The terms are as follows:
t₃ = -62
t₇ = -29.6
tₙ = 10.8n - 105.2
How to find terms of an arithmetic sequence?t₁₄ = 46
t₁₉ = 100
Therefore,
tₙ = a + (n - 1)d
where
a = first termd = common differenceHence,
46 = a + 13d
100 = a + 18d
5d = 54
d = 10.8
46 - 13(10.8) = a
a = 46 - 140.4
a = - 94.4
t₃ = a + 3d = - 94.4 + 3(10.8) = -62
t₇ = a + 6d = - 94.4 + 6(10.8) = -29.6
tₙ = -94.4 + 10.8n - 10.8 = 10.8n - 105.2
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Help asap pleaseeeeeeeeee its due 5 and its 4 for me right now
Answer:
The answer would be A
Step-by-step explanation:
1^2=1×1= 1
2^2 =2×2=4
3^2=3×3=9
4^2=4×4=16
Therefore,
√11 lies between 3 and 4
Answer:
A
Step-by-step explanation:
[tex]since 3 is \sqrt{9} and 4 is \sqrt{16} then it follows that \sqrt{11} is between the two[/tex]
A portion of the Quadratic Formula proof is shown. Fill in the missing reason.
Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ?
Rewrite the perfect square trinomial as a binomial squared on the left side of the equation
Take the square root of both sides of the equation
Multiply both sides of the equation by 2
Square the left side of the equation
The quadratic equation ax²+bx+c = 0 is given and this is illustrated below.
How to illustrate the equation?ax²+bx+c = 0
Step 1: Subtract c from both sides
ax²+bx+c-c = 0-c
ax²+bx = -c
Step 2: Divide both sides of the equation by a
ax²/a + bx/a = -c/a
x² + bx/a = -c/a
Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
Step 4: Square the quantity b/2a on the right side of the equation
x² + bx/a + (b/2a)² = -c/a + b²/4a²
Step 5: Find a common denominator on the right side of the equation which is 4a²
x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²
Step 6: Add the fractions together on the right side of the equation
x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²
Step 7: The equation on the left is to be written as a perfect square as shown
(x+b/2a)² = (-4ac+ b²)/4a²
Step 8: Take the square root of both sides
√(x+b/2a)² = √ (-4ac+ b²)/4a²
(x+b/2a) = √(-4ac+ b²)/2a
Step 9: subtract b/2a from both sides
x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a
x = -b/2a + √(-4ac+ b²)/2a
Step 10: Add the fractions together on the right-hand side
x = -b±√(-4ac+ b²)/2a
This will then gives the required equation.
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^
Find (ff)(0).
f(x) = 3x - 2
a. 1
b. 0
Please select the best answer from the choices provided
ABCD
Answer:
a
Step-by-step explanation:
go it right on a mastery test
which type of data would be best displayed in a box plot
The type of data that would be best displayed in a box plot is the number of votes received by each of four candidate.
What is a box plot?A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%
The whiskers represent the minimum and maximum scores. On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
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The volume of a square pyramid is 50 inches. The length of the base of the pyramid is 5 inches. What is the height of the pyramid?
Answer: the height of the pyramid is 6 inch.
Step-by-step explanation:
V=50 inch³ a=5 inch H=?
Formula of volume square pyramid is:
[tex]\boxed {V=\frac{1}{3}*S_{base}*H },[/tex]
where: Sbase - pyramid base area;
H - pyramid height.
Hence,
[tex]H=\frac{3*V}{S_{base}}\\[/tex].
Since the pyramid is square, its base is a square. ⇒
[tex]S_{base}=a^2\\S_{base}=(5\ inch)^2\\S_{base}=25\ inch^2\\H=\frac{3*50}{25} \\H=3*2\\H=6\ (inch).[/tex]
Good luck!
Show all work to identify the asymptotes and end behavior of the function f(x)= 5x/x-25.
Considering the given function and the asymptote concept, we have that:
The vertical asymptote is of x = 25.The horizontal asymptote is of y = 5.The end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. Hence it also gives the end behavior of the function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex].
The vertical asymptote is found as follows:
x - 25 = 0 -> x = 25.
The horizontal asymptote is found as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5[/tex].
Hence the end behavior is that as [tex]x \rightarrow \infty, f(x) \rightarrow 5[/tex].
