In general, the equations of a line in point-slope form and slope-intercept form are:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y=mx+b \end{gathered}[/tex]respectively. Where m is the slope of the line, b is a constant, and (x_1, y_1) is a point on the line.
Thus, the point-slope form of the line described by the problem is:
[tex]y-3=m(x-5)[/tex]We simply need to calculate the slope of the line. For that, we simply require 2 points, we already have (5, 3) and, since the x-intercept is 6, we can deduce that the line goes through (0,6).
Therefore, the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{0-5}=-\frac{3}{5}[/tex]Then, the solution is:
[tex]y-3=-\frac{3}{5}(x-5)[/tex]Describe how you can use the factors of a quadratic function to find its zeroes. (Please try to answer it specifically)
Oce we have the factors, we must equal each factor to zero, then we solve for x to find the zeroes of the equation.
Ex.
(x - 3)(x + 2) = 0
the factors are (x - 3) and (x + 2)
Equal to zero
x - 3 = 0 x + 2 = 0
Solve for x
x = 3 x = -2 and these are the zeroes of the
equation.
Answer:
To find de ceros you can take each factor and use the 0 product property, then you solve to find the value of the cero.
Solve this problem, please and thank you. Picture included. Algebra 2.
107. Cranky mower To start her old lawn mower, Rita has
S to pull a cord and hope for some luck. On any partic-
ular pull, the mower has a 20% chance of starting.
(a)
Find the probability that it takes her exactly 3 pulls to
start the mower.
(b) Find the probability that it takes her more than 6
pulls to start the mower.
108. 1-in-6 wins Alan decides to use a different strategy for
the 1-in-6 wins game of Exercise 90. He keeps buying
one 20-ounce bottle of the soda at a time until he gets
a winner.
Find the probability that he buys exactly 5 bottles.
(b) Find the probability that he buys at most 6 bottles.
Show
your work.
According to the binomial distribution, there is a 0.128 = 12.8% chance that it will take her precisely 3 pushes to start the mower.
she will need to start the mower more than 10 times.There are just two possible results for each pull. The lawnmower either starts or it doesn't. The binomial distribution is employed to answer this question since the likelihood that the mower will start on a pull is independent of all other pulls.Binomial distribution of probabilitiesThe conditions are: x is the total number of victories.The number of trials is n.P represents the likelihood that a trial will be successful.It has a 20% chance of starting on any given pull, therefore
Item
a:This probability is P(X = 0) when n = 2, multiplied by 0.2, which is the probability that it starts on the third, and it is that it doesn't start on the first two. Hence:
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:When n = 10, this probability is none on the first 10 and is hence P(X = 0):
Her chances of needing more than 10 pushes to start the mower are 0.1074, or 10.74%.
It has a 0.128 = 12.8% chance that she starts the mower with exactly 3 pulls.
Item b:On the first, there is no chance in this.
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The Fishers ate out at a restaurant and paid a total of $68.22, including the tip. If the Fishers tipped 20%, what was the cost of the meal?
Explanation:
Multiply 68.22 by 1.2 to get 81.864 or $81.86
Dilate the figure by the scale factor. Then enterthe new coordinates.A(-1,1)B(4,0)K=5A'( [?],[])B'( 1 )C'([ ],[]).C(1,-3)EnterAnswer
A dilation is a proportional stretch or shrink of an image based on a scale factor. It is represented by:
[tex](x,y)\rightarrow(K\cdot x,\text{ K}\cdot y)[/tex]Then, for the figure on the question tab and scale factor of 5:
[tex]A(-1,1)\rightarrow A^{\prime}(-1\cdot5,1\cdot5)=A^{\prime}(-5,\text{ 5)}[/tex][tex]B(4,0)\rightarrow B^{\prime}(4\cdot5,0\cdot5)=B^{\prime}(20,0)[/tex][tex]C(1,-3)\rightarrow C^{\prime}(1\cdot5,-3\cdot5)=C^{\prime}(5,-15)[/tex]I want to select average students . If the mean score on the qualifying test is 43.2 and the standard deviation is 8.6. find the score that cutt off the middle 50 percent of all scores
The score that cutt off the middle 50 percent of all scores is 43.2
Explanations:For a normal distribution, the normal value is the mean
It divides the curve in 50%-50%
Mean score, μ = 43.2
Standard Deviation, σ = 8.6
P(X≤a)=0.5
Use Z =(X-μ)/δ ~N(0;1)
b =(a-μ)/σ
P(Z≤b)=0.5
The value is b=0 (the mean for Z)
a=(b*σ)+μ
a=(0*8.6)+43.2
a=43.2
Therefore, the score that cutt off the middle 50 percent of all scores is 43.2
Wich expression is equivalent to a+(c+7)
Given the expression:
[tex]a+(c+7)[/tex]To determine an equivalent expression, the first step is to open the bracket.
