[tex]a(n) = 3 + 5n[/tex]
[tex]b(n) = - 2 + 6n[/tex]
[tex]a(n) = b(n) \\ 3 + 5n = - 2 + 6n \\ 5 = n \\ n = 5 \: (6th \: term)[/tex]
[tex]a(5) \: or \: b(5) = 3 + 5(5) = 28[/tex]
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;
The volume of a cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
where r is the radius of its flat surface, and h is its height.
From the given question, we have to determine the value of h using the Pythagoras theorem.
Such that;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]4^{2}[/tex] = [tex]h^{2}[/tex] + [tex]1^{2}[/tex]
16 = [tex]h^{2}[/tex] + 1
[tex]h^{2}[/tex] = 15
h = [tex]\sqrt{15}[/tex]
Thus the volume of the cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{1}{3}[/tex]x [tex]\frac{22}{7}[/tex] x [tex]1^{2}[/tex]x [tex]\sqrt{15}[/tex]
= 4.0574
Therefore the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]
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find (f•g) (k) equations in red letters
The answer is (f . g)(x) = - (34k + 17k⁷ + 17k⁵ + 40k³ + 20k² + 60).
Remember that :
(f . g)(x) = f(x) × g(x)
Hence :
(f . g)(x) = (2k³ + k² + 3)(-17k⁵ - 20)(f . g)(x) = -34k⁸ - 17k⁷ - 17k⁵ - 40k³ - 20k² - 60(f . g)(x) = - (34k + 17k⁷ + 17k⁵ + 40k³ + 20k² + 60)
What is the slope of a line passing through (-5, 5) and
(-4, 10)?
Answer:
5
Step-by-step explanation:
Formula for finding slope:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
Slope of line passing through (-5,5) and (-4,10)
=
[tex] \frac{5 - 10}{ - 5 - ( - 4)} \\ = \frac{ - 5}{ - 5 + 4} \\ = \frac{ - 5}{ - 1} \\ = 5[/tex]
Answer:
Slope = 5
Step-by-step explanation:
Slope:(-5,5) ; x₁ = -5 & y₁ = 5
(-4, 10) ; x₂ = -4 & y₂ = 10
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{10-5}{-4-[-5]}\\\\ =\dfrac{10-5}{-4+5}\\\\=\dfrac{5}{1}\\\\= 5[/tex]
Use the ideal gas law (PV=nRT) to find P. Round answer to 1 d.p.
Given: V = 3 L, n = 2 mol, T = 300 K, R = 0.0821
Answer:
P = 16.4
Step-by-step explanation:
Given the equation PV = nRT and the values we know, we need to isolate P .
Thus, we have:
[tex]PV=nRT\\3P=2*0.0821*300\\P=49.26/3\\P=16.42=16.4[/tex]
How to find the answer?
i) The number of students that come to school by motorcycle only = 8
ii) The number of students that did not take all the three types of transportation = 9
iii) Number of students that did not come to school by car = 28
Solving questions on venn diagramThe total number of students = 40
The number of students that come to school by car alone = 9
The number of students that come to school by motorcycle only = 8
The number of students that come to school by car only = 11
The number of students that come to school by both car and motorcycle = 3
Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)
= 40 - 31
Number of students that did not take all the three types of transportation = 9
Total students that come to school by car = 9+3 = 12
The total number of students that did not come to school by car = 40 - 12 = 28
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1. sonya's salary increases at a rate of 4% per year. her starting salary is $45,000. what is her annual salary, to the nearest $100, after 8 years of service?
Her annual salary after 8 years will be $57,600.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " %". A % is a number with no dimensions; it has no unit of measurement.To find what is her annual salary, to the nearest $100, after 8 years of service:
Find 4% of 45,000
[tex]\frac{x}{45000} *100=4\\\frac{x}{450} =4\\x =1800[/tex]
So, 4% of $45,000 of $1800.
1st year = $45000
2nd year = 45000 + 1800 = $46800
3rd year = 46800 + 1800 = $48600
4th year = 48600 + 1800 = $50400
5th year = 50400 + 1800 = $52200
6th year = 52200 + 1800 = $54000
7th year = 54000 + 1800 = $55800
8th year = 55800 + 1800 = $57600
Therefore, her annual salary after 8 years will be $57,600.
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The salary of Sonya after 8 years will be $61,600 (nearest $100).
What is compound interest?The interest on the a loan or deposit that is calculated using the both initial principal as well as the accrued interest from prior periods is known as compound interest (sometimes known as compounding interest).
