For a geometric sequence
a, ar, ar ², ar ³, …
the n-th term in the sequence is ar ⁿ ⁻ ¹.
The first sequence is
1, 3, 9, 27, …
so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.
The second sequence is
400, 200, 100, 50, …
so of course a = 400, and you can easily solve for r :
200 = 400r ==> r = 200/400 = 1/2
Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.
Similarly, the other sequences are given by
3rd: … 4 × 2ⁿ ⁻ ¹
4th: … 400 (1/4)ⁿ ⁻ ¹
5th: … 5ⁿ ⁻ ¹
6th: … 1000 (1/2)ⁿ ⁻ ¹
7th: … 2 × 5ⁿ ⁻ ¹
If the ratio of raisins to bran flakes in a box of raisin bran flakes cereal is 3:27, how many raisins are there in a box that contains 3,000 raisins and brand flakes?
Answer:
300 raisins
Step-by-step explanation:
sum the parts of the ratio, 3 + 27 = 30 parts
Divide the total by 30 for the value of one part of the ratio.
3000 ÷ 30 = 100 ← value of 1 part of the ratio , then
3 parts = 3 × 100 = 300 ← number of raisins in a box
3x/5=-6
please explain how to do it
Answer: x = -10
Step-by-step explanation:
Given
3x / 5 = -6
Multiply 5 on both sides
3x / 5 × 5 = (-6) × 5
3x = -30
Divide 3 on both sides
3x / 3 = (-30) / 3
x = -10
Hope this helps!! :)
Please let me know if you have any questions
Step-by-step explanation:
3x/5 = - 6
first take 5 to the right: 3x = - 6×5
3x = -30
then divide 3 on both sides
3x/3 = -30/3
x = - 10
I hope this answers your questions.
passes through (−3, 7) and is parallel to y = 4x − 1.
Answer:
Equation of the line is y = 4x + 19
Step-by-step explanation:
slope, m = 4
[tex]y = mx + c[/tex]
consider (-3, 7):
[tex]7 = (4 \times - 3) + c \\ 7 = - 12 + c \\ c = 19[/tex]
equation:
[tex]y = 4x + 19[/tex]
Answer:
y = 4x + 19
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 1 ← is in slope- intercept form
with slope m = 4
Parallel lines have equal slopes, then
y = 4x + c ← is the partial equation
To find c substitute (- 3, 7) into the partial equation
7 = - 12 + c ⇒ c = 7 + 12 = 19
y = 4x + 19 ← equation of parallel line
pleaseee answer this question quickly.. I will give brainliest MAKE SURE ITS RIGHT
Answer:
JKM is acute and MKL is obtuse
Step-by-step explanation:
because an acute triangle's interior angles are always 180° and an obtuse triangle's sum is greater than 90°
1. A rectangular pyramid is intersected by a plane to create the frustum shown. If the height of the original pyramid is 14 m, what is the volume of the frustum?
10 m
4 m
8 m
6 m
12m
The volume of the frustum that is shown in the diagram is: C. 256 m³.
What is the Volume of Frustum?The volume of frustum = Volume of the bigger rectangular pyramid - Volume of smaller rectangular pyramid.
Find the volume of the original (bigger) rectangular pyramid:
Volume of rectangular pyramid = 1/3(lwh) = 1/3(12 × 6 × 14)
Volume of rectangular pyramid = 336 m³
Find the volume of the smaller (the top that was removed) rectangular pyramid:
Volume of rectangular pyramid = 1/3(lwh) = 1/3(10 × 4 × 6)
Volume of rectangular pyramid = 80 m³
The volume of frustum = Volume of the bigger rectangular pyramid - Volume of smaller rectangular pyramid = 336 - 80 = 256 m³.
Thus, the volume of the frustum that is shown in the diagram is: C. 256 m³.
Learn more about volume of frustum on:
https://brainly.com/question/1641223
PLEASE HELPPP I'LL GIVE OUT BRAINLIEST !!!!!
Does (3, 3) make the equation y = 5x true?
Answer:
y = 5x
In the coordinate (3, 3), the first number is the x value and the second number is the y value.
So, does 3 = 5(3).
The answer is no, so this coordinate does not make the equation true.
Let me know if this helps!
Answer: No, the given point does not make the equation true.
===========================================================
Explanation:
There are three different ways to approach this.
One way is to plug x = 3 into the equation to find that
y = 5x
y = 5*3
y = 15
But that doesn't match up with y = 3 from the point (3,3). So we see that (3,3) is not a solution to y = 5x.
------
Or another method we could do is plug x = 3 and y = 3 to find a contradiction
y = 5x
3 = 5*3
3 = 15
The contradiction being that 3 on the left side doesn't match with 15 on the right side. The false equation at the end means y = 5x is false for (x,y) = (3,3), and therefore this point is not a solution to y = 5x.
