Answer:
-2⅓
Step-by-step explanation:
-4 + 5/3 Start out with this sum.
-4 + 1 ⅔ Make 5/3 into a mixed number.
-2 ⅓ Then add them together. The best way to do this is to first add -4 and 1 which makes -3. Then add ⅔ to -3 which is -2 ⅓
Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?
The values of b and c are -4 and 4 respectively
How to determine the values of b and c?The function is given as:
f(x) = x^2 + bx + c
Differentiate f(x)
f'(x) = 2x + b
Set to 0
2x + b = 0
Solve for b
b = -2x
The minimum is (2, 0).
So, we have:
b = -2 * 2
b = -4
Substitute b = -4 in f(x) = x^2 + bx + c
f(x) = x^2 - 4x + c
Substitute (2, 0)
0 = (2)^2 - 4(2) + c
This gives
0 = 4 - 8 + c
Evaluate
c = 4
Hence, the values of b and c are -4 and 4 respectively
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give the answer please
Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:
[tex]x = -\frac{5}{3}[/tex]
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.
The rational function for this problem is given by the function f(x) presented below:
[tex]f(x) = \frac{1}{3x + 5}[/tex]
The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:
3x + 5 = 0
3x = -5
[tex]x = -\frac{5}{3}[/tex]
The solution to the equation above is the only value of x that is not part of the domain of f(x).
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In a model of a construction project, 1 yard is represented as 0.25 inch. What would be the actual area of a garden in square yards, if it is represented by 20 square inches in the model?
Find the missing side length of the triangle.
Answer:
a = 1.5 in.
Step-by-step explanation:
Use the Pythagoras Theorem:
1.7^2 = a^2 + 0.8^2
a^2 = 1.7^2 - 0.8^2
= 2.25
a = 1.5 in.
Answer:
a = 1.5 in.
Explanation:
Using Pythagoras theorem:
a² + b² = c²
insert values
a² + 0.8² = 1.7²
a² = 1.7² - 0.8²
a² = 2.89 - 0.64
a² = 2.25
a = √2.25
a = 1.5
The bottom of a cylindrical container has an area of 10 cm2 . The container is filled to a height whose mean is 5cm, and whose standard deviation is 0.1 cm. Let V denote the volume of fluid in the container.
The volume of the shape will be 50cm3.
How to calculate the volume?It should be noted that the volume van be found by multiplying the area by the height. The volume will be:
= 10 × 5
= 50cm³
The standard deviation volume will be:
= 0.1 × 50
= 5cm
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What is Permutations and Combinations?
Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
----
Combination can be expressed mathematically as:
[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.
Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.
Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.
Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.
The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.
Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.
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What is the simplified base for the function f(x) = 2rootindex 3 startroot 27 endroot superscript 2 x?
Applying exponential properties, the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
What is the function?The function is represented by the following definition:
[tex]f(x) = 2\sqrt[3]{27^{2x}}[/tex]
As an exponent, the function is given by:
[tex]f(x) = 2(27)^{\frac{2x}{3}}[/tex]
27 can be simplified as follows:
27 = 3 x 3 x 3 = 3³
Hence:
[tex]f(x) = 2(3^3)^{\frac{2x}{3}}[/tex]
Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:
[tex]f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}[/tex]
Hence the simplified base for the function is given as follows:
[tex]f(x) = 2(3)^{2x}[/tex]
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The number of Minghua's stamps is 1 1/2 times that of John's.
Step-by-step explanation:
Let the number of stamps of John be x.
Then number of Minghua's stamps:
1 1/2 * x3/2 * x(3/2)xJohn's: x
Minghua's: (3/2)x
Find the zeros of: [tex]f(x)=-\frac{1}{1500} (x^3+10x^2-275x-1500)[/tex], and the use them to find all of the linear factors of the polynomial function
The linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).
How to find the linear factors of a cubic equation
Cubic equations are polynomials of third grade, whose standard and factor forms are shown below:
Standard form
y = a · x³ + b · x² + c · x + d
Factor form
y = (x - r₁) · (x - r₂) · (x - r₃)
Where r₁, r₂, r₃ are the zeros of the cubic equation.
There are several approaches to find the roots of the polynomial, in this question we decided to use the graphical approach, which offers sufficiency and quickness for analysis. The roots of the polynomials are the points that pass through the x-axis.