Some features of compounding are-
Compound interest is calculated just on initial principal of a deposit or loan, which also takes into account all of the interest accrued from prior periods.The yearly interest rate is raised to a number of compounded periods minus one, and the starting principal amount is multiplied by both of these factors.The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The quantity of compounding periods has a bigl impact on compound interest calculations.Calculation for the amount after 8 years-
The principal amount is $45,000
Rate of interest is 4% per year.
Time duration is 8 years.
The formula for total amount after compounding is -
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period.
t = number of time periods elapsed.
As the rate of interest is applied only one in a year ; n = 1.
Substitute the values in the formula to get the value.
[tex]A=45,000\left(1+\frac{.04}{1}\right)^{8}\\A=45,000\left(1.04}\right)^{8}\\\\A=61585.60[/tex]
Therefore, the salary of Sonya will be $61600 (nearest $100) after 8 years.
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Find the gradient of the tangent to the curve y = (√x + 3)(3√x - 5) at the point where x = 1
Answer:
Gradient (slope) is 5.
Step-by-step explanation:
To find the gradient (slope) of a curve graph at x = x₁ can be done by steps following:
Differentiate the function - this is to find a gradient (slope) at any points (technically function of slope)Substitute x = x₁ in the derived function - you'll receive a slope at x = x₁ point.First, derive the given function which is:
[tex]\displaystyle{y = (\sqrt{x}+3)(3\sqrt{x}-5)[/tex]
Differentiation can be done two ways - go ahead and expand the expression then derive it or you can use the product rule where it states that [tex]\displaystyle{y'=u'v+uv'}[/tex]
I'll be using product rule:
[tex]\displaystyle{y' = (\sqrt{x}+3)'(3\sqrt{x}-5)+(\sqrt{x}+3)(3\sqrt{x}-5)'}[/tex]
Note that the following process will require you to have knowledge of Power Rules:
[tex]\displaystyle{y = ax^n \to y' = nax^{n-1}}[/tex]
Hence:
[tex]\displaystyle{y'=\dfrac{1}{2\sqrt{x}}(3\sqrt{x}-5) + (\sqrt{x}+3)\dfrac{3}{2\sqrt{x}}[/tex]
Now we know the derivative. Next, we find the slope at x = 1 which you substitute x = 1 in derived function:
[tex]\displaystyle{y'(1)=\dfrac{1}{2\sqrt{1}}(3\sqrt{1}-5) + (\sqrt{1}+3)\dfrac{3}{2\sqrt{1}}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(3-5) + (1+3)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=\dfrac{1}{2}(-2) + (4)\dfrac{3}{2}}\\\\\displaystyle{y'(1)=-1 + 2(3)}\\\\\displaystyle{y'(1)=-1 + 6}\\\\\displaystyle{y'(1)=5}[/tex]
Finally, we have found the slope or gradient at x = 1 which is 5.
Please let me know if you have any questions!
Prove that a positive integer is a sum of at least two consecutive positive integers if and only if it is not a power of two.
Answer:
45
Step-by-step explanation:
small brain
what are the domain and range of the graph below.
O domain: [0,00)
range: (-00,00)
O domain: [0,00)
range: (-0,4]
domain: (0,4)
range:
(-00,00)
domain: (-∞,4]
range: [0,00)
Answer:
Domain: [0,∞)
Range: (-∞, 4]
Step-by-step explanation:
The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)
To calculate the domain and range of a function from its graph, you can follow these steps:
Identify the x-coordinates of all the points on the graph. The set of all possible x-coordinates is the domain of the function.Write the domain as an interval or as a set of values, depending on the format of the original problem. For example, if the graph is defined for all real numbers, the domain would be written as (-∞, ∞).Identify the y-coordinates of all the points on the graph. The set of all possible y-coordinates is the range of the function.Write the range as an interval or as a set of values, depending on the format of the original problem.So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)
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If t = 18 and r = 12, find S. Round to the nearest tenth.
Answer:
13.4 or √180
Step-by-step explanation:
Pythagorean theorem states
a² + b² = c²
C^2 is the longest side. The corner of the right angle points to it. The other sides are your a and b squared. They are called the legs or Opposite and Adjacent sides.
Answer: S ≈ 48.2°
Step-by-step explanation:
We can use trigonometry functions to solve.
Looking at angle S, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.
[tex]\displaystyle cos(S) = \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}[/tex]
[tex]\displaystyle cos^{-1} (cos(S)) = (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}[/tex]
[tex]S = 48.189685...\\S \;$\approx$\; 48.2^{\circ}[/tex]
Can some solve for x please?
