Answer:
x^2+11x+10
or
(x+1)(x+10) since you can factor x^2+11x+10
Step-by-step explanation:
Let's do synthetic division.
We are dividing by x+2, so -2 will be on the outside. Like this:
-2 | 1 13 32 20
| -2 -22 -20
|___________________________
1 11 10 0
The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.
The other factor we found by doing this is (x^2+11x+10).
You can find more factors by factoring x^2+11x+10.
Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).
F(x)=x^2 what is g(x)
Answer:
[tex]\large\boxed{C.\ g(x)=3x^2}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2\to f(1)=1^2=1\\\\g(1)=3\to\text{given point (1,\ 3)}\\\\3=3\cdot1=3\cdot1^2=3f(1)\to g(x)=3f(x)=3x^2[/tex]
How many permutations are there of the letters in the word 'PLANTS', if all the letters are used without repetition?
Answer:
6!
or
6*5*4*3*2*1
or
720
Step-by-step explanation:
The word 'PLANTS' contains no letter more than once.
It is say 6 letter word.
_ _ _ _ _ _
There are 6 ways to choose the first blank (after than there are 5 letters left to choose from)
After the first blank, there are 5 letter left to choose from so there are 5 ways to choose the second blank.
Then 4 ways for the third blank.
3 ways for the fourth blank.
2 ways for the fifth blank.
1 way for the sixth blank.
Now to figure out the number of permutations you must multiply the number of different ways we have above for each blank.
That is we are doing 6*5*4*3*2*1 or 6!
There are 720 different permutations of the letters in the word 'PLANTS' when used without repetition. This is calculated as the factorial of the number of letters, which is 6. Therefore, 6 factorial (6!) equals 720.
Explanation:The subject of the question falls under the topic of permutations in Mathematics. The question is asking for the number of different ways that the letters in the word 'PLANTS' can be arranged if all letters are used without repetitions. This is a concept in combinatorics, a subject of discrete mathematics that deals with counting and arranging objects.
To solve this, we need to calculate the factorial of the number of letters in the word 'PLANTS'. There are 6 letters in the word. The factorial of a number (denoted as n!) is the product of all positive integers less than or equal to that number. Therefore, the number of permutations is 6!, which equates to 6 x 5 x 4 x 3 x 2 x 1 = 720.
So, there are 720 different permutations of the letters in the word 'PLANTS' if all the letters are used without repetition.
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If 8(x) is the inverse of f(x) and f(x) = 4x + 12, what is g(x)?
Answer:
[tex]g(x)=\frac{x-12}{4}[/tex]
Step-by-step explanation:
To find the inverse of y=4x+12, all you need to is swap x an y and then remake y the subject.
y=4x+12
Swap x and y:
x=4y+12
Solve for y:
Subtracting 12 on both sides:
x-12=4y
Dividing 4 on both sides:
[tex]\frac{x-12}{4}=y[/tex]
So [tex]g(x)=\frac{x-12}{4}[/tex]
Answer:
[-12 + x]\4 = g(x)
Step-by-step explanation:
x = 4y + 12 [SWAP y and x]-12 + x = 4y [Move -12 to the left side of the equivalence symbol][-12 + x]\4 = g(x) [Divide by 4]If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
PLEASE HELP! Select all the correct answers.
Terry is an up-and-coming florist who specializes in weddings. He uses 5 roses, 3 daisies, and 4 bundles of green filler to make one bouquet. If r is the cost of a rose, d is the cost of a daisy, and f is the cost of a bundle of green filler, which expression represents the cost for making 75 bouquets?
Answer:
im sorry this never got answered but you would put the third one i believe
Step-by-step explanation:
Which represents the solution set of the inequality 5x-9321?
Answer:
The solution set is the interval (-∞ , 6] OR {x : x ≤ 6}
Step-by-step explanation:
* Lets explain how to find the solution set of the inequality
- The inequality is 5x - 9 ≤ 21
∵ 5x - 9 ≤ 21
- At first add 9 to both sides of the inequality to separate x in one
side and the numbers in the other sides
∴ 5x - 9 + 9 ≤ 21 + 9
∴ 5x ≤ 30
- Lets divide both sides of the inequality by 5 to find the values of x
∴ (5x ÷ 5) ≤ (30 ÷ 5)
∴ x ≤ 6
- The solutions of the inequality is all real numbers smaller than
or equal to 6
∴ The solution set is the interval (-∞ , 6] OR {x : x ≤ 6}
- We can represent this inequality graphically to more understand
for the solution
- From the graph the solution set is the purple area
Identify an equation in point-slope form for the line perpendicular to
y= -2x + 8 that passes through (-3,9).
