Answers
The formula for the partial sum of a geometric sequence is given by:
\(S_n=\frac{a(r^n-1)}{r-1}\)From the problem, we identify:
\(\begin{gathered} n=7 \\ a=3 \\ r=2 \end{gathered}\)Finally, using these values in the formula:
\(\begin{gathered} S_7=\frac{3(2^7-1)}{2-1}=\frac{3(128-1)}{1}=3\cdot127 \\ \\ \therefore S_7=381 \end{gathered}\)Related Questions
Fill in the missing value for the coordinate pair that lies on the graph of the function. y=52 (2,
Answers
The missing value for the coordinate pair that lies on the graph of the function. y=5^x (2, 25)
How to determine the missing values?The equation of the function is given as:
y = 5^x
And the x value is given as
x = 2
To determine the missing value, we start by substituting 2 for x in the function y = 5^x
So, we have:
y = 5^2
Evaluate the exponent
y = 25
So, the complete coordinate is (2, 25)
Hence, the missing value for the coordinate pair that lies on the graph of the function. y=5^x (2, 25)
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help me pleaseee...
Answers
x=1
y=1
What is the surface area of the rectangle pyramid below 13 13 13
Answers
Answer:
Step-by-step explanation:
Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:
First, we need to calculate the area of the rectangular base, which is simply length x width:
Area of rectangular base = 13 x 13 = 169 square units
Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.
To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:
a² + b² = c²
where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.
13² + 13² = c²
338 = c²
c ≈ 18.38
Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:
Area of isosceles triangle = (1/2) x base x height
Area of isosceles triangle = (1/2) x 13 x 18.38
Area of isosceles triangle ≈ 119.14 square units
To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:
Area of right triangle = (1/2) x base x height
Area of right triangle = (1/2) x 13 x 18.38
Area of right triangle ≈ 119.14 square units
Since there are two of each type of triangular face, the total surface area of the pyramid is:
Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle
Surface area = 169 + 2 x 119.14 + 2 x 119.14
Surface area = 546.28 square units
Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.
Follow this link to view juan’s work. critique juan’s work by justifying correct solutions and by explaining any errors he made. for any errors made, provide and explain a correct response. be sure to explain each key aspect of the graph.
Answers
Answer:
Step-by-step explanation:
Let the exponential function given in the picture is,
f(x) = a(b)ˣ
Here, a = Initial value
b = Base value
x = Exponent
Since, the graph passes through the points (0, 1) and (1, 3)
For (0, 1),
1 = a(b)⁰
a = 1
For (1, 3),
3 = 1(b)¹
b = 3
Therefore, equation of the given function will be,
f(x) = (3)ˣ
Therefore, Initial value = 1
Base = 3
Asymptote (Horizontal) → y = 0
Vertical asymptote → None
Domain → (-∞, ∞) Or {x | x ∈ R}
Range → (0, ∞) Or {y | y > 0}
Therefore, answers given by Juan are incorrect.
please help if you can!
Answers
Step-by-step explanation:
\(a - 3c = \left(-\dfrac{2}{3}\right) - 3\left(\dfrac{4}{5}\right)\)
\(\:\:\:\:\:\:\:=-\dfrac{2}{3} - \dfrac{12}{5} = -\dfrac{46}{15}\)
Rotation: 180° about the origin
Answers
According to the above, the figure rotated 180° would remain as shown in the image in the fourth quadrant of the Cartesian plane (+ , -)
How to rotate the figure 180°?To rotate the figure 180 degrees we must take into account its initial position. Additionally, we must remember that each quadrant is equivalent to 90°, so we would have to rotate it two quadrants. In this case it is not important to know if it rotates counterclockwise or clockwise because we know it will be in quadrant #4.
In this case, we must be guided by the coordinates that the figure has to draw it again. From the above we can see that it has four coordinates at the top. In the case of the figure rotated in quadrant #4, these four coordinates would be at the bottom because the figure has been rotated 180°.