Answer:
x = 19
Step-by-step explanation:
You would use vertical angles to move the 8x - 14 so that we could use the Consecutive Interior angles theorem. Which says that consecutive angles equal 180. So, you would set up your equation: 8x-14+2x+4 = 180. Add the 8 and 2 = 10. Add the -14 and 4 = -10. You get 10x-10 = 180. 180+10 = 190. 190/10 = 19. X = 19
I am thinking of a two digit number.it is smaller then 5 tens but greater then 4 tens. its ones digit is 3 more than its tens digit.what number am i thinking of?
The two digit number larger than 40 and lesser than 50, and the difference between the ones and tens digits gives the two digit number as 41
How can the two digit number be found?Let XY represent the two digit number;
From the question, we have the following inequalities and equations;
40 < XY < 50X = Y + 3Therefore;
4 ≤ X < 5Y > 0Which gives;
4 ≤ Y + 34 - 3 = 1 ≤ YY = 1
X = 4
Therefore;
XY = 41The two digit number, XY = 41
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Complete the double number line to show the other values of fat and protein.
The double number line which shows the other values of fat and protein is: option B.
What is a number line?A number line is a type of graph with a graduated straight line which contain numerical values that are placed at equal intervals along its length.
For the fat component, we have:
Fat = 2n = 0, 2, 4, 6, 8.
For the protein component, we have:
Protein = 11n = 0, 11, 22, 33, 44.
Note: n represent integers such as 0, 1, 2, 3 and 4.
In conclusion, the double number line which represent the other values of fat and protein is shown in the image attached below.
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Complete Question:
One serving of beef je-rky contains 2 grams of fat and 11 grams of protein. Complete the double number line to show the other values of fat and protein.
The width of a window on a house is 48 inches. The house is shown in a scale drawing. The width of the window in the drawing is 20% of its actual width What is the window’s width in the drawing?
please help!
The windows width in the drawing according to the task content is; 9.6inches.
What is the windows width in the drawing?According to the task content, the window's actual width on the house is given as; 48 inches.
Hence, since, the window's width on the drawing is 20% of the actual width, it follows that;
Windows drawing width = 20% × 48 = 9.6 inches.
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Write an absolute value inequality for each of the following. Then graph the
solution set on a number line.
all numbers less than 7and greater than -7
An absolute value inequality for "all numbers less than 7 and greater than -7" is given by |x| < 7.
How to write an absolute value inequality?Based on the information provided, we can logically deduce that the statement describes an intersection of set because the word "and" was used.
This ultimately implies that, we would use the less than (<) symbol to write an absolute value inequality for the given statement:
|x| < 7
Therefore, this can be translated as follows:
-7 < x < 7 or x < 7 and x > -7.
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2x - y = 4
y = 2x + 4
Solution(s):
PLEASEEE
Use the quadratic model y=-4x^2-3x+4 to predict y if x equals 5
Answer:
y = -4x^2 - 3x + 4
x = 5
y = -4(5)^2 - 3(5) + 4
y = -4(25) - 15 + 4
y = -100 - 15 + 4
y = -114
Step-by-step explanation:
Find the area of a triangle who's side lengths are 13, 14, and 15. (The questions doesn't tell the type of triangle.)
Answer:
84 square units.
Step-by-step explanation:
Area of scalene triangle:[tex]\sf \boxed{\bf Area = \sqrt{s*(s-a)(s-b)*(s-c)}}[/tex]
Here, a, b and c are the sides of the triangle. s is the semi perimeter.
a = 13
b = 14
c = 15
[tex]\sf s= \dfrac{a+b+c}{2}\\\\ =\dfrac{13+14+15}{2}\\\\=\dfrac{42}{2}\\\\s = 21[/tex]
s -a = 21 - 13 = 8
s -b = 21 - 14 = 7
s - c = 21 - 15 = 6
[tex]\sf Area = \sqrt{21*8*7*6}[/tex]
[tex]= \sqrt{ 7* 3 * 2 * 2 * 2 * 7 * 2 * 3}\\\\=7 * 3 *2*2\\\\= 84 \ square \ units[/tex]
Will make BRAINLIEST!!
Complete the congruence statement for the figure below.
An airplane covers 3450 km in an hour. how much distance will it cover in 7 hours?
Answer:
24,150km
Step-by-step explanation:
The plane travels 3450km in 1 hr, since we need the distance traveled in 7 hrs we need to multiply 3450 by 7.
distance in 7hrs: 3450*7 = 24,150km
Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.
The surface area of the cone is calculated to the nearest tenth as: 173.4 cm².
What is the Surface Area of a Cone?Surface area of a cone = πr(r + l),
Given the following:
Radius (r) = 4 cmSlant height (l) = 9.8 cmPlug in the values
Surface area of the cone = π × 4(4 + 9.8)
Surface area of the cone = 173.4 cm²
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One pen is chosen without looking from a bag that has 3 blue pens, 6 red pens, and 3 green pens.
