Answers
Answer:
[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7}[/tex]
[tex]\frac{\sqrt{x+2}-3 }{x-7}[/tex]
[tex]\frac{\frac{1}{2} (x+2)^{-\frac{1}{2} }}{1}[/tex] <-- Take derivative of numerator and denominator expressions
[tex]{\frac{1}{2} (x+2)^{-\frac{1}{2} }}[/tex] <-- Simplify
[tex]\frac{1}{2}(\frac{1}{\sqrt{x+2} })[/tex] <-- Rewrite
[tex]\frac{1}{2}(\frac{1}{\sqrt{7+2} })[/tex] <-- Use direct substitution and plug in the limit x=7
[tex]\frac{1}{2}(\frac{1}{\sqrt{9} })[/tex]
[tex]\frac{1}{2}(\frac{1}3 })[/tex]
[tex]\frac{1}{6}[/tex]
Therefore, [tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]
Related Questions
Sales Geet sells televisions. He earns a fixed amount for each television and an additional $15 if the
buyer gets an extended warranty. If Geet sells 14 televisions with extended warranties, he earns
$910. How much is the fixed amount Geet earns for each television?
The fixed amount Geet earns for each television he sells is $
Answers
Answer:
50
Step-by-step explanation:
15 times 14 = 210
910 - 210 = 700
700 divided by 14 = 50
Which form do you prefer when finding the vertex of a quadratic function, vertex or standard? Why?
Answers
To which of the following sets of numbers does 725 belong?
Prime Number
Negative Number
Positive Number
Answers
It is not a negative number. It is also not a prime number because we can see it is divisible by 5 as the last digit is 5 (or 0).
In order to understand the magnitude of the effect a treatment has on a group of subjects in an experiment, the response from a treatment group is compared with the response from:
A) A different treatment group in the same trial of the experiment
B) The same treatment group in a different trial of the experiment
C) A control group in the same trial of the experiment
Answers
Solve for r (will give Brainliest)
64pi = 1/3 pi r^2 x 3
Answers
Answer:
Step-by-step explanation:
64pi = (1/3)pi r^2 *3 = pi r^2
r^2 =64
r = sqrt(64) = 8
The Smith family plans to purchase a new house in 4 years, and they want to make a down payment of 25% of the estimated purchase price of $250,000. Find the amount they need to invest to make the down payment if funds earn 12% compounded quarterly.
Answers
Answer:
The Smith Family paid $50, 820 as down payment.
Step-by-step explanation:
Total purchase price the Smith Family Paid = $231,000
Percentage of the amount paid in Down Payment = 22%
This means 22% of the total purchase price was paid in down payment.
The formula to calculate percentage in this case will be:
Percentage Price = (Amount Paid in Down Payment/Total Price) x 100%
Using the values, we get:
22% = (Amount Paid in Down Payment) / 231,000 x 100%
0.22 = (Amount Paid in Down Payment) / 231,000
Amount Paid in Down Payment = 0.22 x 231000 = $50, 820
This means, The Smith Family paid $50, 820 as down payment.
Hope this answer helps you :)
Have a great day
Mark brainliest
Some values of a linear function are shown in this table:
х
y
2
4
3
6.5
4
4
9
5
11.5
What is the rate of change of this function?
O A. -2.5
O B. 2.5
O C. 1.625
D. -1.625
Answers
the function of this answer b
please help!!! i’ll give brainliest.
no links
do not comment random things
i need help asap!!
ill give as many points i can
Answers
ihgubhuybh g bh h ygv vgbj uv bu
Answer:
4
Step-by-step explanation:
The scale factor is 4
According to the dimensions given on the right rectangular
prism, what is the volume? Fill in the blank with an answer
rounded to the nearest hundredth.
Just type the number. You do not need to type the units.
Answers
Answer:
26.67
Step-by-step explanation:
8 x 5 x 2/3 = 80/3 = 26.67
Consider the function.
f(x) = x2 + 3
Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?