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If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
The vertex U' is located at (-4, -5)
How to determine the location of U'?The vertices are given as:
U = (-4, 5)
V = (-6, 2)
The rule of transformation is given as:
Reflection across the x-axis
This is represented as:
(x, y) => (x, -y)
So, we have:
U' = (-4, -5)
Hence, the vertex U' is located at (-4, -5)
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Complete question
Quadrilateral UVWX is reflected over the x-axis to form quadrilateral U′V′W′X′. If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −3x+5y=−15? Drag and drop each choice into the boxes to correctly complete the table.
The first line is perpendicular, the second line is not perpendicular and not parallel , the third line is parallel to the above line and the forth line not parallel or perpendicular to the line.
How can the slope of the line be calculate?The slope of the line is been given as −3x+5y=−15
Then [tex]y= \frac{3}{5x} -3[/tex], hence the slope is [tex]\frac{3}{5}[/tex]
Slope of the first line 5x + 3y = 15 after calculation isthe slope is [tex]y= \frac{5}{-3x} +5\\\\\frac{5}{-3}[/tex]
this means that the line is perpendicular to the given line
Slope of the second line 3x + 5y = 15 after calculation is[tex]y= \frac{3}{-5x} +15\\\\\frac{3}{-5}[/tex]
This means that the line is not perpendicular and not parallel
Slope of the Third line -3x + 5y = 15 can be calculated as[tex]y= \frac{3}{5x} +15\\\\\frac{3}{5}[/tex]
This means that the line is parallel to the above line.
Slope of the first line 3x + 5y = 15 after calculation is[tex]y= \frac{-3}{5x} +3\\\\\frac{-3}{5}[/tex]
This means that the line is not parallel or perpendicular to the line
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(6+√-64)(3-√-16) Multiply. This is urgent, please explain this to me!
Answer:
50
Step-by-step explanation:
[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i
[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i
the factors can then be expressed as
(6 + 8i)(3 - 4i) ← expand using FOIL
= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]
= 18 - 24i + 24i + 32 ← collect like terms
= 18 + 32 + 0
= 50
Based off this picture, what would the length of AC- be?
The length of AC- is?
(Giving 70 points!)
Answer:
AC = 9
Step-by-step explanation:
Set the negative value into absolute as length cannot be negative.
⇒ AC = AB + BC
⇒ AC = |-5| + 4
Formula: |-a| = a
⇒ AC = 5 + 4
⇒ AC = 9
Answer: I think the length is 9 units
Step-by-step explanation:
Consider a TV set that consumes 120 W of electric power when it is on, and is kept on for an average of 6 h per day. For a unit electricity cost of 23 cents per kWh, determine the cost of electricity this TV consumes per month (30 days). The cost of electricity the TV consumes per month is $
The cost of electricity consumed by the TV per month is $4.968.
In the question, we are given that a TV set consumes 120W of electric power when switched on. It is kept on for a daily average of 6 hours per day. The number of days in the month is given to be 30 days. The cost per unit of electricity is 23 cents per kWh.
We are asked to find the cost of electricity the TV consumes in the month.
The daily energy consumed by the TV = Power*Daily time = 120*6 Wh = 720 Wh.
The monthly energy consumed by the TV = Daily energy*Number of days in the month = 720*30 Wh = 21600 Wh = 21600/1000 kWh = 21.6 kWh.
Hence, the total cost of electricity the TV consumes = Monthly energy*Per unit cost = 21.6*23 cents = 496.8 cents = $496.8/100 = $4.968.
Therefore, the cost of electricity consumed by the TV per month is $4.968.
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Suppose g(x)=f(x+2)-3
The transformations which map f(x) to g(x) according to the equation are; Translation of f(x) 2 units to the left and 3 units upwards.
Which translations maps f(x) to g(x)?The equation given in the task content is as follows;
g(x)=f(x+2)-3It therefore follows that the transformations which would produce function g(x) from f(x) involves a 2 units translation to the left and a 3 units translation upward.
Remarks:
The complete question requires that the transformations from f(x) to g(x) be identified.
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Consider the equation x^2-5x-24=0 . Write this equation in the form X^2=k
x= 8 , -3
What is Quadratic Equation?Given:
x² - 5x -24 =0
x² - 8x + 3x -24=0
x(x-8) + 3(x- 8)=0
(x-8)(x+3)=0
x= 8 , -3
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find the product (t - sa) (9t + 6sa)
The product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a²
What is the product of two factors?The product of two factors of an expression results in a quadratic or polynomial expression depending on the degree to which their power is being raised.