------
The third method involves graphing the line y = 5x. You can see that (3,3) is not on the line, which visually confirms the results of the previous two sections. So for a point to be a solution, it must be on the line.
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Answer:
a7 = 55 + (7-1) 10
Step-by-step explanation:
See,
It's given that it will take 7 hours for Jiya to move.
$55 are charged for 1 (first) hour. Now, 6 hours are left (unpaid). $10 per every hour after that.
Among the total 7 hours, the payment for first hour is done ($55) so we are left with the other 6 hours multiplied by 10.
Therefore, the correct option is:
a7 = 55 + (7-1) 10
What should I write?
Step-by-step explanation:
Let's say we have (m*x+d)², with m and d representing constant values (a number). If we expand, we can see that
(m*x+d)² = (m*x+d) * (m*x+d) = m²*x²+2*m*x*d + d². Matching that up with
ax²+bx+c, the value multiplied by x² in our factored perfect square is m² (so m²=a), the value multiplied by x is 2md ( so 2md = b), and the constant is d².
Going back to the problem, we want to see how the values of a and c correspond with a perfect square trinomial. In our perfect square of (m*x+d)², our resulting trinomial has m² = a and d² = c. This points to the fact that a must be a square of something (for example, if a = 1, √1=1, so this works) as well as c if they are part of a perfect square trinomial. If a and c are both squares of other numbers, then it is possible that ax²+bx+c is a perfect square trinomial. If they are not, then it is not possible
What is the minimum Valium of this function? F(x)=150•sin(3•x)
A=150
B=-150
C=200
D=-200
Answer:
B -150.
Step-by-step explanation:
The minimum value of a sine is -1
So the answer is 15 * - 1 = -150.
Answer:
-150
Step-by-step explanation:
F(x)=150•sin(3•x)
The minimum that sin takes is negative 1
so 150(-1) = -150
The minimum of f(x) is -150
Find the equation of the linear function represented by the table below in slope-intercept form.
Helpp plzz
Answer:
Let's first find the slope.
-13 - (-8) / 2-1
-5/1
-5
The slope is -5.
The y intercept, or where the line crosses the y=axis, is equal to -3.
So, the equation is y=-5x-3
Let me know if this helps!
Please I need help will get max points as many as
Answer:
ur answer is 199 thank me later
Answer:
194 ft²
Step-by-step explanation:
Area of rectangle R1 = length * width
= 8 * 5
= 40 square feet
Area of rectangle R2 = 14 * 11
= 154 square feet
Area of the figure = 40 + 154 = 194 ft²
help..lol i dont need help just to lazy
Answer:
C. -2(-2)
Step-by-step explanation:
A. -2(-1/5) = 1
B. -2(1/2)=1
C. -2(-2)=4
D. -2(2)=-4
simplify [tex]x^{2} +10x+9[/tex]
Answer:
Step-by-step explanation:
[tex]\displaystyle \Large \boldsymbol{} x^2+10x+9=0 \\\\ x^2+\underbrace{x+9x}_{10x}+9=0 \\\\x^2+x+\underline9x+\underline9=0 \\\\x(x+1)+9(x+1)=(x+9)(x+1)[/tex]
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNKW THE ANSWER!!
Answer: will be D
Step-by-step explanation:
The perimeter of a rectangle is 102 inches. The length is 5 inches greater than the width.
Answer:
w = 23
l = 28
Step-by-step explanation:
w = width
l = w+5
P = 2 (l+w)
102 = 2( w+5+w)
102 = 2(2w+5)
Divide each side by 2
51 = 2w+5
Subtract 5
46 = 2w
Divide by 2
23 = w
The width is 23 and the length is 23+5 = 28
Answer:
Length=28
Width=23
Step-by-step explanation:
All I did was basically trial and error, to be honest.
The entire group your sample is attempting to describe is known as the ____________.
A. population
B. subgroup
C. census
D. organization
Answer:
Population
Step-by-step explanation:
A.
A population is the entire group that is being studied while a sample is a subset of the population that is being studied.
Rút gọn bthuc
7x(4y-x) + 4y(y-7x) - (4y^2 -7x)
¢✓¢==¢=
Step-by-step explanation:
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What is the domain of G
Answer:
D: {-6, 6}
Step-by-step explanation:
The domain are all the possible values for x. For this graph in the x-position, it starts from -6 to +6. Therefore, the domain will be {-6,6}.
Answer:
[tex]-6\leq x\leq 6[/tex]
[tex]x[/tex] ∈ [tex][-6, 6][/tex]
Step-by-step explanation:
The domain is the set of all numbers for which a function is defined. As one can see on the given graph, the function spans between the numbers (-6) and (6). Therefore, the function is defined between the numbers (-6) and (6). The closed dots on either end of the function signify that the function includes these values. Thus, the domain of the function is as follows:
([tex]-6\leq x\leq 6[/tex])
In set notation,
([tex]x[/tex] ∈ [tex][-6, 6][/tex])
What are the end behaviors of f(x) = -2(x-17)^4?
