Answer:
Explicit form: [tex]a_n=8+4n[/tex]
Seventh term: [tex]a_7=36[/tex]
You gave the recursive form:
[tex]a_n=a_{n-1}+4 \text{ with } a_1=12[/tex]
Step-by-step explanation:
You already have the recursive formula which is:
[tex]a_n=a_{n-1}+4[/tex] where [tex]a_1=12[/tex].
Maybe you looking for the explicit form and also the 7th term?
You were just looking for the 7th term. Sometimes you can read the recursive formula pretty easily and understand the pattern that is happening.
[tex]a_{n-1}[/tex] is the term right before [tex]a(n)[/tex]. Just like [tex]a_5[/tex] would be the term right before [tex]a_6[/tex].
Anyways becak to our recursive for a sequence that was given:
[tex]a_{n}=a_{n-1}+4[/tex] says term=previous term+4.
So you adding 4 over and over to generate the terms of a sequence. This is arithmetic sequence because it is going up by same number (or could go down by same number). The common difference is 4.
[tex]a_1=12[/tex]
[tex]a_2=12+4=16[/tex]
[tex]a_3=16+4=20[/tex]
[tex]a_4=20+4=24[/tex]
[tex]a_5=24+4=28[/tex]
[tex]a_6=28+4=32[/tex]
[tex]a_7=32+4=36[/tex]
Now if you don't like that. You could just blindly without trying to understand the meaning of it just plug numbers in:
[tex]a_1=12[/tex]
For if we wanted to know the 2nd term; we would plug in 2 for n:
[tex]a_2=a_{2-1}+4[/tex]
[tex]a_2=a_1+4[/tex]
[tex]a_2=12+4[/tex]
[tex]a_2=16[/tex]
Plug in 3 for the 3rd term:
[tex]a_3=a_{3-1}+4[/tex]
[tex]a_3=a_2+4[/tex]
[tex]a_3=16+4[/tex]
[tex]a_3=20[/tex]
Plug in 4 for the 4th term:
[tex]a_4=a_{4-1}+4[/tex]
[tex]a_4=a_3+4[/tex]
[tex]a_4=20+4[/tex]
[tex]a_4=24[/tex]
Plug in 5 for the 5th term:
[tex]a_5=a_{5-1}+4[/tex]
[tex]a_5=a_4+4[/tex]
[tex]a_5=24+4[/tex]
[tex]a_5=28[/tex]
Plug in 6 for the 6th term:
[tex]a_6=a_{6-1}+4[/tex]
[tex]a_6=a_5+4[/tex]
[tex]a_6=28+4[/tex]
[tex]a_6=32[/tex]
Plug in 7 for the 7th term:
[tex]a_7=a_{6-1}+4[/tex]
[tex]a_7=a_5+4[/tex]
[tex]a_7=32+4[/tex]
[tex]a_7=36[/tex]
Now if you look at the points we just got (I will just go up to 4 terms):
n (treat as x) | 1 2 3 4
a(n) (treat as y| 12 16 20 24
The explicit form in not in terms of other terms of the sequence. You are looking here for an equation that relates n (x) to a(n) (y).
I'm just going to use x and y until the end where I will replace them back in terms of n and a(n).
This is a line because the's rise/run (the slope) is the same per choosing of points.
That is the following is true:
[tex]\frac{16-12}{2-1}=\frac{20-16}{3-2}=\frac{24-20}{4-3}[/tex] son on....
These all the the value 4, the same number that the arithmetic sequence is going up by.
So in an arithmetic sequence, the common difference is the slope of the line.
I'm going to use point-slope formula which is [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
So we have m=4 and [tex](x_1,y_1)[/tex] could be any of the 7 we found, but I will choose (1,12) for it:
[tex]y-12=4(x-1)[/tex]
Add 12 on both sides:
[tex]y=12+4(x-1)[/tex]
[tex]a_n=12+4(n-1)[/tex].
This is actually in the form of most books formulas for an explicit form which is [tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term and d is the common difference.
So another way to do the problem:
You would have to know the following are equivalent:
[tex]a_n=a_{n-1}+d[/tex] with [tex]a_1 \text{ is given}[/tex]
and
[tex]a_n=a_1+d(n-1)[/tex].
If you know these are equivalent then you could compare [tex]a_n=a_{n-1}+d[/tex] to [tex]a_n=a_{n-1}+4[/tex] and determine d is 4.
