Given:-
Callie walked 14.5 km. And also given 8 km=5 miles.
At first we convert 14.5 km to miles. we get,
[tex]\begin{gathered} 14.5\times\frac{5}{8}=\frac{72.5}{8} \\ \text{ =9.0625} \end{gathered}[/tex]So 14.5 km is 9.0625 miles.
Callie's grandmother pledged Rs. 150 for every mile. so for 9.0625 miles it is,
[tex]9.0625\times150=1359.375[/tex]So her grandmother owe Rs. 1359.375
evaluate the expression [tex]2(2 {}^{5)} [/tex]
64
Explanation
[tex]2(2^5)[/tex]Step 1
operate the exponent,so
[tex]\begin{gathered} 2(2^5) \\ 2(2\cdot2\cdot2\cdot2\cdot2) \\ 2(32) \end{gathered}[/tex]Step 2
now, do the multiplication.
[tex]\begin{gathered} 2(32) \\ 64 \end{gathered}[/tex]so, the answer is 64
I hope this helps you
In the cost function below, C(x) is the cost of producing x items. Find the average cost per item when the required number of items is produced. C(x) = 4.1% +9,500 a. 200 items b. 2000 itemsC. 5000 items What is the average cost per item when 200, 2000, and 5000 items ?
Since the function of the cost is
[tex]C(x)=4.1x+9500[/tex]Where x is the number of the items
a) There were 200 items
x = 200
[tex]\begin{gathered} C(x)=4.1(200)+9500 \\ C(x)=820+9500 \\ C(x)=10320 \end{gathered}[/tex]To find the average cost per item, find
[tex]\begin{gathered} \text{Ave. =}\frac{C(x)}{x} \\ \text{Ave. = }\frac{10320}{200} \\ \text{Ave. =51.6} \end{gathered}[/tex]b) There were 2000 items
[tex]x=2000[/tex][tex]\begin{gathered} C(2000)=4.1\times2000+9500 \\ C(2000)=17700 \end{gathered}[/tex]Find the average as the same above
[tex]\begin{gathered} \text{Ave. = }\frac{17700}{2000} \\ \text{Ave. = 8.85} \end{gathered}[/tex]c) There were 5000 items
[tex]x=5000[/tex][tex]\begin{gathered} C(5000)=4.1(5000)+9500 \\ C(5000)=30000 \end{gathered}[/tex]Divide it by 5000 to find the average
[tex]\begin{gathered} \text{Ave. = }\frac{30000}{5000} \\ \text{Ave. = 6} \end{gathered}[/tex]A small regional carrier accepted 23 reservations for a particular flight with 20 seats. 14 reservations went to regular customers who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other. Find the probability that overbooking occurs find the probability that the flight has empty seats
Answer:
P(Overbooking) = 0.0898
P(Empty seats) = 0.7461
Explanation:
The probability that overbooking occurs is the probability that arrives more than 6 passengers from the 9 that remain.
This probability can be calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where n is the total number of remaining passengers, and p is the probability that a passenger will arrive for the flight. So, the probability that x people arrive is:
[tex]P(x)=\frac{9!}{x!(9-x)!}\cdot0.5^x\cdot(1-0.5)^{9-x}[/tex]So, the probability that arrives 7, 8, or 9 people is:
[tex]\begin{gathered} P(7)=\frac{9!}{7!(9-7)!}\cdot0.5^7\cdot(1-0.5)^{9-7}=0.0703 \\ P(8)=\frac{9!}{8!(9-8)!}\cdot0.5^8\cdot(1-0.5)^{9-8}=0.0176 \\ P(9)=\frac{9!}{9!(9-9)!}\cdot0.5^9\cdot(1-0.5)^{9-9}=0.002 \end{gathered}[/tex]Therefore, the probability that overbooking occurs is:
[tex]\begin{gathered} P(\text{Overbooking)}=P(7)+P(8)+P(9) \\ P(\text{Overbooking)}=0.0898 \end{gathered}[/tex]On the other hand, the probability that the flight has empty seats is the probability that arrives fewer than 6 people for the flight.
So, using the same equation for P(x), we get that the probability that the flight has empty sats is:
[tex]\begin{gathered} P(\text{Empty seats)=P(0) +P(1) + P(2) + P(3) +P(4) + P(5)} \\ P(\text{Empty seats) = 0.7461} \end{gathered}[/tex]Therefore, the answers are:
P(Overbooking) = 0.0898
P(Empty seats) = 0.7461
I have no idea how to do this but I have to graph and show work step by step. and graph the answer.
