Answer:for every five red beeds their are 5 black beeds
Step-by-step explanation:
To maintain the relationship of black beads to red beads, we need to know the ratio of black beads to red beads in the existing bracelet or the desired ratio. If the ratio is 1:1, for example, then you would need to use an equal number of black and red beads.
However, based on the information provided, it's not clear what the current or desired ratio is. If Jamie wants to maintain a specific ratio, you need to know that ratio.
For example, if the ratio is 2:1 (2 black beads for every 1 red bead), and you want to use 5 red beads, you would need 5×2=10 black beads to maintain the 2:1 ratio.
Without more information on the desired or existing ratio, it's not possible to determine whether using 5 red beads alone would maintain the relationship of black beads to red beads.
complete step by step
To maintain the relationship of black beads to red beads in a bracelet, we need to understand the existing ratio and then apply it to the new situation.
Let's say the current ratio of black beads to red beads in Jamie's bracelet is 3:2. This means that for every 3 black beads, there are 2 red beads.
Now, Jamie wants to make a bracelet with 5 red beads. To maintain the same ratio, we need to determine the corresponding number of black beads.
The ratio of black beads to red beads is 3:2, which simplifies3x:2x for some positive value of x.
Since Jamie wants 5 red beads, we set up the equation: 2x-5
Now, solve for x:
x- 5/2
Now that we know the value of x, we can find the number of black beads:
Number of black beads - 3x-3 x (5/2) - (15/2) - 7.5
However, since the number of beads must be a whole number, we need to adjust. In this case, Jamie cannot make a bracelet with exactly 5 red beads while maintaining the ratio of 3:2. She would need to choose a different number of red beads that allows for a whole number of black beads according to the established ratio.
In conclusion, to maintain the relationship of black beads to red beads, Jamie cannot make a bracelet with exactly 5 red beads. The number of red beads chosen must allow for a whole number of black beads based on the given ratio.
x + y = 6
3x - 2y = -2
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
x+y=6
3x-2y=-2
---------------
y=6-x
3x-2(6-x)=-2
3x-12+2x=-2
5x-12=-2
5x=-2+12
5x=10
x=10/5
x=2
y=6-(2)=6-2=4
Which of the following situations results in a sum of 1 1/2 ? Select all that apply
A) I cut 3 1/3 inches from my grave. The grass grew 1 5/6 inches over the next week.
B) I used up 1/4 of a pound of coffee and bought 1 1/4 of a pound of coffee from the store
C) I gained 6 1/2 pounds and my wife lost 8 pounds
D) I had 4 1/4 bottles of juice and drank 1 3/4 of them
E) I painted 5/8 of one room and 7/8 of a another
F) I used 3/4 of a pound of ground beef to make burgers and purchased 2 1/4 of a pound of ground beef
Answer:
A if you're subtracting amount grown from amount cut
C if your subtracting husband's gain from wife's loss,
E for sure. 100%. a sum or 1.5 is reached through addition
& F if you're subtracting amount used from amount bought.
Step-by-step explanation:
Please comment & ask for further explanation if you would like it :)
Answer: they are A C E and F
Step-by-step explanation:
My siblings explained it to me
if a population of 5000 doubles in size every 55 years what will the population be 220 years from now
Answer: 40 000
Step-by-step explanation:
Population doubles in first 55 years =
5000 * 2 = 10 000
In 220 years from now, 220/55 = 4
Hence, 10 000 * 4 = 40 000 population
three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle. find the measure of the angle
Answer:
Step-by-step explanation:3(180-x)=8(90-x)
540-3x=720-8x
540=720-5x
-180=-5x
36=x
x=36
the angle is 36,supplement is 144,complement is 54.
The angle is 36, the supplement is 144, complement is 54.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles.
Two angles whose sum is 90° are called complementary angles.
Given;
The three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle.
So, 3(180-x)=8(90-x)
Solve for x;
540-3x=720-8x
540=720-5x
-180=-5x
36=x
x=36
Hence, the angle is 36, the supplement is 144, complement is 54.
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Find the number if:
1.12 of it is 56
Answer:
The number is 50.
Step-by-step explanation:
1.12x=56
x=56/1.12
x=50
Anna walked 8 miles in 3 hours. Juan walked 14 miles in 5 hours. Are these rates in proportion?
These rates are not in proportion. Juan walked faster.
