The limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1
Limit of a functionThe limit of the function given in question can also be written as:
[tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex]
To determine the required limit, we will simply substitute the value of x into the function as shown:
[tex]\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{ (-3)^2-8}\\\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{9-8}=1\\[/tex]
Hence the limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1
Learn more on limit here: https://brainly.com/question/1444047
#SPJ4
Answer: the answer is b. 1
Step-by-step explanation: just got it right on edge
Casho invests money in an account paying simple interest. She invests $30 and no
money is added or removed from the investment. After one year, she has $32.40.
What is the simple percent interest per year?
Answer:
8%
Step-by-step explanation:
Divide ( 32.40 / 30 ). This outputs the answer 1.08, or 108%. This means that the outcome is 108% of the original, or 8% greater.
The simple interest in which Casho invests money was 8%.
What is simple interest?
Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.
We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, p = 30, SI = (32.40 - 30) = $2.40 and t = 1.
Therefore, 2.40 = (30×r×1)/100.
240 = 30r.
r = 240/30.
r = 24/3.
r = 8.
So, The rate of simple interest is 8%.
learn more about simple interests here :
https://brainly.com/question/11564235
#SPJ2
How do I solve
x² - 10x-3=0
Answer:
x = 5±2√7
Step-by-step explanation:
This quadratic cannot be factorised via the factorisation method, so we use the quadratic formula :
x = [tex]\frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex] or x = [tex]\frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]
(The reason I did 2 equations is because brainliest does not allow me to do the ± in the equation insert thing )
x = [tex]\frac{-(-10) + \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex] or x = [tex]\frac{-(-10) - \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex]
x = [tex]\frac{10 + \sqrt{100+12} }{2}[/tex] or x= [tex]\frac{10 - \sqrt{100+12} }{2}[/tex]
x = [tex]\frac{10 + {4\sqrt{7}} }{2}[/tex] or x = [tex]\frac{10 - {4\sqrt{7}} }{2}[/tex]
x = [tex]5+2\sqrt{7}[/tex] or x = [tex]5 -2\sqrt{7}[/tex]
Hope this helped and brainliest please
Find the indicated side of the
right triangle.
45°
y
y =
45%
88
The indicated side of the right triangle is [tex]44\sqrt{2} =\frac{88}{\sqrt{2} }[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says:[tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:
[tex]sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\[/tex]
The question asks to find one of the legs (y). Then, you can find y applying the trigonometric ratio (sin 45°).
[tex]sin(45\°)=\frac{y}{88}[/tex]
Like sin45° is equal to [tex]\frac{\sqrt{2} }{2}[/tex], you have
[tex]\frac{\sqrt{2} }{2} =\frac{y}{88}\\ \\ 2y=88\sqrt{2} \\ \\ y=44\sqrt{2} \\ \\ Thus\\ \\ y=\frac{88}{\sqrt{2}}[/tex]
Learn more about trigonometric ratios here:
brainly.com/question/11967894
#SPJ1
Answer: 88[tex]\sqrt{2}[/tex]
Step-by-step explanation:
hope it helps
Alex's favorite number is 175% of Winnie's favorite number. Winnie's favorite number is 48 less than Alex's favorite number. What is Winnie's favorite number?
Answer:
64
Step-by-step explanation:
The information can be written as:
Let Alex's number = x
Winnie's number = y
x = 1.75y
x = y + 48
Substitute 1.75y for x:
1.75y = y +48
0.75 y = 48
3/4 y = 48
y = 64
Winnie's favourite number = 64.
Calvin throws 12 sheets of paper up in the air and randomly catches one of the sheets as they float down. Of the 12 sheets of paper, 9 are white and 3 are red.
The probability that Calvin caught a white sheet is
. It is
that this event occurs. The probability that Calvin caught a red sheet is
. It is
that this event occurs.
Reset
Answer:Calvin throws 12 sheets of paper up in the air.
He randomly catches one of the sheets as they float down.
Of the 12 sheets of paper, 9 are white and 3 are red.
Probability = Number of favorable outcomes/ total number of outcomes
The probability that Calvin caught a white sheet is = or 75%.
It is likely that this event occurs as above 70% we say that the event is likely and here the probability is 75%.
The probability that Calvin caught a red sheet is = or 25%
This is unlikely to happen. Thus, we can say that it is not likely event.
