Answer:
6Step-by-step explanation:
[tex]f(n+1)=f(n)-2\\\\f(1)=10\\f(2)=f(1)-2=10-2=8\\f(3)=f(2)-2=8-2=6[/tex]
Answer:
B) 6
Step-by-step explanation:
Solve 4x+2=12 for using the change of base formula logby=logy over logb
Answer:
log₄ 10 = log₁₀ 10 / log₁₀ 4
Step-by-step explanation:
Taking the x to be a power then;
[tex]4^x +2 =12[/tex]
[tex]4^x = 12-2[/tex]
[tex]4^x=10[/tex]
Introduce log on both sides
x log 4= log 10
x= log 10/log 4
log₄ 10 = log₁₀ 10 / log₁₀ 4
Answer: x = log₄(3/4) = -0.207
Step-by-step explanation:
when you have the equation:
n^x = b
whe have that:
Logₙ(b) = x
in this case we have the equation:
4^(x+2) = 12
(4^x)*(4^2) = 12
16*4^x = 12
4^x = 12/16 = 3/4
x = log₄(3/4) = -0.207
Write 6.92 x 10-8 in standard notation
Answer:
0.0000000692
Step-by-step explanation:
We are given the following number in scientific notation and we are to express it in standard notation:
[tex] 6 . 9 2 \times 1 0 ^ - 8 [/tex]
We know that:
[tex] 6 . 9 2 \times 1 0 ^ { - 8 } = \frac { 6 . 9 2 } { 1 0 ^ { 8 } } = \frac { 6 . 9 2 } { 1 0 0 , 0 0 0, 0 0 0 } = 0 . 0 0 0 0 0 0 0 6 9 2 [/tex]
Therefore, the answer in standard notation is 0.0000000692.
Answer:
0.0000000692
Step-by-step explanation:
6.92 x [tex]10^{-8}[/tex]
= 6.92 x 0.00000001
= 0.0000000692
Rewrite the equation below in standard form y=-4x-2
Answer:
4x + y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = - 4x - 2 ( add 4x to both sides )
4x + y = - 2 ← in standard form
Answer:
4x + y = -2
Step-by-step explanation:
Please help me with question 5
Answer:
99x +84 ≤ 1,150
Step-by-step explanation:
Her budget is $1,150, this means that the price of all her purchases cannot exceed it. In other words, the sum of all her purchases must be less or equal to 1,150.
To find how many watches she can buy, you need to multiply it by the price of the watches, which is $99, so it will be 99x.
As for the shirts, she spent $84.
So the inequality equation you will need will be the sum of the price of watches and shirts is less than or equal to 1,150.
99x + 84 ≤ 1,150
What is the definition of a base number
Answer:
main number
Step-by-step explanation:
Final answer:
A base number in mathematics is the number raised to a power, where in scientific notation it is always 10, whereas in economic terms, a base year is a reference year for economic measurements.
Explanation:
The definition of a base number in mathematics generally refers to the number that is being raised to a certain power. In the context of scientific notation, the base number is always 10. This is used to succinctly represent very large or very small numbers in the form N x 10^n, where N is a number greater than or equal to 1 and less than 10, and n is a positive or negative integer; for example, 10^0 = 1. However, the concept of a base extends beyond just the number 10; any number can act as a base in different mathematical contexts.
When discussing numbers in a positional numeral system, the base determines the value of each digit in the number and how those digits are combined to represent the overall number. For instance, in the base-10 system, the digits 0 through 9 are used, and the position of each digit indicates how many multiples of powers of 10 it represents. Finally, in the context of economic indexes, a base year is a reference year against which economic growth or inflation is measured.
The diagram below gives the dimensions of a swimming pool.
- 18 ft
What is the total area of the swimming pool? Show your work. (2 points)
b. What is the perimeter of the swimming pool? Show your work. (2 points)
Click or tap here to enter text.
Answer:
[tex]area = base \times hight 36 \times 18 \: ad perimeter \: base \times base \times hight \times hight36 \times 36 \times 18 \times 18[/tex]
Area is given by base * the Hight which gives the area of the pool
which of the following is an arithmetic sequence?