Answers
Answer:
b
Step-by-step explanation:
edge 2021
The solution is:
B. f(x) domain: x ≥ 1
f–1(x) range: y ≥ 1
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, we have,
Because the two functions are inverse to each other, so we all know that the domain of f(x) will be the range of f^-1(x) and the range of f(x) will be the domain of f^-1(x)
As can be seen from the attached photo,
f(x) extends to the right of x=1, so its domain is x ≥ 1.
<=> f^-1(x) range is y≥ 1.
Therefore, we choose answer B
To learn more on function click:
brainly.com/question/21145944
#SPJ3
complete question:
Which answer pairs a possible domain restriction for f(x) and its corresponding impact on f-1(x)
identify the postulate (if any) that can be used to show the two triangles are congruent.
Answers
Answer:
Step-by-step explanation:
1) SSS
2) SAS
3) SSA
4) SSA
no, don't say Angle Side Side... :P
The lines shown below are parallel. If the green line has a slope of -3/7, what is
the slope of the red line?
10-
3
O A.
O
IN
OB.
B.
5
10
16
.5
O c. 1 /
O D. 1
102
Answers
Answer: the slope of green line = [tex]-\frac37[/tex]
Step-by-step explanation:
We know that,
If two lines are parallel then their slopes(rate of change of y with respect to x) are equal.
Given: The red line and the green line are parallel.
The slope of red line = [tex]-\frac37[/tex]
Then, the slope of green line = [tex]-\frac37[/tex] [Slopes of two parallel lines are equal]
Hence, the slope of green line = [tex]-\frac37[/tex]
Name two lines that contain point K. *
Answers
Answer:
sf and st
Step-by-step explanation:
help me I have hard times in algebra
Answers
Can I get some help with this?
Answers
Find the value of 3 + 2 • (8 – 3)
(a) 25,
(b) 13,
(c) 17,
(d) 24,
(e) 15.
Answers
Answer:
Step-by-step explanation:
3+2(8-3)
3+2*5
3+10
13
use BODMAS rule (Bracket Of Division Multiplication Addition and Subtraction).
Solve for A.
-11 + a/15= -13
Please show work.
Answers
Answer:
A/15 = -13+11
A/5=-2
A= -2*5
A = -10
Answer:
-30
Step-by-step explanation:
-11+a/15=-13
a/15=-13-(-11)
a/15=-13+11
a/15=-2
a=-2*15
a=-30
a park is 9/10 mile long and 4/5 mile wide. What is the area of the park? ENTER ANSWER AS A FRACTION FOR EXAMPLE: 4/10.
Answers
The park formed like a rectangle so :
Area = length × width
Area = ( 9/10 ) × ( 4/5 )
Area = 9 × 4 / 10 × 5
Area = 9 × 2 × 2 / 5 × 5 × 2
Area = 18 / 25
△ABC is reflected across the y-axis on a coordinate plane, resulting in △A′B′C′. If the measure of ∠A is 50 degrees, what is the measure of ∠A′?
Answers
Answer:
Reflections across the line y = x
A reflection across the line y = x switches the x and y-coordinates of all the points in a figure such that (x, y) becomes (y, x). Triangle ABC is reflected across the line y = x to form triangle DEF. Triangle ABC has vertices A (-2, 2), B (-6, 5) and C (-3, 6).
Find the volume of the L shaped composite prism, show clearly how you got your answers
Answers
9514 1404 393
Answer:
510 cm³
Step-by-step explanation:
The overall height of the front face is 9+2 = 11 cm.
The overall width of the front face is 6+4 = 10 cm.
Out of that 11 cm by 10 cm rectangle, a cutout is made in the upper right corner. The area of that cutout (in the plane of the front face) is 2 cm high by 4 cm wide.
Then the area of the front face is ...
(11 cm)(10 cm) -(2 cm)(4 cm) = 110 cm² -8 cm² = 102 cm²
The volume of the prism can be found using the formula ...
V = Bh
where B is the area of the "base" of the prism, and h is its height. Here, the "base" is the front face, and the height is the dimension marked 5 cm. The volume is ...
V = (102 cm²)(5 cm) = 510 cm³
The volume of the prism is 510 cm³.
