The limit of the expression [tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]a s x approaches 3 is -1/2
How to determine the limit?The expression is given as:
[tex]f(x) = \frac{x^2 - 12}{x^2 - 3}[/tex]
As the variable x approaches 3, the limit is represented as:
[tex]\lim_{x \to 3} f(x)[/tex]
So, we have:
[tex]\lim_{x \to 3} = \frac{3^2 - 12}{3^2 - 3}[/tex]
Evaluate the exponents
[tex]\lim_{x \to 3} = \frac{-3}{6}[/tex]
Evaluate the quotient
[tex]\lim_{x \to 3} = -\frac{1}{2}[/tex]
Hence, the limit of the expression as x approaches 3 is -1/2
Read more about limits at:
https://brainly.com/question/5313449
#SPJ4
Answer:
B. 7/3
Step-by-step explanation:
Took the final test and this was the correct answer
Solve for x.
x =
30
27
33
Answer:
the answer is 27
Step-by-step explanation:
3x+9+90=180
3x+99=180
3x=180-99
x=81/3
x=27
Answer:
Step-by-step explanation:
3x + 9 + 90 = 180
3x + 99 = 180
3x = 81
x = 81/3
x = 27
3(27) + 9 = 81 + 9 = 90
What is the slope of the line that passes through the points (-9,-5) and
(-1,-9)? Write your answer in simplest form.
Answer:
slope= (y2-y1)/x2-x1
Step-by-step explanation:
(-5-(-9))/(-9-(-1))
=-1/2
[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]
-1/2
Step-by-step explanation:
To findSlope
Given[tex] \sf let \: ( - 9, - 5) = (x_1,y_1) \\ \\ \sf ( - 1, - 9) = (x_2,y_2)[/tex]
Solution[tex] \sf Slope(m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Substituting the values
[tex] \sf \implies m = \frac{ - 9 - ( - 5)}{ - 1 - ( - 9)} \\ \\ \\ \sf \implies m = \frac{ - 9 + 5}{ - 1 + 9} \\ \\ \\ \sf \implies m = \frac{ - 4}{8} \\ \\ \\ \sf \implies m = - \frac{1}{2} [/tex]
1
maining:
out of
question
Is it a Function?
Instructions: Determine whether the following relationship is a function.
You're headed to the bank with two friends to exchange your American dollars for the South
African currency rand, for an upcoming trip to South Africa. You and one friend both plan to
exchange $100. If you go first and then your friend goes right after you, think about what you
would expect about the amount of rand you both get back. Does the relationship between dollars
turned in and rand received represent a function?
Is it a function? No
Check
The relationship between dollars delivered and rand received represents a function.
What is a function?Corresponds to a mathematical relationship between two variables, x and y, where the set of x values is associated with a y value. Being expressed by the formula:
y = f(x)Therefore, in the exchange rate question, x is the independent variable, that is, the value of $100, and y will correspond to the dependent variable, which is the value of rand that will be received in relation to the dollar.
Find out more about function here:
https://brainly.com/question/2833285
#SPJ1
Please help!! Last question!
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
There is no flaw in the steps. Hence, the correct option is A.
Learn more about Midpoint:
https://brainly.com/question/5127660
#SPJ1
Help...
25 pts and will give BRAINLIEST!
Answer:
hope u understand...........
Work out the equation of the line which has a gradient of 1/2 and passes through the point (2, -5)
Answer:
y=½x-6
Step-by-step explanation:
m= ½
equation of the line: y-y1=m(x-x1)
y+5=½(x-2)
y=½x-6
Answer:
[tex]y =\dfrac{1}{2}x-6[/tex]
Step-by-step explanation:
Point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]
where:
[tex]m[/tex] = slope (gradient)[tex](x_1,y_1)[/tex] = point on the lineGiven:
Gradient (m) = ¹/₂Point = (2, -5)Substitute the given values into the formula:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}[/tex]
It took Shane 2 hours to drive 120 miles. If she continues at this rate, how far will she travel in 4 hours and 30 minutes?
Answer:
270 miles
Step-by-step explanation:
If she drove 120 miles in 2 hours, that means she drives at 60 miles per hour. 4 hours and 30 minutes can be seen as 4.5, since 30 minutes is half an hour. So then you multiply 60 by 4.5 and get 270.
I don’t understand this, can someone please explain and show the answers please
your answer would be A. 122/27
41
The table shows a bacterial population y after a days.
Day, x
0 1
2
3
4
Population, y 5 35 245 1715 12,005
a. Write an exponential function that represents the population.
y=|lx|
b. Find the population after 5 days.
There are
bacteria after 5 days.
An exponential function that represents the population is y = 5 (7)ˣ. And the population after 5 days will be 84035.
What is an exponent?The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.
The table is shown.
