The distance between two points is defined as follows:
[tex]d(a,b)=\sqrt[]{(x_2-x_1)^2-(y_2-y_1)^2}[/tex]Replacing the points in the equation:
[tex]\begin{gathered} a\to(-4,1) \\ b\to(3,-4) \\ d(a,b)=\sqrt[]{(3_{}-(-4))^2-(-4_{}-1_{})^2} \\ d(a,b)=\sqrt[]{(7)^2-(-5_{})^2} \\ d(a,b)=\sqrt[]{49-25} \\ d(a,b)=\sqrt[]{24} \\ d(a,b)=4.8989 \end{gathered}[/tex]The distance between the two points is 4.89 aprox 4.9
You need to arrange five of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the booksmakes a difference to you?
For the first place in the shlef you have 5 possibilities to choose, for the second place you have 4 possibilities, for the third you have three possibilities and so on. This means that we can find the number of ways to arrange the books with a factorial, that is:
[tex]5!=5\cdot4\cdot3\cdot2\cdot1=120[/tex]Therefore, there are 120 ways to arrange your books in the shelf.
12 Bernadette has recently opened her own soup store. It costs her $360 a month plus $2.50 for each bowl of soup she makes. Bernadette brings in $5.50 on each bowl of soup she sells. How many bowls of soup would Bernadette need to sell to make money each month? Explain.
Answer:
So, to make money each month, Bernadette would need to sell at least 121 bowls of soup.
Step-by-step explanation:
Cost function:
Has a fixed cost($360), and a variable cost($2.5 per bowl). So the cost of each making b bowls is given by:
C(b) = 360 + 2.5b
Profit function:
She earns $5.5 for each bowl of soup she sells. So the earnings of selling b bowls are given by:
P(b) = 5.5b
How many bowls of soup would Bernadette need to sell to make money each month?
Bernadette will make money if the profit is higher than the cost, that is:
P(b) > C(b)
Then
5.5b > 360 + 2.5b
5.5b - 2.5b > 360
3b > 360
b > 360/3
b > 120
So, to make money each month, Bernadette would need to sell at least 121 bowls of soup.
Pls help fast !!!!!!!!!!!
Answer: last one
Step-by-step explanation:
I'm not 100% sure but I would like to help you and I think it is. I say this because the 7 can't have a different outcome.
Can I get a in depth explanation to simplifying non perfect roots with quotients? Ex: image
To get the answer, we will attempt to simplify the first expression into its simplest format.
[tex]\sqrt[]{\frac{126xy^5}{32x^3}}[/tex]We begin by dividing both the numerator and the denominator by 2:
[tex]\sqrt[]{\frac{63xy^5}{16x^3}}[/tex]Since x appears in both the numerator and the denominator, we can simplify such that
[tex]\frac{x}{x^3}=\frac{1}{x^2}[/tex]Hence, we have the expression to be
[tex]\sqrt[]{\frac{63y^5}{16x^2}}[/tex]Let us compare the both expressions to each other now:
[tex]\sqrt[]{\frac{63y^5}{16x^2}}=\sqrt[]{\frac{63y^5}{ax^b}}[/tex]Therefore,
[tex]\begin{gathered} a=16 \\ b=2 \end{gathered}[/tex]find the exact area of a sector if the radius of the circle is 4 cm, and the angle of the sector is π radian.
Area of sector = 8π cm²
Explanation:For angle in degrees:
Area of sector = θ/360 × πr²
For angle in radians:
Area of sector = 1/2 r²θ
radius = 4 cm
angle of the sector = π radian
Area of sector = 1/2 × (4)² × π = 16/2 × π
Area of sector = 8π cm²
A customer recelves a discount on each purchase. If thecustomer's bill is $1,600 before the discount and the bill is $1,460after the discount what is the percent discount?O A) 8.8%B) 9.5%C) 11.4%D) 91.3%searchC
The customer's bill before the discount is $1600.
The customer's bill after the discount is $1460.
Determine the discount on the customer's bill.
[tex]\begin{gathered} D=1600-1460 \\ =140 \end{gathered}[/tex]The discount is applied on the customer's bill before the discount. Let the percent discount is d%.
Determine the discount percent on the customer bill.
[tex]\begin{gathered} \frac{d}{100}\cdot1600=140 \\ d\cdot16=140 \\ d=\frac{140}{16} \\ =8.75 \\ \approx8.8 \end{gathered}[/tex]So percent discount is 8.8%.
Commute Time to Work The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume thatcommuting times are normally distributed and that the standard deviation is 6.1 minutes, find the probabilities. (b) The selected commuter spends less than 11 minutes commuting one way.P (x<11) =
mean: 25 minutes
standard deviation: 6.1 minutes
A 11 minutes commute time is 2.30 standard deviations away from the mean. In this case, we have, for a normal distribution:
[tex]P(x<11)=P(x<\mu-2.3\sigma)=0.0107[/tex]The ratio of students who play video games to those who don't play video games if 7:2. If a class has 126 students that play video games, how many students do not play video games?