You could also see that [tex]a_1[/tex] is give as 12.
Then you just plug into:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=12+4(n-1)[/tex].
You could also simplify this equation just a bit.
You could distribute and then combine a pair of like terms.
Like so,
[tex]a_n=12+4(n-1)[/tex]
[tex]a_n=12+4n-4[/tex]
[tex]a_n=8+4n[/tex]
A:what are the solutions to the Quadratic equation
x^2 +4=0?
B:what is the factored form of the quadratic equation x^2+4?
Answer:
The correct answer for question A is x=2i or x= -2i
The correct answer for question B is (x+2i)(x-2i)
Step-by-step explanation:
Solution of question A:
x²+4=0
Subtract 4 from both sides.
x²+4-4=0-4
x²=-4
Take square root of both sides
√x²=+/-√-4
We know that i=√-1
So,
x=+/-(√4)(√-1)
x=+/-2i
Therefore x= 2i, x= -2i
Solution of question B:
x²+4
It cannot be factored using real number coefficient. You have to use complex numbers.
As we know -4 =(2i)², so we can write as:
x²+4=x² - (-4)= x²-(2i)²
Now factor using the difference of squares:
x²+4=(x+2i) (x-2i)....
Identify an equation in point-slope form for the line parallel to y=-2/3x+8 that
passes through (4,-5).
O A. y+5 = (x-4)
O B. y 4= {(x+5)
O C. y-5--}(x+4)
O D. 4+5--xx-4)
Answer:
[tex]\large\boxed{y+5=\dfrac{2}{3}(x-4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
Parallel lines have the same slope.
We have the equation in the slope-intercept form (y = mx + b)
[tex]y=-\dfrac{2}{3}x+8\to m=\dfrac{2}{3}[/tex]
Put to the point-slope equation value of the slope and the coordinates of the point (4, -5):
[tex]y-(-5)=\dfrac{2}{3}(x-4)\\\\y+5=\dfrac{2}{3}(x-4)[/tex]
The equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The equation of a line in point-slope form is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is a point on the line.
We are given that the line we want to find is parallel to y = (-2/3)x + 8, which means it has the same slope of -2/3.
We are also given that the line passes through the point (4, -5).
Substituting the values into the point-slope form equation, we get:
y - (-5) = (-2/3)(x - 4)
Therefore, the equation in point-slope form for the line parallel to y = (-2/3)x + 8 that passes through (4, -5) is y - (-5) = (-2/3)(x - 4), which is option C.
Learn more about equations here:
brainly.com/question/10413253
#SPJ7
Kate used 555 grams of wool to knit a sweater, a hat, and a scarf. She used 5 times fewer grams for the hat than for the sweater. She used 5 grams more for the hat than for the scarf. How many grams of wool did she use to knit each item?
Answer:
Sweater =400 grams
Hat =80 grams
Scarf =75 grams
Step-by-step explanation:
The amount of wool used to make a sweater, a hat and a scarf=555 grams
Let the amount of wool used to make a sweater be = x
The amount of wool for the sweater =x/5
The amount of wool used for the scarf=x/5 -5
Total amount of wool used = x+(x/5)+(x/5-5)
x+x/5 +x/5-5=555
Multiply all through by the LCM 5
5x+x+x-25=2775
7x=2800
x=400
Sweater =400 grams
Hat=400/5=80 grams
Scarf =400/5 -5=75 grams
P^-4q^3r^-7 over p^-2q^3p^-2 simplify
[tex]\bf \cfrac{p^{-4}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^{-7}}{p^{-2}~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^{-2}}\implies \cfrac{1}{p^{4}p^{-2}p^{-2}r^7}\implies \cfrac{1}{p^{4-2-2}r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}[/tex]
Answer:
[tex]\large\boxed{r^{-7}=\dfrac{1}{r^7}}[/tex]
Step-by-step explanation:
[tex]\dfrac{p^{-4}q^3r^{-7}}{p^{-2}q^3p^{-2}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=p^{-4-(-2)-(-2)}q^{3-3}r^{-7}\\\\=p^{-4+2+2}q^0r^{-7}\\\\=p^0q^0r^{-7}\\\\=r^{-7}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{r^7}[/tex]
The function that represents a geometric sequence.
Answer:
C
Step-by-step explanation:
c is the answer to your question
Answer:
C
Step-by-step explanation:
The function f(x) = 2x is a logarithmic function. true or false
Answer:
False.