Explanation:
First, we want to make these ratios to have the same denominator so we can compare the numerators. To do this, do 3x5 and 8x5 to get 40:15. Then, we do 5x3 and 14x3 to get 42:15. Now we can just compare the numbers 40 and 42, and since 42 < 40, we know Juan walked faster.
The rates of 8/3 miles per hour and 14/5 miles per hour are not in proportion.
To determine whether the rates of Anna and Juan are in proportion, we can compare the rates of their walking speeds by forming a ratio and seeing if the ratios are equivalent. Anna walked 8 miles in 3 hours, which gives us a rate of 8/3 miles per hour. Juan walked 14 miles in 5 hours, resulting in a rate of 14/5 miles per hour.
To check the proportion, we set up a ratio of Anna's speed to Juan's speed: (8/3) / (14/5). If these rates are proportional, the cross-products of the ratios will be equal. However, when you cross-multiply, you get 8 * 5 = 40 and 3 * 14 = 42. Since 40 is not equal to 42, the rates are not in proportion.
how can you tell that the following number is a rational number? 0.251
The number 0.251 is a rational number because it can be expressed as the fraction 251/1000, which has both integers as its numerator and denominator, with the denominator not being zero.
Explanation:To determine whether 0.251 is a rational number, one must understand the definition of rational numbers.
Rational numbers include all numbers that can be expressed as a fraction where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not zero.
The number 0.251 meets this criterion because it can be written as the fraction 251/1000, where 251 and 1000 are both integers, and 1000 is not zero.
If we look at different numerical expressions, such as ones resulting from operations on fractions or converting numbers into scientific notation, the underlying principle is that the operations maintain equality and the representations still refer to rational numbers as long as they can be expressed as a ratio of integers.
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 0 100 200 300
y 2.5 97.5 192.5 287.5
Answer:
[tex]y=0.95x+2.5[/tex]
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
(0,2.5) and (100,97.5)
substitute in the formula
[tex]m=\frac{97.5-2.5}{100-0}[/tex]
[tex]m=\frac{95}{100}[/tex]
[tex]m=0.95[/tex]
Find the y-intercept b
we have
[tex]m=0.95[/tex]
[tex]point\ (0,2.5)[/tex]
substitute i the linear equation [tex]y=mx+b[/tex]
[tex]2.5=0.95(0)+b[/tex]
solve for b
[tex]b=2.5[/tex]
Note It was not necessary to calculate the value of b because the value is given in the table
Remember that the y-intercept is the value of y when the value of x is equal to zero (the y-intercept is the point (0,2.5))
The linear equation is
[tex]y=0.95x+2.5[/tex]
To write the equation of a linear relationship in slope-intercept form, find the slope and y-intercept. Use the formula y = mx + b, where m is the slope and b is the y-intercept. Calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b.
Explanation:To write the equation of the linear relationship in slope-intercept form, we need to find the slope (m) and the y-intercept (b). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Choosing any two points from the given data, we can calculate the slope.
Let's use the points (0, 2.5) and (100, 97.5):
m = (97.5 - 2.5) / (100 - 0) = 95 / 100 = 0.95
Next, we can substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b:
2.5 = 0.95(0) + b
b = 2.5
Therefore, the equation of the linear relationship is: y = 0.95x + 2.5
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find the coordinates of the midpoint of VW with endpoint V(-2,-6) and W(x+2,y+3)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-6})\qquad W(\stackrel{x_2}{x+2}~,~\stackrel{y_2}{y+3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{(x+2)-2}{2}~~,~~\cfrac{(y+3)-6}{2} \right)\implies \left( \cfrac{x}{2}~~,~~\cfrac{y-3}{2} \right)[/tex]
Choose the equivalent factored form
2x-5=3x^2 find the root of X
For this case we must solve the following quadratic equation:
[tex]3x ^ 2-2x + 5 = 0[/tex]
Where:
[tex]a = 3\\b = -2\\c = 5[/tex]
The roots are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values we have:
[tex]x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {2 \pm \sqrt {4-60}} {6}\\x = \frac {2 \pm \sqrt {-56}} {6}[/tex]
By definition we have to:
[tex]i ^ 2 = -1\\x = \frac {2 \pm \sqrt {56i ^ 2}} {6}\\x = \frac {2 \pm i \sqrt {56}} {6}\\x = \frac {2 \pm i \sqrt {2 ^ 2 * 14}} {6}\\x = \frac {2 \pm 2i \sqrt {14}} {6}\\x = \frac {1 \pm i \sqrt {14}} {3}[/tex]
We have two complex roots:
[tex]x_ {1} = \frac {1+ i \sqrt {14}} {3}\\x_ {2} = \frac {1- i \sqrt {14}} {3}[/tex]
Answer:
[tex]x_ {1} = \frac {1+ i \sqrt {14}} {3}\\x_ {2} = \frac {1- i \sqrt {14}} {3}[/tex]
In regular mathematics what is nine times nine
Answer:
81
Step-by-step explanation:
PLS HURRY! 15 PTS!