The exponential equation is given as
y = abˣ
Then at x = 1, y will be 35. Then we have
35 = ab ...1
Then at x = 2, y will be 245. Then we have
245 = ab² ...2
On solving equations 1 and 2. Then we have
a = 5 and b = 7
Then the exponential function will be
y = 5 (7)ˣ
Then the population after 5 days will be
y = 5 (7)⁵
y = 5 x 16807
y = 84035
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ1
The volume of a sphere is 9,198.m3 To the nearest ,meter what is the radius of the sphere? Use 3.14 for .pi
Using the given information, the radius of the sphere to the nearest meter is 13m
Calculating Volume of a sphereFrom the question, we are to determine the radius of the sphere
Using the formula for calculating the volume of a sphere,
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the given information,
V = 9198 m³
Then,
[tex]9198 = \frac{4}{3} \times \pi r^{3}[/tex]
[tex]9198 = \frac{4}{3} \times 3.14 \times r^{3}[/tex]
[tex]4 \times 3.14 \times r^{3} = 9198 \times 3[/tex]
[tex]4 \times 3.14 \times r^{3} = 27594[/tex]
[tex]r^{3} = \frac{27594}{4 \times 3.14}[/tex]
[tex]r = \sqrt[3]{\frac{27594}{4\times 3.14} }[/tex]
r = 12.99995 m
r ≅ 13 m
Hence, the radius of the sphere to the nearest meter is 13m.
Learn more on Calculating volume of a sphere here: https://brainly.com/question/21209558
#SPJ1
Which function could be represented by the graph on the coordinate plane? f(x) = (x – 8)2 6 f(x) = (x 8)2 6 f(x) = (x 8)2 – 6 f(x) = (x – 8)2 – 6
Considering it's vertex, the quadratic equation that could be represented on the plane is given as follows:
f(x) = (x - 8)² - 6.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Researching the problem on the internet, it is found that the given graph has vertex at (8,-6), hence h = 8, k = -6 and considering a = 1 the equation is given as follows:
f(x) = (x - 8)² - 6.
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
#SPJ4
en una optica se ofrece la siguiente promoción: se descuenta de la compra de anteojos un porcentaje idéntico a la edad correspondiente del cliente, es decir, si el cliente tiene 23 años, el descuento se le aplica de un 23%. El abuelo de Andrés dice: esos anteojos de $40.000 me costarían tan solo $4.000. ¿Qué edad tiene el abuelo de Andrés?
We will see that the percentage in which the price decreases is 90%, thus the age is 90 years.
How old is Andrés?
We know that the percentage in which the price decreases is equal to the age of Andrés.
We can write:
P = $4,000 = $40,000*(1 - k)
Where k is the percentage in decimal form.
Solving for k:
k = ($40,000 - $4,000)/$40,000 = 0.9
To obtain the percentage, we multiply by 100%.
0.9*100% = 90%
We conclude that Andrés is 90 years old.
If you want to learn more about percentages.
https://brainly.com/question/24554492
#SPJ1
Find the zeros of the function.
y = (x + 1)(x − 3)(x - 6)
Is 23/√3 a rational number? Again is 23 over root 3 a rational or irrational number.
Answer: irrational number
Step-by-step explanation:
Let us write it out.
[tex]\displaystyle \frac{23}{\sqrt{3} }[/tex]
Next, we will define ratoinal and irrational.
A rational number is a number that can be written as a whole number, fraction, or decimal that ends / repeats.
An irrational number is any number that cannot be turned into a fraction.
Let us see which category the number given falls into.
[tex]\displaystyle \frac{23}{\sqrt{3} } = 13.27905619\;\;\;\;\;\;\text {it goes on...}[/tex]
This means [tex]\frac{23}{\sqrt{3} }[/tex] is an irrational number.
Congruent figures Practice -2 measurement of angle F
Answer:
m∠F = 45°
because
Corresponding
Parts of
Congruent
Triangles are
Congruent
To get from home to her friend Rhianna's house, Grace would have to walk 1 mile due north.
To get from home to her friend Elise's house, Grace would have to walk 3 miles due east.
What is the straight-line distance between Rhianna's house and Elise's house? If necessary,
round to the nearest tenth.
Answer: All you would do is 3 miles north 4 miles east
Step-by-step explanation:
That is what gogle said lol
Find the surface area of the pyramid to the nearest whole number.