Nathaniel works as a baker and makes several batches of muffins every morning. each batch requires 1 1/7 cups of sugar. for a large meeting, nathaniel needs 4 4/7 times more nuffins than what a regular batch makes. how much sugar will he use? if each batch fills 3 boxes, how many boxes will be needed to pack the muffins for the meeting?
The amount of sugar he will use is 5.22 cups of sugar, and the number of boxes needed to pack the muffins is 13.71 boxes.
How do we solve a word problem?This word problem question can be solved as follows:
Amount of sugar he will use = 1 1/7 * 4 4/7 = 1.142857142857143 * 4.0.571428571428571 = 5.22 cups of sugar
Number of boxes needed to pack the muffins for the meeting = 4 4/7 * 3 = 4.0.571428571428571 * 3 = 13.71 boxes
Learn more about how to solve word problems here: https://brainly.com/question/13732946.
#SPJ1
Nick walked 5 miles to reach his aunt's house. from there he traveled 8 miles to the shopping mall on a bicycle. he traveled 80% faster on the bicycle than on foot. let r represent his rate of walking in miles per hour. identify the expression that represents the number of hours nick took to reach the shopping mall in terms of r. then find the time taken by nick to reach the shopping mall if he walked at an average speed of 3 miles per hour.
The expression of time in terms of r is T = 85/9r. If he walked at an average speed of 3 miles per hour. Then the time taken by nick to reach the shopping mall will be 3 hours and 60 minutes.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Nick walked 5 miles to reach his aunt's house.
From there he traveled 8 miles to the shopping mall on a bicycle.
He traveled 80% faster on the bicycle than on foot.
Let r represent his rate of walking in miles per hour. Then the 1.8r will be the rate of cycling in miles per hour.
Then the number of hours nick took to reach the shopping mall in terms of r will be
T = t₁ + t₂
Where t₁ is the time taken to reach his aunt's house and t₂ is the time taken to reach the shopping mall from his aunt's house. Then we have
T = 5 / r + 8 / 1.8r
T = 1/r (5 + 8/1.8)
T = 85/9r
If r is 3 miles per hour, then the time taken by nick to reach the shopping mall will be
T = 85 / (9 x 3)
T = 3.15 hours
T = 3 hours and 9 minutes
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ1
consider the following pattern: 5;8;11; ... ; ...
a) determine the common difference of the pattern
b) write the next two terms of the pattern
c) determine the general term
d) determined T²⁰ of the pattern
Answer:
Step-by-step explanation:
The common difference is 8-5 = 3
The first next term is 11 + 3 = 14
The next (second) term is 14 + 3 = 17
tn = 5 + (n - 1)*3 This is part c
t20 = 5 + (20 - 1)*3
t20 = 5 + 19*3
t20 = 5 + 57
Answer t20 = 62
Whoever answers correctly gets BRAINLIESTand 100 points
A rectangular prism with a length of 3.8 meters and a width of 1.5 meters has a volume of 16.53 cubic meters.
What is the height of the prism?
2.9 m
6.525 m
11.23 m
21.83 m
Answer:
2.9 meters.
Step-by-step explanation:
First we multiply the length, 3.8, by the width, 1.5, to get the base, 5.7 (this step is not entirely necessary, but makes it much easier). Then we divide the volume, 16.53, by the base, 5.7, to get the height, 2.9 meters.
Answer:
i think its 21.83 i may be wrong but im pretty sure its 21.83
Step-by-step explanation:
Which of the following equations has a slope of 5 and y-intercept of 4 ?
Answer:
Equation in Slope intercept form :
y = 5x + 4
Simplify the expression. Write your answer as a power.
3^2x3^2
The simplified expression is
Answer:
3^4
Step-by-step explanation:
when both constants have equal base then powers are added
Find the center and radius of the circle with this equation:
x² + 16x + 64 + y² - 2y + 1 = 144
By completing squares, we will see that the radius is 12 units and the center is (-8, 1).
How to find the center and radius of the circle?The circle of center (x₁, y₁) and radius r is written as:
(x - x₁)² + (y - y₁)² = r²
Now we go to our equation:
x² + 16x + 64 + y² - 2y + 1 = 144
Now we need to complete squares:
(a + b)² = a² + 2ab + b²
Then we can rewrite:
(x² + 2*8*x + 8*8) + (y² - 2y + 1) = 12²
(x + 8)² + (y - 1)² = 12²
So the center is the point (-8, 1) and the radius is 12 units.