Answer:
98 students play videogames
28 students dont play videogames
Step-by-step explanation:
we have to make n equation using 7:2=126 so we are going to intaduce x witch will give us 7x+2x=126
9x=126 then we divide it with 9 witch gives us x=14 then we multiply x by 7 and agen x by 2
Andrew buys 975 green peppers and 1,250
hot chili peppers. He uses all of those
peppers to make two types of sauce.
part A
Write a system of equations that shows how
Andrew can use the peppers to make x pints
of Sauce I and y pints of Sauce II.
The system of equation is given by
x + y = 975
x + y = 1250
What is system of equation?
Systems of equations are sets of equations where the solution is the intersecting point (s) between the equations. Most of the systems of equations you see in algebra are sets of two linear equations in the standard form Ax + By = C.
Andrew buys :
green peppers = 975
hot chilli peppers = 1,250
Part A
He uses green peppers (975) to make,
x pints of Sauce I
y pints of Sauce II
So, equation will be,
=> x + y = 975 .........(i)
Simillarly he uses hot chilli peppers (1,250) to make,
x pints of Sauce I
y pints of Sauce II
So, 2nd equation will be,
=> x + y = 1,250 .........(ii)
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What is a formula for the nth term of the given sequence? Also how do I find it with further questions
option (D) aₙ = 300 (5 / 3)¹⁻ⁿ is a formula for the nth term of the given sequence.
The sequence given is:
300, 180, 108
The initial term = a = 300
We will first calculate the common ratio between the terms:
Common ratio = r
r = 180 / 300
r = 18 / 30
r = 3 / 5
Also,
108 / 180 = 3 / 5
Now, the formula for the nth term is given by:
aₙ = a rⁿ⁻¹
Substitute the values:
aₙ = 300 (3 / 5)ⁿ⁻¹
which can also be written as:
aₙ = 300 (5 / 3)¹⁻ⁿ
Therefore, we get that, option (D) aₙ = 300 (5 / 3)¹⁻ⁿ is a formula for the nth term of the given sequence.
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Solve the equation. Justify each step using the word bank provided. *Properties may be used more than once! Given Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Distributive Property Combine Like Terms 2(x − 4) − 9 = 3(2x + 1) + 4
The result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6
The equation is
2(x-4)-9 = 3(2x+1)+4
The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.
2(x-4)-9 = 3(2x+1)+4
Apply distributive property in the equation
2x-8-9 = 6x+3+4
Add the like terms in the equation
2x-17 = 6x+7
Rearrange the terms and combine the like terms in one terms
2x-6x = 7+17
Combine the like terms
-4x = 24
x = 24/-4
x = -6
Hence, the result of the equation 2(x-4)-9 = 3(2x+1)+4 is x= -6
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Solve in simplest form
3x(9/8)
Answer:
27x/8
Step-by-step explanation:
3*9/8
3x*9/8
27x/8
If Ariana writes 6 pages in 2 minutes in a 50-page novel, what is the constant of proportionality, unit rate in one minute?
Let k be the constant of proportionality
Let p be the number of pages
Let t be the time taken
P ∝ t
p = kt
K = p/t
k = 6/2 = 3/1
The unit rate is 3 pages in one minute
What is the area in square feet of the lawn ?
Given:
Find-:
Area of shape
Explanation-:
The area of a rectangle is:
[tex]\text{ Area }=\text{ Length }\times\text{ Width}[/tex]The shape is:
For the first region:
[tex]\begin{gathered} \text{ Length }=80 \\ \\ \text{ Width }=40 \end{gathered}[/tex]The area of the first region is:
[tex]\begin{gathered} \text{ Area }=\text{ Length}\times\text{ Width} \\ \\ =80\times40 \\ \\ =3200\text{ ft}^2 \end{gathered}[/tex]The area of the second region is:
[tex]\begin{gathered} \text{ Length }=80-60 \\ \\ \text{ Length }=20 \\ \\ \text{ Width }=60 \end{gathered}[/tex]The area of the second region is:
[tex]\begin{gathered} \text{ Area }=\text{ Length}\times\text{ Width} \\ \\ \text{ Area }=20\times60 \\ \\ \text{ Area }=1200\text{ ft}^2 \end{gathered}[/tex]The total area of the lawn is:
[tex]\begin{gathered} \text{ Area }=3200\text{ ft}^2+1200\text{ ft}^2 \\ \\ \text{ Area }=4400\text{ ft}^2 \end{gathered}[/tex]The area of lawn is 4400 ft²
An object is traveling at a steady speed of 9 9/10 mi/h. How long will it take the object to travel 2 1/10 miles? First round to the nearest integer to find the estimated answer. Then find the exact answer.
