(x +2) (x +6) ------> x^2 +8X + 12
(2x + 8) (x +2) -------> 2x^2 +12x + 16
(x +8) (x+4) ------------> x^2 +12x +32
(x + 2) (2x+6) ----------> 2x^2 +10x +12
how many km/h equals 880ft/min? Explain how you solved this problem
The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour
How does km/h relate to ft/ min?Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.
In other words, 1 km / h is equal to 54.6807 feet per minute.
If there are 880 ft / minute therefore, the number of kilometers per hour is:
= Speed in feet per minute / feet per minute per kilometer per hour
= 880 / 54.6807
= 16.09 kilometers per hour
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A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
Choose the left side that makes a True statement, and shows at the sum of the given complex numbers is 10Choose the left side that makes a true statement, and shows that the product of the given complex numbers is 40
For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40
Referring to the figure, find the value of x in circle C.
The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
which are thrwe ordered pairs that make the equation y=7-x true? A (0,7) (1.8), (3,10) B (0,7) (2,5),(-1,8) C (1,8) (2,5),(3,10)D (2,9),(4,11),(5,12)
In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.
If we substitute the points from option A, we get
[tex]\begin{gathered} 7=7-0 \\ 7=7 \end{gathered}[/tex]for (1,8), we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option A is false.
Now, if we substitute the points in option B, for point (2,5), we have
[tex]\begin{gathered} 5=7-2 \\ 5=5 \end{gathered}[/tex]which is correct. Now, for point (-1.8) we obtain
[tex]\begin{gathered} 8=7-(-1) \\ 8=8 \end{gathered}[/tex]Since all the points fulfil the equation, then option B is an answer.
Lets continue with option C and D.
If we substitute point (1,8) from option C, we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option C is false.
If we substite point (4,11) from option D, we get
[tex]\begin{gathered} 11=7-4 \\ 11=2\text{ !!!} \end{gathered}[/tex]then, option D is false.
Therefore, the answer is option B.
Find the present value that will grow to $6000 if the annual interest rate is 9.5% compounded quarterly for 9 yr.The present value is $(Round to the nearest cent as needed)
We need to know how to calculate compound interest to solve this problem. The present value is $2577.32
Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.
A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]
where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest
A=$6000
r=9.5%
t=9 yrs
n=4
6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]
6000= P x 2.328
P=6000/2.328=2577.32
Therefore the present value that will grow to $6000 in 9 years is $2577.32
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*You will use the following scenario forquestions 1-4*On the Wechsler Adult IntelligenceScale a mean IQ is 100 with a standarddeviation of 15. You may assume thatIQ scores follow a normal distribution.What percent of people have an IQscore less than 90?*Write your answer as a percent andround to 2 decimal places*
The Solution:
Given:
[tex]\begin{gathered} x=90 \\ \mu=100 \\ \sigma=15 \end{gathered}[/tex]By formula,
[tex]Z=\frac{x-\mu}{\sigma}=\frac{90-100}{15}=\frac{-10}{15}=-0.6667[/tex]From the z-score tables:
[tex]P(Z\leq90)=0.25248[/tex]Convert to percent by multiplying with 100.
[tex]0.25248\times100=25.248\approx25.25\text{\%}[/tex]Thus, the number of people that have an IQ score less than 90 is 25.25%
Therefore, the correct answer si 25.25%
13. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
what would be the value if m in a angle on 50 degrees and 10m
50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.
10m = 90 - 50
10m = 40
m = 40/10
m = 4
Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
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Calculate the probabilities of each of these situations. A standard deck of cards has 52 cards and 13 cards cards in each suit (Spades, Clubs, Hearts, & Diamonds). Which of the following is LEAST likely to occur? a) Selecting any spade card from a standard deck of cards, keeping it, then selecting the queen of hearts. b) Selecting a spade from a standard deck of cards, not putting it back, then selecting another spade. c) Selecting an ace from a standard deck of cards, not replacing it, then selecting a king.Event CEvent AEvent B
Answer
The least likely to occur is Event C
Explanation
A.
P(spade card) = 13/52
P(queen) = 4/51 Note: Without replacement
⇒ 13/52 x 4/51
= 52/2652
= 0.0196
B.
P(a spade) = 13/52
P( another spade) = 12/51 Note: Without replacement
⇒ 13/52 x 12/51
= 156/2652
= 0.0588
C.
P(an ace) = 4/52
P(king) = 4/51
⇒ 4/52 x 4/51
= 16/2652
= 0.006
∴ The least likely to occur is Event C
Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
30 randomly selected students took the statistics final. If the sample mean was 84, and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students
The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}
What is confidence interval?Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.
How to construct a 99% confidence intervalGiven data form the question
99% confidence interval
30 randomly selected students
mean sample = 84
Standard deviation = 12.2
Definition of variables
confidence level, CI = 99%
mean sample, X = 84
standard deviation, SD = 12.2
Z score, z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 30
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]
=[tex]=84+2.576*2.2274[/tex]
= 84 + 5.7378 OR 84 - 5.7378
= 89.7378 OR 78.2622
= 89.73 to 78.26
The confidence interval for the mean score of all students is 78.26 to 89.78
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g(x) = 2x - 5f(x) = 4x + 2Find g(f(x))
Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=2x-5 \\ \text{and} \\ f(x)=4x+2 \end{gathered}[/tex]then
[tex]\begin{gathered} g(f(x))= \\ g(x)=2x-5 \\ g(f(x))=2(4x+2)-5 \\ \text{apply distributive property} \\ g(f(x))=8x+4-5 \\ g(f(x))=8x-1 \end{gathered}[/tex]I hope this helps you
3. The sum of two consecutive odd integersis 168. What are the integers?
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]Use area under the curve to complete probability for continuous probability dentist functionsuse the uniform distribution to compute probabilityfind the mean and standard deviation Love the uniform distribution1.One type of card stock which may be used for the cover of a booklet is uncoated paper with waymark as 65 pounds the standard thickness of 65# of card stuck is 9.5 points (0.0095”). A manufacturer determines that the thickness of 65# of card stuck produced followed a uniform distribution varying between 9.25 points and 9.75 points.A)Sketch the description for this situation.B)compute the mean and standard division of the thickness of the 65# cards stuck producedC)compute the probability that a randomly selected piece of 65# card stark has a thickness of a list 9.4 points.D)Compute the probability that a randomly selected piece of 65# card stock has thickness between 9.75 points.