If you want to learn about circles:
https://brainly.com/question/1559324
#SPJ1
If x = -7, evaluate the following expression:
(x − 2)(x+14)
——————-
x(x + 8)
Answer:
9
Step-by-step explanation:
[tex]\text{Given that}~ x = -7\\\\\dfrac{(x-2)(x+14)}{x(x+8)}\\\\\\=\dfrac{(-7-2)(-7+14)}{-7(-7+8)}\\\\\\=\dfrac{(-9)(7)}{-7(1)}\\\\\\=\dfrac{-63}{-7}\\\\\\=9[/tex]
Find the 14th term of the geometric sequence 5,-10,20
In this specific case, the initial term (a) is 5 and the common ratio (r) is -2
Henceforth, after determining what a and r are, we use the formula for the nth term. Which is:
[tex]a_n = a \times r^{n-1} [/tex]
Therefore, the 14th term is :
[tex]\implies 5 \times { (- 2)}^{14 - 1} \\\implies 5 \times {( - 2)}^{13} \\ =\boxed { -40,960} [/tex]
Hope it helps!
2-53. a message is released at 1930 hours greenwich mean time on 2 january 1991. what is the correctly stated date-time group (dtg) assigned to the me
Step-by-step explanation:
. In Figure 5.144, of ΔABC, where
m(∠C) = 30, m(∠ABD) = 5x,
m(∠A) = 4x. Find m(∠ABC) in
degrees.
help please! marking brainliest
Answer:
see explanation
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]
Then
(a)
[tex]5^{4}[/tex] × [tex]5^{5}[/tex] = [tex]5^{(4+5)}[/tex] = [tex]5^{9}[/tex]
(b)
[tex]2^{7}[/tex] × 2 = [tex]2^{(7+1)}[/tex] = [tex]2^{8}[/tex]
(c)
[tex]6^{5}[/tex] ÷ 6² = [tex]6^{(5-2)}[/tex] = 6³
(d)
[tex]9^{7}[/tex] ÷ [tex]9^{6}[/tex] = [tex]9^{(7-6)}[/tex] = [tex]9^{1}[/tex] = 9
------------------------------------------------
(a)
3² × [tex]3^{4}[/tex] = [tex]3^{(2+4)}[/tex] = [tex]3^{6}[/tex]
(b)
[tex]5^{7}[/tex] × 5³ = [tex]5^{(7+3)}[/tex] = [tex]5^{10}[/tex]
(c)
[tex]6^{7}[/tex] ÷ 6² = [tex]6^{(7-2)}[/tex] = [tex]6^{5}[/tex]
(d)
[tex]9^{4}[/tex] ÷ 9³ = [tex]9^{(4-3)}[/tex] = [tex]9^{1}[/tex] = 9
The graph of y=x² + 11x + 24 is equivalent to the graph of which equation?
y=(x+8)(x+3)
y=(x + 4)(x+6)
y=(x +9)(x + 2)
y=(x + 7)(x+4)
Answer:
y = (x+8)(x+3)
Step-by-step explanation:
If you multiply
(x+8)(x+3),
you get x^2 + 3x + 8x + 24
This simplifies to x^2 + 11x + 24, same as the original question.
The graph of y=x² + 11x + 24 is equivalent to the y=(x+8)(x+3).
What is Polynomial?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.
We have Graph whose equation is
y=x² + 11x + 24
Now, factories the above equation using splitting the middle term
y=x² + 11x + 24
y=x² + 8x + 3x + 24
y = x(x+8) + 3(x+8)
y= (x+3)(x+8)
Thus, the factors are (x + 3)(x+8).
Learn more about Polynomial here:
https://brainly.com/question/1509089
#SPJ2
Which equation represents a population of 300 animals that increases at an annual rate of 23% ?
Answer:
300+(300 + 0.23x)
Step-by-step explanation:
I'm not sure what you are asking but this is the only equation I can get
A number, increased by four times the number, is 35. Find the number.
need help on a worksheet due early tomorrow
The correct numbers to get to the media or mean are 10, 33, 3, and 2.
What is the difference between median and mean?The media is obtained by organizing the values given and selecting the one that is in the middle; while the mean is obtained by adding all values and dividing the total by the number of values.
