-1 shows the answer as none
Find the median of the following set of data: 52,84,94,102,94,89,73
Answers
Answer:
Step-by-step explanation:
the median is 89, the mode is 94, and the mean is 84
Find the value of x,
Answers
Answer: x = -7
Concept:
From the given graph, we can see that it is an isosceles triangle since the two base angles are congruent.
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.
Solve:
Given information
First Side = 7
Second Side = x + 14
Given expression deducted from the definition of an isosceles triangle
Second Side = First Side
Substitute values into the expression
x + 14 = 7
Subtract 14 on both sides
x + 14 - 14 = 7 - 14
[tex]\boxed{x=-7}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
solve 4x+y=24 and y=-4x+24 using substitution
Answers
Answer:
no solutions
Step-by-step explanation:
[tex]4x + y = 24 - - - (a) \\ y = - 4x + 24 - - - (b)[/tex]
substitute for y in (a) with (b):
[tex]4x + ( - 4x + 24) = 24 \\ 0x = 0[/tex]
Answer:
infinite solutions
Step-by-step explanation:
substitute y in the first equation
4x+(-4x+24)=24
4x and -4x cancel out
24/24=1
or solve for x, you should also get 1
Find the distance between the points (3, –8) and (0, –9).
A. 3.16
B. 17.26
C. 2.98
D. 1.06
Answers
Answer:
a. 3.16
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-9 - (-8)]² + (0 - 3)²
√(-1)² + (-3)²
√(1) + (9)
√(10)
= 3.16
How do i reflect triangle ABC if A (2,3), B (1,1), C(4,-3) over the x axis. Also rotating the triangle 90 degrees clockwise about the origin.
Answers
9514 1404 393
Answer:
see attached. red = reflected; blue = rotated
Step-by-step explanation:
The relevant coordinate transformations are ...
(x, y) ⇒ (x, -y) . . . . . reflection over the x-axis
(x, y) ⇒ (y, -x) . . . . . rotation 90° CW
In the attached figure, the red triangle A'B'C' is reflected. The blue triangle A"B"C" is rotated.
__
Additional comment
Learning to visualize these transformations can take a little practice. It can help to draw the figure on a graph, trace it on another piece of paper or transparency, then move the copy to the new position relative to the old axes.
For reflection across the x-axis, the x-axis of the copy is aligned with the original, but the copy is flipped over so the old +y axis is aligned with the -y axis, and vice versa.
For rotation 90° CW, what was the +y axis becomes aligned with the +x axis, and what was the +x axis becomes aligned with the -y axis. That is, the figure is rotated 90° CW about the origin so anything in the first quadrant is moved to the 4th quadrant.
Suppose that an individual has a body fat percentage of 14.5% and weighs 184 pounds. How many pounds of his weight is made up of fat? Round your
answer to the nearest tenth.
Answers
9514 1404 393
Answer:
26.7 lb
Step-by-step explanation:
The weight of fat is ...
14.5% × 184 lb = 0.145 × 184 lb ≈ 26.7 lb
About 26.7 pounds of his weight is made up of fat.
Anthony has a bank balance of $45. Sara has a bank balance of -$90. Sean has a bank balance of -$208. Marsha has a bank balance of $153. Which is the smallest debt?
Answers
9514 1404 393
Answer:
Marsha and Anthony
Step-by-step explanation:
Here a negative bank balance represents a debt. The larger the magnitude of the negative number, the more debt it represents. A positive bank balance corresponds to no debt.
Anthony and Marsha -- no debt . . . . smallest debt
Sara -- $90 in debt . . . . smallest non-zero debt
Sean -- $208 in debt
On those with non-zero debt, Sara has the smallest debt. Overall, Anthony and Marsha have the smallest debt: zero debt.
The meter is defined as the _______________ traveled by _______________ in absolute vacuum in 1⁄299,792,458 of a second
Answers
Answer:
1.) Distance
2.) Speed of light
Step-by-step explanation:
How would I write a number subtracted from 2 times a number is 19 as an equation?
Answers
Answer:
[tex]let \: the \: number \: be \:2 x \\ 2x - x = 19 \\ x = 19 [/tex]
This is the answer
if wrong please correct me ! :)
Help please due today
Answers
Answer:
3.2=6
4.2=8
5.2=10
the scale factor is 2
What is 3x+5=2x-2x+29?
Answers
Answer:
3+5=2−2+29
3x+5=2x-2x+293x+5=2x−2x+29
Solve
1
Combine like terms
}+293x+5=2x−2x+29
3+5=29
3x+5=293x+5=29
2
Subtract
5
55
from both sides of the equation
3
Simplify
2 more steps
Solution
=8
The answer you are looking for is
Solution/Explanation:
First, writing out the equation,
3x+5=2x-2x+29.
Next, making the equation more simple by subtracting 2x-2x, which is 0,
3x+5=0+29.
3x+5=29.
Now, subtracting 5 from both sides of the equation,
3x+5-5=29-5.