Find the probability of choosing a green pen.
The probability of choosing. a green pen is 0.25
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected/Total outcome
If a bag has 3 blue pens, 6 red pens, and 3 green pens, then;
Total pen = 3+6+3
Total pen = 12
If a green pen is chosen, then
Pr(choosing a green pen) = 3/12
Pr(choosing a green pen) = 0.25
Hence the probability of choosing. a green pen is 0.25
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Determine the measure of the interior angle at vertex E. A. 135 B. 67.5 C. 60 D. 90
Answer:
90
Step-by-step explanation:
Why cant people just answer questions without guessing or answer them correctly.
Find the length of BC¯¯¯¯¯¯¯¯
Answer:
B
Step-by-step explanation:
I love trig lol,
Assuming you know trig, Cos(17)=BC/42
Cos(17)*42=BC
Cos(17)~0.956
0.956*42=40.152=BC
Since this is a approximation, B is the closest to our estimate.
hellooo please i need help on these question
( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60. The answers are option D and B
There are different type of FunctionDifferent types of function demands different ways of solving them. Different types are simple function, function by substitution and function of function.
Given that
f(x) = [tex]x^{2}[/tex] + 9x - 14 and g(x) = [tex]x^{2}[/tex] - x + 3
( f - g )(x) will be the difference between f(x) and g(x)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - ( [tex]x^{2}[/tex] - x + 3)
( f - g )(x) = [tex]x^{2}[/tex] + 9x - 14 - [tex]x^{2}[/tex] + x - 3
( f - g )(x) = 10x - 17
Also, if f(x) = [tex]3x^{2}[/tex] - 15 and g(x) = 1 - 2/3 x
( f ° g)(-6) means that we will evaluate g at -6, then evaluate f at the result of g(-6)
g(-6) = 1 - 2/3 (-6)
g(-6) = 1 + 4
g(-6) = 5
f(g(-6)) = 3([tex]5^{2}[/tex]) - 15
f(g(-6)) = 3 x 25 - 15
f(g(-6)) = 75 - 15
f(g(-6)) = 60
Therefore, ( f - g )(x) = 10x - 17 and ( f ° g)(-6) = 60
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What is the slope of a line that passes through the point (-3,0) and has a y-intercept of 12
The slope of a line that passes through the point (-3,0) and has a y-intercept of 12 is 4.
How to find the slope of a line?Using the point slope equation,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (-3, 0)
0 = -3m + 12
-12 = -3m
divide both sides by -3
m = -12 / -3
m = 4
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Find the coefficient of t to the 4th power in the expansion of (-9t-9) to the 7th power select one: a. -25,515 b. -100,442,349 c. -167,403, 915 d. -4,782, 969
The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
What is an expansion?An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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(-1/2 - 1/8) + (3/4 + 5/6) A.1/12
Answer:
23/24
Step-by-step explanation:
Let's convert all the fractions to a common denominator
(-12/24 - 3/24) + (18/24 + 20/24)
Combine like terms and you get 23/24
1. Drew ran the first 2 3/4 miles of a 5-mile race in 1/2 hour. What was his average rate, in miles per hour, for this first part of the race? Describe how you solved the problem.
Answer:
5 1/2
Step-by-step explanation:
Rate x Time = Distance. If you know 2 of the parts, you can figure out the 3rd part. You know the time and the distance, so plug those in and solve.
Let R = rate
R(1/2) = 2 3/4 Let's change 2 3/4 into a improper fraction.
R(1/2) = 11/4 Multiply 4x2 and then add 3 that gets you 11 and the bottom number stays the same. Next, multiply both sides of the equation by 2.
R = 22/4 or 11/2 or 5 1/2 miles per hour.
A tank of water contains 35 liters of water that leaks 6 liters of water an hour another container contains 29 liters of water that leaks 3 an hour if no the the tank and container start leaking at the same time how long does it takes for both the tank and container to have the same amount of water
Answer:
Step-by-step explanation:
Let the # of liters in both containers = y when equality is reached.
Container 1: loses 6 liters / hour
Container 2: loses 3 liters / hour
Equation
35 - 6x = 29 - 3x
Solution
35 - 6x = 29 - 3x Subtract 29 from both sides
35 - 29 - 6x = 29 - 29 - 3x Combine
6 - 6x = - 3x Add 6x to both sides
6 - 6x + 6x = - 3x + 6x Combine
6 = 3x Divide both sides by 3
6/3 = 3x/3
2 = x
After 2 hours they should have the same amount of water.
35 - 6(2) = 35 - 12 = 23
29 - 3*2 = 29 - 6 = 23
Answer
After 2 hours have passed, both containers should have 23 Liters each.