Therefore:
[tex]undefined[/tex]List the sides of ABC from shortest to longest.CB AB ACАВ, СВ, АСАВ, АС, СВCB AC AB
First we need to calculated the missing angle
the intern angles of a triangle must be 180°
angle +63+60=180
angle=57
the shortest side is AB
the next side is AC
and the longest side is CB
t
For her phone service, Lucy pays a monthly fee of $15, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is$84.75What are the possible numbers of minutes she has used her phone in a month?Use m for the number of minutes, and solve your inequality for m.
m ≥ 1395 minutes
Explanation:Monthly fee = $15
fee paid per minute of use = $0.05
let the number of minutes she used = m
The least amount she has been charged = $84.75
least is written as ≥ $84.75
The equation:
Monthly fee + fee per minute(number of minutes) = The total charge
The equal sign changed below since the question mentioned the least amount
$15 + 0.05(m) ≥ $84.75
15 + 0.05m ≥ 84.75
To get the possible number of minutes, we will solve for m:
15 + 0.05m ≥ 84.75
subtract 15 from both sides:
0.05m ≥ 84.75 - 15
0.05m ≥ 69.75
divide both sides by 0.05:
m ≥ 69.75/0.05
m ≥ 1395 minutes
The possible number of minutes she has used her phone in a month is at least 1395 minutes
Eric needs to manufacture a turntable with a circumference of `140pi` centimeters. If the allowed error tolerance in the circumference is `+-5` centimeters, how close to the ideal radius must he control the radius of the turntable?
A. `10/pi`
B. `2/pi`
C. 5/(2pi)`
D. `5/(4pi)`
Answer: is C. `5/(2pi)`
The correct option is C 5/(2π) . The ideal radius must he control the radius of the turntable will be 5/(2π) .
What is meant by circumference?circle's circumference 22 inches around make up the circle. Periphery from the center to the sphere's circumference: 2: an object or figure's external boundary or surface The circumference, which in geometry refers to a circle or ellipse's perimeter, is derived from the Latin circumferens, which means "carrying around." In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. Any great circle's circumference, or the distance between any two planes that cross a sphere's center, is measured in meters. Any large circle that traverses a pole-designated point is known as a meridian. The shortest path between any two locations on a sphere is referred to as a geodesic.
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A card is chosen at random from a deck of 28 cards. The deck contains red, 12 black 7 blue, and 2 green cards. Thend the card is returned to the deck and New card is cosen. the table below shows the results of choosing 14 cards. for which color of card is the experimental probability the same as the theoretical probabicaras.Results red= 10 black=2 blue=1green=1
From the question, we can find that we have 7 red cards
so, the probability of chosen at random a card is
p(red)= 7/28
p(black)= 12/28
p(blue) = 7/28
p(green)=2/28
As after picking a card we return the card to the deck, and given that we chose 14 cards, our theoretical number of chosen cards should be around
p(red) = (7/28)x14 = 3.5
p(black) = (12/28)x14 = 6
p(blue) = (7/28)x14 = 3.5
p(green)= (2/28)x14=1
so the color that the experimental probability is the same as the theoretical probability is green
Cual es el resultado de (5)⁶
Answer:
15625
Step-by-step explanation:
5x5x5x5x5x5=15625
5 times itself 6 times
Fibonacci, Pythagoras and Descartes went out for breakfast. The total bill was $38.50. The tax rate was 7% and they left a 20% tip. Determine the total bill. Round to the nearest hundredth.so how much will each person pay if the bill was equally divided?
