Answer: Explicit Rule: a_n=30,000 • 2^n-1
Recursive Rule: a_n = 2a_n-1; a_1 = 30,000
Step-by-step explanation: the explicit rule for a geometric sequence is a_n = a_1 • r^n-1 and the recursive rule is a_n= r • a_n -1.
a_1 is the first term of the sequence, which is this case is 30,000. R is the common ration, which is 2 since it doubles each time. Substitute those numbers into the formulas and that’s what you’ll get. Hope this helps. God bless you!!!
If circumference of a circle x^2 +y^2 -6x+2y+c =0 be 6pie units, find c
Circumference = 2× pie × r
Circumference = 6pie
Thus ;
2pie × r = 6pie
r = 3
____________________________________________
[tex]r = \frac{1}{2} \sqrt{ ({ - 6})^{2} + {2}^{2} - c} \\ [/tex]
[tex]3 = \frac{1}{2} \sqrt{ 36 + 4 - c} \\ [/tex]
[tex]6 = \sqrt{40 - c} [/tex]
[tex]( {6})^{2} = ({ \sqrt{40 - c} })^{2} [/tex]
[tex]36 = 40 - c[/tex]
[tex]c = 4[/tex]
4. 10 Unit Test: Surface Area and Volume - Part 1
UNIT TEST:
Surface Area and Volume - Part 1
Which net represents this solid figure?
The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.
What is a solid figure?A solid figure is a three dimensional shape having length, width and height. Examples of solid figures are cylinders, cone, pyramid and prism.
The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.
Find out more on solid figure at: https://brainly.com/question/8774322
using the rule y= 7 x-5,find the value of y when x is 3
Answer:
16
Step-by-step explanation:
If x = 3, then all we must do is substitute.
y=7(3)-5
y= 21 -5
y= 16
---
Hope I helped :)
What is the volume of this pyramid? 32 cm 9 cm 15 cm
Answer:
720cm^3
Step-by-step explanation:
The volume of the pyramid with a = 9cm, b = 15cm and l = 32cm is 720cm^3.
Answer:
720³ cm
The formula for volume is...
length ×width ×heightWith that information, we should multiply the smaller numbers first.
[tex]B = \frac{1}{2} xy[/tex]
Replace the substituted parameters with 9 and 15, then multiply them and solve.[tex]B = \frac{1}{2}(9)(15) = \frac{135}{2}[/tex]
UseV for volume.[tex]V = \frac{1}{3} * \frac{135}{2} * 32 = 45 * 16[/tex]
Reducing the expression ↓[tex]V = 720^3~cm[/tex]
Hence, the volume is 720³ cm
Anyone know how to answer this question? Need help quickly pls!!
Answer:
500miles
Step-by-step explanation:
use the Pythagorean theory
What is the mean of the data set?
{7, 9, 5, 4, 3, 6, 8}
Enter your answer in the box.
A web browser is open on your computer screen. The area of the browser window is 24 square inches. Find the length of the browser window x. The browser covers 3/13 of the screen. What are the dimensions of the screen?
We will see that the length of the browser window is 4.9 inches, and the screen is a square of sidelength 10.2 in
How to find the length of the browser window?
We know that the area of the browser window is 24 in^2, we will assume that the window is a perfect square, then the area is equal to the square of the length x, we have:
x^2 = 24 in^2
x = √(24 in^2) = 4.9 in
How to get the dimensions of the screen?We know that the browser covers 3/13 of the screen, so the area of the screen is 13/3 times the area of the browser:
A = (13/3)*24 in^2 = 104 in^2
Again, if the screen is square of sidelength s, we have:
s^2 = 104 in^2
s = √(104 in^2) = 10.2 in
If you want to learn more about areas, you can read:
https://brainly.com/question/24487155
Find the surface area of each solid.