Janine is running at 10 kilometers per hour. How long will it take Janine to travel 15 kilometers?
Answers
Step-by-step explanation:
janine is running 10 kilometer per 60 minutes
means janine runs 1 km in
=60/10
=6
since,Janine runs 1 km per 6 minutes
how much time does janine takes to run 15 km
=15 ×6
=90
Therefore Janine takes 90 minutes to run 15 km ie1 hour 30 minutes
Solve for R.
3/4r-3 1/4=49/16
Answers
Answer:
101/12
Step-by-step explanation:
3/4r-3 1/4=49/16
3 1/4=13/4
3/4r-13/4=49/16
3/4r=49/16+13/4
3/4r=49/16+52/16
3/4r=101/16
r=(101/16)/(3/4)
r=(101/16)(4/3)
r=101/12
whats the balance point for 3,7,8
Answers
Answer:
The balance point is the,number in between your set of numbers so you need to find The middle of 3 and 7, and then when you get that answer you find the number in between 8 and the,number you just found
Step-by-step explanation:
I'm not good at figuring this out myself but, I know the steps
A scale drawing of a school playground in the shape of a rectangle is shown
19 cm
School playground
8 cm
Scale
1 centimeter : 4.5 meters
What is the area, in square meters of the playground?
A. 152
OB. 684
C 1094
D3078
Answers
Answer:
b
Step-by-step explanation:
8×19= 152 [tex]cm^{2}[/tex]
1 [tex]cm^{2}[/tex] : 4.5 [tex]m^{2}[/tex]
152×4.5=684 [tex]cm^{2}[/tex]
on a piece of paper graph y>=2x-3
Answers
Answer:
Omsk internet pra mim é um vídeo de um dia
Given P(A)=0.34P(A)=0.34, P(B)=0.45P(B)=0.45 and P(A\text{ or }B)=0.517P(A or B)=0.517, find the value of P(A\text{ and }B)P(A and B), rounding to the nearest thousandth, if necessary.
Answers
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answers
Answer:
Hello! answer: c = 4
Step-by-step explanation:
triangle area formula: base × height ÷ 2 or base × height × 1/2
6 × 4 = 24
24 ÷ 2 = 12 therefore c = 4 Hope that helps!
Solve for x. Thank you
Answers
Given:
A figure of a right angle triangle.
To find:
The value of x.
Solution:
First, label the vertices figure as shown below.
In triangle ABC and DBA,
[tex]\angle BAC\cong \angle BDA[/tex] (Right triangles)
[tex]\angle ABC\cong \angle DBA[/tex] (Common angle)
[tex]\triangle ABC\sim \triangle DBA[/tex] (AA property of similarity)
We know that the corresponding sides of similar triangles are proportional.
[tex]\dfrac{BC}{BA}=\dfrac{AB}{DB}[/tex]
Substituting the given values from the below figure, we get
[tex]\dfrac{x}{8\sqrt{3}}=\dfrac{8\sqrt{3}}{12}[/tex]
[tex]x=\dfrac{8\sqrt{3}}{12}\times 8\sqrt{3}[/tex]
[tex]x=\dfrac{192}{12}[/tex]
[tex]x=16[/tex]
Therefore, the value of x is 16 and correct option is B.
Find the missing length of the triangle.
Answers
Answer:
12 =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
7.2 ^2 + 9.6 ^2 = c^2
51.84+92.16= c^2
144 = c^2
Taking the square root of each side
sqrt(144) = sqrt(c^2)
12 =c
Answer:
Let's find the hypotenuse.
7.2^2 + 9.6^2
51.84 + 92.16 = 144
√144(square root of 144) = 12, c = 12
What is the area of the triangle in centimeters squared?
Answers
Answer:
[tex]{ \tt{base = \sqrt{ {23}^{2} - {16}^{2} } = 16.5 \: cm}} \\ area = \frac{1}{2} \times base \times height \\ area = \frac{1}{2} \times 16.5 \times 16 \\ { \tt{area = 132 \: {cm}^{2} }}[/tex]