Consider the function f(x)=x^3+2x^2-3. (a) Graph the function. (b) What are the x- and y-intercepts of the graph? BE SURE TO ANSWER (a) & (b). also pls show work!
Answer:
x-intercept = 1 and y-intercept = -3
Step-by-step explanation:
The graph of the function is attached with this answer.
I have used some computer program to draw graph but you can draw a rough graph manually on a graph sheet. For that
first of all you need to know basic structure of a cubic polynomial * which is somewhat like a wave (you can have a look at the graph attached to know the basic structure).Then plot some important points which are point of local maxima ** and local minima ***, point of intercepts (which is the second part of the question - has to be done first in order to draw a more accurate rough diagram of the function).To Calculate Some Important Points :
Local Maxima and Minima :These are the points where the the first derivative of the function becomes zero. This means that at these points the graph takes turn, if it was increasing behind this point then it will start decreasing after this point or the other way. The second derivative of the function at these points are either positive or negative (positive for local minima and negative for local maxima).
Intercepts :To calculate the x-intercept, first you need to analyse the graph to know how many x-intercepts are there. According to this graph only one intercept is there, it means that only one real root of this cubic equation is there (a cubic equation has 3 roots in which either one is real and two are imaginary or all the three are real). To calculate roots of a cubic equation there is no specific way. Generally, the first root is through hit and trial method. So, let's start with the simplest number which is x=0
[tex](0)^{3}+2(0)^{2}-3 \neq 0[/tex]
∴ 0 is not a root.
Now, let x=1
[tex](1)^{3}+2(1)^{2}-3=0[/tex]
∴ 1 is a root.
Since 1 is the only real root of the equation, therefore (1,0) is the only x-intercept of the graph.
To calculate y-intercept, simply put x=0 in the equation which is
[tex]f(0)=(0)^{3}+2(0)^{2}-3=-3\\\therefore f(0)=-3[/tex]
Therefore the y intercept is (0,-3).
* Cubic Polynomial : Polynomials which have a degree (highest power of the variable) of 3 are called cubic polynomials.
** Local Maxima : Points at which the left and right neighbours have less function value are called local maxima.
*** Local Minima : Points at which the left and right neighbours have more function value are called local minima.
Answer:
x = 1 and the y = -3
Step-by-step explanation:
here below hope this helps
2. Shilo is riding her bicycle across the state of Georgia to raise money for her favorite charity. The distance
in miles that she can travel varies directly with the length of time in hours she spends riding. Assume that
her constant of proportionality is 18. What does the constant of proportionality represent in this problem?
help me
Answer:
Below.
Step-by-step explanation:
Let the distance in miles be d and the time taken = t hours.
Then the direct proportion is d = kt where k is some constant.
In this case k = d/t = 18.
d = 18t is the equation relating distance and time.
In this case the 18 represents Milo's speed in miles per hour.
How many kilograms of lentils will each person get if 3 people share 1/5 of a kilogram of lentils equally?
Answer:
1/15 of a kilogram
Step-by-step explanation:
Answer:1/15 of a kilograms
Step-by-step explanation:
1/5 divided by three is the same as 1/5*1/3. 1*1 =1 and 5*3 =15
Which function describes the range to be equal to four less than half of the domain? Question 3 options: f(x)=12(x−4) f(x)=4−12x f(x)=12(4−x) f(x)=12x−4
Answer:
[tex]f(x)=\frac{1}{2}x-4[/tex]
Step-by-step explanation:
Given:
The range is 4 less than half of the domain.
The domain of a function is its input values represented by 'x'. The range of a function is its output values represented by 'y' values.
Domain is 'x'. So, half of domain is [tex]\frac{1}{2}x[/tex].
Now, range is 4 less than half of domain. Hence,
[tex]y=\frac{1}{2}x-4[/tex]
So, the correct option is the last option.
