hello
to solve for angle x, let's collect like terms
[tex]11x+30=54-5x[/tex]step 1
collect like terms to do this, we'll take variables of x one side of the eqaution and keep non-variables at the other side
[tex]\begin{gathered} 11x+30=54-5x \\ 11x+5x=54-30 \\ 16x=24 \\ \text{divide both sides by 16} \\ \frac{16x}{16}=\frac{24}{16} \\ x=\frac{24}{16}=\frac{6}{4} \end{gathered}[/tex]2 1' 15 = 1 2. 2 1 1 = 1 5 . (Type a whole number, fraction, or mixed number.)
Step 1
Write out your question.
[tex]1\frac{2}{5}\frac{.}{.}\text{ 1}\frac{1}{2}[/tex]Step 2
Convert mixed fractions to improper fractions.
[tex]\frac{7}{5}\text{ }\frac{.}{.}\text{ }\frac{3}{2}[/tex]Step 3
Convert division to multiplication and invert the fraction after the division.
[tex]\begin{gathered} =\text{ }\frac{7}{5}\text{ x }\frac{2}{3} \\ =\text{ }\frac{7\text{ x 2}}{5\text{ x 3}} \\ =\text{ }\frac{14}{15} \end{gathered}[/tex]A ball is thrown in the air from a platform. The path of the ball can be modeled by the function h(t)=-16 t^{2}+32t+4 where h(t) is the height in feet and t is the time in seconds.How long does the ball take to reach its maximum height?
Answer:
1 second
Explanation:
The equation that models the path of the ball is given below:
[tex]h\mleft(t\mright)=-16t^2+32t+4[/tex]To determine how long it takes the ball takes to reach its maximum height, we find the equation of the line of symmetry.
[tex]\begin{gathered} t=-\frac{b}{2a},a=-16,b=32 \\ t=-\frac{32}{2(-16)} \\ =-\frac{32}{-32} \\ t=1 \end{gathered}[/tex]Thus, we see that it takes the ball 1 second to reach its maximum height.
) Which ratios hiqve a unit rate greater than 1: 7 Choose ALL that apply. 1 >) 4 miles: 3- hours 33 1 3 mile : 2-hours 8 2 1 0) 2 miles : 3 hours 2 3 0) 7 miles : hour 4 13 9 miles : 3 hours 9 5 miles: hour 8 6
To calculate the ratio or the unit rate, we have to divide each ratio:
[tex]\frac{4\text{ miles}}{3+\frac{1}{3}\text{ hours}}=\frac{4}{\frac{10}{3}}\frac{\text{ miles}}{\text{ hour}}=4\cdot\frac{3}{10}=\frac{12}{10}=1.2\frac{\text{ miles}}{\text{ hour}}[/tex][tex]\frac{\frac{1}{3}}{2+\frac{3}{8}}=\frac{\frac{1}{3}}{\frac{16+3}{8}}=\frac{\frac{1}{3}}{\frac{19}{8}}=\frac{1}{3}\cdot\frac{8}{19}=\frac{8}{57}\approx0.14\frac{\text{ miles}}{\text{ hour}}[/tex][tex]\frac{2+\frac{1}{2}}{3}=\frac{\frac{5}{2}}{3}=\frac{5}{2}\cdot\frac{1}{3}=\frac{5}{6}\approx0.83\frac{\text{ miles}}{\text{ hour}}[/tex][tex]\frac{7}{\frac{3}{4}}=7\cdot\frac{4}{3}=\frac{28}{3}\approx9.33\frac{\text{ miles}}{\text{ hour}}[/tex][tex]\frac{\frac{9}{5}}{3}=\frac{9}{5}\cdot\frac{1}{3}=\frac{3}{5}=0.6\frac{\text{ miles}}{\text{ hour}}[/tex][tex]\frac{\frac{9}{8}}{\frac{5}{6}}=\frac{9}{8}\cdot\frac{6}{5}=\frac{54}{40}=1.35\frac{\text{ miles}}{\text{ hour}}[/tex]Answer:
The ratios that are greater than 1 are:
4 miles : 3 1/3 hours
7 miles : 3/4 hour
9/8 miles : 5/6 hours
4. Suppose that you receive a movie-rental bill for the month that is much higher thanit usually is. Currently you are paying $3.99 for each movie you rent. Switching to asubscription would allow you to watch unlimited movies for only $7.99 per month. However,during a normal month you don't have much time to sit and watch movies. You do not reallywant to waste your money on a monthly subscription. You decide to check your onlinebilling statements and make a probability distribution for the number of movies you mightwatch each month.The results are in the following table:Number of Movies, X 0 1 2 3 4 5Probability, P(X) 0.10 0.15 ? 0.35 0.14 0.13a) What is the probability you will watch 2 movies next month, i.e., P(X=2)?b) What is the probability that you will watch more than 2 movies next month, i.e., P(X<4) orP(X<=3)?c) How much would you expect to spend, on a per-month basis, should you continue to pay foreach movie separately? Explain your answer
For the given table representing the probability distribution, the probability of watching 2 movies is unknown.
