Answer:
40/41
Step-by-step explanation:
cos = adjacent/hypotenuse
adj = 40, hyp = 41
A quadratic sequence is defined as:2;12;28;50
Calculate the first difference between Tn and Tn-1 where Tn= 688
The first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The quadratic sequence:
2, 12, 28, 50
a + b + c = 2
10, 16, 22 (first difference)
3a + b = 10
6, 6 (second difference)
2a = 6
a = 3
b = 1
c = -2
Tterm:
T(n) = 3n² + n - 2 = 688 (given)
After solving the quadratic equation:
n = 15, n = -46/3(n cannot be nagatve)
n = 15
n - 1 = 14
T(14) = 600
T(n) - T(n-1) = 688 - 600 = 88
Thus, the first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50
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Step 1: Place the graph paper in landscape orientation. Measure from the top left hand corner 6 inches right and 5 inches down. This will be your starting point for
your diagram.
Step 2: Using a ruler and index card/protractor create an isosceles Right triangle. Drawing the triangles legs 1 inch straight up from the starting point and 1 inch to the
right of the starting point. Connect the endpoints of the two segments to create your right isosceles triangle.
Step 3: On a separate piece of paper, use the Pythagorean Theorem to calculate the length of the hypotenuse. You only need to do this for the first 8 if you discover a
pattern.
Step 4: Using your original Right triangle, add another leg measuring 1 inch and right angle to the hypotenuse of your original Right triangle. Connect the endpoints
to form a new hypotenuse for your new Right triangle.
Step 5: Show the calculations to find the length of the new hypotenuse.
Step 6: Continue to repeat this process of connecting and drawing new triangles with a side length of 1 inch, using the previous hypotenuse as the other side. Draw
triangles until you are able to measure the square root of 17. You must show all calculations (Step 3) on a separate piece of paper.
T
How to determine the hypotenuse?Step 1 and 2: Draw an isosceles right triangle
See attachment (figure 1) for this triangle
The legs of this triangle have a length of 1 inch
Step 3: The hypotenuse
This is calculated using the following Pythagoras theorem
[tex]h^2 = 1^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 2[/tex]
Step 4: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 2) for this triangle
The legs of this triangle have lengths of 1 inch and 2 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 2^2 + 1^2[/tex]
This gives
[tex]h = \sqrt 5[/tex]
Step 5: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 3) for this triangle
The legs of this triangle have lengths of 1 inch and 3 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 3^2 + 1^2[/tex]
This gives
[tex]h = \sqrt {10[/tex]
Step 6: Draw another isosceles right triangle
Add 1 inch to one of the legs
See attachment (figure 4) for this triangle
The legs of this triangle have lengths of 1 inch and 4 inches, respectively
This hypotenuse is calculated using the following Pythagoras theorem
[tex]h^2 = 4^2 + 1^2[/tex]
This gives
[tex]h = \sqrt{[17[/tex]
See that the hypotenuse is the square root of 17
Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17
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Man's needs help ASAP
A linear function graph of the x-axis and y-axis has a diagonal line that passes the x-axis at (minus 0.5, 0), and the y-axis at (0, 1) In the function above, the slope will be multiplied by 2, and the y-value of the y-intercept will be increased by 3 units. Which of the following graphs best represents the new function?
A. X
B. Z
C. W
D. Y
The graph that best describes the new function is shown in the image attached below.
How to Determine the Graph of a Linear Function?The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.
Given a linear function graph passes the points (-0.5, 0) and (0, 1):
Y-intercept (b) = 1 (value of y when x = 0)
Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2
If the slope (1) is multiplied by 2, the new slope would be: 2
If the y-intercept (2) is increased by 3 units, the new y-intercept would be: 5
The equation of the new function would be: y = 2x + 5
The graph that best represents the function is shown in the image attached below.
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Solve x≥0 or x≥−5 and write the solution in interval notation.
The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:
[a, b] ⇒ All numbers between a and b including both a and b.
(a, b) ⇒ All numbers between a and b excluding both a and b.
(a, b] ⇒ All numbers between a and b excluding a but including b.
[a, b) ⇒ All numbers between a and b including a but excluding b.
We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.