Answer:
B
Step-by-step explanation:
And arithmetic sequence is a sequence in which the difference between each of the numbers are constant.
It is not A, because the difference between 3 and 9 is positive 6, and the difference between 9 and 81 is positive 72.
It is not C, because the difference between 4 and 1 is -3, and the difference between 1 and 4 is positive 3.
It is not D, because the difference between 2 and -2 is -4, and the difference between -2 and 2 is positive 4.
And it is B because the numbers maintain a constant difference between each other, which is -3.
Answer:
B
Step-by-step explanation:
An arithmetic sequence has a common difference (d) between consecutive terms.
The only sequence with a common difference is B
1 = 4 = - 3
- 2 - 1 = - 3
- 5 - (- 2) = - 5 + 2 = - 3
PLZ HURRY IT'S URGENT!
Jeff is buying an ice-cream sundae. There are 2 sizes of sundaes, 14 different ice-cream flavors, and 4 different toppings.
How many ways can Jeff choose a sundae?
A.
20
B.
56
C.
32
D.
112
Jeff can make his choices independently so there are a total of
[tex] 2 \times 14 \times 4[/tex]
different sundaes.
Answer: D. 112
Answer:
D 112
Step-by-step explanation:
Just multiply the number of different ways to choose things to come up with all your possibilities.
That is you just do 2(14)(4)=28(4)=112
Which is 6 3/4 (2/9) simplified?
Answer:
3/2
Step-by-step explanation:
6 3/4 (2/9)
(27/4)(2/9)
4 divided by 2 is 2.
27 divided by 9 is 3.
Answer: 3/2
Find the lateral area of a rectangular prism with l=6, w=4, h=2
Answer:
40 square units
Step-by-step explanation:
The surface area is given by
LA = 2(wh+lh)
where h is the height l is the length and w is the width
We do not include the top or bottom
We know l=6 w=4 and h=2
LA = 2 ( 4*2 + 6*2)
lA = 2( 8+12)
= 2 (20)
= 40
Consider a triangle ABC like the one below. Suppose that A = 27°, C = 78°, and b = 66. (The figure is not drawn to scale.) Solve
the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
We don't get to see the figure but we don't need it.
The remaining angle B is
B = 180 - 27 - 78 = 75°
The Law of Sines gives the remaining sides
[tex]\dfrac{a}{\sin A} =\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]a = \dfrac{b \sin A}{\sin B} = \dfrac{66 \sin 27}{sin 75} \approx 31.0203[/tex]
[tex]c = \dfrac{b \sin C}{\sin B} = \dfrac{66 \sin 78}{sin 75} \approx 66.8350[/tex]
Answer: B=75°, a=31.0, c=66.8
No need for "or" on this one. That happens when we know the sine of an angle so there are two possibilities for the angle, an acute one and an obtuse one that's supplementary.
14. Which of the following is the largest?
2^50 3^40 4^30 5^20
2. 3^40
3. 4^30
4. 5^20
1. 2^50
A 700 4/7 meter long cloth is cut into equal pieces measuring 1 2/5 meter each how many such small pieces are there?
Step-by-step explanation:
(700 4/7) ÷ (1 2/5)
Write the fractions in improper form:
(4904/7) ÷ (7/5)
To divide by a fraction, multiply by the reciprocal:
(4904/7) × (5/7)
24520/49
500 20/49
There are 500 pieces.
Answer:
(700 4/7) ÷ (1 2/5)
Write the fractions in improper form:
(4904/7) ÷ (7/5)
To divide by a fraction, multiply by the reciprocal:
(4904/7) × (5/7)
24520/49
500 20/49
There are 500 pieces.
The midpoint M of CD has coordinates (6, 6). Point D has coordinates (10, 4). Find the coordinates of point C.
Write the coordinates as decimals or integers.
Final answer:
To find the coordinates of point C when given the midpoint M and point D, we find the average of the endpoints' coordinates. Solving the equations, we find that the coordinates of point C are (2, 8).