Given fx)= 10-2x, find f(7)
-4
3
7
56
Answer:
A) -4
Step-by-step explanation:
f(x)=10-2x
f(7)=10-2(7)
f(7)=10-14
f(7)=-4
fx)= 10-2x
f(7)=10-2(7)
do the bracket first
-2(7)=-14
f(7)=10-14
f(7)=-4
answer:
-4
1/2,-4,32,-256 find an explicit formula for the sequence
The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 * (-8)^(n-1), where n represents the position of each term in the sequence.
Explanation:To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the sequence. Upon examination, we notice that each term is obtained by multiplying the previous term by -8.
The first term, a1, is 1/2. The second term, a2, is 1/2 times -8, which is -4. If we continue this pattern, the nth term of the sequence can be described by the formula an = 1/2 * (-8)^(n-1).
Therefore, the explicit formula for the nth term of this sequence is an = 1/2 * (-8)^(n-1).
Final answer:
The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 × (-8)(n-1), where n represents the nth term. This is derived from the pattern that each term is -8 times the previous term, indicating a geometric sequence.
Explanation:
To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the terms of the sequence. Upon inspection, we see that each term is -8 times the previous term. This is a geometric sequence with a common ratio of -8.
The formula for the nth term of a geometric sequence is given by an = a1 × r(n-1), where a1 is the first term and 'r' is the common ratio.
Applying this to the given sequence with a1 = 1/2 and r = -8, the explicit formula for the nth term (an) is:
an = ½ × (-8)(n-1)Explain how to solve W/26=35. Then solve
Answer:
multiply 35(26)
Step-by-step explanation:
35(26)=910
and 910/26=35 ,
so w=910
Answer:
910
Step-by-step explanation:
Your equation is w ÷ 26 = 35
To solve for 'w,' you have to get 'w' alone on one side. To do that, you multiply both sides by 26, getting rid of the '÷ 26' on the left side of the equation.
w ÷ 26 = 35
w = 910
So your answer is 910 ^-^
please help with question below!
Answer:
45
Step-by-step explanation:
45 is constant, because no mater how many miles you drive, you will always be charged $45. It stays the same
Answer:
45
Step-by-step explanation:
your equation would be y= 45+22x and no matter what x equals, you will always have the set $45, so that is your constant.
Plz help plz plz plz plz plz plz plz
Answer:
10
Step-by-step explanation:
To solve this, we have to do 4 divided by 2/5, because there are stops every 2/5 mile of a 4-mile track.
To make dividing easier, you can write 4 as a fraction, which would be 4/1
Now, divide:
4/1 ÷ 2/5
Remember that when you divide a fraction by another fraction, you can multiply the first fraction by the reciprocal of the second fraction and get the same fraction.
The reciprocal of 2/5 is 5/2.
So 4/1 x 5/2 = 20/2, which can be simplified as 10.
So there are 10 stops. ^-^
What is the tangent ratio for F ?
13/12
12/5
5/12
12/13
Answer:
12/5
Step-by-step explanation:
The tangent ratio is the ratio of the opposite side (GH) to the adjacent side (FG). The mnemonic SOH CAH TOA can help you remember this:
Tan = Opposite/Adjacent
In this triangle, ...
tan(F) = GH/FG = 12/5
A shade of green paint is to be mixed with 3 parts blue and 2 parts yellow Ten gailions of green paint are to be mixed
How many gallions of yellow paint must be used?
4
2
5
6 2/3
Answer:
4
Step-by-step explanation:
If we were to work backwards, 4 would be the 2 part in the equation, already done. 2x2=4. so that means that the other number must also be multiplied by 2, making the number 6. 6+4 is 10, meaning ten gallons. message me with any remaining questions!
There are 4 gallons of yellow paint are needed to mixed with the ten gallons of green paint.
To calculate how many gallons of yellow paint must be used to mix with blue paint in order to make ten gallons of green paint, using a ratio of 3 parts blue to 2 parts yellow, we first need to understand the total ratio parts. The ratio given is 3:2, which means there are 3 + 2 = 5 parts in total. Since we want to mix ten gallons of green paint, we need to split these ten gallons according to the ratio.
First, we calculate the value of one part by dividing the total gallons of green paint by the total number of parts:
10 gallons / 5 parts = 2 gallons per part
Now, since we have 2 parts yellow, we need:
2 parts imes 2 gallons per part = 4 gallons
Therefore, to make ten gallons of green paint with the given ratio, 4 gallons of yellow paint must be used.