Step-by-step explanation:
The function f(x) =2x is not an logarithmic function. Rather, it is a linear function. The reason for this is that in f(x) = 2x, there is no log or ln involved on the right hand side of the equation. It is the polynomial of the first degree, which means it is a straight line function. It is important to note that for any value of x, the value of the function changes with the same proportion. This is because the derivative of the function is a constant, which means that the rate of change is constant. The graph of the function will be a line passing from the origin and (1,2) and will have the positive slope. Therefore, f(x) is not a logarithmic function, which means that the statement is false!!!
Alexis has a stamp collection of 3 cent stamps and 8 cent stamps. She has 1 less 8 cent stamps as 3 cent stamps. If the collection has a face value of 69 cents, how many of each does she have?
She has ____ 3 cent stamps and _____ 8 cent stamps.
Answer:
She has seven 3 cents stamps and six 8 cents stamps.
Step-by-step explanation:
7*3 = 21
6*8 = 48
48 + 21 = 69
Answer: She has SEVEN 3 cent stamps and SIX 8 cent stamps.
Step-by-step explanation:
Let be "x" the number of 8 cent stamps and "y" the number of 3 cent stamps.
Set up the following system of equations:
[tex]\left \{ {{x=y-1} \atop {8x+3y=69}} \right.[/tex]
Substitute the first equation into the second one and the solve for "y":
[tex]8(y-1)+3y=69\\\\8y-8+3y=69\\\\11y=77\\\\y=7[/tex]
Substitute the value of "y" into the first equation:
[tex]x=7-1\\\\x=6[/tex]
PLZ QUICK ILL GIVE U BRAINLIEST I NEED HELP FAST!!!
Based on the figure below, what is the value of x? A right angle is shown divided in two parts. The measure of the angle of one part is 30 degrees and the measure of the other part is 5x plus 15 degrees. 3 9 12 15
Answer:
x=9
Step-by-step explanation:
90-30= 60
now set 60 = 5x + 15
solve for x
45= 5x
divide by 5
x = 5
what is the slope of the line graphed below (1,1) (2,-2)
Answer:
slope is
Step-by-step explanation:
slope of line is -3
Answer:
The answer is -3.
Step-by-step explanation:
I just got it correct.
What is the surface area of the cone? (radius 10in height 26in)
A) 425pi in2
B) 460pi in2
C) 360pi in2
D) 390pi in2
Answer:
C) 360pi in2
Step-by-step explanation:
Given:
radius, r= 10in
height, h=26in
surface area of the cone, T.S.A= ?
T.S.A=πrl +πr^2
=π(10)(26) +π(10)^2
=260π+100π
=360π^2 !
10.
A bookstore is having a sale. All comic books are reduced 15%. Fill in the blank to show a
correct representation of this sale.
A $20 comic book is reduced to?
[tex]20-20\cdot0.15=\boxed{17}[/tex]
Comic book cost is reduced from 20 dollars to 17 dollars.
Hope this helps.
r3t40
Answer:
A $20 comic book is reduced to $17
Step-by-step explanation:
Consider the provided information.
A bookstore is having a sale. All comic books are reduced 15%.
We need to Fill the blank to show a correct representation of this sale.
A $20 comic book is reduced to?
The cost of books are reduced to 15% that means now you need to pay only 85% of the price.
Therefore,
[tex]\frac{85}{100}\times 20=0.85\times20 =17[/tex]
Hence, A $20 comic book is reduced to $17
What angle is included by AB and BC?
Answer:
B
Step-by-step explanation:
The answer is in the the question "What angle is included by line segments AB and BC?".
I see B in both of those line segments so they both must share the angle B.
Answer:
<B
Step-by-step explanation:
The included angle is the angle between the two sides AB and BC
The included angle is angle B
What is the equation of the line, in general form, that passes through the point (1,1) and has a y-intercept of 2.
(
x - y + 2 = 0
@dry-2=0
Ox-y-2=0
Answer:
x + y - 2 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept.
Put the given y-intercept b = 2 and the coordinates of the point (1, 1) to the equation:
[tex]1=1m+2[/tex] subtract 2 from both sides
[tex]-1=m\to m=-1[/tex]
The equation of a line:
[tex]y=-1x+2\to y=-x+2[/tex]
The general form of an equation of a line:
[tex]Ax+By+C=0[/tex]
Convert:
[tex]y=-x+2[/tex] add x to both sides
[tex]x+y=2[/tex] subtract 2 from both sides
[tex]x+y-2=0[/tex]
how do i do these using the following functions
Step-by-step explanation:
(f+g)(x) means f(x) + g(x).
