Applying it's properties, the limits of the functions are given as follows:
1. 9.
2. -2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. Algebraically, for continuous functions, we have that:
[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex].
Hence, applying the property above, for item 1, we have that:
limx→0 f(x−1)g(x) = f(0 - 1)g(0) = f(-1)g(0) = -3 x 3 = 9.
For item 2, we have that:
limx→0 f(x+4)+g(x) = limx→4 f(x) + limx→0 g(x) = 3 - 5 = -2.
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Uber charges $3 plus $0.75 per mile driven. lyft charges $5.00 plus $.50 per mile driven. write the equations for both companies
The linear equation for both Uber and Lyft will be Y = 0.75x + 3 and
Y = 0.5x + 5 .
A linear equation is an algebraic equation of the form y = mx+b. Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Here we have,
Uber charge $3 fix on every trip and additional charges on per mile $0.75
So, linear equation be
Y = 0.75x + 3 where, x = no. of mile covered
Similarly, lyft charge $5 fix and $0.5 as an additional
So, linear equation be
Y = 0.5x + 5 where, x = no. of mile covered
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which of the following pairs of ratios form a proportion? a. 9 boys to 5 girls and 12 boys to 8 girls
Answer:
12 to 8
Step-by-step explanation:
cuz i am smart pls mark me brainliest
12. −7.5 • −2³/4
19
Answer:
-9.5
Step-by-step explanation:
8. A total of $36,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in
bonds is to exceed that in CDs by $5,000, how much will be invested in each type of investment?
The amount invested in CDs is $
The amount invested in bonds is $
Using a system of equations, it is found that:
The amount invested in CDs is $20,500.The amount invested in bonds is $15,500.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested in CDs.Variable y: amount invested in bonds.The total invested is of $36,000, hence:
x + y = 36000.
The amount invested in bonds is to to exceed that in CDs by $5,000, hence:
x = y + 5000.
Replacing in the first equation:
y + 5000 + y = 36000.
2y = 31000
y = 15,500.
x = y + 5000 = 20,500.
Hence:
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Given m|n, find the value of x.
Answer:
127°
Step-by-step explanation:
The angle that's represented with x and the angle with the measure 127 are alternate exterior angles because line m and line n are parallel.
And alternate angles has equal measures so if one is 127 then so is the other.
Therefore the value of x = 127
Find the equation of the line.
Use exact numbers.
y=
#+
Evaluate.
10/1⋅(−4)
Enter your answer in the box.
Answer:
Step-by-step explanation:
-40
Factoring All Methods
Answer:
5(3n - 4)(3n - 10)
Step-by-step explanation:
15n² - 110n + 200 ← factor out 5 from each term
= 5(3n² - 22n + 40) ← factor the quadratic
consider the factors of the product of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × 40 = 120 and sum = - 22
the factors are - 12 and - 10
use these factors to split the n- term
3n² - 12n - 10n + 40 ( factor the first/second and third/fourth terms )
3n(n - 4) - 10(n - 4) ← factor out (n - 4) from each term
(n - 4)(3n - 10)
then
15n² - 110n + 200 = 5(n - 4)(3n - 10)
Answer:
Hello,
Step-by-step explanation:
[tex]15n^2-110n+200=15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )\\[/tex]
1. I am thinking about 2 numbers with sum=22/3 and product=40/3.
Those numbers are 4 and 10/3 since 4*10/3=40/3 and 4+10/3=22/3
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n-\dfrac{10}{3} )(n-4)=5*(3n-10)(n-4)[/tex]
2.
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n^2-2*\dfrac{11}{3} x+(\dfrac{11}{3})^2 -\dfrac{121}{9} +\dfrac{120}{9})\\\\=15((n-\dfrac{11}{3})^2 -\dfrac{1}{9})\\\\=15( n-\dfrac{11}{3} -\dfrac{1}{3})*(n-\dfrac{11}{3} +\dfrac{1}{3})\\=15(n-\dfrac{10}{3})(n-4)\\\\=5(3n-10)(n-4)\\[/tex]
3.
Using discriminant ...
Explain why researchers formulate a null hypothesis in addition to a hypothesis when designing an experimental study.
A null hypothesis outlines what a researcher should see if the tested hypothesis is incorrect. In essence, it presents an "alternative" theory to the first.
What is the null hypothesis?The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the result of chance. It is claimed to be a claim made by surveyors who wish to look at the data.