3x=24.
Finally, dividing both sides of the equation by 3,
3x/3=24/3.
x=8.
So, therefore, the final answer is x=8.
I hope this has helped answer your question. Enjoy your day, and take care!
Use the slope formula to find the slope of the line through the points (−3,−6) and (0,3).
Answers
So far we have 9/x, now on to the x coordinates. -3 and 0, -3 + 3 = 0
9/3 is the slope
now simplify and the slope is 3
What is the slope of the line represented by the equation y = 4/5x-3?
Answers
Answer:
The slope is 4/5
Step-by-step explanation:
The slope in a y=mx+b equation is always in front of the x. Remember that! :)
Step-by-step explanation:
4/5.
this equation is slope in intercept form following the template of y=mx+b .m is your slope and by looking at the corresponding part tell you 4/5 is the slope
You need to make 48 servings of roast beef gravy. Each serving takes .75 cups of brown stock. How many quarts of brown stock do you have to make
Answers
Answer:16 q
Step-by-step explanation:
How can I multiply this without a claculator 4103 x 25?
Answers
You just mutiple 4103×25and it =102575
X 25
———-
The answer is 102575!
state the domain: A= {(-3,2), (5,4), (7,-3)}
Answers
The required domain is [tex]\{-3,5,7\}[/tex].
Given:
A set of ordered pairs is:
[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]
To find:
The domain of the given set of ordered pairs.
Solution:
Domain is the set of input values.
In the set of ordered pairs [tex](x,y)[/tex], then the set of all the [tex]x[/tex]-values is domain and the set of all the [tex]y[/tex]-values is range.
We have,
[tex]A=\{(-3,2),(5,4),(7,-3)\}[/tex]
In the above set of ordered pairs, the x-values are [tex]-3,5,7[/tex].
[tex]Domain=\{-3,5,7\}[/tex]
Therefore, the domain of the given set of ordered pairs is [tex]\{-3,5,7\}[/tex].
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3. Multiply: (x + 8)(x - 12)
Please show work
Answers
Answer:
x^2-4x-96
Step-by-step explanation:
x^2-12x+8x-96
=x^2-4x-96
Answer:
[tex] {x}^{2} + 20x + 96[/tex]
Step-by-step explanation:
[tex](x + 8) \times (x - 12)[/tex]
➡️ [tex]x \times (x + 12) + 8(x - 12)[/tex]
➡️ [tex] {x}^{2} + 12x + 8x + 96[/tex]
➡️ [tex] {x}^{2} + 20x + 96[/tex]
A fine jewelry store leased a space at the mall with a base rent of $1,800 a month, plus 4% of all sales over $200,000. If the gross sales were $325,000, what was the total amount of rent paid by Heinz Fine Jewelry at the end of the year?
Answers
Answer:
So, first, we have to establish how much the base rent ends up costing. So to find that, we do 1,800x12=21,600. So the base rent is $21,600. Then, we add the 4% of sales which is 125,000x0.04=5,000. So, we add $21,600 with $5,000 and we get a final answer of $26,600 owed at the end of the year :)
Step-by-step explanation:
Find the area of each shaded region. Show your reasoning.
Answers
maybe we could answer if there waas a pic=]
Can anyone help?
Plis
Answers
Answer:
B. 50%
Step-by-step explanation:
7/20 = 35%
35% + 15% = 50%
100% - 50% = 50%
white → 15%
red → 7/20 · 100% = 35/100 · 100% = 35%
blue → 100% - 35% - 15% = 50%
Answer: B)
Help! given 2(x-9)=-10 prove x=4 with statements and reasons
Answers
Step-by-step explanation:
Proof:
2 ( x - 9) = - 10 when x = 4
2 ( 4 - 9) = -10
8 - 18 = -10
-10 = -10 ..........hence proven
Reasons
- When you replace X with 4, you can clearly see that the equation is equal to -10.
sorry I couldn't answer accurately, but I hope this helps
help with this plzzzzzzz
Answers
Answer:
x = 6
Step-by-step explanation:
According to the rules of segment addition, AB+BC=AC.
Since the length of AB is x+5, length of BC is 2x+10, and total length of AC is 33, we can create the equation: (x+5) + (2x+10) = 33.
To solve, we combine like terms: 3x + 15 = 33.
Subtract 15 from both sides: 3x = 18.
Divide both sides by 3: x = 6.
Identify a pair of supplementary angles in the diagram below.
Answers
Answer:
a & b
Step-by-step explanation:
Supplementary angles add up to 180°
Angles a and b are both on a straight line which the sum is 180°
I hope this helps.
Solvin
Is 5.787787778... a rational or irrational number?
Explain.
Answers
Answer:
For a number to be rational, it must:
-terminate (0.5) or repeat (0.3333...)
-be able to be written as a fraction
If a number does not meet this criteria, then it is irrational. Thus, 5.787787778... is irrational.
Step-by-step explanation:
BRAINLIEST, PLEASE!