Answer:
y - 9 = 1/2(x + 3)
Step-by-step explanation:
For the equation y = -2x + 8, your slope, m, is -2. To find the slope for a line perpendicular to the original line, we do the opposite reciprocal of this number. The slope of the perpendicular line is 1/2.
Point-slope form is: y - y1 = m(x - x1) where x1 and y1 are the x- and y-coordinates of an ordered pair.
With this new slope for the perpendicular line, and the point we are given, we just plug in the info.
Your equation is: y - 9 = 1/2(x + 3)
THANK U!!✔
for answering
Answer:
-8.95 ,, -8.36 ,, 7/28 ,, 8 22/40
Step-by-step explanation:
Answer:
-8.95, -8.36, 7/28, 8 22/40
Step-by-step explanation:
1,2,and 3 please I really need help
Answer:
1) yes
2) Option B
3) 9200
Step-by-step explanation:
1) yes
The exponential function is: y=-(x)^3
Putting the values of x in the given function we get the values of y.
x =1 , y= -(1)^3, y=-1
x= 2, y= -(2)^3, y = -8
x= 3, y= -(3)^3,y = -27
x= 4, y= -(4)^3,y = -64
2) f(x) = 160.2^x
if value of x = 2
then f(2) = 160.2^(2)
f(2) = 160.4
f(2) = 640
So, Option B is correct.
3) f(x) = 2300.2^x
if value of x = 2 decades then
f(2) = 2300.2^2
f(2) = 2300.4
f(2) = 9200
Since all options are not visible, so correct answer is 9200
The Coffee Counter charges $10 per pound for Kenyan French Roast coffee and $9 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $ 9.50 per pound?
10 pounds of each type of coffee should be mixed to make a 20 pound blend that sells for $9.50 per pound.
Charges for Kenyan French Roast coffee = $10 per pound
Charges for Sumatran coffee = $9 per pound
Let the amount of Kenyan French Roast used = K pound
And the amount of Sumatran coffee used = S pound
If the total amount of the mixture = 20 pounds
Equation for the total amount will be,
K + S = 20 ------- (1)
If the cost of this mixture = $9.50
Equation for the cost of the mixture will be,
10K + 9S = 20×9.50
10k + 9S = 190 ------- (2)
Multiply equation (1) by 9 and subtract this equation from equation (2),
(10k + 9S) - (9K + 9S) = 190 - 180
K = 10 pounds
Substitute the value of K in equation (1),
10 + S = 20
S = 10 pounds
Therefore, 10 pounds of each blend of coffee should be mixed.
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To make a 20 pound blend of coffee that costs $9.50 per pound using Kenyan French Roast coffee ($10 per pound) and Sumatran coffee ($9 per pound), you should use 10 pounds of each type.
Explanation:To solve this problem, we can set up a system of equations to represent the given information. Let x represent the amount of Kenyan French Roast coffee and y represent the amount of Sumatran coffee. We have the following equations:
x + y = 20 (equation 1 - representing the total weight of the blend)
10x + 9y = 9.50 * 20 (equation 2 - representing the total cost of the blend)
To solve this system, we can first multiply equation 1 by 10 to get:
10x + 10y = 200 (equation 3)
We can then subtract equation 3 from equation 2 to eliminate the variable x:
10x + 9y - (10x + 10y) = 9.50 * 20 - 200
9y - 10y = 190 - 200
-y = -10
y = 10
Substituting this value back into equation 1 gives us:
x + 10 = 20
x = 10
Therefore, we should use 10 pounds of Kenyan French Roast coffee and 10 pounds of Sumatran coffee to make the 20 pound blend.
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someone help me with this
2a. 14,9; 2b. 15,4; 2c. 30,8; 3. 32
For 2a., you have to set it up like this: csc 48° = 20⁄x [OR sin 48° = ˣ⁄20]. Then you would have to isolate the variable by getting rid of the denominator. The cosecant function has an extra step because you will get xcsc 48° = 20. As stated, isolate the variable; this time, divide by csc 48°. This is what 20 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.