The sum of all probabilities should be equal to 1. We can use that to calculate the unknown probability:
Adding all probabilities and equating to 1:
[tex]0.1+0.15+P(x=2)+0.35+0.14+0.13=1[/tex]Solving for P(x=2)
[tex]\begin{gathered} 0.87+P(x=2)=1 \\ P(x=2)=1-0.87 \\ P(x=2)=0.13 \end{gathered}[/tex]Then: A. The probability of watching 2 movies next month is 0.13.
The complete table of probability distribution will look like this:
xP(x)
00.1
10.15
20.13
30.35
40.14
50.13
To calculate the probability of watching more than two movies we need to add the probabilities of watching 3, 4 or 5 movies. Those should be added because those are the cases where more than 2 movies are watched.
[tex]\begin{gathered} P(x>2)=P(x=3)+P(x=4)+P(x=5) \\ P(x>2)=0.35+0.14+0.13 \\ P(x>2)=0.62 \end{gathered}[/tex]Then, B. The probability of watching more than 2 movies is 0.62.
The probability of watching 2 movies is equivalent to P(x>2) or P(x>=3).
On the other hand, to calculate P(X<4) or P(X<=3) we need to add the probabilities of watching 3 movies or less. That is, probabilities of watching 0, 1, 2 or 3:
[tex]\begin{gathered} P(x<4)\text{ or }P(x\le3)=P(x=0)+P(x=1)+P(x=2)+P(x=3) \\ P(x<4)\text{ or }P(x\le3)=0.1+0.15+0.13+0.35 \\ P(x<4)\text{ or }P(x\le3)=0.73 \end{gathered}[/tex]The probability of watching 3 movies or less next month is 0.73.
To estimate how much we would expect to spend per month if we pay for each movie sepparately we need to calculate the expected value of movies per month.
We can estimate that with the probability distribution given in the table.
The expected value is the sum of the products between each event and their probabilities:
[tex]\text{Expected Value}=\sum ^{}_{}x\cdot P(x)[/tex]Let's call EV the expected value:
[tex]\begin{gathered} EV=(0\cdot0.1)+(1\cdot0.15)+(2\cdot0.13)+(3\cdot0.35)+(4\cdot0.14)+(5\cdot0.13) \\ EV=2.67 \end{gathered}[/tex]Then, we should expect to watch about 2.67 movies per month, on average.
I each individual movie costs $3.99, then, the total expenses per month will be:
[tex]2.67\cdot3.99\approx10.65[/tex]Then, C. According to the given probability distribution, we should expect to watch about 2.67 movies per month, on average, and spend in total $10.65 per month. We would be spending more than we would if we selected the unlimited movies plan which costs only $7.99 per month, then, it would be wise to decide to change our subscription to that plan.
Is it wise to use the rational theorem at the beginning when finding all real roots of polynomial function.
Explanation:
Definition or rational roots theorem:
Rational root theorem is used to find the set of all possible rational zeros of a polynomial function (or) It is used to find the rational roots (solutions) of a polynomial equation
We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate algebra Use the rational zeros theorem to find all the real zeros of the polynomial function.
Rational Zero Theorem. If a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p / q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Hence,
The final answer is TRUE
A cone has a height of 15 yards and a radius of 11 yards. What is its volume?Use a ~ 3.14 and round your answer to the nearest hundredth.cubic yardsSubmit+
Okay, here we have this:
Considering the provided information, we are going to calculate the volume of the cone, so we obtain the following:
We will substitute in the following formula for the volume of a cone:
[tex]V=\frac{1}{3}\pi R^2h[/tex]Replacing we obtain:
[tex]\begin{gathered} V=\frac{1}{3}\pi(11yd)^2\cdot(15yd) \\ V=\frac{1}{3}\pi121yd^2\cdot15yd \\ V=5yd\cdot121yd^2\cdot\pi \\ V=605\pi yd^3 \\ V=605(3.14)yd^3 \\ V=1899.7yd^3 \end{gathered}[/tex]Finally we obtain that the volume of the cone is approximately 1899.7yd^3.