Here, we want to graph the given inequality
To do this, we need to get the intercepts of the normal line with the inequality replaced by an equality sign
Thus, we have;
[tex]y\text{ = }\frac{2}{3}x-1[/tex]Generally, we have the equation of a linear graph as;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and b represents the y-intercept
With respect to this question, -1 is y-intercept of the line
Thus, the point of the y-intercept is (0,-1)
Now, we proceed to get the x-intercept.
To do this, we simply substitute the value 0 for y
We have;
[tex]\begin{gathered} 0\text{ = }\frac{2}{3}x\text{ - 1} \\ \\ \frac{2x}{3}\text{ = 1} \\ \\ 2x\text{ =3 } \\ \\ x\text{ = }\frac{3}{2} \\ \\ x\text{ = 1.5} \end{gathered}[/tex]The x-intercept here is thus the point (1.5,0)
Normally, to plot the graph of the line, we simply connect the two intercepts with a straight line
In the case of this inequality too, we are going to join the two points, but this time with dots and not straight lines
And also, since the inequality is greater than, we are simply going to shade the side above the dotted line
Kindly note that if there was an inequality sign, wherein, we have greater than or equal to, we are going to join with a thick line and shade
Let us check what we have in the plot below;
4. [-/12.5 Points]DETAILSAUFEXC4COREQ 13.2.005.MY NOTESASK YOUR TEACHERFind the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.4.3, 4.8, 2.4, 4.1, 2.5, 2.6rangestandard deviationvariance5. [-/12.5 Points]DETAILSAUFEXC4COREQ 13.2.007.MY NOTESASK YOUR TEACHERFind the range, the standard deviation, and the variance for the given samples. Round non-integer results to the nearest tenth.61, 82, 58, 74, 56, 47, 73, 52, 65rangestandard deviationvariance
Range = greatest number - smallest number
Range= 4.8 - 2.4 = 2.4
Mean = 2.4 + 2.5 + 2.6 + 4.1+ 4.3+4.8 = 20.7/6 = 3.45
[tex]\begin{gathered} SD=\sqrt{\frac{\sum_{i=1}^n(x1\text{ - }x)^2}{n\text{ - }1}} \\ SD=\sqrt{\frac{(2.4\text{ - 3.45\rparen}^2+(2.5\text{ - 3.45\rparen}^2+(2.6\text{ - }3.45)^2+(4.1\text{ - }3.45)^2+(4.3\text{ - }3.45)^2+(4.8\text{ -}3.45)^2}{6\text{ - }1}} \\ \\ SD=\sqrt{\frac{(\text{ -1.05\rparen}^2\text{ + \lparen- 0.95\rparen}^2\text{ + \lparen-0.85\rparen}^2\text{ + \lparen0.65\rparen}^2\text{ + \lparen0.85\rparen}^2\text{ + \lparen1.35\rparen}^2}{5}} \\ \\ SD=\text{ }\sqrt[\placeholder{⬚}]{\frac{(1.1025)\text{ + \lparen0.9025\rparen + \lparen0.7225\rparen + \lparen0.4225\rparen + \lparen0.72259\rparen + \lparen1.8225\rparen}}{5}} \\ \\ SD=\text{ }\sqrt[\placeholder{⬚}]{\frac{5.6954}{5}} \\ \\ SD=\sqrt[\placeholder{⬚}]{1.13908} \\ \\ SD=\text{ 1.067} \\ \\ Variance=\text{ }\sqrt[\placeholder{⬚}]{SD} \\ V=\text{ 1.13908} \end{gathered}[/tex]Rounding to the nearest tenth:
Standard deviation: 1.1
Variance: 1.1
Range: 2.4
Given the lengths of the three sides for ∆ABC, please list the angles in order from largest to smallest.
1. AB = 15, BC = 14, AC = 10
2. AC = 20, AB = 10, BC = 15
Answer:
1. ∠B, ∠A, ∠C2. ∠C, ∠A, ∠B
Step-by-step explanation:
We know smaller side is opposite to smaller angle and the larger side is opposite to larger angle.