What is the equation?
Step-by-step explanation:
the segments are equal to each other because O is the midpoint of the segment
10 • 1/10 =1 a) This is an example of the additive inverse property
b)This is an example of the additive identity property.
c)This is an example of the multiplicative inverse property.
d)This is an example of the multiplicative identity property.
Answer:
C) Multiplicative Inverse Property
Step-by-step explanation:
Because 1/10 is the inverse of 10.
For example, 15*(1/15)=1.
Answer:
C
Step-by-step explanation:
The diameter of a truck tire is 22inches Approximately how fat will the truck have traveled after 5 rotations of these tires
Answer:
The truck have travelled 345.5 inches after 5 rotations of the tires
Step-by-step explanation:
Given:
Diameter of the tyre= 22 inches
Number of rotations= 5
To find:
Distance travelled after 5 rotations=?
Solution:
We have given with diameter,
So let radius be r
r= [tex]\frac{diameter}{2}[/tex]
[tex]r=\frac{22}{2}[/tex]
r=11 inches
The distance covered by one rotation is given by circumference
Circumference =[tex]2\pi r[/tex]
Substituting the values, we get
Circumference =[tex]2\times\pi\times r[/tex]
Circumference =[tex]2\times\pi\times 11[/tex]
Circumference =[tex]2\times\3.14\times 11[/tex]
Circumference =[tex]6.28\times 11[/tex]
Circumference = 69.11
Now for 5 rotation,
Distance travelled = [tex]5\times(\text{circumference value})[/tex]
Distance travelled = [tex]5\times(69.11)[/tex]
Distance travelled = [tex]5\times(69.11)[/tex]
The truck will travel 345.5 inches.
2y=5x+1
Not a direct variation
Direct variation, constant of variation is -
Direct variation, constant of variation is
Direct variation, constant of variation is 1--
Answer:
Step-by-step explanation:
he whole assignment seems to deal only with one simple concept, a direct variation
Sometimes text or your notes have definitions that are difficult to understand.
Here is the definition that is easy to understand:
A direct variation gives you an equation that contains no constants, and there are no exponents on the two variables.
e.g. y = 8x is a direct variation,
but y = 8x + 4 is NOT, since I see a constant of 4
a direct variation can be written in the form
y = kx , where k is the constant of variation
#1, not a variation, I see a +1 sitting there as a constant
#2, yes it is a direct variation:
-12x = 6y
6y = -12x
y = -2x
so the constant of variation is -2 , if y varies directly with x
or
-12x = 6y
x = -(1/2)x
now the constant of variation is -1/2 , if x varies directly as y
so it depends how you express the equation, either in terms of x or in terms of y
#3,
.7x - 1.4y = 0
.7x = 1.4y
1.4y = .7x
y = (.7/1.4)x = (1/2)x
so , yes it is, and the constant of variation is 1/2
From #4 on, you have to first find the equation.
I will do #4, you try the remaining.
#4, they tell us it is a direct variation, so it must look like
y = kx
They give us x=2 when y = -10
let's plug in those values:
-10 = k(2)
2k = -10
k = -5
aaahhhh, so y = -5x is our equation
#6, same way, just some fractions to deal with
#7, to graph, pick any x, and find the y to get ordered pairs,
e.g. let x = 3, then y = (1/3)(3) = 1, --> point(3,1)
let x = 9, then y = (1/3)(9) = 3 ---> point (9,3)
plot those two points, and join with a straight line
Notice how I picked multiple of 3's for my x's so I could take 1/3 of the x without ending up with fractions?
#8 , same as #7, pick multiples of 2 for your x's
#9 and #10 are the same type
#9
assume it is a direct variation, then its equation must be
y = kx
use the first given data: x = 3, y = 5.4
then 5.4 = k(3)
3k = 4.5
k = 1.5
equation is y = 1.5x
do the other points satisfy our equation?
for (7, 12.6)
is 12.6 = 1.5(7) ?