In accordance with the image attached below, the polynomial has three real roots: r₁ = - 20, r₂ = - 5, r₃ = 15. Then, the linear factors of the polynomial function are f(x) = - (1/1500) · (x + 20) · (x + 5) · (x - 15).
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For limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 minus = and limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 plus= . these limits indicate there is an asymptote of .
The given limit indicates that there is a vertical asymptote at x = 2.
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator. When x tends to these values laterally, the limit of f(x) goes to infinity.
In this problem, the function is:
[tex]f(x) = \frac{x^2 - 4x - 12}{x - 2}[/tex]
The vertical asymptote is:
x - 2 = 0 -> x = 2.
Hence:
[tex]\lim_{x \rightarrow 2^+} f(x)[/tex] and [tex]\lim_{x \rightarrow 2^-} f(x)[/tex] are either positive infinity or negative infinity.
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Point W is on line segment \overline{VX} VX . Given VX=4x,VX=4x, VW=3x,VW=3x, and WX=5,WX=5, determine the numerical length of \overline{VX}. VX .
The numerical length of VX is undefined
How to determine the numerical length of VX?The given parameters are
VX = 4x
VW = 3x
WX = 5x
Point W is on line segment VX
So, we have
VX = VW + WX
This gives
4x = 3x + 5x
Evaluate
4x= 8x
The above equation is false
Hence, the numerical length of VX is undefined
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the cost of 4 ice cream cones from the snack bar was $10.40. if each ice cream costs the same amount, which model correctly illustrates the relationship? check all that apply
Jay went to an amusement park. the park charges an entrance fee of $10.50 and $4.50 for every ride. jay spent $46.50 on entrance fees and rides. which fuction can be used to find the number of rides he went on? f (x) = 4.5 x + 10.5 f (x) = 4.5 x f (x) = 4.5 x minus 10.5 f (x) = negative 4.5 x
The function that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.
Also, on solving the function we get that, Jay went on 8 rides.
We assume the number of rides Jay spent to be x.
The cost of each ride is given to be $4.50.
Thus, the total amount Jay spent on rides = $4.50x.
The entrance fee to the park is given to be $10.50.
Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).
But, in the question we are given that Jay spend $46.50 altogether.
Thus, the function to find the number of rides Jay went on can be shown as:
f(x) = 4.5x + 10 = 46.5.
Hence, the first option is the right choice.
To find the number of rides he went, we can solve this function as:
4.5x + 10 = 46.5,
or, 4.5x = 46.5 - 10.5 = 36,
or, x = 36/4.5 = 8.
Thus, Jay went on 8 rides.
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What is the best example of elasticity demand in the context university of rwanda
Answer:
Step-by-step explanation:
Elasticity Demand
The flexibility of interest is a significant minor departure from the idea of interest. Request can be delegated as versatile, inelastic, or unitary.Flexible interest is one in which the adjustment of the amount requested because of an adjustment of cost is huge. An inelastic interest is one in which the adjustment of the amount requested because of an adjustment of cost is little.The equation for processing versatility of interest is:(Q1 - Q2)/(Q1 + Q2)
(P1 - P2)/(P1 + P2)
In the event that the recipe makes an outright worth more prominent than 1, the interest is flexible. At the end of the day, the amount changes quicker than the cost. On the off chance that the worth is under 1, the request is inelastic. All in all, the amount changes more slowly than the cost. In the event that the number is equivalent to 1, the flexibility of interest is unitary. All in all, the amount changes at a similar rate as the cost.An illustration of items with a flexible interest is purchaser durables. These are things that are bought inconsistently, similar to a clothes washer or an auto, and can be deferred assuming the cost rises. For instance, vehicle refunds have been extremely fruitful in expanding car deals by diminishing costs.#SPJ10
The graph of the piecewise function f(x) is shown.
On a coordinate plane, a piecewise function has 2 connecting lines. The first line has a closed circle at (negative 2, negative 5) and goes up to a closed circle at (2, negative 1). The second line has a closed circle at (2, negative 1) and goes down to an open circle at (4, negative 2).
What is the range of f(x)?