Given:
• Total bill = $38.50
,• Tax rate = 7% = 0.07
,• Tip = 20% = 0.20
Let's find the total bill after tax and tip.
Now, to find the total bill we have:
Total bill = bill + tax amount + tip amount
Where:
[tex]\begin{gathered} \text{ tax amount = 0.07}\times38.50=2.695 \\ \\ Tip\text{ amount = 0.20 }\times38.50=7.7 \end{gathered}[/tex]The tax amount is $2.695
The tip amount is $7.70
Now, to find the total bill, we have:
Total bill = $38.50 + $2.695 + $7.7 = $48.895 ≈ $48.90
Therefore, the total bill rounded to the nearest hundredth is $48.90
Part B.
To find the amount each person will pay if the bill was equally divided, let's divide the total bill by the number of people.
Where:
Number of people = 3
Hence, we have:
[tex]\frac{48.90}{3}=\text{ 16.30}[/tex]Therefore, the amount each person will pay is $16.30
ANSWER:
(a). $48.90
(b). $16.30
A small pool can hold 72.5 gallons of water . The pool is currently 3/4full how many gallons are in the pool ?
If we have that the pool is currently 3/4 full, we need to multiply this fraction by the total the small pool can hold. That is (with no units):
[tex]T=72.5\Rightarrow\frac{3}{4}T=\frac{3}{4}\cdot72.5=54.375[/tex]Therefore, the pool currently has 54.735 gallons (3/4 of its total capacity) (we multiply 3 times 72.5, and then we divide this result by 4).
Find the exact value of the expression:4^log16^(7)A) ✓7B) 2✓3C) 8D) 49
Answer:
A) ✓7
Explanation:
Given the expression:
[tex]4^{\log _{16}7}[/tex]First, we can rewrite 4 as a root of 16.
[tex]=16^{\frac{1}{2}\log _{16}7}[/tex]Next, by the power law of logarithm:
[tex]a\log x=\log x^a\implies\frac{1}{2}\log _{16}7=\log _{16}7^{\frac{1}{2}}[/tex]Thus, our given expression becomes:
[tex]=16^{\log _{16}\sqrt{7}}[/tex]Using the logarithm property below:
[tex]\begin{gathered} x^{\log _xa}=a \\ \implies16^{\log _{16}\sqrt[]{7}}=\sqrt[]{7} \end{gathered}[/tex]The exact value of the expression is ✓7.
Option A is correct.
Please help me quickly I don’t need the explanation I just need the answer I’m sorry I just need a fast
Notice that the area is equivalent to the area of the complete rectangle minus the area of the 3km x 4km rectangle.
[tex]A=TA-AS\text{.}[/tex]Now, the area of a rectangle is given by the following formula:
[tex]A=\text{width}\cdot\text{lenght.}[/tex]Therefore:
[tex]A=9km\cdot16km-3km\cdot4km\text{.}[/tex]Simplifying the above result, we get:
[tex]A=(144-12)km^2=132km^2.[/tex]Answer:
[tex]132km^2.[/tex]given the parent function f(x)=ab^x how could changing from a 2 to -2 cause f(x) to change? use words like "increasing" "decreasing" "positive" "negative" "domain" and "range" to describe the similarities and differences in the graph
Here, we want to get the response of the given function with respect to the change in the value of the leading coefficient
As we can see from the question, what we have is an example of an exponential function
Generally, with exponential function with a positive value for a, as the value of x moves closer to negative infinity, we have that the value of f(x) moves closer to 0. What this mean is that with a decrease in the value of x, the value of f(x) moves closer to 0
Hence, as the domain value moves closer to negative infinity, the value of the range moves closer to 0. Furthermore, as the value of the domain moves closer to positive infinity, the value of the range also close in on positive infinity
The above situation is for a being positive (given as 2)
Now, when a becomes negative, we have an opposite direction for the plot
Although, as the domain value moves closer to negative infinity, we have the value of f(x) being closer to zero. This is directly as above
However, as the domain moves towards positive infinity, the value of the range moves closer to negative infinity
In summary;
[tex]\begin{gathered} \text{for a = 2} \\ x\Rightarrow\text{ +}\infty\text{ , f(x)}\Rightarrow+\infty \\ x\Rightarrow-\infty,\text{ f(x) }\Rightarrow0 \\ \text{for a = -2} \\ x\Rightarrow+\infty,\text{ f(x)}\Rightarrow-\infty \\ x\Rightarrow-\infty,\text{ f(x)}\Rightarrow0 \end{gathered}[/tex]Match the equation in Column I with the correct description in Column II
As given by the question
There are given that the equations:
Now,
According to the given question,
The correct matching values are;
[tex]\begin{gathered} (a)\rightarrow E \\ (b)\rightarrow D \\ (c)\rightarrow C \\ (d)\rightarrow B \\ (e)\rightarrow A \end{gathered}[/tex]Evaluate each complex number.