Considering this we have the following1. AB = 15, BC = 14, AC = 10
Put in ascending order:
AC < BC < ABSo the opposite angles are:
B < A < C----------------------------------------------------------------------
2. AC = 20, AB = 10, BC = 15
Put in ascending order:
AB < BC < ACSo the opposite angles are:
C < A < BI'm not the best at word problems Find the probability of obtaining exactly seven tails when flipping eight coins. Express your answer as a fraction in the lowest terms or a decimal rounded to the nearest millionth.
When you flip a coin, there are only two possible outcomes, heads (H) or tail (T).
If you consider the coin to be fair, then both outcomes have the exact same probability which can be calculated as the number of favorable outcomes divided by the total number of outcomes.
For the event "flip a coin" the probability of obtaining tail is:
[tex]\begin{gathered} P(T)=\frac{nº\text{favorable outcomes}}{total\text{ outcomes}} \\ P(T)=\frac{1}{2} \end{gathered}[/tex]The experiment consists on flipping the coin 8 times:
The coin is flipped 8 times, so the number of trials of the experiment is fixed (n=8).
Each trial has only two possible outcomes "Head"(failure) or "Tail" (success)
The probability of the result being tail is the same for each time the coin is flipped, this represents the probability of success of the experiment (p=0.5).
Each trial of the experiment (flipping the coin) is independent.
This experiment meets the binomial criteria, which means that it is a binomial experiment.
To calculate the probability you can apply the formula for the binomial probability:
[tex]P(X)=\frac{n!}{(n-X)!X!}\cdot(p)^X\cdot(q)^{n-X}[/tex]Where
n is the number of trials
X is the number of successes
p is the probability of success
q is the probability of failure and is complementary to p
For this experiment:
The number of trials is n=8
The number of successes is X=7
The probability of success is p=0.5
The probability of success is q=1-p=1-0.5=0.5
Use these values to calculate the probability of obtaining 7 tails:
[tex]\begin{gathered} P(X=7)=\frac{8!}{(8-7)!7!}\cdot(0.5)^7\cdot(0.5)^{(8-7)} \\ P(X=7)=\frac{8!}{1!\cdot7!}\cdot(0.5)^7\cdot(0.5)^1 \\ P(X=7)=\frac{40320}{1\cdot5040}\cdot\frac{1}{128}\cdot\frac{1}{2} \\ P(X=7)=8\cdot\frac{1}{128}\cdot\frac{1}{2} \\ P(X=7)=\frac{1}{32}\cong0.03125 \end{gathered}[/tex]The probability of getting 7 tails when flipping the coin 8 times is
P(X=7)= 0.03125
☆
13. The amount of ice cream in an ice cream cone has a distribution with a mean amount of 3.2 ounces
per cone and a standard deviation of 0.6 ounces. If there are 40 kids at a birthday party, what is
the probability that more than 138 ounces of ice cream will be served? (Hint: Find average amount
of ice cream served per kid at the party)
The probability that more than 138 ounces of ice cream will be served is; 0.33845 or 33.845%
How to find the probability from the z-score?
The formula for calculation of the test statistic or z-score of a population in normal distribution is given as;
z = (x' - μ)/σ
where;
z is z-score
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
Population mean; μ = 3.2
Standard deviation; σ = 0.6
We don't have sample means but we are told that there are 40 kids and we want to find the probability that more than 138 ounces of ice cream will be served. Thus;
Sample mean; x' = 138/40 = 3.45
Thus;
z = (3.45 - 3.2)/0.6
z = 0.417
From online p-value from z-score calculator, we have;
probability = 0.33845 = 33.845%
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Jerry attended a computer software conference.He pause $12.00 for admission.He spent $11.50 for lunch. He paid $1.50 for each workshop tickets. If jerry had a total of $35.00 to spend at the conference which inequalities could be used to determine n, the maximum number of workshop tickets that jerry could have purchased?
Given he spent the following:
Admission = $12.00
Lunch = $11.50
Each workshop ticket = $1.50
Total amount Jerry had = $35.00
Here, the total amount Jerr
The inequality to determine the maximum number of tickets that Jerry could have purchased is:
12.00 + 11.50 + 1.50t ≤ $35.00
(a) Which function has the graph with a y-intercept closest to 0 ?(b) Which function has the graph with the greatest slope?(c) Which functions have graphs with y-intercepts greater than 3? (Check all that apply.)
We need to find the slope-intercept equation for all cases:
Function 1.