If x is uniformly distributed over the interval [ a , b ] then,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{b-a}\text{ , a }\leq\text{ x }\leq\text{ b} \\ f(x)\text{ = 0 , otherwise} \end{gathered}[/tex]Also ,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Std deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \end{gathered}[/tex]It is given that ,
[tex]\begin{gathered} a\text{ = 9.25} \\ b\text{ = 9.75} \\ b\text{ - a = 9.75 - 9.25 = 0.5} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{0.5}\text{ 9.25 }\leq\text{ x }\leq\text{ 9.75} \\ f(x)\text{ = 0 otherwise} \end{gathered}[/tex](a)The distribution is as follows :
(b)The mean is calculated as,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Mean = }\frac{9.25\text{ + 9.75}}{2} \\ \text{Mean = 9.5} \end{gathered}[/tex]Standard deviation is calculated as,
[tex]\begin{gathered} \text{Standard deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \\ \text{Standard deviation = }\sqrt[]{\frac{(0.5)^2}{12}} \\ \text{Standard deviation }\approx\text{ 0.1443} \end{gathered}[/tex](c) The probability is calculated as,
[tex]\begin{gathered} P(\text{ atleast 9.4 points ) = P( x }\ge\text{ 9.4)} \\ P(\text{ atleast 9.4 points ) = }\int ^{9.75}_{9.4}(\frac{1}{0.5})dx \\ P(\text{ atleast 9.4 points ) = }\frac{9.75\text{ - 9.4}}{0.5} \\ P(\text{ atleast 9.4 points ) = 0.7} \end{gathered}[/tex](d) The probability is calculated as,
[tex]\begin{gathered} P(\text{between 9.45 and }9.75\text{ ) = P( 9.45 }\leq\text{ x }\leq\text{ 9.75 )} \\ P(\text{between 9.45 and }9.75\text{ ) = }\int ^{9.75}_{9.45}(\frac{1}{0.5})dx \\ P(\text{between 9.45 and }9.75\text{ ) =}\frac{9.75\text{ - 9.45}}{0.5} \\ P(\text{between 9.45 and }9.75\text{ ) = 0.6} \end{gathered}[/tex]If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.70Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B
Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]I would like to make sure my answer is correct ASAP please
step1: Write out the formula for exponential growth
[tex]y=a(1+r)^n[/tex][tex]\begin{gathered} a=\text{initial population} \\ r=\text{rate} \\ n=\text{years} \end{gathered}[/tex]Hence we have
[tex]a=800,r=3\text{ \%, n=x}[/tex]Step2: substitute into the formula in step 1
[tex]\begin{gathered} y=800(1+\frac{3}{100})^x \\ y=800(1+0.03)^x \\ y=800(1.03)^x \end{gathered}[/tex]Hence the right option is A
h(x) = x2 + 1 k(x) = x-2 (h - k)(3) = DONE
We are given two functions:
h(x) = x^2 + 1
and k(x) = x - 2
We are asked to find the value of:
(h - k) (3) (the value of the difference of the two functions at the point x = 3
So we performe the difference of the two functions:
(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3
So, this expression evaluated at 3 gives:
(h-k)(3) = 3^2 - 3 + 3 = 9
One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:
h(3) = 3^2 + 1 = 10
k(3) = 3 - 2 = 1
Then, the difference is : h(3) - k(3) = 10 - 1 = 9
So use whatever method feels more comfortable for you.
What does the slower car travel at Then what does the faster car travel at
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
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I got the first part I’m not sure of the 2nd is it 38.5
We will have the following:
The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:
[tex]A_s=4\pi(\frac{3.5}{2})^2\Rightarrow A_s\approx38.5[/tex]Given slope of m=2/3 and y-intercept b=1 graph the line
ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)
graph that
because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)
we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)
create a line connecting all the points
The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
Кр2.345 67 8Identify each angle as acute, obtuse, or right123345678.
we have the following:
Therefore:
5)Which of the following is a critical number of the inequality x^2+5x-6<0 ?
Answer:
B. 1
Explanation:
Given the inequality:
[tex]x^2+5x-6<0[/tex]To find the critical number, first, change the inequality sign to the equality sign :
[tex]x^2+5x-6=0[/tex]Next, solve for x:
[tex]\begin{gathered} x^2+6x-x-6=0 \\ x(x+6)-1(x+6)=0 \\ (x-1)(x+6)=0 \\ x-1=0\text{ or }x+6=0 \\ x=1\text{ or }x=-6 \end{gathered}[/tex]Therefore, from the options, 1 is the critical number.
The correct option is B.
Put the equation y = x2 - 10x + 16 into the form y = =(x - h)² + ki Answer: y = > Next Question
To complete the perfect square ((x-h)²) we add and subtract constants:
[tex]\begin{gathered} y=x^{2}-10x+16 \\ y=x^{2}-10x+25-25+16 \\ y=x^{2}-10x+5^{2}-9 \\ y=(x-5)^{2}-9 \end{gathered}[/tex]an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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