Explanation:
The student is asking to find the coordinates of point C given that the midpoint M of line segment CD is at (6, 6), and point D is at (10, 4). To find point C, we use the concept that the midpoint's coordinates are the average of the coordinates of the endpoints of the segment. That means:
The x-coordinate of C can be found by the equation 6 = (xC + 10) / 2 which leads to xC = 2(6) - 10,
The y-coordinate of C can be found by the equation 6 = (yC + 4) / 2 which leads to yC = 2(6) - 4.
Solving for xC and yC, we find:
xC = 12 - 10 = 2,
yC = 12 - 4 = 8.
Therefore, the coordinates of point C are (2, 8).
find a ordered pair to represent a in the equation a=b+c if b= (6,3) and c =(-4,8)
Answer:
So ordered pair a is (2,11)
Step-by-step explanation:
We are given
a = b+c
and ordered pair b =(6,3) and ordered pair c =(-4,8)
Putting values of b and c in the given equation and adding x and y coordinates of b and c we can find ordered pair a.
a=(6,3)+(-4,8)
a =(6-4,3+8)
a =(2,11)
So ordered pair a is (2,11)
Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis
The volume of the solid is:
(Type an exact answer
cubic units)
Check the picture below, that enclosed area is pretty much our "washer".
now, to get the outer radius, or "farther" radius from the axis of rotation, what I usually do is, use the f(x) - g(x) to get the area under the curve, using the axis of rotation for g(x).
[tex]\bf \stackrel{\textit{top, f(x)}}{4\sqrt{x}}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{farthest radius}}{4\sqrt{x}-0\implies 4\sqrt{x}} \\\\\\ \stackrel{\textit{top, f(x)}}{x}~~-~~\stackrel{\textit{bottom, g(x)}}{(0)}\implies \stackrel{\textit{closest radius}}{x-0\implies x} \\\\[-0.35em] ~\dotfill\\\\ 4\sqrt{x}=x\implies \stackrel{\textit{squaring both sides}}{16x=x^2\implies }16x-x^2=0[/tex]
[tex]\bf x(16-x)=0\implies x= \begin{cases} 0\\ 16 \end{cases}\qquad \qquad \impliedby \textit{these are the bounds} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int\limits_{0}^{16}~\pi [(4\sqrt{x})^2-(x)^2]dx\implies \pi \int\limits_{0}^{16}[16x-x^2]dx\implies \pi \int\limits_{0}^{16}16x~~-~~\pi \int\limits_{0}^{16}x^2[/tex]
[tex]\bf \pi \left. 16\cdot \cfrac{x^2}{2} \right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16}\implies \left. \pi 8x^2 \cfrac{}{}\right]_{0}^{16}-\left. \cfrac{\pi x^3}{3} \right]_{0}^{16} \\\\\\ \left( \pi [2048]-\pi [0] \right)-\left(\left[ \cfrac{4096\pi }{3} \right]-[0] \right)\implies 2048\pi -\cfrac{4096\pi }{3} \implies \cfrac{2048\pi }{3}[/tex]
Mon wants to make 5 lbs of the sugar syrup. How much water and how much sugar does he need to make 1.5% syrup?
Answer:
He needs 0.075 lbs of sugar and 4.925 lbs of water.
Step-by-step explanation:
Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.
Note
5 lbs - 100%
x lbs - 1.5%
Write a proportion:
[tex]\dfrac{5}{x}=\dfrac{100}{1.5}[/tex]
Cross multiply:
[tex]100x=5\cdot 1.5\\ \\100x=7.5\\ \\x=\dfrac{7.5}{100}=0.075[/tex]
So, he needs 0.075 lbs of sugar and 5 - 0.075 = 4.925 lbs of water.
Is 6 a solution to the equation below. Yes or No?
6x + 4 = 42
Answer:
no
Step-by-step explanation:
6 times 6 is 36 and 36 plus 4 is 40 not 42
convert 7.2•10•-3 to standard form
Answer:
0.0072
Step-by-step explanation:
7.2 x [tex]10^{-3}[/tex]
=7.2 x 0.001
=0.0072
Answer:
0.0072
Step-by-step explanation:
The given expression is as follows:
7.2 * 10^(-3)
This expression is in scientific notation, We need to convert it to standard notation for which we will convert the power of 10 to 0.