In this case, we have the following points
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(0,-4) \end{gathered}[/tex]Then, its slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4+2}{0-1}=2[/tex]Since the line crosses the y-axis at y=-4, the line equation is:
[tex]y=2x-4[/tex]Function 2.
We can choose 2 points of the table, for instance,
[tex]\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]and get the following slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-5}{1-0}=-1[/tex]since the line crosses at y=5, the equation is:
[tex]y=-x+5[/tex]Function 3.
From the given information, the equation is
[tex]y=-4x-1[/tex]Function 4.
From the given information, the equation is:
[tex]y=5x+2[/tex]In summary, we have obtained the following equations:
1) y=2x-4
2) y=-x+5
3) y=-4x-1
4) y=5x+2
Then, we have obtained:
a) Which function has the graph with a y-intercept closest to 0? Answer. As we can note, function 3 because its y-intercept is -1
(b) Which function has the graph with the greatest slope? Answer. From the above result, we can note that function 4 has the greatest slope because it is equal to 5
(c) Which functions have graphs with y-intercepts greater than 3? Answer. Only function 2 has y-intercept greater than 3 because the value is 5
In summary, the answers are:
a) Function 3
b) Function 4
c) Function 2
find the slope of the line
Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Two clear points are visible in the graph of the figure: (0,1) and (4,0).
Note: I'm assuming each division of the grid has a measure of one unit.
Applying the formula:
[tex]\displaystyle m=\frac{0-1}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]The slope of the line is -1/4.
maya sells homemade spice mixes in different sizes at the creft fair. the graph shows the proportional relationship between tsp of cumin and tsp of chili powder in one recipe. what does the origin represent
The origin represents the quantities of chili powder and cumin are zero tsp in the recipe.
Maya sells homemade spice mixes in different sizes at the craft fair.
The given graph shows the proportional relationship between tsp of cumin and tsp of chili powder in one recipe.
As per the given graph,
The y-axis represents the tsp of chili powder in the recipe.
The x-axis represents the tsp of cumin in the recipe.
In the recipe, the proportions of chili powder and cumin are zero teaspoons which are represented by the origin of the given graph.
Therefore, the origin represents the quantities of chili powder and cumin are zero tsp in the recipe.
Learn more about graph here:
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b -6(46 - 2) = 150A) 4-6 B) -5C) 9 D) (3)
To solve this equation, we need to follow the next steps:
1. Apply the distributive property:
[tex]b-6\cdot4b+6\cdot2=150\Rightarrow b-24b+12=150[/tex]2. Add the like terms, and subtract 12 to both sides of the equation:
[tex]-23b+12=150\Rightarrow-23b=150-12[/tex]3. Divide both sides of the equation by -23 (to isolate b):
[tex]\frac{-23}{-23}b=\frac{150-12}{-23}\Rightarrow b=\frac{138}{-23}\Rightarrow b=-6[/tex]Then, the answer to this equation is {-6} (option A).
According to an oil company. In a particular year, a certain country used 15.881,567 barrels of ol a day, and worldwide, people used around 85,993,660 barrels of oil per day. This includes oil used for (among other things) fuel and manufacturingthere were 303 million people in the country for this year, what was the daily consumption rate per person in the country?The daily consumption rate is about barrels per day per person in the country(Round to the nearest hundredth as needed.)
In this case the answer is very simple. .
Step 01:
Data
country = 158,815,67 barrels / day
people = 85,993,660 barrels / day
303,000,000 people in the country
Step 02:
daily consumption per day
[tex]\frac{85993660\text{ barrels/day}}{303000000\text{ people}}[/tex]0.28 barrels/day / people
The answer is:
The daily consumption rate per person in the country is 0.28
Select the correct answer from each drop-down menu. А D F B f G С In the diagram, ZADE & ZABC. The ratios and are equal. Reset Next FB : GC AE: EC
Consider the given figure, in the triangle ADE and ABC,
Angle A is common in both the triangles.
Already given that angle ADE is equal to angle ABC.
Consider the property that the sum of all three angles of a triangle is 180 degree,
[tex]\angle A+\angle ADE+\angle AED=\angle A+\angle ABC+\angle ACB\Rightarrow\angle AED=\angle ACB[/tex]Therefore, by the AAA criteria, the triangles ADE and ABC are similar.