what is the vertex of y=2(x-3)^2+6 and determine if it’s maximum or minimum value
The general equation of a vertex of a parabola is given by
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ \text{The coordianates of the vertex are} \\ (h,k) \end{gathered}[/tex]If we compare the general equation with that given in question 2
[tex]y=2(x-3)^2+6[/tex]We can infer that
[tex]\begin{gathered} -h=-3 \\ \text{Hence} \\ h=3 \\ \text{Also} \\ k=6 \end{gathered}[/tex]Thus, the vertex is
[tex](h,k)=(3,6)[/tex]To determine if it is maxima or minima, we will use the graph plot
We can observe that we have a minimum value.
Usually, we can determine this also from the value of a.
If a is negative, we have a maxima
If a is positive, we have a minimum
The value of a =2 (Positive)
Hence, we have a minimum
A volcano on a recently discovered planet rises to a height of 22.187 mi. Use the table of facts to find the height of the volcano in feet. Round your answer to the nearest tenth.
22.187 mi
1 mi = 5280 ft
22.187 mi = 22.187 x 5280 ft = =117147.36 ft
Answer:
117,147.36 ft
find the mean median and mode Numbers 1,2,2,6,5,1,1
Solution:
We are required to find the mean median and mode of 1,2,2,6,5,1,1.
[tex]Mean=\frac{1+2+2+6+5+1+1}{7}=\frac{18}{7}=2.5714[/tex]Median:
Sort the data
1, 1, 1, 2, 2, 5, 6
The median = 2
Mode = 1 (because it appears the most (3 times) )
A figure skater is facing north when she begins to spin to her right. She spins at 2250 degrees. Which direction is she facing when she finishes her spin?
step 1
Divide 2250 degrees by 360 degrees
so
2,250/360=6.25
that means
6 complete circles and 0.25 circle
0.25 circle is equal to 90 degrees and she is facing East
The answer is EastIf figure the skater is facing north when she begins to spin to her right. She spins at 2250 degrees. She faces the east direction when she finishes her spin.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that, a figure skater is facing north when she begins to spin to her right. She spins at 2250 degrees.
Since one rotation of the circle form 360 degree.In order to find the angle when she finishes her spin is,
=2,250/360
=6.25
6.25 shows that 6 complete circles and 0.25 circles and 0.25 circle is equal to 90 degrees and she is facing East.
Thus, if figure the skater is facing north when she begins to spin to her right. She spins at 2250 degrees. She faces the east direction when she finishes her spin.
Learn more about circle here:
brainly.com/question/11833983
#SPJ2
Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 17 m. What are the lengths of the three sides? What is the length of the two sides that have the same length? m
Let the common sides have length x, i.e, we have 2 sides measuring x
the third side would measure 2x - 3.
The perimeter = x + x + 2x - 3 = 4x - 3 = 17
so, 4x = 17 + 3 ,
4x = 20
x = 20/4 = 5m
Therefore, the three sides are 5m , 5m and 2( 5 )-3 = 10 - 3 = 7m
when f(x)=-3(2)^-× what is the value of f(-3)
Let the function be,
[tex]f(x)=3\times2^{-x}[/tex]Put -3 for x in the function to find f(-3) implies,
[tex]\begin{gathered} f(-3)=3\times2^{-(-3)} \\ =3\times2^3 \\ =3\times8 \\ =24 \end{gathered}[/tex]Thus, f(-3) is 24.
The perimeter of a rectangle is less than 10 inches. The length is x and the width is x - 5. If the solution is x<5, ThEn the length is less than 5. Is this viable solution.A. ViableB. Non - viable
Problem
The perimeter of a rectangle is less than 10 inches. The length is x and the width is x - 5. If the solution is x<5, ThEn the length is less than 5. Is this viable solution.
Solution
For this case the perimete rof a rectangle is given by:
P= 2x+2y
x= lenght y = width
And we also know that y= x-5
And replacing the condition given: P<10 we got:
2x +2y <10
2x +2(x-5)<10
4x -10 >10
And we can rewrite as:
4x >20
x>5
So then the best answer would be:
B. non viable
How many millimeters are there in 16 meters?A. 160 millimetersB. 1,600 millimetersC. 160,000 millinersD. 16,000 millimeters
It is known that 1 meter = 1000millimeter.