{x | −2 ≤ x < 4}
{x | −2 < x ≤ 4}
{y | −5 < y < −1}
{y | −5 ≤ y ≤ −1}
Answer: {y | −5 ≤ y ≤ −1}
Step-by-step explanation:
The extreme values are -5 and -1.
There is a closed circle at (-2, -5), so -5 is in the range.There is a closed circle at (2, -1), so -1 is in the range.So, the answer is {y | −5 ≤ y ≤ −1}.
On a coordinate plane, kite U V W X with diagonals is shown. Point U is at (negative 2, 5), point V is at (5, 4), point W is at (8, negative 5), and point X is at (negative 1, negative 2).
Prove that the diagonals of kite UVWX are perpendicular.
Step 1: Determine the slope of XV.
The slope of XV is
.
Step 2: Determine the slope of UW.
The slope of UW is
.
Step 3: The slopes of the diagonals are
.
The diagonals of kite UVWX are
.
The information about the coordinate plane shows that the slope of XV is 1.
How to illustrate the information?From the information, the slopes of the diagonals are negative reciprocals. Therefore, the slope of UW is -1 and the slope of XV is 1.
The diagonals of kite UVWX are perpendicular.
It should be noted that negative reciprocals in a kite create a perpendicular bisector. So the two lines share a midpoint so they are perpendicular.
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Answer:
Step-by-step explanation:
The slope of XV is
1
The slope of UW is
–1
The slopes of the diagonals are
negative reciprocals
The diagonals of kite UVWX are
perpendicular
.
Maria buys some soft drinks for her friends. she buys a total of 13 drinks for a total of $32. if medium drinks, m, cost $3 and small, s, drinks $2, write a system of equations which can be used to find how many small drinks and medium drinks she bought.
The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
What is system of linear equations?A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).
Formation of the linear equation for the drinks bought by Maria:
The total number of drinks bought by the Maria is 13.
Lets say 'm' represents the number of medium drink.
's' represents the number of small drink.
Total drinks comprises of medium drinks and small drinks.
Thus,
s + m = 13, is the first linear equation.
Now medium drinks cost $3.
Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)
Total price for medium drinks = 3×m
Similarly,
Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)
Total price for small drinks = 2×s
Total cost = total cost of medium drink + total cost of small drink
32 = 3×m + 2×s, is second linear equation.
From equation first substitute the value of 'm' in second equation to fine the total number of drink.
32 = 3×(13 - s) + 2×s
32 = 39 - 3s + 22
s = 7
Put s = 7 in first equation and calculate 'm'.
m = 13 -7
m = 6
Therefore, The total number of small drinks 's' bought by Maria is 7.
The total number of medium drinks 'm' drinks bought by Maria is 6.
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1. Determine the most precise name for the quadrilateral.
rhumbos
it is the most precise name because it gives more information about the quadrilateral
Solve 5x=125 using the one-to-one property of exponents.
A) X=In(125)
B) x = 1
C) x = 3
OD) x = 5
Anyone is here
Answer:
Step-by-step explanation:
hello :
A) X=In(125)
Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called _____ variables.
The independent variable that caused a change in the dependent variable is called cofounding variable.
Given the Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called _____ variables.
These are variables in statistics other than the dependent and independent variables which can also be important to a researcher because it affects the dependent variable.
Confounding variables can also be called influences, external factors or third variables because they mostly affect the outcome of a research and prevent a researcher from achieving its objectives.
Hence, Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called cofounding variables.
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Does (5,-8),(3,5),(3,-3),(2,8) represent a function
Answer:
No
Step-by-step explanation:
So to determine whether this is a function, we first need to know what a function is. A function is defined as for each input, there is only 1 output.
This output doesn't have to be unique and other inputs can output this output, but it only matters that each input outputs only one output.
So let's look at what you provided and specifically these two points:
(3, 5)
(3, -3)
This input 3, outputs 5 and -3, which is not a function since this input outputted 2 different outputs. One thing to note is had you provided the two points: (3, 5), (3, 5) instead then it would still be a function because the input outputted the same output of 5 both times.
A survey was conducted in the class about their favorite subjects. 35% of the class voted for Math and Science. 45% of the class voted for Math. Find the percent of the class who voted for Math also voted for Science.