We first write each inequality in interval notation:
x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.
x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.
Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:
[0, ∞) ∪ [-5, ∞) = [5, ∞).
Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.
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the answer has to be as a fraction
Answer:
49/100
Step-by-step explanation:
So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: [tex]\pi r^2[/tex]
Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is [tex]\pi(3.5)^2[/tex] which is [tex]12.25\pi[/tex].
The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is [tex]\pi (2)^2[/tex] which is [tex]4\pi[/tex]. Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: [tex]12.25\pi-4\pi[/tex] which equals [tex]8.25\pi[/tex].
Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: [tex]\pi(5)^2[/tex] which is equal to [tex]25\pi[/tex].
Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: [tex]\frac{12.25\pi}{25\pi}[/tex] but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction [tex]\frac{49}{4}=12.25[/tex]. So now all we have to is divide the two values: [tex]\frac{\frac{49}{4}}{\frac{25}{1}}[/tex]. If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: [tex]\frac{49}{4} * \frac{1}{25}[/tex] which becomes [tex]\frac{49}{100}[/tex] which is the answer
HELLPPPPPPPP !!!!!!???
Answer:
C
Step-by-step explanation:
12 /13 is definitely less than 36/30 because 36/30 = 1 1/5
PLEASE HELP ITS URGENT i need number 20 & 21
!!!!!
Answer:
Put the equations in the form y=mx+c and after that, take any two values for x, fill in the equation of y=mx+c to get the corresponding y coordinate and take any value for y, to get the corresponding x coordinate. For this example i took x=0 and y=0, feel free to try it again with any other value. If you get a fraction and don't what to work with fractions, just do a trial and error till you get a whole number (as i did for Question 21 for the x and y coordinates)
The farmer wants ratio horses : cows to equal 5 : 3.
He keeps his 45 horses but buys some cows.
Work out the number of cows he must buy.
Answer
He needs to buy 27 Cows
Step-by-step explanation:
if the ratio from horses to cows is 5-3 then you multiply 5 by the number to get 45 and also multiply it by 3
5 x 9 = 45
3 x 9 = 27
Find the solution set for this equation:
-a2+4a=0
(Separate the two values with a comma)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: \{ 0,4 \}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0[/tex]
[tex]\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0[/tex]
[tex]\qquad \tt \rightarrow \: {a}^{2} - 4a = 0[/tex]
[tex]\qquad \tt \rightarrow \:a(a - 4) = 0[/tex]
The two cases are :
a = 0or
a -4 = 0, that leads to a = 4We can conclude :
[tex]\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex] \quad \quad \quad \quad\huge \tt \pink ❆ AnSweR \pink ❆[/tex]
[tex]\quad\quad \tt-a^2+4a= 0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \quad\quad\tt⇢-1(a^2 - 4a) = 0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\quad\quad\tt⇢-1(a-4)a = 0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\quad\quad\tt⇢a-4=0[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\quad\quad\tt⇢a = 0[/tex]
-----------------------------------------------------------
[tex] \boxed{ \tt \blue{a = 0}}[/tex]
[tex]\boxed{ \tt\blue{a = 4}}[/tex]
This problem is lowkey tricky. Can someone help me out
Answer:
x = 10
Step-by-step explanation:
Proof: If a line is parallel to one side of the triangle, then it divides the other two sides proportionally.
6/9 = x/15
9x = 90
x = 10
If 55% of the people at a certain conference are doctors, 49% are women, and 29% are female doctors, what is the probability that a person selected at random at this conference is a doctor or woman (or both)?
[tex]doctors = 55\% \\ woman = 49\% \\ both = 29\%[/tex]
[tex]p(a) =0.55 + 0.49 - 0.29 \\ p(a) = 0.75[/tex]
can someone please help me
The answer is [tex]11c^3[/tex].
Charlie's Pizzeria made 11 thin-crust pizzas and 24 thick-crust pizzas. What is the ratio of the number of thin-crust pizzas to the total number of pizzas? Charlie's Pizzeria made 11 thin - crust pizzas and 24 thick - crust pizzas . What is the ratio of the number of thin - crust pizzas to the total number of pizzas ?