Therefore, 16 meters = 16X 1000 millimeters
16 meters = 16, 000 millimeters.
Hence, option D is the correct answer.
You pick a card at random put it back and then pick another card at random what is the probability of picking a number greater than 5 and then picking a 5 right and then picking a 5 write your answer as a percentage
You have four cards numbered 4, 5, 6, and 7.
Step 1
To calculate the probability of picking a card at random, and that this card has a number greater than 5, you have to divide the number of successes by the number of possible outcomes.
Successes: You want to pick a card with a number greater than 5, there are only two cards that meet this condition, the card numbered 6 and the card numbered 7, so for this scenario, there are 2 successes.
Total outcomes: The number of outcomes is equal to the total number of cards you can pick from, in this case, the total number of outcomes is 4.
Next, calculate the probability of picking a card with a number greater than 5:
[tex]\begin{gathered} P(X>5)=\frac{nºsuccesses}{Total\text{ }outcomes} \\ P(X>5)=\frac{2}{4} \\ P(X>5)=\frac{1}{2}=0.5 \end{gathered}[/tex]The probability of picking a card with a number greater than 5 is 0.5.
Step 2
Next, you put the card back and pick another one at random.
You have to calculate the probability that this time you will pick the card numbered 5.
To calculate this probability you have to divide the number of successes by the total number of outcomes.
Successes: there is only one card with the number 5, so the number of successes is 1.
Total outcomes: since the first card that was drawn was returned to the deck, the total number of outcomes is still 4.
Calculate the probability of drawing a 5:
[tex]\begin{gathered} P(X=5)=\frac{nºsuccesses}{Total\text{ }outcomes} \\ P(X=5)=\frac{1}{5}=0.2 \end{gathered}[/tex]The probability of drawing a 5 is 0.2.
Finally, the probability that you have to determine is to "draw a card with a number greater than 5 and then pick a 5"
The event described is the intersection of both events "drawing a card greater than 5" and "picking a 5". Since the first card was returned to the deck before drawing the second card, both events are independent, which means that the probability of their intersection is equal to the product of the individual probabilities of the events, so that:
[tex]P(X>5\cap X=5)=P(X>5)*P(X=5)=0.5*0.2=0.1[/tex]The probability is 0.1.
Multiply the result by 100 to express it as a percentage:
[tex]0.1*100=10\%[/tex]The probability of picking a number greater than 5 and then picking a 5 is 10%.
1. In which number is the value of the 4 one thousand times more than the value of the 4 in 45? 43,853 458,329 894,256 34,914
The answer is 43 853
If we multiply 45 times 1000, we have:
[tex]45\text{ }\times\text{ 1000 = 45000}[/tex]The value of 4 in 45000 is similar to the value of 4 in 43853
Hence, the choice
10. Explain how you would prove the following.Given: HY = LY:WH LFProve: A WHY = AFLY
It is being proved that triangle Δ WHY ≅ Δ FLY by ASA rule.
In triangle Δ WHY and Δ FLY, we have that:
HY ≅ LY ( given)
∠WHY = ∠ FLY (alternate interior angles as WH || LF)
∠WYH = ∠ FYL ( Vertically opposite angles)
We get that:
Δ WHY ≅ Δ FLY ( ASA rule)
It is proved that Δ WHY ≅ Δ FLY by ASA rule.
Therefore, we get that, it is being proved that triangle Δ WHY ≅ Δ FLY by ASA rule.
Learn more about triangle here:
https://brainly.com/question/17335144
#SPJ9
What is the equation of the line that passes through the point (-2,-4) and has a slope of 1/2
Answer:
[tex]y=\frac{1}{2}x-3[/tex]
Step-by-step explanation:
[tex]y+4=\frac{1}{2}(x+2) \\ \\ y+4=\frac{1}{2}x+1 \\ \\ y=\frac{1}{2}x-3[/tex]
what’s the equation for points (2,13) and (4,6)
The points we have are:
(2,13) and (4,6)
I will label this points as follows:
[tex]\begin{gathered} x_1=2 \\ y_1=13 \\ x_2=4 \\ y_2=6 \end{gathered}[/tex]To find the equation for this line, first we need to find the slope between the points with following slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope.