Answer:
See below
Step-by-step explanation:
Distance / rate = time
2 1/10 mi / 9 9/10 mi/hr
21/10 / 99/10 = 21/99 hr = 12.73 minutes
ZERO hr if rounded to nearest integer hr
= 13 minutes as nearest integer minutes
exact is 21/99 hr = 7/33 hr
The mean number of blue m&m's in a fun size bag is 3.4 with a standard deviation of .2. What is the probability of getting more than 4 blue
m&m's in a bag? Write your answer as a percentage. Do NOT include the percentage sign
If the mean number of blue m&m's in a fun size bag is 3.4 with a standard deviation of .2. The probability of getting more than 4 blue m&m's in a bag is 0.00135.
How to determine the probability?Given data:
Mean = 3.4
Standard deviation = .2
Now let find or determine the z-score before finding the probability of getting more than 4 blue
Z = 4 blue - mean / standard deviation
Hence,
Z = 4 - 3.4 / .2
Z = 0.6 / .2
Z = 3
The probability was determine using the normal distribution table
P(x > 4) = P( Z=3)
= 0.00135
Therefore we can conclude that the probability is 0.00135.
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The following table represents a linear function. use the value in the tables to find the slope of the line.
true or false3. The expression 78 − 22 + − 4 is a polynomial of degree 8
The expression is:
[tex]7x^8-2x^2+x-4^{}[/tex]In general, a polynomial has the form:
[tex]a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,a_n\ne0[/tex]And we say that the polynomial is the degree n.
In our expression. a_n=7 and that is not equal to zero. Then, the expression is of degree 8 since a_n=7=a_8. The answer is true.
Find the complex zeros of the following polynomial function and write F in factored form.
Answer:
The complex zeros are:
[tex]\begin{gathered} x_1=-2i \\ x_2=2i \end{gathered}[/tex]The factored polynomial is:
[tex]f(x)=(x-1)(x-3)(x^{2}+4)[/tex]Step-by-step explanation:
Factoring the polynomial, we'll have:
[tex]f(x)=(x-1)(x-3)(x^2+4)[/tex]To find the complex zeroes, let's solve for the quadratic term as following:
[tex]\begin{gathered} x^2+4=0 \\ \rightarrow x^2=-4 \\ \rightarrow x=\pm2i \end{gathered}[/tex]Cann you prove the two triangles below to be congruent, if so which postulate did you use to prove them congruent
The angles shown in each triangle are congruent. Then, by SAS postulate, the triangles are congruent
all you need is on the photo please just give me the answer don't do step-by-step is so confusing is homework
You have the following function:
f(x) = x² - x
- In order to determine the vertex of the function, consider that for the general form of a quadratic function:
f(x) = ax² + bx + c
the value of x at the vertex is:
x = -b/2a
for the given function you have a = 1, b = -1, c =0:
x = -(-1)/2(1) = 1/2 = 0.5
next, replace the previous value of x into the function:
f(1/2) = (1/2)² - (1/2) = 1/4 - 1/2 = -1/4 = -0.25
Hence, the vertex is (0.5 , -0.25)
- The axis of symmetry is the value of x atthe vertex:
x = 0.5
- The x-intercepts are the zeros of the function:
x² - x = 0 by factorizing
x(x - 1) = 0
Then, the zeros are:
x =0
x = 1
Hence, the x-intercepts are x=0 and x=1
- Due to the coefficient a is positive and the term ax² is the dominant term, this curve has a minimum. This minimum is the vertex (0.5 , -0.25)
- The minimum value of the function is -0.25
- The y-intercept is the value of y when x=0:
f(0) = 0² - 0 = 0
Find the greatest common factor.6m, 2mWrite your answer as a constant times a product of single variables raised to exponents.
For 6m and 2m the comun factor corresponds to 2m, because 2 can divide 6 and 2 and m appears on both expressions with the same exponent.
Kathleen and ednardo both ran from the park entrance along the loop Kathleen started walking from the park entrance and gets a five mile Head Start of aarona the graph shows how far they have both traveled
Answer:
75
Step-by-step explanation:
They meet up when their distance traveled is the same (in other words, when the graphs intersect).
The graphs intersect x=75.