From the information given, we have:
= (t - sa) (9t +6sa)
= 9t² + 6tsa - 9tsa - 6(sa)²
= 9t² - 3tsa - 6s²a²
Therefore, we can conclude that the product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a².
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In the triangle below, what is the measure of ZZ?
OA. 65°
B. 7°
O C. 90°
D. 50°
65
7
Can you answer my question please and thank you
Answer:
50
Step-by-step explanation:
I did this by inspection because {7, 24, 25} is a common trio, but ill just break it down for you.
Let the hypotenuse be x
Then [tex]14^2+48^2=50^2[/tex]
2500 = [tex]x^2[/tex]
x=50 or -50 (not applicable because you cannot have a negative length).
So the hypotenuse is 50.
Note: Common trios such as {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17} are worth remembering as you can often multiply them in such questions. Such as in this question, {7, 24, 25} times 2 is {14, 48, 50}.
Hope you have a nice day!
Create a scatterplot displaying the data in the table. Be sure to include a linear trend line. (2 points)
The scatter plot is shown in the attached picture, and the line of best is also shown.
What is scatter plot?Scatter plots are graphs representing individual data points and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one on the y-axis for each point.
We have the data shown in the table.
We can plot the data on the coordinate plane such as:
(x, y) = (54, 92), (46, 80) and so on
We can find the equation of best fit:
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
y = mx + c
Thus, the scatter plot is shown in the attached picture, and the line of best is also shown.
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2. The name of the 1500-meter gold medal winner for each of the Olympics
from 1896 to 2000 is placed in a jar. (If a man has won the race more than
once, his name will be included for each race he won.)
A. If one name is drawn from the jar, which country has the best chance
of having a name drawn?
B. Three names are drawn without replacing the name after it is drawn.
What is the probability that the three winners will be from either
New Zealand or Australia?
pLEASE HELP
The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.
How to calculate probability?It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.
Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.
The probability that the winners will be from either New Zealand or Australia will be:
= 3/29 + 2/29
= 5/29
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Answer
A. Great Britain
B. 3/29+2/29=5/29
please give me the brainliest.
A rectangle has a length of 6x-5y+1 if the perimeter of the rectangle is 16x-4y-4 determine an expression for its width
Answer:
Width = 3y - 3
Step-by-step explanation:
P = 2l + 2w
12x - 4y - 4 = 2(6x - 5y + 1) + 2w
12x - 4y - 4 = (12x - 10y + 2) + 2w
6y - 6 = 2w
w = 3y - 3
93a²xy - 124a²x - 62a²x³y²
Step-by-step explanation:
the ans is 19 a6 x5 y3
93-12-62×a2xy×a2x×a2x3y2
ans. 19 a6 x5 y3 add all the spuare and cube
Answer:
[tex]31a^2x(3y-4-2x^2y^2)[/tex]
Step-by-step explanation:
So the given equation is : 93a²xy - 124a²x - 62a²x³y². In this form you'll notice they all have a, and specifically a^2, and they also have x, but we only factor out x^1 since the first variable only has a degree of 1. So this gives us the equation: [tex]a^2x(93y-124-62x^2y^2)[/tex]. Now if we look at the coefficients you'll notice that they have a GCF of 31. So we can factor that out to. This gives you the equation: [tex]31a^2x(3y-4-2x^2y^2)[/tex] Which is your completely factored equation. You could also technically group 2xy^2 and 3y to get: [tex]31a^2x(y(3-2xy)-4)[/tex], although I'm not sure if that's considered "simplifying it"
Write the standard form of the line that passes through the given points. include your work in your final answer. (-1, -3) and (2, 1)
The standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
The slope of the given line, m = (1 - (-3))/(2 - (-1)) = (1 + 3)/(2 + 1) = 4/3.
Computed using the formula for the slope of a line, m = (y₂ - y₁)/(x₂ - x₁), when a line passes through the points (x₁, y₁) and (x₂, y₂).
The point intercept form of a line is y - y₁ = m(x - x₁) when the line passes through the point (x₁, y₁) and has the slope m.
Thus, the given line in the point intercept form can be written as:
y - 1 = (4/3)(x - 2).
The standard form of a line is ax + by = c.
To convert the point intercept form to the standard form, we do as follows:
y - 1 = (4/3)(x - 2),
or, 3(y - 1) = 3(4/3)(x - 2) {Multiplying both sides by 3},
or, 3y - 3 = 4x - 8 {Simplifying},
or, 8 - 3 = 4x - 3y {Rearranging},
or, 4x - 3y = 5 {Rearranging and simplifying}.