The power of 10 here is -3. So we will move the decimal point 3 places to the left and get:
= 0.0072 x 10^0
= 0.0072 x 1
= 0.0072
find f (-3) if f(x) = x^2
Konichiwa~! My name is Zalgo and I am here to help you out today. If f were to equal -3, first we need to put -3 into the equation. It would look like "f(-3)=x^2". The answer to that equation is 9.
I hope that this helps! :T
"Stay Brainly and stay proud!" - Zalgo
33
Ebony is making a scale drawing of her farm. The farm has a circular well with a circumference
of 47 feet. In the drawing, the area of the well will be 0.641 square centimeters.
What scale is Ebony using?
A 1 cm = 0.16 ft
B 1 cm = 2.5 ft
C 1 cm = 5 ft
D 1 cm = 6.25 ft
Answer:
B
Step-by-step explanation:
Circumference of a circle is:
C = 2πr
Area of a circle is:
A = πr²
The circumference of the well is 47 ft and the area of the well in the drawing is 0.641 cm². If we say r is the radius of the circle on the drawing in centimeters and R is the actual radius of the well in feet, then:
47 = 2πR
0.641 = πr²
Solving for each:
R = 47 / (2π) ≈ 7.48 feet
r = √(0.641 / π) ≈ 0.452 cm
The scale is the ratio of R / r:
R / r = (7.48 ft) / (0.452 cm) = 16.6 ft/cm
So 1 cm = 16.6 ft.
This isn't one of the options. Are you sure you copied the problem correctly?
Maybe you meant that the circumference is 4π feet, and the area is 0.64π cm². If so:
R = 4π / (2π) = 2 feet
r = √(0.64π / π) = 0.8 cm
R / r = (2 feet) / (0.8 cm) = 2.5 ft/cm
So 1 cm = 2.5 ft.
Which of the following shows the polynomial below written in descending order
When it asks for descending order of the polynomial it wants you to put the exponents in order from largest to smallest like so...
C. [tex]x^{12} +3x^{7} + 4x^{3} -9x[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Option C
Step-by-step explanation:
In this question the given polynomial is 4x³ + 3x⁷ - 9x + x¹²
If we rewrite it in the descending order of the powers then the polynomial will be
x¹² + 3x⁷ +4x³ + 9x
This polynomial matches with option C.
Option C is the answer.
What is the sum of 4ft 4 in and 1 ft 11in
Answer:
6ft 3in
Step-by-step explanation:
4ft + 1ft = 5ft
4in +11in= 15in
15in =1ft and 3in
5ft+ 1ft 3in= 6ft 3in
The formula F=mv^2/r gives the centripetal force F of an object of mass m moving along a circle of radius r, where v is the tangential velocity of the object. Solve the formula for v. Rationalize the denominator. Calculate the tangential velocity of a 100kg object with a force of 50 Newton, moving along a circular path with a diameter of 150 meters.
Answer: (It didn't say what to have the units in so I assumed as is)
(pm) 5sqrt(6)/2
(pm) 6.12372 (rounded version)
Step-by-step explanation:
F=mv^2/r (Given)
rF=mv^2 (Multiply both sides by r)
rF/m=v^2 (Divide both sides by m)
v=(pm) sqrt(rF/m) (Square root both sides)-(pm means plus or minus)
v=(pm) sqrt(rF)/sqrt(m)
v=(pm) sqrt(rF)sqrt(m)/m (I had multiply top and bottom by sqrt(m))
v=(pm) sqrt(rFm)/m
*sqrt( ) means square root of whatever is in the ( ) that follows the sqrt
Now find v if F=50, m=100 kg, and r=150/2=75 so plug in
v=(pm) sqrt(75*50*100)/100
v=(pm) sqrt(375000)/100 OR
v=(pm) sqrt(100*25*3*25*2)/100
v=(pm) 10*5*sqrt(3)*5*sqrt(2)/100
v=(pm) 250sqrt(6)/100
v=(pm) 2.5sqrt(6)
v=(pm) 5sqrt(6)/2
Or if you want a decimal number rounded, it would be (pm) 6.12372
The formula for calculating the centripetal force of an object in circular motion can be rearranged to find velocity. You compute the tangential velocity of a 100kg object with a force of 50N, moving on a circular path with a diameter of 150m, by plugging these values into this rearranged formula. This calculation results in a value of approximately 61.24 m/s for the tangential velocity of the object.