What value makes the median 5 and 25?A. 2,4,5,9,1,7 = 1,2,4,5,7,9,10 x= 10B.32,23,15,30,12 = 12,15,23,25,30,32,33 x= 33What value makes the mean 5 and 3?A. 7+8+2+5 +3 = 25/5 = 5 x= 3B. 6+1+7+4+1+0+2= 21/7 =3 x=2Learn more about numbers in: https://brainly.com/question/17429689
#SPJ1
In 20 words or fewer write a conjecture about rectangles and quadrilaterals
A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.
What is conjecture?A conjecture is a conclusion made on the basis of speculation rather than proof.
Rectangle has four sides and is a polygon. The internal angle total is 360 degrees. The opposing sides of a rectangle are parallel and equal, and each angle is 90 degrees.
In the first place, your search for a pattern before making an educated assumption or hypothesis about it. In the introduction, you look for a pattern and then form an educated guess or conjecture about it.
A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.
To learn more about the conjecture, refer to https://brainly.com/question/11224568
#SPJ1
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
A correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
What is a circle?A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.
The general form of the equation of a circle is given as:-
( x - h )² + ( y - k )² = r²
By comparing the given equation we can see the following results:-
x² + (y – 3)² = 36
( x - ( 0 ))² + ( y - 3 )² = 6²
We can see that the coordinate of the center are ( 0, 3 ) and the radius is 6 so the diameter is 12.
Therefore the correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.
To know more about circles follow
https://brainly.com/question/24375372
#SPJ1
Answer:
A and E (first and last, ending in "=36")
x2 + (y – 3)2 = 36
x2 + (y + 8)2 = 36
Step-by-step explanation:
just took the quiz
MATHH!!! find the surface area of the composite figure. Please answer correctly & tell me how you got your answer
The total area of the given composite figure is; 84.8 ft²
How to find the area of a composite figure?
We are given;
Area of triangle = 5.6 ft²
Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²
Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)
Area of rectangles = 14.4 + 16 + 43.2
Area of rectangles = 73.6 ft²
Total Area of composite figure = 73.6 ft² + 11.2 ft²
Total Area of composite figure = 84.8 ft²
Read more about area of composite figure at; https://brainly.com/question/21135654
#SPJ1
Pls help!!!
Write an exponential equation for the graph shown
below.
Explain how you determined the equation.
The exponential equation of the graph is y = 1.59 * 1.26^x
How to determine the exponential equation?On the graph, we have the following points
(x,y) = (2,1) and (4,4)
An exponential function is represented as;
y = ab^x
So, we have:
ab^1 = 2 and ab^4 = 4
Divide both equations
b^3 = 2
Take the cube root of both sides
b = 1.26
Substitute b = 1.26 in ab^1 = 2
1.26a = 2
Divide both sides by 1.26
a = 1.59
So, we have:
y = ab^x
y = 1.59 * 1.26^x
Hence, the exponential equation of the graph is y = 1.59 * 1.26^x
Read more about exponential equation at:
https://brainly.com/question/11832081
#SPJ1
I need the answers with work someone please help if not ima fail math
Answer:
I am sorry if you feel mad but I do not know this question I am very sorry . . . . . . . . . .
Help I’m confused on what to do
The correct answer for the Function in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5
Meaning of FunctionA function can be defined as a set of outputs that its varying is dependent on the inputs.
In this case the functions given have a designated outputs.
(f+g)(x) = f(x) + g(x) - because its held by an addition
(f+g)(x) = [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5
In conclusion, The correct answer for the question in the diagram is: (B). [tex]\frac{1}{X}[/tex] + [tex]x^{2}[/tex] + 2x - 5
Learn more about function: https://brainly.com/question/25638609
#SPJ1
a circle has a radius of 8cm the measure or the arc of the shaded region is 72 which is closest to the area of the shaded region of the circle
Answer:
just tell me when you find the answer
A vendor sells apples, pears and oranges. He has 120 oranges. Given that he has 20% more apples than oranges and 40% fewer oranges than pears, find the tal number of fruits he has.
Answer:
144 apples 72 pears
Step-by-step explanation:
Apples 120 + 20% = 144
Pears 120 - 40% = 72
Hope This Helped
what's the domain of the function?
please i need this the soon as possible...
-286 divided by 457.6