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The salaries of 4 players on a professional basketball
team average $200,000 per year. If a fifth player is hired
for $400,000 per year, what will be the average salary
for the 5 players?
Answers
If salary average of 4 players is making $200,000/yr, what's the total payroll? It should be $200K x 4 or $800,000.
Now if you add in that 5th player at $400,000 what is the total payroll of all 5 players? It should be $800,000 + $400,000 = 1,200,000. From there you can find the average of the 5 players by dividing!
The points (0,3) and (1,12) are solutions of an exponential function. What is the equation of the exponential function?
A) h(x) = 3(4)x
B) h(x) = 4(3)x
C) h(x) = 4(1∕3)x
D) h(x) = 3(0.25)x
Answers
Answer:
A
Step-by-step explanation:
An exponential function has the form
y = a\((b)^{x}\)
Use the given solutions to find a and b
Using (0, 3 ) , then
3 = a\(b^{0}\) [ \(b^{0}\) = 1 ] , so
a = 3
y = 3\((b)^{x}\)
Using (1, 12 ) , then
12 = 3\(b^{1}\) = 3b ( divide both sides by 3 )
4 = b , then
h(x) = 3\((4)^{x}\) → A
Which of the following expressions is equivalent to 5 + 2(10 – 3)?
1. 7(10 – 3)
2. 70 – 3
3. 5 + 20 – 3
4. 5 + 2(7)
Answers
Answer:
4
Step-by-step explanation:
1. 7(10-3)
7×7
49
2. 70-3
67
3. 5+20-3
25-3
22
4.5+2(7)
5+14
24
5+2(10-3)
5+2×7
5+14
24
Each of the samples below is randomly selected from a company with 320 employees. Choose which samples are representative samples for the company. Select all that apply. A. 25 employees on the company email list B. 25 employees with 10 years of service or more C. 25 employees as they begin their shifts at 3:00 pm D. 25 employees at a company-wide assembly E. 25 employees from the human resources department
Answers
Step-by-step explanation:
For all the recent strides we’ve made in the math world, like how a supercomputer finally solved the Sum of Three Cubes problem that puzzled mathematicians for 65 years, we’re forever crunching calculations in pursuit of deeper numerical knowledge. Some math problems have been challenging us for centuries, and while brain-busters like the ones that follow may seem impossible, someone is bound to solve ‘em eventually. Maybe.
For now, take a crack at the toughest math problems known to man, woman, and machine.
1. The Collatz Conjecture

DAVE LINKLETTER
Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.
A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.
Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.
The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.
The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.
Answer:
Sorry brillant26 or whatever gave you a invalid answer. its actually A (25 employees on the company email list) and D (25 employees at a company wide assembly)
Hope this helps!!
Have a nice day!!
Step-by-step explanation:
aisha places 6 counters into this place value chart
list all the possible numbers she could represent
Answers
Answer:
All the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
Step-by-step explanation:
Please refer to the attached diagram for this question.
We are asked to list all the possible numbers she could represent using the counters.
The possible numbers are:
When there is 0 counter in the "ones" place and 6 counters in the "tenths" place.
0.6
When there is 1 counter in the "ones" place and 5 counters in the "tenths" place.
1.5
When there are 2 counters in the "ones" place and 4 counters in the "tenths" place.
2.4
When there are 3 counters in the "ones" place and 3 counters in the "tenths" place.
3.3
When there are 4 counters in the "ones" place and 2 counters in the "tenths" place.
4.2
When there are 5 counters in the "ones" place and 1 counter in the "tenths" place.
5.1
When there are 6 counters in the "ones" place and 0 counter in the "tenths" place.
6
Therefore, all the possible numbers she could represent using the counters are:
0.6 | 1.5 | 2.4 | 3.3 | 4.2 | 5.1 | 6
In AHIJ, h = 160 inches, i = 910 inches and ZJ=28°. Find the area
of AHIJ, to the nearest square inch.