√-49=
√-48=
√-5 x √-8=
Answer:
Step-by-step explanation:
the sophomores are planning a homecoming dance they want to hire a band band a charges $600 to play for the night Band B charges $375 plus $10 for each ticket sold at the sophomore sold 30 tickets which band Chargers higher
• Charges $600 to play for the night.
Notice that this cost is to play the whole night, it's a fixed cost.
[tex]A=600[/tex]Band B.• Charges $375 plus $10 for each ticket sold.
,• The sophomore sold 30 tickets.
This band has a fixed cost plus a fee of $10, which is $300 more because they sold 30 tickets.
So, the cost of this band would be
[tex]B=350+10(30)=350+300=650[/tex]Therefore, Band B will charge more than Band A.solve the value of the variable7(3x-4)=6x-4+3x+12
7(3x-4) = 6x -4 +3x +12
Distributing:
7(3x) -7(4) = 6x -4 +3x +12
21x - 28 = 6x -4 +3x +12
Combining similar terms:
21x - 28 = (6x + 3x) + (-4 +12)
21x - 28 = 9x + 8
9x is adding on the right, then it will subtract on the left
28 is subtracting on the left, then it will add on the right
21x - 9x = 8 + 28
12x = 36
12 is multiplying on the left, then it will divide on the right
x = 36/12
x = 3
Which of the following things is not contained at the plane B?
Related with the picture and your question, you should notice that an element is not contained in a set, that in your case is the plane B, when any of its points is outside of this one.
Then by the picture we could notice that the line q is not contained at the plane B, because the point G is inside q but it is not in B.
find the solution to the system of equations given below x=-4 5x+4y=-16
We have the following system of equations:
[tex]\begin{gathered} x=-4\ldots(A) \\ 5x+4y=-16\ldots(B) \end{gathered}[/tex]Solving by substitution method.
If we substitute equation A into equation B, we get
[tex]5(-4)+4y=-16[/tex]since 5(-4)= -20, we have
[tex]-20+4y=-16[/tex]If we move -20 to the right hand side as +20, we obtain
[tex]\begin{gathered} 4y=-16+20 \\ \end{gathered}[/tex]since -16+20=20-16 = 4, we get
[tex]4y=4[/tex]and finally, y is equal to
[tex]\begin{gathered} y=\frac{4}{4} \\ y=1 \end{gathered}[/tex]Since equation A tells us that x=-4, the solution of the system is
[tex]\begin{gathered} x=-4 \\ y=1 \end{gathered}[/tex]Which rule describes the transformation used tocreate GHI from DEF?A. (x,y) → (-y, x)B. (x,y) → (-X, -y)C. (x,y) → (x, -y)D. (x,y) → (y, -x)
Explanation:
We can see that the points are mapped as:
[tex]\begin{gathered} G(5,-1)\rightarrow D(-5,1) \\ H(5,2)\rightarrow E(-5,-2) \\ I(-1,2)\rightarrow F(1,-2) \end{gathered}[/tex]Therefore the coordinates of each point change to its opposite.
Answer:
The rule is:
B. (x, y) → (-x, -y)
Why aren't there infinitely many semi-regular tessellations?