O A. Both ends go up.
O B. The left end goes down; the right end goes up.
C. The left end goes up; the right end goes down.
о
D. Both ends go down.
Answer:
D. Both ends go down.
Step-by-step explanation:
f(x) = -2(x-17)^4
As x goes to -∞
f(-∞) = -2(-∞)^4 = -2 (∞) = -∞
As x goes to ∞
f(∞) = -2(∞)^4 = -2 (∞) = -∞
Both ends go to -∞, or go down
What is the volume of the rectangular prism in simplest terms?
Answer:
V=w*h*l
Step-by-step explanation:
w=width
h=height
l=length
volume = w*h*l
volume = w*h*l
volume = w*h*l
y is inversely proportional to V1+x.
When x = 8, y = 2.
Find y when x = 15.
Answer:
y = 1.5
Step-by-step explanation:
Given x is inversely proportional to [tex]\sqrt{1+x}[/tex] , then the equation relating them is
y = [tex]\frac{k}{\sqrt{1+x} }[/tex] ← k is the constant of proportion
To find k use the condition when x = 8, y = 2
2 = [tex]\frac{k}{\sqrt{1+8} }[/tex] = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )
6 = k
y = [tex]\frac{6}{\sqrt{1+x} }[/tex] ← equation of proportion
When x = 15 , then
y = [tex]\frac{6}{\sqrt{1+15} }[/tex] = [tex]\frac{6}{\sqrt{16} }[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
Hello!! Please help me ASAP
Using special right triangles show and explain all work for each problem. Each solution and work should demonstrate your understanding of Special Right Triangles (30-60-90 and 45-45-90)
Find the missing side length and angle of this triangle. I've attached the triangle.
Answer:
Step-by-step explanation:
The basic 30-60-90 triangle ratio is:
Side opposite to 30° angle is : x
Side opposite to 60° angle is : x √3
Side opposite to 90° angle is : 2x
From the diagram we learn that
x√3 = 10
[tex]x = \frac{10}{\sqrt{3}}=\frac{10*\sqrt{3} }{\sqrt{3}*\sqrt{3}}\\\\x=\frac{10\sqrt{3}}{3}= 5.77\\[/tex]
∠T = 30°, Side opposite to ∠T is AC = 5.77
∠A = 90°, side opposite to ∠A is TC = 2x = 2*5.77 = 11.54
write the expression fourteen added to the product of seven and a number
Answer:
(7×x)+14
Step-by-step explanation: Because we have 14 added to something, we will need a + to whatever we are adding to. The product of 7 and a number is 7×x because product is the number you get after multiplication. So we get 7×x+14. You dont need parenthesis
Hope this helps!
6 times a number increased by 11 is equal to 17. What is the number?
Let the no be x
ATQ
[tex]\\ \sf\longmapsto 6x+11=17[/tex]
[tex]\\ \sf\longmapsto 6x=17-11[/tex]
[tex]\\ \sf\longmapsto 6x=6[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{6}{6}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Answer:
1
Step-by-step explanation:
let the number be x
and solve it
Can anyone help me with this?
Answer:
baba booey
Step-by-step explanation:
444
factor the quadratic expression x2 +16x+48
Answer:
(x+4)(x+12)
Step-by-step explanation:
Answer:
(x +4) (x+12)
Step-by-step explanation:
product 48
Sum 16 ( 12 and 4)
(x2 +12x) +(4x +48)
=(x+4) (x+12)
What is the domain of the function shown below?
[tex]y = log_{3}(x + 2) [/tex]
A. All real numbers greater than -2
B. All real numbers less than 2
C. All real numbers
D. All real numbers greater than 0
Answer:
A
Step-by-step explanation:
A logarithmic function, log(x) has a domain x>0. For this logarithmic equation x+2>0, x>-2.
What is the answer to this geometry problem?
Answer:
[tex]x=29[/tex]Step-by-step explanation:
Here, MN= NP
→ [tex]128=2x+70[/tex]
→ [tex]2x=128-70[/tex]
Subtract :-
→ [tex]2x=58[/tex]
Divide both sides by 2:-
→ [tex]\frac{2x}{2}=\frac{58}{2}[/tex]
→ [tex]x=29[/tex]
OAmalOHopeO
What is the measure of an interior angle of a regular octagon? O A) 120° OB) 135° O C) 145° OD) 160
Answer:
B = 135
Step-by-step explanation:
An octagon has 8 equal sides, and in total is 1080 degrees. Each angle is 135 degrees which adds up to 1080. Or:
135 × 8 = 1080.
Hope this helped.
Find the least length of a rope which can be cut into whole number of pieces of lengths 45cm, 75cm and 81 cm