Substituting our known values:
[tex]\begin{gathered} m=\frac{6-13}{4-2} \\ m=\frac{-7}{2} \end{gathered}[/tex]Next, we need to use the point-slope equation:
[tex]y=m(x-x_1)+y_1[/tex]And substitute our values, including the slope:
[tex]y=-\frac{7}{2}(x-2)+13[/tex]Using the distributive property to multiply -7/2 by x and by -2:
[tex]\begin{gathered} y=-\frac{7}{2}x+7+13 \\ y=-\frac{7}{2}x+20 \end{gathered}[/tex]Answer:
[tex]y=-\frac{7}{2}x+20[/tex]Write the English sentence as an equation in two variables. Then graph the equation.The y-value is three less than twice the X-value.
Given the sentence:
The y-value is three less than twice the X-value.
Let's write the sentence as an equation then graph the equation.
The equation that represents the sentence is:
y = 2x - 3
To graph the eqautaion, let's find and plot three points, then connect the points using a straight edge.
• When x = 1:
Substitute 1 for x and solve for y.
y = 2(1) - 3
y = -1
• When x = 2:
Substitute 2 for x and solve for y.
y = 2(2) - 3
y = 4 - 3
y = 1
• When x = 3:
Substitute 3 for x and solve for y.
y = 2(3) - 3
y = 6 - 3
y = 3
• When x = 0:
y = 2(0) - 3
y = -3
Thus, we have the points:
(1, -1), (2, 1), (0, -3), and (3, 3)
The graph is attached below.
ANSWER:
Equation: y = 2x - 3
5. Match the equation with its graph.4x + 8y = 32
In order to find the corresponding graph, let's find two points that are on the line.
To do so, let's choose values of x and then calculate the corresponding values of y:
[tex]\begin{gathered} x=0\colon \\ 0+8y=32 \\ y=\frac{32}{8}=4 \\ \\ x=8\colon \\ 32+8y=32 \\ 8y=0\to y=0 \end{gathered}[/tex]So we have the points (0, 4) and (8, 0).
Looking at the options, the graph that has these points is the fourth graph.
How many perfect squares less than 1000 have a ones digit of 2,3 or 4?
There are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
To check that perfect squares that have a ones digit of 2,3 or 4 :
First we will check the squares of 0-10 numbers.
[tex]0^{2} = 0[/tex] [tex]1^{2} = 1[/tex] [tex]2^{2} = 4[/tex]
[tex]3^{2} = 9[/tex] [tex]4^{2} = 16[/tex] [tex]5^{2} = 25[/tex]
[tex]6^{2}=36[/tex] [tex]7^{2}=49[/tex] [tex]8^{2}=64[/tex]
[tex]9^{2}=81[/tex] [tex]10^{2}=100[/tex]
As we can see, only 2,8 have the squares which have 2,3 or 4 at ones place.
So, only numbers like 12,18,24,28.........,998 have a ones digit of 2,3 or 4.
Hence, there are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
Learn more about perfect squares on:
https://brainly.com/question/385286
#SPJ1
Answer: 6
Step-by-step explanation:
We can use brute force for this, because there are 31 numbers to try(32^2 is 1024, which is over 1000).
To begin with, there is no number that ends in 2 or 3 in the first 10 squares. If we move onto the ones digit of 4, we can see that:
2
8
12
18
22
28
Are the only numbers which end in a 4.
We add these up and we get the answer of 6.
b. Shirley was given the following points and asked to calculate the area, but her graph paper is not big enough. Calculate the area of Shirley's rectangle, and explain to her how she can determine the area without graphing the points. Shirley's points (352, 150), (352, 175), (456, 150), and (456, 175)
The given points are
(352, 150)
(352, 175)
(456, 150)
(456, 175)
Each point represents one vertex of the rectangle.
The points that have the same x-coordinate are in the same vertical line, this means that the diference between the y-coordinates of the point determine the length of the width of the rectangle.
Since is a rectangle both vertical sides are equal.
Using the points
(352, 150)
(352, 175)
You can calculate the width as:
[tex]\begin{gathered} w=y_2-y_1 \\ w=175-150 \\ w=25\text{units} \end{gathered}[/tex]The points that have the same y-coordinate are in the same horizontal line, if you calculate the difference between the x-coordinates of said points, you can determine the length of the rectangle.