Answers
Answer:
34178
Step-by-step explanation:
deltamath
Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is 60°. What is the length of the third side
of the
triangle?
A. 43
B. 13
C. 3
D. 5
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Answer:
B
explanation:
I am sorry that I am not sure how to expalin but this is the correct answer.
can someone solve this with an explanation?
Answers
Jim drove 455 miles in 7 hours.
At the same rate, how many miles would he drive in 5 hours?
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six times an integer minus 5 equals the square of the integer
Answers
The value of the the integer is 1 or 5
What is an integer?An integer is a whole number that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1
Let's represent the integer by x, therefore
six times an integer minus 5 equals the square of the integer can be put into equation as:
6x-5 = x²
x² - 6x +5 = 0
x²-5x - x + 5 = 0
(x²-5x)(-x+5) = 0
x(x-5) - 1 ( x -5) = 0
(x-1)(x-5) = 0
therefore x-1 = 0 or x-5 = 0
x = 1 or 5
therefore the value of the integer can either be 5 or 1
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(x-8) + (x - 2) pls
Answers
Answer:
2x - 10
Step-by-step explanation:
group like terms: (x+x) + (8 - 2)
simplify: 2x - 10
Factor each polynomial. Look for a GCF first.
2x²-8k-90
O
2 (x-9) (x - 5)
2 (x + 9) (x + 5)
2 (x − 9) (x + 5)
2 (x + 9) (x - 5)
Answers
Answer:
Step-by-step explanation:
First, you could factor 2 out of the whole thing. The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)
c.) 4. Solve the system of equations
and write the solution in the blank.
y = -3x + 4
y = 4x – 10
Answers
In triangle JKL, if angle J is seven less than angle L and angle K is 21 less than twice angle L, find the measure of each angle
Answers
Answer:
j=45 k=83 L=52
Step-by-step explanation:
j=x-7
k=2x-21
L=x
x-7+2x-21+x=180
4x-28=180
4x=208
x=52
The measure of the angles are; J = 48, K = 57 and L = 75
What is linear pair?Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
In order to determine the measure of these angles, we have to set J as x. then find the measure of all of these angles.
J = x
K = x + 9
L = 2x - 21
Now, we can add them all together and set equal to 180;
x + x + 9 + 2x - 21 = 180
4x - 12 = 180
4x = 192
x = 48
Now that we have;
J = x = 48
K = x + 9 = 48 + 9 = 57
L = 2x - 21 = 2(48) - 21 = 96 - 21
L = 75
Hence, The measure of the angles are; J = 48, K = 57 and L = 75
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A carpenter is measuring a cabinet to
ensure the sides create a right angle.
Determine whether the triangle is a right
triangle
Answers
Answer:
It is a right angle triangle.
Step-by-step explanation:
Use the pythagoras theorem. c^2 = a^2 + b^2.
5^2 = 4^2 + 3^2
25 = 16 + 9
25 = 25
GIVING BRAINLIST IF YOU HELP FAST!
Which statement about the arrow is true?
A)
The arrow does not have rotational symmetry.
B)
The arrow has rotational symmetry after a 90° rotation.
C)
The arrow has rotational symmetry after a 180° rotation.
D)
The arrow has rotational symmetry after a 270° rotation.
Answers
Answer:
B
Step-by-step explanation:
Answer:
Though you said that you would give " BRAINLIST IF YOU HELP FAST!" It doesn't mean that it is going to be the right answer. The correct answer is "ACTUALLY" C) The arrow has rotational symmetry after a 180° rotation.
Step-by-step explanation:
Graph the circle (x - 3)^2 + (y + 3)^2= 36.
Answers
The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.
To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.
The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.
Using this information, we can proceed to plot the circle on a graph:
Plot the center point: (3, -3).
From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.