(f−g)(x) means f(x) − g(x).
So all you have to do is add them and subtract them.
1. (f+g)(x) = f(x) + g(x)
(f+g)(x) = (3x − 7) + (2x − 4)
(f+g)(x) = 5x − 11
2. (f−g)(x) = f(x) − g(x)
(f−g)(x) = (3x − 7) − (2x − 4)
(f−g)(x) = 3x − 7 − 2x + 4
(f−g)(x) = x − 3
3. (f+g)(x) = f(x) + g(x)
(f+g)(x) = (2x + 3) + (x² + ½ x − 7)
(f+g)(x) = x² + 2½ x − 4
4. (f−g)(x) = f(x) − g(x)
(f−g)(x) = (2x + 3) − (x² + ½ x − 7)
(f−g)(x) = 2x + 3 − x² − ½ x + 7
(f−g)(x) = -x² + 1½ x + 10
The volume of a cone is 3.x cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
Answer:
Radius of the cone's base is 3x ....
Step-by-step explanation:
We have given that the volume of a cone is 3πx³
Height = x units.
The volume of a cone of radius r and height h units is given by:
V= 1/3 π r² *h
Simply plug the values given in the question into the above mentioned equation:
1/3πr²*x = 3*π*x³
1/3r²*x= 3x³
r² = 3*3*x³/x
r²=9x²
Taking square root at both sides we get:
√r² =√9x²
r = 3x
Thus the radius of the cone's base is 3x.
Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x. So THE CORRECT Answer is: A) r = 3x
Step-by-step explanation: I just paid for this answer
14. Find the average of the 1000 whole numbers
from 1 to 1000 inclusive.
(A)499.5
(B) 500.0
(C) 500.5
(D) 501.0
Answer:
500.5
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the number of numbers.
The sum of all whole number form 1 to n is n(n + 1)/2.
The sum of all whole numbers from 1 to 1000 is
1000(1000 + 1)/2 = 1000(1001)/2 = 500,500
The average is the sum of the numbers divided by the number of numbers.
average = 500,500/1000 = 500.5
if 2x - 3 + 3x equals -28 what is the value of x
Chapter : Linear equations
Lesson : Math of Junior High School
2x - 3 + 3x = -28
= 5x - 3 = -28
= 5x = -28 + 3
= 5x = -25
= x = -25 / 5
= x = 5
For this case we must find the value of "x" of the following expression:
[tex]2x-3 + 3x = -28[/tex]
We add similar terms:
[tex]5x-3 = -28[/tex]
We add 3 to both sides of the equation:
[tex]5x = -28 + 3[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]5x = -25[/tex]
We divide between 5 on both sides of the equation:
[tex]x = \frac {-25} {5}\\x = -5[/tex]
ANswer:
[tex]x = -5[/tex]
Find the center of a circle with the equation:
x2+y2+10x−16y+75=0
Answer: (-5,8)
Step-by-step explanation: since the radius of a circle square root of 14 so
x² + y² + 10x − 16y + 75 = 0
x² +10x + y² − 16y = -75
x² +10x + 25 + y² − 16y + 64 = -75 + 25 + 64
(x + 5)² + (y − 8)² = 14
ANSWER
The center is
[tex](-5,8)[/tex]
EXPLANATION
The given circle has equation
[tex] {x}^{2} + {y}^{2} + 10x - 16y + 75= 0[/tex]
An easy way to find the center is by comparing to the general equation of the circle
[tex] {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0[/tex]
where (-g,-f) is the center.
By comparing, we have
[tex]2gx = 10x[/tex]
[tex] \implies \: 2g = 10[/tex]
Divide both sides by 2.
[tex]g = 5[/tex]
Also,
[tex]2fy = - 16y[/tex]
[tex]2f = - 16[/tex]
Divide both sides by 2
[tex]f = - 8[/tex]
Therefore the center is
[tex](-5,- - 8) = (-5,8)[/tex]
Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure of ∠ACB is determined to be 38.833°. Find the distance between points A and B (to the nearest meter).