Then the sides of the triangle are proportional,
[tex]\frac{AD}{DB}=\frac{AE}{EC}[/tex]This can also be written as,
[tex]AD\colon DB=AE\colon EC[/tex]This is the required answer.
4 Find the slope of the line that passes through the points (- 4.6) and (-4,-2)
to finde the slope of the poins we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]after replacing on the formula we obtain
[tex]\begin{gathered} m=\frac{-2-6}{-4-4} \\ m=\frac{-8}{-8} \\ m=1 \end{gathered}[/tex]the slope for the line will be 1
The width of a rectangle measures (3u - 4v) centimeters, and its length measures
(10u + 2v) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle
Answer:
Step-by-step explanation:
Ok lets get rolling
So far as we know, perimeter is the sum of all sides of a figure
in a rectangle opposite sides are equal, therefore we after some machinations we get this equation
P of rectangle = 2(10u+2v) + 2(3u-4v)
P of rectangle = 20u+4v + 6u - 8v
P of rectangle = 26u - 4v
and thats ur answer
hope this helps
-20x - 10y = 2010x + 5y = -10
We have here a system of linear equations. In this case, to find the solutions for this system, we can start by multiplying by 2 the second equation:
3) The sofa is $45.00. Discount is 15%. What is the total? A) $75 B) $38.25 C) $42.60 D) $120
Answer:
B) $38.25
Explanation:
If we have a discount of 15% then the price of the item now is 100% - 15 = 85% of the original price.
85% of $45 is
[tex]\frac{85}{100}\times45=\$38.25[/tex]Hence, the discount price is $38.25 and therefore,
please see image, use this information to solve the problem.
The coordinates of the point B is,
[tex](56,7)[/tex]A data set whose original x values ranged from 241 through 290 was used to generate a regression equation of ŷ = -0.06x + 9.8. Use the regression equation to predict the value of y when x=240.24.2-4.6Meaningless result4.6
we have the equation
[tex]\begin{gathered} ŷ=-0.06x+9.8 \\ For\text{ x=240} \\ ŷ=-0.06(240)+9.8 \\ ŷ=-4.6 \end{gathered}[/tex]The answer is -4.6How would I solve this equation by rewriting it as a proportion?
To rewrite the given expression as a proportion multiply the 1/2 by a fraction that makes it have the same denominator as 1/2x (that fraction is x/x):
[tex]\begin{gathered} \frac{1}{2}*\frac{x}{x}+\frac{1}{2x}=\frac{x^2-7x+10}{4x} \\ \\ \frac{x}{2x}+\frac{1}{2x}=\frac{x^2-7x+10}{4x} \end{gathered}[/tex]Sum the fractions in the left of the equal:
[tex]\frac{x+1}{2x}=\frac{x^2-7x+10}{4x}[/tex]Then, the correct answer is third optionA rectangle is inscribed with its base on the -axis and its upper corners on the parabola y = 7 - x ^ 2 What are the dimensions of such a rectangle with the greatest possible area?
The width = 3.06
The height = 4.66
Explanation:The rectangle is inscribed with its base on the -axis and its upper corners on the parabola
Width = 2x
Height = 7 - x²
Area of the inscribed rectangle:
Area = width x height
A = 2x (7 - x²)
A = 14x - 2x³
Take the derivative of the area (A) and equate to zero
A' = 14 - 6x²
0 = 14 - 6x²
6x² = 14
x² = 14/6
x² = 2.33
x = √2.33
x = 1.53
The width = 2x
The width = 2(1.53)
The width = 3.06
Substitute x = 1.53 into the equation y = 7 - x² to solve for the height
y = 7 - 1.53²
y = 4.66
The height = 4.66
What is the sum of a 7-term geometric series if the first term is −11, the last term is −45,056, and the common ratio is −4? A −143,231B −36,047C 144,177D 716,144
the first term is −11
the last term is −45,056
the common ratio is −4
the formula for geometric series is
[tex]\begin{gathered} a+ar+ar2+ar3+\ldots \\ \sum ^n_1a_1r^{n-1} \\ \text{solution formula:} \\ S_n=a_1\frac{1-r^n}{1-r} \end{gathered}[/tex]where
r = -4
a1 = -11
n = 7
therefore,
[tex]S_7=(-11)\frac{1-(-4)^7}{1-(-4)}[/tex]let's simplify
[tex]\begin{gathered} S_7=(-11)\frac{1-(-4)^7}{1-(-4)}=-11\cdot\frac{1-(-16384)}{1+4}=-11\cdot\frac{1+16384}{1+4}=-11\cdot\frac{16385}{5} \\ S_7=-11\cdot\: 3277 \\ S_7=-36047 \end{gathered}[/tex]Thus, the answer is -36047
How can i solve this?