Answer:
11:37
Step-by-step explanation:
11 thin-crust pizzas
11+24=37 total pizzas
=>11:37
Which expression is equivalent to -21.8 - (-18.3)?
O-21.8+18.3
-21.8-18.3
21.8+18.3
21.8-18.3
GUYS PLS HELP ME
The expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple.
The given expression is
-21.8 - (-18.3)
So, open the bracket and distribute the negative;
-21.8 (+18.3)
Thus, the expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.
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Answer: A
Step-by-step explanation: –21.8 – (–18.3) = -3.5 and –21.8 + 18.3 = -3.5
Graph the exponential model
y = 3(6)^x Which point lies on the graph?
(-9 2)
(2, 9)
(- 1, - 18)
(1, 18)
(1,18)
Let's verify
18=3(6)118=3(6)18=18Verified
Solve c= 5/9(F-32) for F
Answer:
F=9/5c+32
Step-by-step explanation:
c=5/9f-160/99c=5f-160-5f=-160-9cf=32+9/5cf=9/5c+32Simplify
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Answer:
55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
Step-by-step explanation:
To simplify this equation, follow these steps:
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Multiply 7.5x² by all the terms in the right parenthesis.
7.5x² (7.4x² -2.1x +7.7)=55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²
Then multiply 5.4x by all the terms in the right parenthesis.
5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x
Now multiply 3.7 by all the terms in the right parenthesis.
3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49
Add all of those answers together.
55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=
=55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
The answer is 55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49
Hope this helps!
If not, I am sorry.
there were three parts to Rita's race. she ran the first part, which was 4/9 of the total distance, in 20 minutes. She ran the second part, which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meters per minute.
a) How long was the third part of the race?
20+12+15= 32+15 = 47 minutes in total
300 meters per minute
300 * 47 = 14100 meters in total
with this we can see the first race was 4/9 that distance meaning the first race was 6266.6 meters long
14100 - 6266.6 = 7833.3
2/5 of 7833.3 is 3133.32
therefore 7833.3 - 3133.32 will give the distance of the third part of the race
meaning of course the answer is 4699.98 or rounding up 4700 meters for the third race
Kenya worked from 2:00 pm to 11:00 pm and made $79.11. What was her rate of pay per hour?
Answer:
[tex]\huge\boxed{\sf \$ \ 8.79\ per\ hour}[/tex]
Step-by-step explanation:
Given that:Work hours = 2:00 pm - 11:00 pm
This makes a total of 9 work hours.So,
9 hours = $79.11
Rate of pay per hour:Using unitary method
9 hours = $79.11
Divide both sides by 9
1 hour = $79.11/9
1 hour = $8.79
So, Kenya is being paid $8.79 per hour.
[tex]\rule[225]{225}{2}[/tex]
Evaluate the following expression. -8 \times (-10 + (-7))−8×(−10+(−7))minus, 8, times, left parenthesis, minus, 10, plus, left parenthesis, minus, 7, right parenthesis, right parenthesis
The value of the given expression is 136
Simplifying an expressionFrom the question, we are to evaluate the give expression
The given expression is
−8×(−10+(−7))
The expression can be simplified as follows
−8×(−10+(−7))
−8×(−10−7)
−8×(−17)
= 136
Hence, the value of the given expression is 136
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Can someone help me on these problems and show work
The simplified expression are as follows;
6mn³ - mn² + 3mn³ + 15mn² = 9mn³ + 14mn²
a⁴b³ + 8a⁴b³ = 9a⁴b³
How to simplify an expression?A simplified expression is express to its lowest term.
Therefore,
6mn³ - mn² + 3mn³ + 15mn²
combine like terms
6mn³ + 3mn³ - mn² + 15mn²
9mn³ + 14mn²
a⁴b³ + 8a⁴b³ = 9a⁴b³
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Need help with this problem
Answer:graph a
Step-by-step explanation:
bc if you subtract 3
from 2 you find the one you line your numbers up with
Write the ratio of sin X and cos X
The ratio of sin X and cos X are as follows;
sin X = √119 / 12
cos X = 5 / 12
How to find the sides of right angle triangle?Right angle triangle has one of its angle as 90 degrees. The side and angles can be found using trigonometric ratios.
