Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
What is implicit differentiation?Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
[tex]\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}[/tex]
Since dx/dt=−2, we have that:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
When y = π/4, x is given by:
xcos(y) = 2.
[tex]x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}[/tex]
Hence:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}[/tex]
Since cot(pi/4) = 1, we have that:
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]
Which means that option a is correct.
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PLEASE HELP!!! WILL MARK BRAINLIEST!!!!!
The piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
How to determine the piecewise functions?On the domain of t = 0 to 2, we have:
f(0) = 800
f(1) = 1200
f(2) = 1800
The above function is a piecewise function with the following definition
f(0) = 800 --- initial value
r = 1200/800 = 1.5 --- rate
The function is then represented as:
f(t) = f(0) * r^t
This gives
f(t) = 800 * 1.5^t
On the domain of t = 3 to 9, we have:
f(3) = 2700
f(4) = 2835
The above function is a piecewise function with the following definition
f(3) = 800 --- initial value
r = 2835/2700 = 1.05 --- rate
The function is then represented as:
f(t) = f(3) * r^t-3
This gives
f(t) = 2700 * 1.05^t-3
Hence, the piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
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The graph of the absolute value parent function
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
How to find a resulting function by applying rigid transformations
Herein we must modify a parent function to get a resulting function by the use of rigid transformations, defined as those transformations applied on geometric loci, including functions, such that Euclidean distance is conserved.
Based on the statement seen in the picture, the enlargement of the parent function can be done by a rigid transformation known as dilation, whose definition is shown below:
g(x) = k · f(x), where k is the stretch factor and is greater than 1. (1)
If we know that f(x) = |x| and k = 5, then the resulting function is:
g(x) = 5 · |x| (1)
This expression is also equivalent to the expression g(x) = |5 · x| by definition of absolute value.
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
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X+2y=5 and 4x-12y=-20 solve using elimination and substitution
Answer:
(1,2)
Step-by-step explanation:
Substitution:
x + 2y = 5 Solve for x
x = -2y + 5 Substitute -2y + 5 in for x in the second equation
4x - 12y = -20
4(-2y + 5) - 12y = -20 Distribute the 4
-8y + 20 - 12 y = -20 Combine the y term
-20y + 20 = -20 Subtract 20 from both sides
-20y = -40 Divide both sides by -20
y = 2
Plug y into either of the 2 original equations to get x.
x + 2y = 5
x + 2(2) = 5
x + 4 = 5
x = 1
The answer is (2,1).
Elimination:
x + 2y = 5 4x - 12y = -20. We want to eliminate with the x or the y. I am going to eliminate the x's that means that I have to multiply the first equation all the way through by -4
(-4)(x + 2y) = (5) (-4) That makes the equivalent expression
-4x - 8y = -20 I will add that to 4x - 12y = -20
4x - 12y = -20
0x -20y = -40
-20y = -40
y = 2. Plug 2 into either the 2 original equation to find x. This time I will select the second original equation to find x.
4x -12y = -20
4x - 12(2) = -20
4x - 24 = -20
4x = 4
x = 1
evaluate the following using powers of ten rules: 10 to the 4th times the square root of 1.042
The value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
Evaluating an expressionFrom the question, we are to determine the value of the given expression
The given expression is
10 to the 4th times the square root of 1.042
That is,
10⁴ × √1.042
The expression can be evaluated as shown below
10⁴ × √1.042
= 10⁴ × 1.02078
= 1.02078 × 10⁴
≈ 1.021 × 10⁴
OR
= 1.02078 × 10⁴ = 10207.8
Hence, the value of the given expression is approximate equal to 1.021 × 10⁴ OR 10207.8
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Number lineWhich of these numbers represents the difference between -3 and -2
The number which represents the difference between the numbers given -3 and -2 as in the task content is; 1.
Which number represents the difference between -3 and -2 in the task content?It follows from the task content that the difference between the given numbers -3 and -2 is to be determined by means of the number line.
On this note, since, it follows that the difference between two numbers in the number line is given by the absolute value of their arithmetic difference.
It follows that the number which is required in this scenario is; |-3-(-2)| = |-1| = 1.
This follows from the fact that the absolute value big any number is that number with a positive polarity.