The percent of the class who voted for Math also voted for Science is 38.8%
How to find the percent who voted math and also voted for science?Therefore,
1 = p(m) + p(s) - p(m ∩ s)
Hence,
p(m) = 45% = 0.45
p(s) = ?
p(m ∩ s) = 35% = 0.35
Therefore,
1 = 0.45 + p(s) - 0.35
1 - 0.45 + 0.35 = p(s)
p(s) = 0.9
Therefore,
p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%
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For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet can fill the tub in 8 minutes. If both faucets are used together, how long will it take to fill the tub
If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.
What is the concept of time and work?Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.
When the amount of work is constant, efficiency is inversely proportional to the length of time required.
Important Time and Work Formula:
Work Done = Time Taken × Rate of Work.Rate of Work = 1 / Time Taken.Time Taken = 1 / Rate of Work.If a piece of work is done in x number of days, then the work done in one day = 1/x.Total Wok Done = Number of Days × Efficiency.Efficiency and Time are inversely proportional to each other.Calculation for the time taken by both faucet to fill the tub.
The unit should be tub per minute.
Then, do the reciprocal of the result to have minute per tub.
The hot water faucet can fill the tub in 12 minutes.
The cold water faucet can fill the tub in 8 minutes.
The filling rate for both faucets filling the tub at the same time is the sum of their rates.
Let 't' be the time taken by both faucets.
Then,
[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]
[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]
[tex]\frac{1}{t} =\frac{20}{96}[/tex]
[tex]\frac{t}{1} =\frac{96}{20}[/tex]
t = 4.8
Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.
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Helen had $12 but spent $3 of it. What per cent did she spend?
12%
25%
30%
33 1/3%
Answer:
25%
Step-by-step explanation:
3/12 = 0.25 = 25%
Answer:
25%
Step-by-step explanation:
$3 pent out of the original $12. We can ask what is the percentage of $12 that is equal to $3? This can be written as:
X($12) = $3, where X is the percentage.
X = (3/12)
X = 0.25 or 25%
URGENT WHOEVER ANSWERS CORRECTLY AND FAST GETS BRAINLY
40% of the house plants were watered today. 320 house plants were watered. Which equation can be used to find how many plants there were?
40x = 320
0.40x = 320
x
=
0.40
--------
320
x = 0.40(320)
Answer:
0.40x = 320
Step-by-step explanation:
If 40% of the total houseplants watered = 320
0.40 times x (total houseplants) = 320
Answer:
[tex]\frac{x}{0.40} = 320 Plants[/tex]
Step-by-step explanation:
[tex]\frac{x}{0.40} = 320 Plants[/tex]
[tex]X = (0.40)(320)Plants[/tex]
[tex]X = 128Plants[/tex]
Given the series below, find S29.
{13+4+(−5)+(−14)+(−23)+...}
Select one:
a. -2,480
b. -2,752
c. -3,016
d. -3,277
Answer:
d
Step-by-step explanation:
there is a common difference between consecutive terms in the series, that is
4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 13 and d = - 9 , then
S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]
= 14.4(26 + (- 252))
= 14.5(26 - 252)
= 14.5 × - 226
= - 3,277
find the volume of a sphere with a raduis of 3 in.
Answer:
V≈113.1in³.
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What is the type? f(x)=-1/5x³-5+10x²
Select the correct answer.
What is the zero of the function represented by this graph?
x = 5
x= -6
x=-5
x=6
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the explanation ~
Zeros or roots of a function is the value of independent variable (usually x - coordinate or absicca) where the value of dependent variable (y - coordinate or ordinate) is 0.
That is :
The point where it cuts the x - axis, it has an x - coordinate = -6
Therefore, we can conclude that The zero of given function is -6
Answer:
x = -6.
Step-by-step explanation:
It is where the graph cuts the x-axis (where the function is zero).
That is -6.
URGENT!!! PLEASE HELP!!!
Find the value of x that makes the parallelogram a square. Show your steps.
(13x + 5.5)°
You will be awarded 5 points for the correct answer and 5 points for the supporting
work.
Answer: 6.5
Step-by-step explanation:
Since all squares are rhombi, and diagonals of a rhombus intersect at right angles, this means that
[tex]13x+5.5=90\\\\13x=84.5\\\\x=6.5[/tex]