Therefore,
sin X = opposite / hypotenuse
sin X = √119 / 12
Therefore,
cos X = adjacent / hypotenuse
cos X = 5 / 12
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A state seal, which is round, hangs in the capitol building. it has a radius of 2 feet. what is the seal's circumference?
Answer:
12.56637ft
Step-by-step explanation:
Formula: c=2π*r
c=2π*2 = 12.56637ft
(1) Triangle ABC is an isosceles triangle.
Find the altitude h.
B
45°
Step-by-step explanation:
45+45
90
I guess is the answer
Tina spent a total of $14.90 on 4 identical notebooks and 3 identical pencils. She
had some money left. If she bought another identical pencil, she would have $0.30
left. If she bought another identical notebook instead, she will be short of $1.50.
How much more does a notebook cost than a pencil?
$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.
Which method can be used to calculate the difference in costs?Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;
4•x + 3•y = 14.9...(1)
Let a represent the total money Tina has, which gives;
4•x + 4•y = a - 0.3...(2)
5•x + 3•y = a + 1.5...(3)
Subtracting equation (2) from equation (3) gives;
5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8
Which gives;
x - y = 1.8...(4) From the above, we have that the difference between the cost of a notebook and pencil is 1.8Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;
4 × (x - y) = 4 × 1.8 = 7.2
4•x - 4•y = 7.2
4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7
7•y = 7.7
y = 7.7 ÷ 7 = 1.1The cost of a pencil, y = $1.1x - y = 1.8
x = 1.8 + 1.1 = 2.9
Cost of a notebook, x = $2.9The difference between the cost of a notebook and the cost of a pencil is therefore;
x - y = $2.9 - $1.1 = $1.8
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The cost of a 6 ounce can of tomato paste is 29
cents. A 16 ounce can sells for 65 cents.
Which is the better deal?
Answer:
16 ounce can sells for 85 cents
Step-by-step explanation:
29cents / 6 ounce = 4.833cents/ounce
65cents / 16 ounce = 4.0625cents/ounce
4.0625 < 4.833
then:
the better deal is:
16 ounces per 65 cents
A horse holds the all time record for running a 2 kilometer race in 1 min and 59.4 sec. which conversions are necessary to find the horses average speed for the race in miles per hour?
To calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.
The average speed thus calculated is 393.2722 miles per hour.
The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.
Thus, Average speed = Total Distance/Time taken.
In the question, we are informed that a horse holds the all-time record for running a 2-kilometer race in 1 min and 59.4 sec.
We are asked for the necessary conversions required to calculate the average speed of the horse for the race in miles per hour.
The necessary conversions that will be required will be:
Distance: 2 kilometers to miles.
Time: 1 minute 59.4 secs to hours.
To convert from kilometers to miles, we follow the conversion rate:
1 kilometer = 0.621371 miles.
Thus, distance = 2 kilometers = 2 * 0.621371 miles = 1.24274 miles.
For the time, we first convert seconds to time, using the conversion rate:
1 second = 1/60 minutes,
Therefore, 59.4 seconds = 59.4/60 minutes = 0.99 minutes.
Thus, the total time = 1.99 minutes.
To convert from minutes to hours, we follow the conversion rate:
1 minutes= 1/60 hours.
Thus, time = 1.99 minutes = 1.99/60 hours = 0.03316 hours.
Thus, the average speed of the horse = Distance/Time = 1.24274/0.003316 miles per hour = 393.2722 miles per hour.
Thus, to calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.
The average speed thus calculated is 393.2722 miles per hour.
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Select the function that represents a geometric sequence.
OA. A(n) = P+ (n-1)i P, where n is a positive integer
B. A(n) = (n-1)(P. )", where n is any real number
O C. A(n) = P(1 + i)-1, where n is a positive integer
OD. A(n) = n+ (P-1)i P, where n is a positive integer
The function that represents a geometric sequence is given by:
C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
Following this pattern, a function that is also a geometric sequence is:
C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.
For the function, we have that:
[tex]a_1 = P, q = 1 + i[/tex].
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What is the solution to the following system of equations?
Answer:
no solutionStep-by-step explanation:
The lines do not intersect