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Write a quadratic function fwhose zeros are 2 and 8.
f(x) = 0
Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount. Part B: Explain how you would solve this problem by organizing a sample calculation.
Assuming you had a bill of $120 when you went to the restaurant with your three friends, the 20% tip would come out to $24.
What would be the tip?First assume an amount that the meal you ate cost. Let's assume that amount if $120.
If the tip rate if 20%, it means that you need to find out what 20% of the bill of $120 is.
If you don't want to use a calculator, there are other ways you can calculate the tip.
An easy method would be to find 10% of the bill. To find 10%, all you have to do is to move the decimal point from right to left.
The decimal point in $120 is at the far right so the 10% amount would be:
= $12.0
Now that you have the 10% amount, remember that 20% is simply twice the amount of 10% so:
= 12 x 2
= $24
The total amount then becomes:
= 120 + 24
= $144
In conclusion, your tip amount would be $24.
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Use a calculator to explore the pattern. Write a conjecture based on what you observe. i did the whole calculator bit, but I just am clueless about the conjecture bit. Could someone please explain this to me?
Check the picture below.
now hmmm let's observe, hmmmm 11 has two digits, and low and behold, the 2 is right in the middle, then 1 and 1 on flanking it.
let's check 111 hmmmm has three digits and has a 3 right in the middle as well, and low and behold, is flanked by a regressing count, namely an "outwards" count.
let's check 1111 and 11111, same happens, one has a digit of 4 in the middle and the other 5, and yes, the "outwards" count on each, outwards count towards 1 each time btw.
so, if we were to take that pattern, we can say that eight 1's, namely 11111111 x 11111111, will have an 8 in the middle, and will look like 1234567 8 7654321.
10. Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. a) Draw a graph with two lines that represent the bike rides of Lin and Andre. b) For each line, highlight the point with coordinates (1, k) and find k. c) Who was biking faster?
According to the data, it can be inferred that Lin is faster than Andre because she is going at 0.3 km/min speed while he is going at 0.25 km/min speed.
How to calculate who goes faster?To calculate who goes faster we must divide the time into the distance traveled by each character as shown below:
1.5km ÷ 5min = 0.3km/min2km ÷ 8min = 0.25km/minWhat is the K point for each character?According to the above, the point K of each would be equal to the distance that each of them travels in one minute. As shown in the graph, after 5min (Lin) and 8min (Andre), each one reaches their respective destination located 1.5km and 2km away, respectively, taking the point (0,0) as the starting point.
Lin: (1,0.3)Andrew: (1,0.25)The graph is attached.
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HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Write each expression in the standard form for the complex number a + bi.
1. [ 4 ( cos (7pi/9) + i sin (7pi/9))]^3
2. The complex fifth roots of 5 - 5 sqrt(3)i
1. By de Moivre's theorem,
[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]
2. First write the given number in exponential/trigonometric form.
[tex]z = 5-5\sqrt3\,i[/tex]
has modulus
[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]
and since it lies in the second quadrant of the complex plane, its argument is
[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]
So, we have
[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]
Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are
[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]
[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]
[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]
[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]
[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]
List the sides of triangle RST in acsending order (Shortest to longest.)
The sequence of angles from smallest to largest is m∠T,m∠S,m∠R.
Given three angles be m∠T=4x-52°,m∠S=x+38°,m∠R=2x+47°.
We are required to arrange the angles in ascending order.
Ascending order means values that are written in a way that smallest values come first and larger values comes last.
First we have to find the angles at one value of x.
The values will differ as the values of x differ so we have to choose point or value of x.
Suppose x=20.
Then the angles are:
m∠T=4x-52°
=4*20-52
=80-52
=28°
m∠S=x+38°
=20+38
=58°
m∠R=2x+47°
=2*20+47
=40+47
=87°
Hence the sequence of angles from smallest to largest is m∠T,m∠S,m∠R.
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PLEASE HELP ME WITH THIS QUESTION ASAPP
Answer:
Trapezoid
Step-by-step explanation:
One pair of parallel sides.
Sarah, Tony, and Megan are helping their parents plan the layout of the backyard. The patio is as wide as the fire pit, and 5 feet long. The pool is enlarged to yield the following layout:
If the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
Given that the patio is as wide as the fire pit, and 5 feet long.
We are required to form an equation which can describe the area of the backyard.