The basic idea behind null hypothesis testing is to gather data and calculate the probabilities of a particular set of data during an experiment on a random sample, presuming that the null hypothesis is correct.
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Match the angle with its classification
Answer:angels
Step-by-step explanation:bea
Madelyn read 45 pages in 1 1/3 hours . At what rate , in pages per hour , did she read?
Madelyn reads at the rate of 33.75 pages per hour.
Here rate is defined as the number of pages read per hour. Rate or unit rate is defined as the quantity that is done in 1 unit of time(second, minute or hour). Distance per time is called speed. Velocity per time is called acceleration.
Here it is given Madelyn reads 45 pages in [tex]1\frac{1}{3}[/tex] hours.
Now to find the unit rate we have to divide the number of pages read in the total time taken to read 45 pages.
Unit rate= [tex]45\div 1\frac{1}{3}[/tex]
[tex]=45\div \frac{4}{3}\\=\frac{135}{4} \\=33.75[/tex]
Madelyn reads at the rate of 33.75 pages in 1 hour .
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10. A Cube-root function with a reflection across the y-axis; a vertex of (4,0).
We need to know about cube-root function and reflection to solve this problem. The function is f(x)=[tex]-\sqrt[3]{x-4}[/tex]
A cube-root function is the inverse of a cubic function, a cubic function can be given by f(x)=[tex]x^{3}[/tex], the inverse of this is a cube-root function which can be given by f(x)=[tex]\sqrt[3]{x}[/tex] with vertex at (0,0). The general formula for a cube root function is given be
f(x)=a[tex]\sqrt[3]{x-h} +k[/tex] where a is the measure of how horizontally compressed the graph is and (h,k) is the vertex of the graph. In the question we have to find a cube root function which has been reflected about the y-axis, which means our a will be negative. The vertex of the graph is at (4,0) so (h,k) is (4,0). Thus the cube root function we need is
f(x)=-[tex]\sqrt[3]{x-4}[/tex]
Therefore we found the cube root function that has been reflected about y-axis and the vertex at (4,0) to be f(x)=[tex]-\sqrt[3]{x-4}[/tex]
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Calculate the surface area of the object provided.
A. 56 cm
B. 64cm³
C. 80cm²
D. 112cm²
Answer:
112cm^2
Step-by-step explanation:
A=2(wl+hl+hw)=2·(2·8+4·8+4·2)=112
Answer: B. 64 cm³
Step-by-step explanation:
Let's lenth of the object set is a, width - b and height - h
Thus,
V=abh
a=8 cm b=2 cm h=4 cm
Hence,
V=8*2*4
V=64 cm³
385 people get on an empty train at a station. At the first stop, 264 more people get on the train, and 89 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train.
How many people get off the train at the final destination?
385 people get on an empty train at a station. At the first stop, 264 more people get on the train, and 89 people get off. There are no more stops until the train reaches it final destination, where everybody gets off the train.
560 is the answer
560 people get off the train at the final destination.
Given that 385 people get on an empty train. At the first stop, 264 more people get on, and 89 people get off.
There are no more stops until the train reaches it final destination,
We need to find the number of the people who get off the train at the final destination.
To find out how many people get off the train at the final destination, let's break down the information given step by step.
385 people get on the empty train at the station.
At the first stop, 264 more people get on the train, bringing the total number of people on the train to 385 + 264 = 649.
Additionally, 89 people get off the train at the first stop.
After the first stop, there are no more stops until the final destination.
To find out how many people get off at the final destination, we need to subtract the number of people who got off at the first stop from the total number of people on the train after the first stop.
Total number of people on the train after the first stop = 649 (from step 2)
People who got off at the first stop = 89 (from step 3)
Number of people who get off at the final destination = Total number of people on the train after the first stop - People who got off at the first stop
Number of people who get off at the final destination = 649 - 89 = 560
Therefore, 560 people get off the train at the final destination.
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In the figure, angles ABC and AST are right angles. If AC = 35, AT = 11, and BT = 9, then what is AS?