140 in2
40 in2,
180 in2
80 in2.
taking a peek at the pyramid, is really just 4 triangles stemming from a common top and touching a squarish base at the edges.
so hmmm to get the surface area of the pyramid, we can simply get the area of all those four triangles and the square and sum them up.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{4}) \right]}~~ + ~~\stackrel{square}{(10)(10)}}\implies 80~~ + ~~100\implies 180~in^2[/tex]
Sela is making 400 scones.
she use butter ,sugar and flour in the ratio 2:1:9
here the cost of those ingredients
butter-2.50 per 500g
sugar-1.60 per kilogram
flour-60p per 1.5kg
the total mass of the butter ,sugar and flour in each scone is 30g
work out the total cost of these ingredients for the 400
scones
Answer:
£15.20
Step-by-step explanation:
butter : sugar : flour = 2 : 1 : 9
Total mass for 1 recipe = 30 g
2 + 1 + 9 = 12
12x = 30
x = 30/12
x = 2.5
For 1 scone:
butter = 2x = 2(2.5) g = 5 g
sugar = x = 2.5 g
flour = 9x = 9(2.5) g = 22.5 g
Cost for 1 scone:
butter: 5 g × £2.50/(500 g) = £0.025
sugar: 2.5 g × £1.60/(1000 g) = £0.004
flour: 22.5 g × £0.6/(1500 g) = £0.009
Cost for 1 recipe = £0.025 + £0.004 + £0.009 = £0.038
Cost for 400 scones = 400 × £0.038 = £15.20
Answer: £15.20
What expression is equivalent to 7/12
Answer:
14/24 is one expression equivalent to 7/12.
Answer:
14/24,21/36,28/48,35/60,42/72,49/84,56/96 are equivalent to 7/12...
In American football, a touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points. If a team scored a total of 24 points, how many combinations of plays is possible
The number of combinations of plays that is possible will be 2.
How to calculate the combination?Let the number of combinations be represented by x.
From the information given, we are informed that the touchdown scores 7 points, a field goal scores 3 points, and a safety scores 2 points.
Therefore, this will be:
7x + 3x + 2x = 24
12x = 24
x = 24/12
x = 2
Therefore, there are 2 combinations.
Learn more about combinations on:
brainly.com/question/11732255
#SPJ1
What’s the Value of y and x
Answer:
x=86 y=111
Step-by-step explanation:
i think ita right on edmentum it makes sense
Please help will give brainliest!!!!
Answer:
12
Step-by-step explanation:
Which of the following statements best describes the lines?
Find the values of x and y in parallelogram PQRS. PT=y, TR=2x+1, QT=5y, TS=6x+13 x= ? and y= ?
Answer:
Step-by-step explanation:
Six hundred thirty-one and fifthy eight thousandths in standard form
The number in standard form is 632.058
How to represent the number in standard form?The number is given as:
Six hundred thirty-one and fifty-eight thousandths
This means:
Six hundred thirty-one + fifty-eight thousandths
Express Six hundred thirty-one as 631
632 + fifty-eight thousandths
Express fifty-eight thousandths as 58/1000
632 + 58/1000
Express as decimal
632 + 0.058
Evaluate the sum
632.058
Hence, the number in standard form is 632.058
Read more about standard forms at:
https://brainly.com/question/1708649
#SPJ4
121. How much sand is needed to fill a sandbox
8 feet by 6 feet to a depth of 18 inches?
A. 64 cu
B. 62 cu ft.
C. 74 cu ft.
D. 72 cu ft.
E. 68 cu ft.
Answer: The answer is D. 72 cu ft.
Step-by-step explanation:
What is the area of the composite figure?
500
490.62
245.31
745.31
Answer:
745.31
Step-by-step explanation:
20x25=500
(2(12.5)pie)/2=245.435
245.435+500=745.31
A box contains 20 uckets mmbered from 1 to 20 tetor de candowm. find the probability it is divisible by 3 and 4
Answer:
that 2 out of 20 ratio you have 18 to 1 odds of getting these
Darcy gave her hair hairstyles a $4.90 tip the tip was 7% of the cost of the haircut Write an equation to find b, the cost of the haircut
A class made a line plot of the weight of each science book in pounds. a line plot. short description, a line plot. ,long description,
the line plot is entitled weight of science books in pounds. it goes from 2 pounds to 3 pounds with marks at some numbers:
one mark is at two and one eighth. two marks are at two and one fourth. one mark is at two and three eighths. two marks are at two and one half. three marks are at two and three fourths. one mark is at two and seven eighths. question
sonya carried ,begin emphasis,all,end emphasis, the books weighing 2 and one-fourth pounds and 2 and three-eighths pounds to the library. how many pounds of books did sonya carry?
The total pounds of science books that sanya carried is; 6⁷/₈ pounds
How to Interpret Line Plots?
From the attached Line Plot, we can see the book weights.
Now, we are told that Sanya carried all the books weighing 2¹/₄ pounds and 2³/₈ pounds.
From the line plot we see that;
Number of books weighing 2¹/₄ pounds are 2 books
Number of books weighing 2³/₈ pounds is 1 book
Thus;
Total weight of books carried by Sanya = 2(2¹/₄) + 1(2³/₈)
Total weight = 4¹/₂ + 2³/₈
Total Weight = 6⁷/₈ pounds
Read more about Line Plots at; https://brainly.com/question/3493733
#SPJ1