12.6 = 10.5 ??? NO, so the given data is NOT a direct variation
#10 same way
Answer:1. 2y=5x+1 answer is A Not a direct variation
2. -12x=6y answer is D Direct variation, constant of variation is -2
3. 0.7x-1.4y=0 answer is B Direct variation, constant is 1/2
4. y=-10 when x=2 answer is A y=-5x
5. y=7 1/2 when x=3 answer is C y=5/2 x
6. y=10.4 when x=4 answer is D y=2.6x
7. y=1/3 x answer is A the graph that reads (6, 2) where the green arrow is on the top right portion and on the bottom left is (-6, -2)
8 y=-1/2 x answer is C graph
9. the table x is first 3, 7, 12 y is next 5.4, 12.6, 21.6 answer is B Direct variation, y=1.8x
10. the table x is first -2, 3, 8 y is next 1, 6, 11 answer is A not a direct variation
p.s. this is for the direct variation practice
hope i helped
Step-by-step explanation:
If sin(x) =-1/2 and tan(x) is negative what is cos(2x)
[tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
Given that [tex]\( \sin(x) = -\frac{1}{2} \) and \( \tan(x) \)[/tex] is negative, we can find \[tex]( \cos(2x) \)[/tex]using the trigonometric identities.
First, let's find the value of [tex]\( \cos(x) \)[/tex] using the Pythagorean identity:
[tex]\[ \cos^2(x) = 1 - \sin^2(x) \][/tex]
Given [tex]\( \sin(x) = -\frac{1}{2} \),[/tex] we have:
[tex]\[ \cos^2(x) = 1 - \left(-\frac{1}{2}\right)^2 \][/tex]
[tex]\[ \cos^2(x) = 1 - \frac{1}{4} \][/tex]
[tex]\[ \cos^2(x) = \frac{3}{4} \][/tex]
Taking the square root of both sides, since [tex]\( \cos(x) \)[/tex] is positive in the first and fourth quadrants:
[tex]\[ \cos(x) = \pm \frac{\sqrt{3}}{2} \][/tex]
Given that [tex]\( \tan(x) \)[/tex] is negative, we know that ( x ) lies in either the second or fourth quadrant. In the second quadrant, both [tex]\( \sin(x) \) and \( \cos(x) \)[/tex] are negative. In the fourth quadrant, [tex]\( \sin(x) \)[/tex] is negative but [tex]\( \cos(x) \) i[/tex]s positive.
Since [tex]\( \cos(x) = \pm \frac{\sqrt{3}}{2} \),[/tex] we conclude that [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \)[/tex] (since [tex]\( \cos(x) \)[/tex] is negative in the second quadrant).
Now, using the double angle identity for cosine:
[tex]\[ \cos(2x) = 2\cos^2(x) - 1 \][/tex]
Substituting [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \):[/tex]
[tex]\[ \cos(2x) = 2\left(-\frac{\sqrt{3}}{2}\right)^2 - 1 \][/tex]
[tex]\[ \cos(2x) = 2\left(\frac{3}{4}\right) - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - 1 \][/tex]
[tex]\[ \cos(2x) = \frac{3}{2} - \frac{2}{2} \][/tex]
[tex]\[ \cos(2x) = \frac{1}{2} \][/tex]
So, [tex]\( \cos(2x) = \frac{1}{2} \).[/tex]
Which formula can be used to describe the sequence? -2/3,-4,-24,-144...
The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
Step-by-step explanation:
The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where
a is the first term of the sequencer is the common ratio between each two consecutive terms[tex]r=\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex]∵ The sequence is [tex]\frac{-2}{3}[/tex] , -4 , -24 , -144 , .......
∵ The 1st term is [tex]\frac{-2}{3}[/tex]
∵ The 2nd term is -4
∴ [tex]\frac{-4}{\frac{-2}{3}}=6[/tex]
∵ The 3rd term is -24
∴ [tex]\frac{-24}{-4}=6[/tex]
∵ The 4th term is -144
∴ [tex]\frac{-144}{-24}=6[/tex]
∵ [tex]\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex] = [tex]\frac{a_{4}}{a_{3}}[/tex] = 6
∴ There is a constant ratio between each two consecutive terms
∴ The sequence is a geometric sequence
∵ The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex]
∵ a = [tex]\frac{-2}{3}[/tex]
∵ r = 6
∴ The formula of the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]
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Answer:
c - f(x) = -2/3(6)^x − 1
Step-by-step explanation:
Edge 2020
If there are 32 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
4/7
Step-by-step explanation:
32/56=4/7
Answer:
The number of boys = 32
The number of girls = 56
therefore, to fine the possible ratio, you divided 32 and 56 to their lowest terms.
i.e 32: 56. 32÷8 : 56÷8 = 4:7