AS=6.28
First, draw a line joining C and T;
Two triangles TBC and TSC are formed;
Also, AC=35, AT=11,BT=9;
AB=AT+BT=11+9=20
Using pythagoras theorem;
AB² + BC² = AC²
BC²=35²-20²=825
Using pythagoras theorem on triangle TBC;
BC² + TB²= CT²
825 + 9²=CT²
CT²=906;
In triangle CST, using pythagoras theorem;
CS²+ST²=CT²=906 -1
In triangle AST, using pythagoras theorem;
AS²+ST²=AT²=11²=121 -2
Subtract 1 from 2;
AS²+ST²-CS²-ST²=121-906
AS²-CS²=-785
AS²-(AC-AS)²=-785
AS²-(35-AS)²=-785
AS²-AS²-35²+70AS=-785
AS=6.28
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Find the sum of all multiple 3 between 5 and 64
Answer:
690
Step-by-step explanation:
The multiples of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57+60+63 which gives you 690.
Hope this helps, have a good day! :D
Answer: ∑=690
Step-by-step explanation:
Let's use the formulas for an arithmetic progression:
[tex]a_1=6 \ \ \ \ \ a_n=63\ \ \ \ d=3\\a_n=a_1+(n-1)d\\63=6+(n-1)3\\63=6+3n-3\\63=3+3n\\63-3=3+3n-3\\60=3n\\[/tex]
Divide both parts of the equation by 3:
[tex]20=n[/tex]
Thus,
[tex]\displaystyle\\\sum=\frac{a_1+a_n}{2} n\\\\\sum=\frac{6+63}{2}20 \\\\\sum=\frac{69*20}{2} \\\\\sum=69*10\\\\\sum=690[/tex]
A composite figure is shown.
6 ft
6 ft
6 ft
20 ft
What is the total surface area of the figure?
A. 180 sq ft
B. 60 sq ft
C. 480 sq ft
D. 720 sq ft
4 ft
The total surface area of the given figure is 720 ft² that is option (D).
The Lateral Surface Area( LSA) of an object is the area covering all the sides of the object except it top and bottom .
Let us divide the given Composite figure into three parts ,
Part(a) = top part having shape of pyramid
First we will calculate the LSA of the top pyramid.
Given that
base = 6ft
perpendicular distance = 4ft
Slant height(l) = [tex]\sqrt{(\frac{base}{2} )^{2} +(perpendicular . distance )^{2} }[/tex]
On substituting the values we get
l=√(3²+4²)
l=√25
l=5 ft
LSA of pyramid = (1/2)* perimeter of base * slant height
Substituting the values we get ;
=(1/2)*(4*6)*5
=60 ft² ....(i)
Part (b)
the 2nd part is a rectangular prism with length = 20 ft
and breadth = 6 ft
Surface area of rectangular prism = 4*Area of side
=4*20*6
=480 ft² ...(ii)
Part(c)
The last part is a cube with only 5 sides of side 6ft.
Surface Area of the cube = 5*Area of side
=5*6*6
=180 ft² ....(iii)
Total surface area of the figure= LSA of pyramid + Surface area of rectangular prism + Surface Area of the cube
Substituting the values from equation (i) , (ii) and (iii) we get ,
Total surface area of the figure = 60+480+180
=720 ft²
Therefore , the total surface area of the given figure is 720 ft².
hence option (D) 720sq ft is correct.
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Solve:
4(x+3)-2=6
SHOW ALL WORK
Answer:
[tex] \sf \large \: x=−1[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
4(x+3)−2=6
Step 1: Simplify both sides of the equation.
4(x+3)−2=6
(4)(x)+(4)(3)+−2=6(Distribute)
4x+12+−2=6
(4x)+(12+−2)=6(Combine Like Terms)
4x+10=6
4x+10=6
Step 2: Subtract 10 from both sides.
4x+10−10=6−10
4x=−4
Step 3: Divide both sides by 4.
4x/4 = −4/4
x=−1
HURRY PLS!!
A company orders 22 boxed lunches from a deli for $273.90. If each boxed lunch costs the same amount, how much do 16 boxed lunches cost?
Answer:
Step-by-step explanation:
1 box costs x amount
18 boxes cos 223.20
Cross multiply
223.20 * 1 = 18 x
Divide by 18
223.20 / 18 = 18x / 18
x = 12.40
Cost of 1 box is 12.40
Answer:
It should be 199.20 for 16 boxes
Step-by-step explanation:
I divided 273.90 by 22 which came out to 12.45
so then i multiplied 12.45 by 16 and it gave me 199.20
5a + 2b = 40 solve for b
Answer:
5a-40=-2b
5a-40/-2=-2b/-2
-5a/2+20=b
what is the formula of (a+b)²
Hey there!