Answer:
3791m
Explaation:
We are given the following from the diagram;
Ocean surface = adjacent side = x
hypotenuse = 3900m
Angle of depression = 76.4 degrees
According to SOH
sin theta = opp/hyp
sin 76.4 = opp/3900
Opp = 3900sin76.4
Opp = 3900*0.9719
Opp = 3,790.41
The distance below the ocean surface is approximately 3791m
Given f(x)=1/x-2 and g(x)=square root of x+2, what is the domain of f (g(x))?.A. ℝB. [–2, ∞)C. [–2, 2) ∪ (2, ∞)D. (–∞, 2) ∪ (2, ∞)
we have the functions
[tex]\begin{gathered} f(x)=\frac{1}{x-2} \\ \\ g(x)=\sqrt{x+2} \end{gathered}[/tex]Find out f(g(x))
[tex]f\mleft(g\mleft(x\mright)\mright)=\frac{1}{\sqrt{x+2}-2}[/tex]Remember that
The radicand must be greater than or equal to zero and the denominator cannot be equal to zero
so
step 1
Solve the inequality
[tex]\begin{gathered} x+2\ge0 \\ x\operatorname{\ge}-2 \end{gathered}[/tex]the solution to the first inequality is the interval [-2, infinite)
step 2
Solve the equation
[tex]\begin{gathered} \sqrt{x+2}-2\ne0 \\ \sqrt{x+2}\operatorname{\ne}2 \\ therefore \\ x\operatorname{\ne}2 \end{gathered}[/tex]The domain is the interval
[–2, 2) ∪ (2, ∞)
The answer is the option CState the domain and range of the relation. Then determine whether the relation is a function, write yes or no.
Solution:
The domain is the set of independent values of a relationfor which the reltion is valid.
The range is the set of dependent values of a relation for which he relation is valid and real
Given:
From the above image, we have
[tex]\begin{gathered} Domain:\text{ -2, 3} \\ Range:\text{ 4, -2, 0, 2} \end{gathered}[/tex]For a relation to be a function, for every value of x there is only one corresponding value for y.
Since the value of domain in the above figure outputs more than one value, the relation is not a function.
Hence, the correct answer is NO
Can I find a tutor to help me with this answer?
Explanation:
We have the equation of a quadratic function:
[tex]f(x)=(x-2)^2+2[/tex]And we need to find and plot the vertex of the equation.
We start by remembering that a quadratic equation is represented by a parabola and that the vertex is the point where the parabola changes direction, usually represented by (h, k) as shown in the following example:
• How do we find the vertex using the given equation?
We find it by comparing our equation with the general vertex form of the quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]where
[tex](h,k)[/tex]is the vertex, and a is a constant.
Using the given equation, we find the h and k values:
[tex]\begin{gathered} f(x)=(x-2)^{2}+2 \\ \downarrow \\ h=2 \\ k=2 \end{gathered}[/tex]Therefore, the vertex is at (2, 2).
Answer:
The point (2,2) representing the vertex is shown in the image:
Can you please help me out with a question
Explanation
we have a rigth triangle, then
Let
leg1=radius= 7
leg2=QP
hypotenuse= radius+18=25
now, we can use the Pythagorean theorem:
Pythagorean theorem, the geometric theorem that states the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
[tex]a^2+b^2=c^2[/tex]hence, replace
[tex]\begin{gathered} 7^2+QP^2=25^2 \\ 49+QP^2=625 \\ \text{subtract 49 in both sides} \\ 49+QP^2-49=625-49 \\ QP^2=576 \\ \text{square rot in both sides} \\ \sqrt[\square]{QP^2}=\sqrt[\square]{576} \\ QP=24 \end{gathered}[/tex]so, the answer is
[tex]J.24[/tex]I hope this helps you
cupid is ordering a new bow for valentine's day. there are 5 styles of bows, 2 lengths, and 4 colors of bows to choose from. how many different bows are possible formula n!/ k!*k2!*k3!.....