Equation is relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or many more depending on the powers of the variable.
If we see the figure carefully then we can find that the length of the backyard is 2x+6 and the breadth of the backyard is 5+x and backyard is in shape of rectangle.
Area of rectangle =Length *breadth
=(2x+6)*(5+x)
=30+10x+6x+2[tex]x^{2}[/tex].
Hence if the patio is as wide as the fire pit, and 5 feet long then area of backyard can be expressed as [tex]2x^{2}+16x+30[/tex].
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Someone pls help with this<3
Answer: No
Step-by-step explanation:
The sum of exterior angles in a polygon is always equal to 360 degrees.
A student says that 3% is equal to 0.3 when written as a decimal. Is their thinking correct? Explain.
The answer is no.
Always remember when converting from percent to decimal, divide by 100%.
3% ÷ 100%0.03 ≠ 0.3Hence, the student's thinking is not correct.
Answer:
no
Step-by-step explanation:
0.3 = 30% not 3%
to change a percentage to a decimal fraction, divide by 100
3% = [tex]\frac{3}{100}[/tex] = 0.03
One number is 6 more than another. The difference between their squares is 204. What are the numbers?
Answer: 20 and 14
Step-by-step explanation:
Using a little guess and check, we can figure out that the numbers are 6 apart and the difference between their squares is 204.
[tex]20^2 = 400\\14^2=196[/tex]
[tex]20^2-14^2 = 204[/tex]
A trick to doing this is to start with a number that is easily squared like 10 or 20 and see if the difference between their numbers is larger or smaller and change your numbers based on them.
Hope this helped :)
Answer:
14 and 20
Step-by-step explanation:
Let x and y be two numbers where x < y.
We are given :
y - x = 6
y² - x² = 204
Then
y - x = 6
(y - x)(y + x) = 204
Then
y - x = 6
6 × (y + x) = 204
then
y - x = 6 (Equation 1)
y + x = 34 (Equation 2)
Then
(Equation 1) + (Equation 2) ⇒ 2y = 40 ⇒ y = 20
Now ,we substitute y by 20 in equation 1 :
y - x = 6
⇔ 20 - x = 6
⇔ 20 - 6 = x
⇔ x = 14
A community college employs 88 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 88. Complete parts (a)
-Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 3, column 6. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample.
The numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
How to determine the number that will be included in the sample?The complete question is added as an attachment
The given parameters are:
Row = 3
Column = 6
From the attached figure, the entries in row 3 are:
4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7 1
From the attached figure, the entries in column 6 are:
1, 6, 9, 5, 4, 9
Hence, the numbers that would be included in the sample are 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
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List these fractions from
least to greatest 3/8 5/8 4/8 2/8 7/8
Answer: 2/8, 3/8, 4/8, 5/8, 7/8
Step-by-step explanation:
Since they all have a common denominator, we can list them based on their numerator without having to worry about the denominator.
2/8 < 3/8 < 4/8 < 5/8 < 7/8
Determine the domain:
[tex]f(x) = \frac{ln(ln(x + 1))}{e {}^{x} - 9 } [/tex]
The denominator cannot be zero, so
[tex]e^x - 9 = 0 \implies e^x = 9 \implies x = \ln(9)[/tex]
is not in the domain of [tex]f(x)[/tex].
[tex]\ln(x)[/tex] is defined only for [tex]x>0[/tex], and we have
[tex]\ln(x+1) > 0 \implies e^{\ln(x+1)} > e^0 \implies x+1 > 1 \implies x>0[/tex]
so there is no issue here.
By the same token, we need to have
[tex]x+1 > 0 \implies x > -1[/tex]
Taking all the exclusions together, we find the domain of [tex]f(x)[/tex] is the set
[tex]\left\{ x \in \Bbb R \mid x > 0 \text{ and } x \neq \ln(9)\right\}[/tex]
or equivalently, the interval [tex](0,\ln(9))\cup(\ln(9),\infty)[/tex].
$2,870 per month. He pays $574 a month for rent. What percent of his monthly pay goes to rent?
we know that 2870 is the 100%, what is 574 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2870 & 100\\ 574& x \end{array} \implies \cfrac{2870}{574}~~=~~\cfrac{100}{x} \\\\\\ 5=\cfrac{100}{x}\implies 5x=100\implies x=\cfrac{100}{5}\implies x=20[/tex]
The percent of his monthly pay which goes to rent if he earns a total of $2,870 per month is 20%.
What percent of his monthly pay goes to rent?Amount earned per month = $2,870
Amount paid for rent = $574
Let
The unknown percent = x
x% of $2,870 = $574
x/100 × 2,870 = 574
2,870x/100 = 574
cross product
2,870x = 57,400
divide both sides by 2,870
x = 57,400/2,870
x = 20%
Ultimately, 20% of the monthly pay goes to rent.
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If a number is tripled & the result is increased by 5, we get 50. Find the number.
Solution:
Let x be the number
Triple the number=3x
According to the question,
3x+5=50
⇒3x+5−5=50−5 [Subtract 5 from both sides]
⇒3x=45
⇒ x = 45/3
[Divide 3 from both sides]
⇒x=15
∴15 is the required number. When it is tripled and increased by 5, we get 50.
5. Here are two copies of the same figure. Show two different ways for
finding the area of the shaded region. All angles are right angles.
(Photo below)
The two different ways of finding the area are,
Case 1 = assume horizontal rectangles,
Case 2 = assume vertical rectangles.
the rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
Here,
case 1,
As shown in the image
Area = sum of horizontal rectangles
Area = 10 * 3 + 2 * 5 + 2 * 1
Area = 30 + 10 + 2
Area = 42
Case II,
As shown in right figure,
Area of the vertical rectangles
Area = 3 * 5 + 5 * 3 + 2 * 6
Area = 15 + 15 + 12
Area = 42
Here, the area in case 1 is equal to case 2.
Thus, the two different ways of finding the area have shown above.
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Write down the answer for Q 7 and 8
The answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
Addition operationFrom the question, we are to add the given numbers
7. 6 Hundredths add to 4 tenths add to 6 ones is equal to
6 Hundredths = 0.06
4 tenths = 0.4
6 ones = 6
Thus, we get
0.06 + 0.4 + 6 = 6.46
8. 82 Hundredths add to 9 tenths add to 4 tens is equal to
82 Hundredths = 0.82
9 tenths = 0.9
4 tens = 40
Thus, we get
0.82 + 0.9 + 40 = 41.72
Hence, the answers to the given addition operations are
7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46
8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72
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Find the value of x
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 35°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:4x + 1 + x + 4 = 180[/tex]
[ by linear pair ]
[tex]\qquad❖ \: \sf \:5x + 5 = 180[/tex]
[tex]\qquad❖ \: \sf \:5(x + 1) = 180[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 180 \div 5[/tex]
[tex]\qquad❖ \: \sf \:x + 1 = 36[/tex]
[tex]\qquad❖ \: \sf \:x = 36 - 1[/tex]
[tex]\qquad❖ \: \sf \:x = 35[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 35°Use the rational zeroes theorem to write the
function in factored form and find all zeroes.
Note a = 1.
Y =x²-23x² 18x+40
The y factors of the given quadratic equation is -1 and 40/22.
According to the statement
we have given that the equation and we have to find the factors of those equation.
So, The given equation is:
[tex]Y =x^2-23x^2 + 18x+40[/tex]
where y is the factors of that equation.
So, we have to find the factors of the given quadratic equation.
[tex]x^2-23x^2 + 18x+40 = 0[/tex]
Then after solving it become
[tex]-22x^2 + 18x+40 = 0[/tex]
Then take negative sign common from it then
[tex]22x^2 - 18x - 40 = 0[/tex]
Make the factors of this quadratic equation
[tex]22x^2 + 22x -40x - 40 = 0[/tex]
Now take common values 22x and 40 from the equation then
[tex]22x (x + 1) -40 (x + 1) = 0[/tex]
Then it become
[tex](22x - 40) (x + 1) = 0[/tex]
Then the values of x become from the equation is
[tex]x = -1, x= 40/22[/tex]
The value of the factors y is -1 and 40/22.
So, The y factors of the given quadratic equation is -1 and 40/22.
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graph 3/6 3/4 and 3/12 on a number line
The number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.
When fractions are represented on a number line, we can plot them on a number line just like we do with whole numbers and integers. Parts of a whole are represented by fractions. As a result, fractions on the number line are represented by splitting a whole into equal parts, ranging from 0 to 1, and the number of those equal parts would match the denominator of the fraction.
To graph the given fractions on the number line, we first convert them to like fractions.
3/6, 3/4, and 3/12
= 6/12, 9/12, and 3/12, which are like fractions.
Now we divide the number line with the minimum mark as 1/12, the least fraction, with 12 as denominator.
Now, we can mark the points 6/12, 9/12, and 3/12, as shown.
Thus, the number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.
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x+2y=5 and 4x-12y=-20 substitution and elimination method
By solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.
Given two equations x+2y=5 and 4x-12y=-20.
We are required to solve the equations through elimination and substitution method.
Firstly we will solve the equations through elimination method.
x+2y=5-------------1
4x-12y=-20--------2
Multiply the equation 1 by 4 and then subtract the equation 2 from equation 1.
4x+8y-4x+12y=20+20
20y=40
y=2
Use the value of y in 1
x=5-2*2
x=5-4
x=1
From substitution method.
First find the value of x from first equation in terms of y.
x=5-2y-----4
Now put this value in second equation to get the value of y.
4(5-2y)-12y=-20
20-8y-12y=-20
20-20y=-20
-20y=-40
y=2
Put the value of y in equation 4.
x=5-2y
x=5-2*2
x=5-4
x=1
Hence by solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.
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need this answered asap Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5
The function that has a minimum and is transformed to the right and down from the parent function is; g(x) = 8(x² - 3²) - 5
How to Interpret Functions?By inspection, only Functions B) and D) have a minimum.
For the first function in option B, we have:
g(x) = 4(x²- 6x + 9) + 1
This can be simplified to;
g(x) = 4( x - 3 )² + 1
Thus, we can say that this first function is transformed to the right and up from the parent function.
For the second function in option D, we have;
g(x) = 8(x² - 6x + 9 ) - 5
The function can be simplified to get;
g(x) = 8( x - 3 )² - 5
Thus, we can say that it is transformed to the right and down.
The function that has a minimum and is transformed to the right and down from the parent function is D
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Answer: option D
Step-by-step explanation:
PLEASE HELP ALOT OF POINYSAshlee is working with a local construction firm to improve Interstate 35.
The construction firm has created steel supports that will be arranged
into triangular shapes with side lengths of 6 feet, 9 feet, and where the
third side of each triangle has various lengths. They have asked Ashlee to
design a package that she could guarantee would fit all the materials. She
decided to use constructions to determine the maximum value for the
unknown side, x, and then ship all her materials in a box of length x feet.
Which is the best conclusion for Ashlee to make?
The best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.
How to determine the maximum lengths?
The side lengths of the triangle are given as:
6 feet and 9 feet
Let the third side be x.
By triangle inequality theorem, we have:
a + b > c
So, we have
6 + 9 > x
6 + x > 9
9 + x > 6
Evaluate the inequalities
15 > x
x > 3
x > -3
Remove the negative inequality
15 > x
x > 3
Combine the inequalities
3 < x < 15
So, the maximum side is less than 15
Hence, the best conclusion for Ashlee to make is (c) Ashlee determined that the box must be less than 15 feet by verifying the triangle inequality theorem.
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sin theta =-(1)/(\sqrt(17))and (3\pi )/(2)<=\theta <=2\pi then tan\theta =
Using a trigonometric identity, and considering that the angle is in the fourth quadrant, the tangent of the angle is given as follows:
tan(theta) = -1/4
Which trigonometric identity relates the sine and the cosine of an angle?The following identity is used to relate the measures, considering an angle [tex]\theta[/tex]:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
For this problem, the sine is given as follows:
[tex]\sin{\theta} = -\frac{1}{\sqrt{17}}[/tex]
Then the cosine, which we need to find the tangent, is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\left(-\frac{1}{\sqrt{17}}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{1}{17} + \cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{16}{17}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{16}{17}}[/tex]
Since the angle is in the fourth quadrant, the cosine is positive, hence:
[tex]\cos{\theta} = \frac{4}{\sqrt{17}}[/tex]
What is the tangent of an angle?It is the sine of the angle divided by the cosine of the angle, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{-\frac{1}{\sqrt{17}}}{\frac{4}{\sqrt{17}}} = -\frac{1}{4}[/tex]
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