Answer:
232 in^2
Step-by-step explanation:
This rectangle has 6 surfaces:
Front: 10 x 8 = 80
Back: 10 x 8 = 80
Top: 10 x 2 = 20
Bottom: 10 x 2 = 20
Side: 8 x 2 = 16
Side: 8 x 2 = 16
Total surface area: 232 in^2
How can you decompose the composite figure to determine its area? as a pentagon and four semicircles as two rectangles and four circles as a square and four semicircles as two triangles and four circles
Answer: as a square and four semicircles
Step-by-step explanation:
The composite shape area can be found by first decomposing the figure as: a square and four semicircles.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
to Find the Area of a Composite Figure:
To find the area of a composite figure, the first thing to do is to identify the individual shapes that make up the figure, then find the area of each shape before adding all the areas together.
For a composite figure that is comprised of a square and 4 semicircles, the composite figure would be decomposed into: a square and four semicircles.
Hence, The composite shape area can be found by first decomposing the figure as: a square and four semicircles.
Learn more about composite figures on:
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The table shows input and output values for a liner function f(x). What is the positive difference of outputs for any two outputs that are two values apart? H E L P. 10 Points award!!
Answer:
If you observer the value of x=0 and x=1, you can conclude that every 1 value of x increased,
the f(x) will be increased by 0.5. The graph function should be:
f(x)= x/2A positive difference means that the value should be always positive.
To find 3 the positive difference of f(x) with 3 values of x apart, let use x=0 and x=0+3= 3. The difference would be:
f(x+3) - f(x)f(3)- f(0)=1.5 - 0= 1.5The answer would be: 1.5
 which equation represents the line that passes through the points (3, 7) and (-1, -1)?
points: (3, 7) and (-1, -1)
slope (m) :
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
========
[tex]\hookrightarrow \dfrac{-1-7}{-1-3}[/tex]
[tex]\hookrightarrow \dfrac{-8}{-4}[/tex]
[tex]\hookrightarrow 2[/tex]
Equation:
[tex]\sf y-y_1 = m(x-x_1)[/tex]
==============
[tex]\rightarrow \sf y-7 = 2(x-3)[/tex]
[tex]\rightarrow \sf y = 2x-6+7[/tex]
[tex]\rightarrow \sf y = 2x+1[/tex]
Answer:
[tex]y = 2x- 1[/tex]
Step-by-step explanation:
To determine which equation passes through the points (3, 7) and (-1, -1), we need to determine the slope of the equation. Then, we shall use point slope form to determine the equation of the line.
Determining the slope of the line:
[tex]\text{Slope} = \dfrac{\text{Rise}}{\text{Run} } =\dfrac{\text{y}_{2} - \text{y}_{1} }{\text{x}_{2} - \text{x}_{1} }[/tex]
Substituting the points in the slope formula:
[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]
Simplifying the slope:
[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]
[tex]\text{Slope} =\dfrac{-8}{-4 } = 2[/tex]
Determining the equation of the line:
We shall use point slope form to determine the equation of the line.
[tex]\text{Point slope form:} \ y - y_{1} = m(x- x_{1} )[/tex]
Substitute the slope and the coordinates of any two points stated above.
[tex]y -7= 2(x- 3 ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using the point (3,7)}][/tex]
Simplify the equation and organize it to slope intercept form:
[tex]y -7= 2x- 6[/tex]
[tex]y = 2x- 6 + 7[/tex]
[tex]y = 2x+ 1[/tex]
pls answer this fasttt
got a deadline
Answer: 1.a equal 158 over 33 1.b equals 34 over 33
1.c equals negative 31 over 15
3.a equals 106 over 35
3.b equals negative 293 over 72 .
Step-by-step explanation: I am very sorry but I answered what I know . Hope it helps you . Sorryyy. Thanks . .
The first three steps in writing f(x) = 40x 5x2 in vertex form are shown. write the function in standard form. f(x) = 5x2 40x factor a out of the first two terms. f(x) = 5(x2 8x) form a perfect square trinomial. (eight-halves) squared = 16 f(x) = 5(x2 8x 16) – 5(16) what is the function written in vertex form? f(x) = 5(x 4) – 80 f(x) = 5(x 8) – 80 f(x) = 5(x 4)2 – 80 f(x) = 5(x 8)2 – 80
The function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
What is the vertex form of parabola?Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.