For 2b., you have to set it up like this: sec 39° = ˣ⁄12 [OR cos 39° = 12⁄x. Then you would have to isolate the variable by getting rid of the denominator. The cosine function has an extra step because you will get xcos 39° = 12. As stated, isolate the variable; this time, divide by cos 39°. This is what 12 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.
For 2c., you have to set it up like this: cot 64° = 15⁄x [OR tan 64° = ˣ⁄15]. Then you would have to isolate the variable by getting rid of the denominator. The cotangent function has an extra step because you will get xcot 64° = 15. As stated, isolate the variable; this time, divide by cot 64°. This is what 15 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.
Now, for 3., it is unique, but similar concept. In this exercise, we are solving for an angle measure, so we have to use inverse trigonometric ratios. So, we set it up like this: cot⁻¹ 1⅗ = m<x [OR tan⁻¹ ⅝ = m<x]. We simply input this into our calculator and we get 32,00538321°. When rounded to the nearest degree, we get 32°.
WARNING: If you use a graphing calculator, you have to input it uniquely because most graphing calculators do not have the inverse trigonometric ratios programmed in their systems. This is how you would write this: tan⁻¹ 1⅗⁻¹. You set 1⅗ to the negative first power, ALONG WITH the inverse tangent function, because without it, your answer will be thrown off. Since Cotangent and Tangent are multiplicative inverses of each other, that is the reason why the negative first power is applied ALONG WITH the inverse tangent function.
**NOTE: 1⅗ = 8⁄5
Take into consideration:
sin θ = O\H
cos θ = A\H
tan θ = O\A
sec θ = H\A
csc θ = H\O
cot θ = A\O
I hope this helps you out alot, but if you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains.
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.
He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.
He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.
Answer:
He is incorrect. The path will have an area of (4)(40) = 160 ft². The yard has an area of 600 ft². The area of the lawn will be the difference of the yard and path, so it is 440 ft².
Step-by-step explanation:
1. Original area of yard
A = lw = 40 × 15 = 600 ft²
2. Area of path
The path is a parallelogram.
A = bh = 4 × 40 =160 ft²
3. Remaining area
Remaining area = original area - area of path = 600 - 160 = 440 ft².
Answer:
A is correct
Step-by-step explanation:
I got 100 on edg
seven sixteeths wrote as a decimal
Answer:
The answer is 0.4375 .
Hope this helps!
Maria has a swimming pool in her backyard. Calculate the volume of the swimming pool. Round your answer to the nearest whole number. a0 cubic feet
Answer:
108 feet cubed
Step-by-step explanation:
i think its 24 because you do l*w*h so 4 times 6 equals 24, times 4.5 and its 108.
Answer : The volume of the swimming pool is, [tex]142ft^3[/tex]
Step-by-step explanation :
In the given figure, there are two figures are included which are cuboid and 2 hemisphere.
As we know that 2 hemisphere combine to form a sphere.
Volume of swimming pool = Volume of cuboid + Volume 2 hemisphere
Volume of swimming pool = Volume of cuboid + Volume sphere
Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]
where,
l = length of cuboid = 6 ft
b = breadth of cuboid = 4 ft
h = height of cuboid = 4.5 ft
r = radius of sphere = [tex]\frac{Diameter}{2}=\frac{4ft}{2}=2ft[/tex]
Now put all the given values in the above formula, we get:
Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]
Volume of swimming pool = [tex](6ft\times 4ft\times 4.5ft)+(\frac{4}{3}\times 3.14\times (2ft)^3)[/tex]
Volume of swimming pool = [tex]108ft^3+33.49ft^3[/tex]
Volume of swimming pool = [tex]141.49ft^3[/tex]
Volume of swimming pool ≈ [tex]142ft^3[/tex]
Therefore, the volume of the swimming pool is, [tex]142ft^3[/tex]
13, 29, 427, 881
Is the sequence geometric? If so, identify the common ratio.
Final answer:
The sequence 13, 29, 427, 881 is not geometric because each term is not obtained by multiplying the previous term by a constant ratio. The ratios between successive terms vary, so there is no common ratio.