Thus, the standard form of a line passing through the points (-1, -3) and (2, 1) is 4x - 3y = 5.
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HEEEEELLLLLLLLLPPPPPPPMEEEEEEEE!!!!!!!!!!!
Answer: a = 18
Step-by-step explanation:
The pythagorean theorem says that the sum of the square of the two legs of a triangle is equal to the square of the hypotenuse.
The two legs are 80 and a, and the hypotenuse is 82 which gives us
80² + a² = 82²
a² = 324
a = 18.
Answer:
18
Step-by-step explanation:
a² + b² = c²
a² + 80² = 82²
a² + 6400 = 6724
a² = 324
a = √324
a = 18
If the product of two integers is 420 and one of the integer is (-5) then the other is__________
Answer:
-84.
Step-by-step explanation:
n * -5 = 420
n = 420/ -5 = -84.
Answer:
- 84
Step-by-step explanation:
let the other integer be x , then
- 5 × x = 420
- 5x = 420 ( divide both sides by - 5 )
x = 420 ÷ - 5 = - 84
A girl has 3 shirts (red, yellow, blue) and 6 pairs of socks (red, blue, green, orange, white, black). What is the probability her socks will be orange and her shirt will be red?
Answer:
1/18
Step-by-step explanation:
P(Orange AND Red)
= P(Orange socks)*P(Red shirt)
= 1/3*1/6
= 1/18
solve:
-2(6)^x=-432
Answer:
x = 3
Step-by-step explanation:
1) Divide both sides by -2.
[tex]6^x=\frac{-432}{-2}[/tex]
2) Two negatives make a positive.
[tex]6^x=\frac{432}{2}[/tex]
3) Simplify [tex]\frac{432}{2}[/tex] to 216.
[tex]6^x=216[/tex]
4) Convert both sides to the same base.
[tex]6^x=6^3[/tex]
5) Cancel the base of 6 on both sides.
x = 3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{-2(6)^x = -432}[/tex]
[tex]\huge\textbf{DIVIDE -2 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{6^x = 216}[/tex]
[tex]\huge\textbf{Solve for the current exponent:}[/tex]
[tex]\mathbf{6^x = 216}[/tex]
[tex]\huge\textbf{Log them:}[/tex]
[tex]\mathbf{Log \ 6^x = log = 216}[/tex]
[tex]\huge\textbf{Take the log to both of the sides:}[/tex]
[tex]\mathbf{x \times log (6) = log(216)}[/tex]
[tex]\huge\textbf{Convert it:}[/tex]
[tex]\mathbf{x = \dfrac{log(216)}{log(6)}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = 3}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Find the image vertices for a dilation with center
Image vertices are mathematically given as:
A' = (-12 , 4) B' = (16 , -12) C' = (8 , 12) D' = (-4 , 16)What are the image vertices for dilation with the center?Generally, Multiplying the vertices by a scale factor of four is required in order for us to locate the picture vertices for dilation with center (0, 0).
In conclusion,, the image vertices are :
A' = (-12 , 4) B' = (16 , -12) C' = (8 , 12) D' = (-4 , 16)Read more about vertices
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Which of the following lines will have a negative slope? Select all that apply
Which graph shows the solution to the system of linear inequalities?
y> x+3
ys-x+2
VO
Next
Submit
The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality shows the non equal comparison of two or more numbers and variables.
Given the inequality y > x + 3 and y < -x + 2.
The solution to the inequality y > x + 3 and y < -x + 2 is the dark green region shown in the graph.
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Probabilities that can be estimated from long-run relative frequencies of events are called _____ probabilities.
Probabilities that can be estimated from long-run relative frequencies of events are called objective probabilities.
What is Objective Probability?In contrast to intuition or guessing, objective probability refers to the chances or odds that an event will occur based on the examination of certain measurements. Each metric is based on factual observation, a documented observation, or a long history of data collection.
Instead of being dependent on anecdotes, firsthand knowledge, or hunches, the objective probability is based on statistics, experiments, and mathematical measures. Using objective probability is crucial in the realm of finance to prevent making irrational investment decisions.
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An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.
What is the largest possible volume of the box?
The largest possible volume of the given box is; 96.28 ft³
How to maximize volume of a box?Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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