Up: (3, -3 + 6) = (3, 3)
Down: (3, -3 - 6) = (3, -9)
Left: (3 - 6, -3) = (-3, -3)
Right: (3 + 6, -3) = (9, -3)
Connect the plotted points to form a circle.
The resulting graph should look like this:
| • (3, 3)
|
| •
| •
__|_____________________________
|
|
|
|
| • (3, -3)
The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.
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(04.04 LC)
On a coordinate grid, point T is at (2,-4) and point Sis at (2,6). The distance (in units) between points T and Sis
numbers, such as 2.) (5 points)
(Input only whole
Answers
Answer:
The distance 'd' between T and S:
\(d=10\)Step-by-step explanation:
As the point 'T' is located at (2, -4)
So, the point 'T' has the coordinates (2, -4)And the point 'S' is located at (2, 6)
So, the point 'T' has the coordinates (2, 6)The distance 'd' between T and S can be computed using the formula:
\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
\(=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}\)
\(=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}\)
\(=\sqrt{0+10^2}\)
\(=\sqrt{10^2}\)
\(d=10\)
Therefore, the distance 'd' between T and S:
\(d=10\)Answer:
t and s
Step-by-step explanation:
what are exchange rates?
Answers
Answer:
Step-by-step explanation:
Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.
Please please help!!!!
Answers
Hope this helps
how do I add fractions
Answers
Step-by-step explanation:
1 Find common denominator (lower numbers)
2 add numerators(top numbers)
3 put the numerator over the denominator
ex 3/4+2/8
3x2=6,4x2=8
3/4=6/8
6/8+2/8=8/8 or 1
Suppose two fractions be
a/b c/dNow
\(\\ \rm\Rightarrow \dfrac{a}{b}+\dfrac{c}{d}\)
Find LCM of b and ddivide LCM by b and d and multiply with a and c respectively\(\\ \rm\Rightarrow \dfrac{ad+bc}{bd}\)
Harper plans to purchase her school pictures. The prints cost $108 plus any add-ons she wants to purchase. If she saves $18 per week, which solution represents how many weeks, x, it will take Harper before she can purchase her school pictures?
A - x < 8
B - x < (underlined) 8
C - x > 8
D - x > (underlined) 8
Answers
Answer:
A - x < 8,,,,,,,,,,,,,,,,,
=6
Bank of America offers a 5-year 8% continuously compounded investment option.
Find the amount accrued if $1450 is invested.
Answers
Answer:
A = $2130.49
Step-by-step explanation:
Given the following data;
Time, t = 5 years
Interest rate, r = 8%
Principal = $1450
To find the future value, we would use the compound interest formula;
\( A = P(1 + \frac{r}{100})^{t}\)
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
t is the number of years for the compound interest.
Substituting into the equation, we have;
\( A = 1450(1 + \frac{8}{100})^{5}\)
\( A = 1450(1 + 0.08)^{5}\)
\( A = 1450(1.08)^{5}\)
\( A = 1450 * 1.4693 \)
A = $2130.49
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at negative 8 comma 1, 0 comma 1, negative 4 comma 5 Determine the coordinates of the image if triangle ABC is translated 8 units to the right. A′(−14, 1), B′(−8, 1), C′(−12, 5) A′(−6, 9), B′(0, 9), C′(−4, 13) A′(0, 1), B′(8, 1), C′(4, 5) A′(2, −7), B′(8, −7), C′(4, −3)
Answers
The cοοrdinates οf the image if triangle ABC is A′(0, 1), B′(8, 1), C′(4, 5).
What is Triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.
A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with vertices A, B, and C is knοwn as triangle ABC. Any three pοints in Euclidean geοmetry that are nοt cοllinear result in a distinct triangle and a distinct plane.
The cοοrdinates οf the image if triangle ABC is translated 8 units tο the right are:
A′(0, 1), B′(8, 1), C′(4, 5).
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