Regular tessellations use identical regular polygons to fill the plane. The polygons must line up vertex to vertex, edge to edge, leaving no gaps.
Semi-regular tessellations have two properties:
• They are formed by two or more types of regular polygon, each with the same side length
,• Each vertex has the same pattern of polygons around it.
There are 8 semi-regular tessellations in total. We know each is correct because again, the internal angle of these shapes add up to 360.
For example, for triangles and squares, 60 × 3 + 90 × 2 = 360.
(credited)
Please answer and explain the problem. This is due soon, please help!!
In all cases use the following formula for the are of a rectangular shape:
A = lw
Plot A:
The area and height are known, then, solve the formula for the length l:
l = A/w
repace the given values
l = (204 ft²)/(10.2 ft)
I = 20 ft
For the perimeter you have:
P = 2l + 2w = 2(20 ft) + 2(10.2 ft) = 60.4ft
Plot B:
The length and the perimeter are known. For the expression for the perimeter solve for w:
P = 2l + 2w
w = (P - 2l)/2
replace the values of P and l:
w = (57.56 ft - 2(12.78 ft))/2 = 16 ft
Then, replace in the formula for the area:
A = lw = (12.78 ft)(16 ft) = 204.48 ft²
Plot C:
The area and the height are known. Use the formula for A to obtain the length:
l = A/w = 204.49 ft/14.3 ft = 14.3 ft
and for the perimeter:
P = 2w + 2l = 2(14.3 ft) + 2(14.3 ft) = 57.2 ft
Hence, you can conclude:
- The plost with the least amount of fencing is the plot with the lowest perimeter, hence, Plot C requires the least amount of fencing.
- The plot with the greatest area is Plot A.
Josslyn placed $4400 in a savings account which earns 3.2% interest, compounded continuously. How much will she have in the account after 8 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
The initial amoud on her savings is $4400, so now we can calculate the interest that she generate in one year:
[tex]4400\cdot\frac{3.2}{100}=140.8[/tex]so in 8 year is going to be:
[tex]140.8\cdot8=1126.4[/tex]So the total amoud will be the initial amound plus the interest she earn so:
[tex]4400+1126.4=5526.4[/tex]and rounded would be like:
[tex]5526\text{ dollars}[/tex]Answer:5684
Step-by-step explanation:
pe
Part 1 - FlooringFor the most part, the floors in Rachel's new house are in good shape. However, there are a couple of rooms that Rachel wants to redo right away. She plans to put new carpet in the family room and living room, and fresh hardwood floors in the foyer and kitchen. She also needs to put a new tile floor in the breakfast nook and mud room. Rachel (with your help) plans to install all the flooring herself, so there are no labor costs. However, she does need to buy the materials.Rachel has already scoped out the local home improvement store and priced out the cost of each material. She found that the carpet she wants will cost $1.80 per square foot, the hardwood flooring will cost $4.50 per square foot, and the tiles will cost $2.30 per square foot.a. How many square feet of carpet does Rachel need?b. How many square feet of hardwood does Rachel need?c. How many square feet of tile does Rachel need?d. How much will the total cost of materials for the re-flooring project be?