Answer:
= 70 Meters
Step-by-step explanation:
We can use the sine rule as follows:
Angle ABC=180-(70.5+38.833)
=70.667°
Using the sine rule and sides AB, AC and angles ABC and ACB:
b/Sin B=c/Sin C
Replacing with the values above we get:
AC/Sin ABC= AB/Sin ACB
105.6/Sin 70.667=AB/Sin 38.833
AB=(105.6 Sin 38.833)/Sin 70.667
=70.17 meters
The distance between the two points to the nearest meter is 70 meters
Answer:
70 m
Step-by-step explanation:
I got it correct on founders edtell
15 MINUTES LEFT PLEASE!
A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x
and the number of seats in each row by the function g(x) = 5x-2
Which function represents the total number of seats?
65x + 26
65x – 26
65x2 + 26x
65x2 – 26x
Answer:
65x^2 – 26x
Step-by-step explanation:
To determine the total number of seats, take the number of rows and multiply by the number of seats per row
f(x) * g(x)
13x * (5x-2)
65x^2 -26x
Answer:d
Step-by-step explanation:A wedding planner is organizing the seating for a wedding. He can represent the number of rows by the function f(x) = 13x and the number of seats in each row by the function g(x) = 5x – 2.Which function represents the total number of seats?65x + 2665x – 2665x2 + 26x65x2 – 26x
How to solve this problem
Answer:
B: (2, -1)
Step-by-step explanation:
1) First isolate the y in both equations
2) Set the equations equal to each other
3) Solve for x (you should get 2 and 5)
4) Insert the x values back in to get your y values
5) You should have gotten (2, -1) and (5, 2)
These are your two answers, but the question is only asking for one solution and (5,2) isn't one of the options, so it has to be (2,-1).
Not sure how to do this
Answer:
Answer in picture.
Step-by-step explanation:
First step: You must plot the point (-3,5).
To graph this point, start at the origin.
The point says move left 3 and up 5 and put your dot (your point).
Second step: Use your slope to find a second point to plot. The slope is [tex]\frac{-1}{2}[/tex].
Slope is rise/run. So it says down 1 and right 2.
So starting at the first point you plotted and you count down 1 and then go right 2 and put your second point.
Third step: Connect the two points with a straight-edge. Extend in both directions.
The two points I used to graph my line is (-3,5) and (-1,4).
Step-by-step explanation:
[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\Delta y-\text{run up (+) or down (-)}\\\\\Delta x-\text{run to the right (+) or to the left (-) }\\\\\text{We have}\ slope=-\dfrac{1}{2}=\dfrac{1}{-2}\to\Delta y=1\ (\text{1 unit up}),\ \Delta x=-2\ (\text{2 units to the left})\\\\\text{Mark the point (-3, 5) in the coordinates system. Go 1 unit up}\\\text{and 2 units to the left. Mark next point.}\\\text{Draw a line passing through the given points.}\\\\\bold{Look\ at\ the\ picture.}[/tex]
Which of the following data represents an actual probability?
A computer randomly generates 6 out of 100 numbers.
An observer notes the number of pepperoni, cheese, vegetarian pizzas are ordered out of 100 orders.
None of the above.
Answer:
(A.)A computer randomly generates 6 put of 100 numbers.
Step-by-step explanation:
This is an actual probability.
Which answer choice correctly describes the inequality?
Answer:
the Answer is: D
Step-by-step explanation:
so that means he makes 11 dollars an hour so at most he can make that because he can work really work however long which means he can't really have less than 11 dollars an hour therefore its D
A dog begins his stay at the kennel with 25 fleas. Each day, the number of fleas triples. Which of the following statements is true about the function that represents this situation?
The relationship is linear with an increase of 3 fleas per day.
The relationship is exponential, and the number of fleas increases by a factor of 3 per day.
The relationship is exponential, and the number of fleas increases by a factor of 25 per day.
The relationship is linear with an increase of 75 fleas per day.
Answer:
It is the second statement.
Step-by-step explanation:
y = 25(3)^(n - 1) where y = the number of fleas and n = the number of days.
On day 1, y = 25 3^0 = 25
On day 2, y = 25(3^1 = 75
On day 3, y = 25(3) ^2 = 225 and so on.
Exponential growth.
Answer: Second Option
Step-by-step explanation:
Initially there are 25 fleas, and each day triples the amount.