The standard equation of the vertex form of parabola is given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) is the vertex point.
The first three steps in writing the function in vertex form are shown.
[tex]f(x) = 40x +5x^2[/tex]
Write the function in standard form.
[tex]f(x) = 5x^2+ 40x[/tex]
Factor out of the first two terms by taking out the common number 5 from the equation,
[tex]f(x) = 5(x^2 +8x)[/tex]
Form a perfect square trinomial with (8/2)² = 16,
[tex]f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80[/tex]
Hence, the function which is the vertex form of the equation whose first three steps shown in writing is f(x)=5(x +4)²- 80.
Learn more about the vertex form of the parabola here;
https://brainly.com/question/17987697
Answer:
c
Step-by-step explanation:
Kiwi fruit contains roughly two and a half times as much vitamin C as the same weight of oranges.
What weight of kiwi fruit contains approximately the same amount of Vitamin C as 1kg of oranges
Using proportions, it is found that 400g = 0.4kg of kiwi fruit contains approximately the same amount of Vitamin C as 1kg of oranges.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Kiwi fruit contains roughly two and a half times as much vitamin C as the same weight of oranges. Hence, if there is 1 kg = 1000g of oranges, the weight of kiwi fruit is given by:
1000/2.5 = 400g = 0.4kg.
More can be learned about proportions at https://brainly.com/question/24372153
Find the area, no need to explain, need this quick!!
Answer:
A = 201.5 m2
Step-by-step explanation:
[tex]A=76.5+65+60=201.5[/tex]
Hope this helps
10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1 copy. How many different ways can the 10 copies be stored
We will see that there are 847,660,528 different ways in which the copies can be stored.
In how many ways can the 10 copies be stored?
So, we know that the copies can be stored in any of 40 computers, such that each computer can get, at most, one copy.
Then what we need to do is find how many different combinations of 10 computers can we make with the set of 40 computers, this is given by using the combination formula:
[tex]C(40, 10) = \frac{40!}{(40 - 10)!*10!} = \frac{40*39*38*37*36*35*34*33*32*31}{10*9*8*7*6*5*4*3*2} = 847,660,528[/tex]
This means that the 10 computes can be selected in 847,660,528 different ways, so there are 847,660,528 different ways in which the copies can be stored.
If you want to learn more about combinations, you can read:
https://brainly.com/question/11732255
Find the volume of the cone. Round your answer to the nearest tenth.
we know the base of the cone has a diameter of 6, thus its radius must be half that or 3.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies \begin{array}{llll} V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi \\\\\\ V\approx 75.4~in^2 \end{array}[/tex]
Food Bill= $48.06 and a 24% tip Tip = $ Total = $
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{24\% of 48.06}}{\left( \cfrac{24}{100} \right)48.06}\implies 11.5344~\hfill \underset{total}{\stackrel{48.06~~ + ~~11.53}{\approx 59.59}}[/tex]
Answer:
59.59$
Step-by-step explanation:
24% of $48.06=11.5344
Total=11.5+48.06=$59.59
Pleaseeeee helppppp meeeee
Answer:
NY or MZ
Step-by-step explanation:
they are both outside of the parallel lines and on opposite sides of the transverse line
2. Draw what might be the missing figure in
the pattern below.
Please helps
Please I’m stuck in the answer
Answer:
PLEASE ATTACH THE FIGURE LIKE THIS.....
Find the surface area of the prism:
Answer: the prism has a surface area with 920
please help if you can xx
Answer:
Below in bold.
Step-by-step explanation:
The angle in a regular octagon = 180 - (360/8) = 135.
Using trigonometry sin (135/2) = k/2 / EF
sin 67.5 = k / 2EF
2EF = k / sin 67.5
EF = k / 2 sin 67.5 = k/1.8478
Perimeter of octagon = 8 * k/1.8478
= 4.33k to the nearest hundredth.
If the slope of a line is -4 find y when (2,y) and (3,8)
(Someone please explain I'm so confused)
Answer:
y=12
Step-by-step explanation:
[tex]slope=\frac{y2-y1}{x2-x1} \\-4=\frac{8-y}{3-2} \\-4=8-y\\y=8+4=12[/tex]
Planet XX is in a stable circular orbit around a star, as shown in the figure. Which of the following graphs best predicts the angular momentum of the planet as a function of its horizontal position from point AA to point BB if the planet is moving counterclockwise as viewed in the figure above?
Answer:
option c iscorrect
Step-by-step explanation:
Speed
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|________________ position
Can someone please help me
Answer:
15
Step-by-step explanation:
f(X)= f(5)
meaning X= 5
x²-2x
5²-2(5) = 15
A theater has 32 rows. The first row has 18 seats, second row has 21 seats, third row
has 24 seats, and so on. Determine the total number of seats in the theater.
Answer:
2064
Step-by-step explanation:
18 + 21 + 24 + ...
This is an arithmetic series with first term 18 and common difference 3.
The nth term is
18 + 3(n - 1)
The 32nd term is the number of seats in the 32nd row:
18 + 3(32 - 1) = 18 + 3(31) = 18 + 93 = 111
The sum of the series is:
n/2(a + L) = (32/2)(18 + 111) = 2064
Traingle Congruence, FlowChart Proof Level2, 10th Grade
Answer:
Step-by-step explanation:
→1.
Statement : AB ≅AD (side)
Reason: Given
→2.
Statement : ∡BAC≅∡CAD (angle)
Reason: Given
→3.
Statement : AC ≅AC (side)
Reason: Reflexive Property -a side is congruent with itself
→
Statement : ΔABC ≅ΔADC
Reason: Side-Angle-Side Theorem of Congruency
(If two corresponding sides of two triangles are congruent and the corresponding angles between those two sides are congruent then the two triangles are congruent)
Can you pls answer the question
Answer:8
Step-by-step explanation: behind the x value (5) there are 2 ages that had a value. You add the two values (5+3) and you get 8.
Final answer is 8.
find the angle between the pair of vectors to the nearest tenth of a degree
6i-4j, 2i-6j
[tex]~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} 6i-4j\\ 2i-6j \end{cases}\implies \stackrel{\qquad a~\hfill b\qquad }{\begin{array}{llll} < 6~~,~~-4 > \\ < 2~~,~~-6 > \end{array}}[/tex]
[tex]\stackrel{\textit{\Large dot product}}{ < 6~~,~~-4 > \cdot < 2~~,~~-6 > \implies (6\cdot 2)+(-4\cdot -6)}\implies 12+24\implies 36 \\\\\\ \stackrel{\textit{\Large magnitudes}}{|| < 6~~,~~-4 > ||\implies \sqrt{6^2+(-4)^2}\implies \sqrt{52}} \\\\\\ || < 2~~,~~-6 > ||\implies \sqrt{2^2+(-6)^2}\implies \sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right)\implies \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right) \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{2080}} \right)\implies \measuredangle \theta \approx 37.9^o[/tex]
Matthew collected different types of leaves for a science project. He measured the lengths of the leaves. This list shows his findings. 2, 2, 234, 214, 3, 234, 3, 234, 314, 312, 3, 234 Create a line plot to display the data.
Answer:
Place 2 X's above the 2 column, and Place 1 X above the 2 1/4 column, place 4 X's in the 2 3/4 column, place 2 X's in the 3 column, place 1 X in the 3 1/4 column, and 1 X in the 3 1/2 column.
Step-by-step explanation:
The key with Line plots is to count the amount of that number. As you can see, there are 2 2's in the 2 columns, 2 3's in the three-column, and so on. And the three main steps of making a line graph are these:
1. Count the Number of what you have
2. Always give your graph a title
3. Keep your graph organized. An unorganized graph can cause confusion.
And you're done! I hope this helped!