Using the points
(456, 150)
(352, 150)
You can calculate the length as
[tex]\begin{gathered} l=x_2-x_1 \\ l=456-352 \\ l=104\text{units} \end{gathered}[/tex]So the rectangle has a length of 104 and a width of 25. Using these values you can calculate the area:
[tex]\begin{gathered} A=wl \\ A=25\cdot104 \\ A=2600\text{units}^2 \end{gathered}[/tex]Find the simple interest on a $4,719 principal deposited for
six years at a rate of 6.11%.
Answer:
The answer is 1,729.99
Step-by-step explanation:
The formula for calculating Simple interest is
Simple interest (A) = P×R×T
where,
P = Principal
R = Rate
T = Time
So after adding the values to the formula
we get
=4719×6.11×6/100
=1,72,998.54/100
=1,729.9854
So The simple interest is 1,729.99
For more Information search Simple Interest in Brainly.com
I am thinking of a number. It has two digits. When I reverse the digits and then add the new number to the original number I get 33. What is the number?
Let x and y be the digits.
The original number has two digits that means that one is the tens and the other the ones, in this case let x be the tens and y the ones, then we have the number:
[tex]10x+y[/tex]if we reverse it this means that the y become the tens and x becomes the ones then we have the number:
[tex]10y+x[/tex]And if we add them the result is 33, then we have the equation:
[tex]\begin{gathered} (10x+y)+(10y+x)=33 \\ 11x+11y=33 \\ x+y=3 \\ y=3-x \end{gathered}[/tex]This means that y has to be 3-x. Now, since we both numbers to have two digits x can't be zero nor 3. Then has to be 1 or 2.
If x=1 then y=2 and the original number is 12.
If x=2 then y=1 and the original number is 21.
Notice how in both cases we get the other one when reversed, therefore the numbers we are looking for are 12 and 21.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
I just need the first one thanks
If the vector is pointing in the opposite direction of [-4,3], we can say it is pointing in the same direction of the vector [4,-3]. We just flipped the direction of the vector by changing the sign of the components.
We have now a vector that is pointing in the same direction of the vector we are looking for. Let's find the length of that vector to see how much it has to be scaled, or if it does not need to be scaled.
The length of the vector is calculated as the square root of the sum of the square of its components:
[tex]\text{Length}=\sqrt[]{x^2+y^2}[/tex]Then, the length of the vector is:
[tex]\begin{gathered} \text{Length}=\sqrt[]{4^2+(-3)^2}=\sqrt[]{16+9}=\sqrt[]{25} \\ \\ \text{Length}=5 \end{gathered}[/tex]Then the length of the vector [4,-3], which is pointing opposite to the vector [-4,3], happens to have a length of 5, then, that is the vector we were looking for. There is no need to scale it.
Then, the components of the vector are 4 and -3. [4,-3]
Representing fractions as repeating decimalsConvert the fraction to a decimal:5/6
ok
5/6 = 0.833333 or
The line means that number three is repeated till infinty
Find the infinite sum of the geometric sequence with a=3,r=3/6 if it exists.S∞=
ANSWER
[tex]S_{\infty}=6[/tex]EXPLANATION
Given:
1. First term (a) = 3
2. Common ration (r) = 3/6
Desired Outcome:
Infinite sum of the geometric sequence.
The formula to calculate the infinite sum of the geometric sequence
[tex]S_{\infty}=\frac{a(1-r^n)}{1-r}[/tex]Now, as n approaches infinity,
[tex]1-r^n\text{ approaches 1}[/tex]So,
[tex]\frac{a(1-r^n)}{1-r}\text{ approaches }\frac{a}{1-r}[/tex]Therefore,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values
[tex]\begin{gathered} S_{\infty}=\frac{3}{1-\frac{3}{6}} \\ S_{\infty}=\frac{3}{1-\frac{1}{2}} \\ S_{\infty}=\frac{3}{\frac{1}{2}} \\ S_{\infty}=6 \end{gathered}[/tex]Hence, the infinite sum of the geometric sequence is 6.
Find the value of x. Assume that segments that appear to be tangent are tangent. 12, x , 6
The value of x is 16.64.
Given that 14 is tangent to the circle and 9 is a radius, this is a right triangle.
From the figure, we have
Using the Pythagoras theorem,
a^2 +b^2 =c^2
9^2+14^2 =x^2
81+196 = x^2
277 = x^2
By taking the square root of each side, we get
sqrt(277) = sqrt(x^2)
sqrt(277) =x
x = 16.64
Pythagoras theorem:
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem. In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.
To learn more about pythagoras theorem visit: https://brainly.com/question/343682
#SPJ9