Drag the tiles to the boxes to form correct pairs.Consider functions fand g.(1) = 1 - 12g(x) = VII – 45Evaluate each combined function, and match it to the corresponding value.0VISV3 - 3-303(9.5) (2)(+) (2)(9 - 1)(-1)(-1)
We have the following functions:
[tex]\begin{gathered} f(x)=1-x^2, \\ g(x)=\sqrt[]{11-4x}\text{.} \end{gathered}[/tex]1) We evaluate (g · f)(2):
[tex](g\cdot f)(2)=g(2)\cdot f(2)=\sqrt[]{11-4\cdot2})\cdot(1-2^2)=-3\cdot\sqrt[]{3}\text{.}[/tex]2) We evaluate (g + f)(2):
[tex](g+f)(2)=g(2)+f(2)=(\sqrt[]{11-4\cdot2})+(1-2^2)=\sqrt[]{3}-3.[/tex]3) We evaluate (g - f)(-1):
[tex](g-f)(-1)=g(-1)-f(-1)=\sqrt[]{11-4\cdot(-1)}-(1-(-1)^2)=\sqrt[]{15}\text{.}[/tex]4) We evaluate (f / g)(-1):
[tex](\frac{f}{g})(-1)=\frac{f(-1)}{g(-1)}=\frac{(1-(-1)^2)}{\sqrt[]{11-4\cdot(-1)}}=\frac{0}{4}=0.[/tex]Answers
[tex]\begin{gathered} (g\cdot f)(2)=-3\cdot\sqrt[]{3} \\ (g+f)(2)=\sqrt[]{3}-3 \\ (g-f)(-1)=\sqrt[]{15} \\ (\frac{f}{g})(-1)=0 \end{gathered}[/tex]If a shape is dilated by a scale factor of 3, what is the resulting perimeter? A.)The new perimeter is 9 times larger than the preimageB.)The same as theperimeter of thepreimageC.)The new perimeter is 4 times the originalD.)The new perimeteris 3 times largerthan the preimage
The perimeter of the figure is sum of the side of the figure. If figure is dilated by factor of 3, means that each side of the figure is dilated by 3.
The addition of dilated side to obtain the perimeter results in 3 times the original perimeter.
So new perimeter is 3 times larger than the preimage. Option D is correct.
Bryson's cat had six kittens this summer. Each kitten weighs 5 1/3 ounces. How much did all the kittens weigh together?
Each kitten weighs 5 1/3 ounces. Converting this weight to improper fraction, it becomes
16/3 ounces
Since the total number of kittens is 6, the weight of all the kittens is
16/3 * 6 = 32 ounces
The total weight is 32 ounces
A 2 1/2-pound box of frozen corn costs $1.65. How much does a 4-ounce serving cost?
Given data:
The given cost of 2 1/2 pound of box is $1.65.
The given expression can be written as,
[tex]\begin{gathered} 2\frac{1}{2}\text{ lb=1.65} \\ 2.5\text{ lb=1.65} \\ 1\text{ lb(}\frac{16\text{ ounce}}{1\text{ lb}})\text{ =0.66} \\ 16\text{ ounces=0.66} \\ \frac{1}{4}\times16\text{ ounces=}\frac{1}{4}\times\text{0.66} \\ 4\text{ ounces=0.165} \end{gathered}[/tex]Thus, the cost of 4 ounces is $0.165.
A carton of eggs contains 12 eggs. Each carton of eggs costs $1.89.A function, f(x), is written to represent the cost of purchasing x cartons of eggs.What is the practical domain for the function f(x)?all whole numbersall real numbersall whole numbers that are multiples of 12all positive integers
Given the information on the problem, we have the following function:
[tex]f(x)=1.89x[/tex]where 'x' represents the numer of cartons of eggs.
Notice that this is a real function, but it can only take integer values. Therefore, the practical domain of the function f(x) is positive integers
What is the approximate slope of the curve with equation-atx=1.2?
a) -25
b) -1/25
c) 25
d) 1/25
The most appropriate choice of slope of a curve will be given by
Slope of the curve at x = 1.2 = -25
First option is correct
What is slope of a curve?
Slope of curve at a point is the tan of the angle that the tangent to the curve at that point makes with the positive direction of x axis.
Here,
f(x) = [tex]\frac{1}{x - 1}[/tex]
[tex]f^{'}(x) = \frac{d}{dx} (\frac{1}{x-1})[/tex]
= [tex]-(x -1)^{-2}[/tex]
= [tex]-\frac{1}{(x-1)^2}[/tex]
At x = 1.2,
Slope = [tex]f^{'}(1.2) = -\frac{1}{(1.2 - 1)^2}[/tex]
= -[tex]\frac{1}{0.04}[/tex]
= -25
First option is correct
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Use the table below. I don’t know how to do ordered pairs I forgot.
Solution
To write in ordered pairs is to arrange it in the form of x and y values
The ordered pairs are
[tex]\begin{gathered} (5.0,4.20) \\ (6.0,5.05) \\ (7.0,5.90) \\ (8.0,6.75) \end{gathered}[/tex]