Explanation:The formula F=mv^2/r calculates the centripetal force (F) of an object of mass (m) moving in a circular path with a radius (r). You can solve this formula for velocity (v) by first multiplying both sides by r, making the formula Fr=mv^2. Then, divide both sides by m, which makes the formula Fr/m = v^2. Finally, take the square root of both sides to get v = √(Fr/m).
To calculate the tangential velocity of a 100kg object with a force of 50 Newton, moving along a circular path with a diameter of 150 meters, you must first divide the diameter of the circle by 2 to get the radius, 75 meters. Next, substitute the given values into the formula; v = √((50N * 75m) / 100kg). Therefore, the tangential velocity is approximately √(3750N·m/kg) = 61.24 m/s.
Learn more about Tangential Velocity here:https://brainly.com/question/33443064
#SPJ3
Which scatterplots display an example of a cluster ? Check all that apply
Answer:
1st and 3rd options
Step-by-step explanation:
We have been given three scatter plots. We are asked to choose the plots with cluster.
We know that cluster in a dot plot is formed when many data points lie in a small interval.
We can see that graphs represented by 1st option and 3rd option have many data points in a small interval, therefore, 1st and 3rd options are correct choice.
Answer:
Step-by-step explanation:
Convert the fraction to a mixed number
5/2=a b/2
Answer:
2 1/2
Step-by-step explanation:
5 is 2 more than 2 so the the first part would be 2.
[tex]\dfrac{5}{2}=\dfrac{2\cdot2+1}{2}=2\dfrac{1}{2}[/tex]
Given x = wavelength and y = frequency, solve for the wavelength for the given type of radiation.
y= 3×10^8 m/s /x
Answer: 1 x 10^27 m
Step-by-step explanation:
what is the period of the function y=2sinx?
Answer:
C. 2π
Step-by-step explanation:
Given a wave of the equation y= a sin bx where a and b are constants, then the amplitude is a while the period is 360°/b.
360°= 2π radians
For the provided function, the value of b =
Thus period = 2π/1
=2π radians
Answer: 2 Pi
Step-by-step explanation:
What is the volume of the sphere shown below with a radius of 6
Answer:
[tex]\large\boxed{V=288\pi}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a sphere:}\\\\V=\dfrac{4}{3}\pi R^3\\\\R-radius\\\\\text{W have the radius}\ R=6.\ \text{Substitute:}\\\\V=\dfrac{4}{3}\pi(6^3)=\dfrac{4}{3}\pi(216)=4\pi(72)=288\pi[/tex]
Is 3[g(x)] = x a linear function?
Answer: no
Step-by-step explanation:
Linear functions are straight lines and are also written in the form y=mx+b
The linearity of 3[g(x)] = x depends on the form of g(x). If g(x) is linear, such as g(x) = ax, then the equation is linear. Otherwise, if g(x) involves non-linear operations, the overall equation will not represent a linear function.
Whether or not the equation 3[g(x)] = x represents a linear function depends on the form of g(x). If g(x) is a linear function, then the equation represents a linear transformation. If g(x) is nonlinear, then the overall function is not linear.
For example, if g(x) = exp(3x), the relationship is non-linear due to the exponential function. However, if the g(x) function is a simple linear function like g(x) = a₁x, with a constant coefficient, the equation maintains its linearity. In this scenario, the function could even represent a constant multiple of the identity function, where g(x) = x/3.
It is important to note that in the context of mathematics, understanding whether a function is linear involves recognizing if it can be written in the form of g(x) = mx + b, where m and b are constants, and the function results in a straight line on a graph.