Explanation:
Is the sequence 13, 29, 427, 881 geometric? To determine if a sequence is geometric, each term should be obtained by multiplying the previous term by a constant number, known as the common ratio.
Let's calculate the ratios between successive terms:
Ratio from 13 to 29: 29 ÷ 13 = 2.23077 (approximately)Ratio from 29 to 427: 427 ÷ 29 = 14.72414 (approximately)Ratio from 427 to 881: 881 ÷ 427 = 2.06324 (approximately)Since the ratios are not the same, the sequence is not geometric. Therefore, there is no common ratio.
Question 3(Multiple Choice Worth 4 points)
(08.03)Solve the system of equations and choose the correct answer from the list of options.
2x + y = −4
y = 3x + 2
negative 6 over five comma negative 8 over 5
negative 8 over 5 comma negative 6 over 5
negative 5 over 6 comma negative 11 over 5
negative 11 over 5 comma negative 6 over 5
Answer:
[tex]\large\boxed{\left(-\dfrac{6}{5},\ -\dfrac{8}{5}\right)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x+y=-4&(1)\\y=3x+2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\2x+(3x+2)=-4\\2x+3x+2=-4\qquad\text{subtract 2 from both sides}\\5x=-6\qquad\text{divide both sides by 5}\\\boxed{x=-\dfrac{6}{5}}\qquad\text{put it to (2)}\\\\y=3\left(-\dfrac{6}{5}\right)+2\\\\y=-\dfrac{18}{5}+\dfrac{10}{5}\\\\\boxed{y=-\dfrac{8}{5}}[/tex]
There are 32 students in Jenny's class. If the teacher randomly picks a student to call on, what is the probability that Jenny will be called on twice? (If necessary, round to the nearest hundredth.)
To find the probability that Jenny will be called on twice, we multiply the probabilities of picking her on the first and second calls, which is 1/992.
Explanation:To find the probability that Jenny will be called on twice, we need to consider the total number of possible outcomes and the number of favorable outcomes.
There are 32 students in Jenny's class, so the total number of possible outcomes is 32.
For the first call, the probability of picking Jenny is 1/32. After the first call, there are now 31 students left, with 1 of them being Jenny. So, the probability of picking Jenny again on the second call is 1/31.
To find the probability of both events happening, we multiply the probabilities together: (1/32) x (1/31) = 1/992.
The probability that Jenny will be called on twice is 1/992.
The probability that Jenny will be called twice in a class of 32 students is 0.00098. This rounds to 0.00 when rounded to the nearest hundredth.
To determine the probability that Jenny is called on twice when there are 32 students in the class, we start by finding the probability for one instance and then consider the repeated scenario.
For the first call, Jenny has a 1 in 32 chance of being called, so the probability is 1/32.For the second call, we're still considering a random selection from the entire class, so Jenny again has a 1 in 32 chance.To find the combined probability of both events happening (Jenny being called twice), we multiply the probabilities of each individual event:
(1/32) * (1/32) = 1/1024
Thus, the probability that Jenny will be called on twice is approximately 0.00098 when rounded to the nearest hundredth.
What is the simplified expression for
for 3^-4 x 2^3 x 3^2/2^4 x 3^-3?
Answer:
3/2
Step-by-step explanation:
3^-4 x 2^3 x 3^2/2^4 x 3^-3
base 3 will be numerator and base 2 will be denominator:
3^-4 * 3^2 * 3^3 / 2^4*2^-3
Now add the exponents of the base:
3^-4+2+3/ 2^4-3
3^-4+5/ 2^1
3/2
The correct option is 3/2 ....
Janelle and her best friend Carmen go shopping. the function p(t) = 5^4-3x^3 +2^2+24 represents how much money each girl spent based on the number of hours they were shopping. If Janelle and Carmen each go shopping for 2 hours how much money did they spend together.
$58
$62
$176
$124
The answer is:
They spent $176 together.
Why?We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.
Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:
[tex]p(t)=5x^{4}-3x^{3}+2x^{2}+24[/tex]
Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:
[tex]p(t)=2(5x^{4}-3x^{3}+2x^{2}+24)[/tex]
Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.
Calculating we have:
[tex]p(2)=2(5*(2)^{4}-3*(2)^{3}+2*(2)^{2}+24)=2(5*16-3*8+2*4+24)[/tex]
[tex]p(2)=2(5*16-3*8+2*4+24)=2(80-24+8+24)=2*88=176[/tex]
Hence, we have that they spent $176 together.
Have a nice day!
Answer:
c
Step-by-step explanation:
Which algebraic expression represents the phrase "four times a number"?
0 4+0
O 0-4
0 4=0
040
Answer:
Step-by-step explanation:
None of them do to me. The last one does not. And certainly the second last one cannot.
In B, you are subtracting 4 from zero which doesn't work.
A adds 0 to 4 which gives 4
Unless I misreading D and O is a variable (sneaky), there is no answer.
what is the value of x?
To solve this you must use Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = 48
b = x
c = 50
^^^Plug these numbers into the theorem
[tex]48^{2} +x^{2} =50^{2}[/tex]
simplify
2304 + [tex]x^{2}[/tex] = 2500
Isolate x^2 by subtracting 2304 to both sides
[tex]x^{2}[/tex] = 196
To remove the square from x take the square root of both sides to get you...
14 = x
Hope this helped!
~Just a girl in love with Shawn Mendes
The graphed line shown below is y=-4x-12. Which equation, when graphed with the given equation, will form a system that has no solution?
I guess one more does not hurt.
Notice that choice D is equivalent to the given equation y = -4x - 12.
The only equation that does not cross the given equation is y = -4x.
They have THE SAME SLOPE. This means they are parallel and thus lead to NO SOLUTION.
ANSWER: y = -4x
Answer:
[tex]y=-4x[/tex]
Step-by-step explanation:
A Linear System with no solution, therefore inconsistent, is graphically represented by a pair of parallel lines.
According to Analytic Geometry, a parallel line shares the same slope.
Given the options, the only parallel line to [tex]y=-4x-12[/tex] is [tex]y=-4x[/tex] Since [tex]y=-4(x+3)[/tex] despite having the same slope, is actually the same line [tex]y=-4x+12[/tex]
So [tex]y=-4x[/tex] will form a system that has no solution.
Simplify [4a^(-6) b^2]^(-3) write your answer using only positive exponent
For this case we must simplify the following expression:
[tex](4a^{ - 6} * b ^ 2)^{ - 3}[/tex]
By definition of power properties we have:[tex]a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex](\frac {4} {a ^ 6} * b ^ 2) ^ {- 3} =\\\frac {1} {(\frac {4} {a ^ 6} * b ^ 2)^3} =\\\frac {1} {(\frac {4b ^ 2} {a ^ 6})^3} =[/tex]
By definition we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
[tex]\frac {1} {\frac {64b ^ 6} {a^{18}}}\\\frac {a^{18}} {64b ^ 6}[/tex]
Answer:
[tex]\frac {a^{18}} {64b ^ 6}[/tex]
The complex numbers w
and z satisfy the relation w= (z + i)/ (iz + 2)
Given that z = 1 + i, find w. giving your answer in the form x + iy, where x and y are real.
[tex]w=\dfrac{1+i+i}{i(1+i)+2}\\\\w=\dfrac{1+2i}{i-1+2}\\\\w=\dfrac{1+2i}{1+i}\\\\w=\dfrac{(1+2i)(1-i)}{1+1}\\\\w=\dfrac{1-i+2i+2}{2}\\\\w=\dfrac{3+i}{2}\\\\w=\dfrac{3}{2}+\dfrac{1}{2}i[/tex]
To find the value of w, substitute the given value of z into the equation for w. Simplify the expression to obtain the value of w in the form x + iy, where x and y are real numbers.
Explanation:To find the value of w, we first substitute the given value of z into the equation for w.
Given z = 1 + i, we have:
w = (1 + i + i) / (i(1 + i) + 2)
Simplifying the numerator:
w = (1 + 2i) / (i + i^2 + 2)
Since i^2 = -1, we can rewrite the equation as:
w = (1 + 2i) / (-1 + i + 2)
Simplifying further:
w = (1 + 2i) / (1 + i)
To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.
w = ((1 + 2i)(1 - i)) / ((1 + i)(1 - i))
w = (1 - i + 2i - 2i^2) / (1 - i^2)
Using i^2 = -1 again:
w = (1 + i + 2i + 2) / (1 - (-1))
Simplifying the numerator:
w = (3 + 3i) / 2
Dividing both terms by 2:
w = 3/2 + 3/2i
Therefore, w = 3/2 + 3/2i in the form x + iy, where x = 3/2 and y = 3/2 are real numbers.
System of equations graphed below had How many equations?
Answer:
A. 0Step-by-step explanation:
The solution of the system of equations are the coordinates of the point of intersection.
We have two parallel lines. The intersection point does not exist.
Therefore, this system of equations has no solution.
Based on Pythagorean identities, which equation is true?
O sin?e 1-cos?
O sec?etan? --1
O -cos?-1--sin
O cote-csc? --1
Answer:
d no is correct
I hope it will help you
The equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]
Pythagoras theoremAccording to the theorem;
[tex]x^2 + y^2 = r^2[/tex]
Given the following
x = [tex]r cos \theta[/tex]
y = [tex]r sin \theta[/tex]
Substitute into the formula
[tex](rcos \theta)^2 + (r sin \theta)^2 = r^2\\cos^2 \theta + sin^2 \theta =1[/tex]
Multiplying through by minus, the equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]
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Write the equation of the line that passes
through the point (3, -3) and has a slope of -2.
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the point (3, -3) and the slope m = -2. Substitute:
[tex]y-(-3)=-2(x-3)[/tex]
[tex]y+3=-2(x-3)[/tex] - point-slope form
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-2(x-3)[/tex] use the distributtive property
[tex]y+3=-2x+(-2)(-3)[/tex]
[tex]y+3=-2x+6[/tex] subtract 3 from both sides
[tex]y=-2x+3[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=-2x+3[/tex] add 2x to both sides
[tex]2x+y=3[/tex] - standard form
Convert to the general form (Ax + By + C = 0):
[tex]2x+y=3[/tex] subtract 3 from both sides
[tex]2x+y-3=0[/tex] - general form
The corporate team-building event will cost $18 if it has 6 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $48? Solve using unit rates.
1) Find the unit rate
$18/6 attendees = 3
2) Apply the unit rate to find the answer
$48/$3= 16 attendees
Therefore, there can be 16 attendees if the budget is $48.
Hope this helps!
ali and jake went on a cross country trip they took a train part of the way and took a bus the rest of the way they traveled a total of 1450 riding on the train 150 more kilometers than on the bus
let x=kilometers traveled by bus
let y = kilometers traveled by train
question how many kilometers did they travel by train?
Answer:
y=800 km
Step-by-step explanation:
Let the distance traveled by train be y and by bus be x.
Bus -x
Train -y
y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)
The sum of the two is equal to 1450
x+y=1450
The two equations form simultaneous equations which when solved simultaneously give the values of x and y.
y+x=1450
y-x=150
Adding the two we get:
2y=1600
Divide both sides by two:
y=800 km
Y is the distance traveled by train= 800 km
Consider the given function. Which statement about the functions is true?
Answer:
the correct answer is D. Funtion 1 and 3 have the same rate of change but funtion 1 has greater y intercept
Step-by-step explanation:
If we organize the funtion 1, we have y= 2x+8
Funtion 2 the need to calculate the slope m = (y2-y1)/(x2-x1) the point on the y represent (y2,x2) and is (4,0) the point onn the x axis is (x1,y1) and is (-2,0)
So, m=(4-0)/(0-(-2) => m=(4/2) => m=2
Then, y=m(X-Xo) + Yo . From the plot, I choose (x2,y2) as (Xo,Yo) So, (0,4)
y=2(X-0) +4 then y= 2x+4
From 3 equation the choose the value x=o and g(x)= 5 and x=1 and g(x)=7 and following the same m=(7-5)/(1-0) the slope is m=2. Following the same procedure before I choose x=0 and y=5
Then the equation is: y=2(x-0) + 5
So, opcion D is true
If a population is ______ , a sample of the population could be _____.
Using sampling concepts, it is found that the sentence is:
C. If a population is all actors, a sample of the population could be movie actors.
A sample is a group taken from the population. It has to come from a more restrict group of the population, that is, an subset of the population.
In option A, baseball players is a subset of all athletes, so all athletes would be the population and baseball players would be the sample. The same can be applied in options B and D.
In option C, movie starts is a subset of all actors, thus the roles of sample and population are correct.
A similar problem is given at https://brainly.com/question/25119689