ANSWERS
a. 863.08 ft²
b. 474 ft²
c. 249 ft²
d. $4,259.24
EXPLANATION
Given:
• Rooms with ,carpet,: Family room and living room
,• Rooms with ,hardwood,: kitchen and foyer
,• Rooms with ,tiles,: breakfast nook and mudroom
• Cost ,carpet,: $1.80 per square foot
,• Cost ,hardwood,: $4.50 per square foot
,• Cost ,tiles,: $2.30 per square foot
First, we have to find the area of each of the mentioned rooms,
a. The family room is in the shape of a square whose sides are all 20 feet and a semicircle whose diameter is 20 feet. The area of the family room is the sum of the areas of each of these figures,
[tex]A_{family-room}=(20ft\cdot20ft)+(\frac{1}{2}\cdot\pi\cdot(20ft/2)^2)[/tex]As shown above, the area of the semicircle is half the area of the full circle with the same diameter. Solve,
[tex]A_{family-room}\approx(400ft^2)+(157.08ft^2)=557.08ft^2[/tex]The living room is in the shape of a rectangle with side lengths 15ft and 22ft, but a right triangle is cut out from the corner. The area of the living room is the area of the mentioned rectangle minus the area of the triangle of the corner,
The side lengths of the triangle are 15ft - 9ft = 6ft and 22ft - 14ft = 8ft. The area of the triangle is,
[tex]A_{triangle}=\frac{6ft\cdot8ft}{2}=24ft^2[/tex]So, the area of the living room is,
[tex]A_{living-room}=(22ft\cdot15ft)-24ft^2=330ft^2-24ft^2=306ft^2[/tex]The area that Rachel wants to cover with a new carpet is,
[tex]A_{carpet}=A_{family-room}+A_{living-room}=557.08ft^2+306ft^2=863.08ft^2[/tex]Hence, the area to be covered with carpet is 863.08 ft².
b. The kitchen is a rectangle with dimensions 24 ft and 15 ft, so its area is,
[tex]A_{kitchen}=24ft\cdot15ft=360ft^2[/tex]The foyer is in the shape of a rectangle with dimensions 10ft and 15ft. However, assuming that the stairs won't be covered with hardwood and that they cover that part of the foyer's floor, to find the area we have to subtract the area the stairs occupy in that room.
The rectangle where the stairs are has dimensions 9ft and (10ft - 6ft ) = 4ft. The area of the Foyer is,
[tex]A_{foyer}=(10ft\cdot15ft)-(9ft\cdot4ft)=(150ft^2)-(36ft^2)=114ft^2[/tex]The area Rachel wants to be covered by hardwood is the sum of the two,
[tex]A_{hardwood}=A_{kitchen}+A_{foyer}=360ft^2+114ft^2=474ft^2[/tex]Hence, the area to be covered with hardwood is 474 ft².
c. The mudroom is in the shape of a rectangle with dimensions 15 ft and 7 ft, so its area is,
[tex]A_{mudroom}=15ft\cdot7ft=105ft^2[/tex]The breakfast nook is in the shape of a trapezoid, where the height is 8ft and the lengths of the bases are 24ft and 12ft. Its area is,
[tex]A_{breakfast-nook}=\frac{(12ft+24ft)}{2}\cdot8ft=\frac{36ft}{2}\cdot8ft=18ft\cdot8ft=144ft^2[/tex]The area Rachel wants to cover with tiles is the sum of these two areas,
[tex]A_{tiles}=A_{mudroom}+A_{breakfast-nook}=105ft^2+144ft^2=249ft^2[/tex]Hence, the area to be covered with tiles is 249 ft².
d. Finally, we have to find the cost of flooring with each material,
[tex]Costs=\begin{cases}C_{carpet}=A_{carpet}\cdot p_{carpet}=863.08ft^2\cdot1.80=1,553.54 \\ C_{hardwood}=A_{hardwood}\cdot p_{hardwood}=474ft^2\cdot4.50=2,133 \\ C_{tiles}=A_{tiles}\cdot p_{tiles}=249ft^2\cdot2.30=572.70\end{cases}[/tex]The total cost of the project is the sum of the three,
[tex]C_{project}=C_{carpet}+C_{hardwood}+C_{tiles}=1,553.54+2,133+572.70=4,259.24[/tex]Hence, the total cost of the re-flooring project will be $4,259.24.
Find the missing angle:
FRT=________
Using the secant-secant theorem,
[tex]m\angle FRT=\frac{140^{\circ}-50^{\circ}}{2}=\boxed{45^{\circ}}[/tex]
Answer: 45 degrees
Step-by-step explanation:
Using the secant-secant theorem
Given the functions:Evaluate the function for . Write your answer in exact simplified form. Select "Undefined" if applicable.
Given:
[tex]\begin{gathered} f(x)\text{ = x}^3\text{ + 6x} \\ g(x)\text{ = }\sqrt{2x} \end{gathered}[/tex]Explanation:
The required function is given as,
[tex]undefined[/tex]