Finding the the answer to the [Binomial]
(a + b)^2
CONVERT:
= (a + b)(a + b)
DISTRIBUTE
= a(a) + a(b) + b(a) + b(b)
= a^2 + ab + ab + b^2
COMBINE the LIKE TERMS
= (a^2) + (ab + ab) + (b^2)
= a^2 + ab + ab + b^2
= a^2 + 1ab + 1ab + b^2
= a^2 + 2ab + b^2
Therefore, your answer should be:
a^2 + 2ab + b^2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the graph of y = -3/4x – 2?
In the graph of y = -3/4x – 2 is represent linear equation.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.The graph is represent a linear equation .
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How many posts does it take to support a straight fence 300 feet long if a post is placed every 25 feet?
12 posts are required to support a straight fence 300 feet long if a post is placed every 25 feet.
The given question can be solved using division. We are given that 25 feet is covered by 1 post. So, we will simply find the number of posts that will cover the 300 feet long fence. Now, calculating the number of posts as shown in steps below -
Number of post that covers 25 feet = 1
So, 300 feet will be covered by number of posts = (1÷25)×300
Performing multiplication and division to find the number of posts required to cover 300 feet long fence
Number of posts required to cover 300 feet long fence = 12 posts
Hence, 12 posts are required to cover 300 feet long fence.
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Ry+z/m-t=x. Solve for y
In linear equation, y = \frac{x}{r} - \frac{z}{mr} + \frac{t}{r} is simple form .
What is a formula for linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.Ry+ z/m-t=x
Ry = x - z/m + t
[tex]y = \frac{x - \frac{z}{m}+ t }{r}[/tex]
[tex]y = \frac{x}{r} - \frac{z}{mr} + \frac{t}{r}[/tex]
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A distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be ______.
A distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.
What is the skewness?A real-valued random variable's probability distribution's asymmetry can be quantified by looking at how skew it is around its known as skewness.
There are three types of probabilities of a value can be:
Positively skewed
negatively skewed
unskewed
From the given question, the distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.
Therefore the correct answer would be an option (D)
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Your question is incomplete, probably the missing part is:
A distribution of scores in which almost the entire class scored very low, but a few students scored fairly high would be ______.
a. normally distributed
b. positively skewed
c. unskewed
d. negatively skewed
Janet weights 20 pounds more than anna if the sum of their weights is 250 lb how much does each girl weigh
Anna's weight is 115 pounds and Janet's weight is 135 pounds.
What is weight?The weight of the object is the force acting on it due to gravity in science and engineering. Weight is defined as a vector quantity in some standard textbooks, as the force of gravity acting on the object. Others define weight as just a scalar quantity, the magnitude of gravity.To find the wight of Anna and Janet:
It is assumed:
Janet is 20 pounds heavier than Anna.This means that if Anna weighs x pounds,Janet's age is then (x+20) pounds.Also,
Their combined weight is 250 pounds.So,
x+x+20 = 2502x+20=250Subtraction of both sides by 20 yields:
2x = 250-202x = 230By dividing both sides by 2, we get:
x = 115So, Anna's weight is 115 pounds and Janet's weight is 115+20=135 pounds.
Therefore, Anna's weight is 115 pounds and Janet's weight is 135 pounds.
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Please help with math question
Answer:
5b+35
Step-by-step explanation:
5*b=5b
5*7=35
The expression √81-√100 represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base?
The distance between home plate and first base is -1 feet
How to determine the numberFrom the information given, we have that;
The expression for the number of feet between home plate and first base is given as;
√81-√100
Where;
√81 is the number of feet at home plate√100 is the number of feet at the first baseTo determine the distance, we take find the square root of the numbers and substitute, we have;
9 - 10
Find the difference
-1 feet
Thus, the distance between home plate and first base is -1 feet
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What is Euclidian Geometry?
Answer:
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these.
Step-by-step explanation:
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Find parametric equations and symmetric equations for the line of intersection of the given planes. x + y + z = 5, x + z = 0
The next set is the parametric equations of the same line .
x = t, y = 5 and z = -t .
What is the meaning of parametric and non parametric?
The assumptions behind parametric statistics relate to the population's distribution from which the sample was drawn. Since no presumptions are made while using nonparametric statistics, data can be gathered from samples that do not fit any particular distribution.x + y + z = 5, x + z = 0
the line satisfies
x + z = 0 , y = 5
thus
x = t, y = 5 and z = -t .
the first one is technically already the symmetric equations of the line.
thus:
x = -z ; y = 5
the next set is the parametric equations of the same line .
x = t, y = 5 and z = -t .
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