So:
Day 1: 25
Day 2: [tex]25 * 3 = 75[/tex]
Day 3: [tex]25 * (3) ^ 2 = 225[/tex]
Day 4: [tex]25 * (3) ^ 3 = 675[/tex]
Day n: [tex]25 * (3) ^ {n-1}[/tex]
Note that the function that models the number of fleas for day n is an exponential growth function with an increase factor of 3 and an initial quantity of 25. Therefore, the answer is the second option.
z varies directly with x4 and inversely with y.
When x = 2 and y = 4, z = 3.
What is the value of z when x = 4 and y = 9?
Answer:
[tex]z=\frac{63}{4}[/tex]
Step-by-step explanation:
When two variables vary in a directly proportional way, it means that when one variable grows, the other also grows.
This is represented by the following equation
[tex]y = kx[/tex]
Where k is the constant of proportionality
When two variables vary in an inversely proportional way, it means that when one variable grows, the other decreases.
This is represented by the following equation
[tex]y = \frac{k}{x}[/tex]
In this case we know that:
z varies directly with [tex]x^4[/tex] and inversely with y.
We write this as:
[tex]z = k\frac{x ^ 4}{y}[/tex]
We know that When [tex]x = 2[/tex] and [tex]y = 4,\ z = 3[/tex].
So we use this information to find the constant k
[tex]3 = k\frac{2 ^ 4}{4}[/tex]
[tex]3 = k\frac{16}{4}[/tex]
[tex]3 = 4k[/tex]
[tex]k = \frac{3}{4}[/tex]
So the equation is:
[tex]z = \frac{3}{4}\frac{x ^ 4}{y}[/tex]
Finally when x = 4 and y = 9 then:
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z = \frac{3}{4}\frac{4 ^ 4}{9}[/tex]
[tex]z=\frac{63}{4}[/tex]
Some polyhedrons are both prisms and pyramids.
True or False?
Answer:
Some polyhedrons are both prisms and pyramids.- False
The provided statement "Some polyhedrons are both prisms and pyramids" is false.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional and three-dimensional figures.
We have a statement:
Some polyhedrons are both prisms and pyramids.
As we know,
A polygon-based solid figure is known as a polyhedron, for instance, a soccer ball, a cuboid, etc.
A strong figure with two equal bases is a prism for instance: Cube. Cylinder, Cuboid, etc.
A polyhedron with a base and an top at the top is called a pyramid, cone, a pyramid with triangles as its base, etc.
Thus, the provided statement "Some polyhedrons are both prisms and pyramids" is false.
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a^-4+b^2 when a=2 and b=3/4 answer as a reduced fraction
[tex]\bf a^{-4}+b^2\implies \cfrac{1}{a^4}+b^2\qquad \begin{cases} a=2\\ b=\frac{3}{4} \end{cases}\implies \cfrac{1}{2^4}+\left( \cfrac{3}{4} \right)^2\implies \cfrac{1}{16}+\cfrac{3^2}{4^2} \\\\\\ \cfrac{1}{16}+\cfrac{9}{16}\implies \cfrac{1+9}{16}\implies \cfrac{10}{16}\implies \cfrac{5}{8}[/tex]
Match each equation to its factorized version and solution.
Answer:
[tex]24x -{6x}^{2} = 0 \: matches \: with \: 6x(4 - x) \: and \: the \: solution \: x = 0 \ \: or \: \: x = 4[/tex]
[tex]2 {x}^{2} + 6x = 0 \: matches \: with \: 2x(x + 3) = 0 \: and \: the \: solution \: x = 0 \: or \: x = - 3[/tex]
[tex]4x - {x}^{2} = 0 \: matches \: with \: x(4 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 4[/tex]
[tex]14x - {7x}^{2} = 0 \: matches \: with \: 7x(2 - x) = 0 \: and \: the \: solution \: x = 0 \: or \: x = 2
[/tex]
what is the volume of a rectangular prism with the base area of 15m2 and height of 5cm?
a. 70m3
b. 60m3
c. 75m3
d. 65m3
Answer:
The correct answer is option C. 75 m³
Step-by-step explanation:
Points to remember
Volume of rectangular prism = Base area * Height
To find the volume of given prism
Here Base area = 15 m² and
Height = 5 m
Volume = base area * height
= 15 * 5
= 75 m³
Volume of prism = 75 m³
Therefore the correct answer is option C. 75 m³
Answer:
Rectangular Prism Volume = length x width x height
Rectangular Prism Volume = 15 x 5
Rectangular Prism Volume = 75 cubic meters
Step-by-step explanation: