Answer:
See Below
Step-by-step explanation:
When you have a negative exponent, you divide by the exponent hence the flipping. Here is an example to make it easier to explain. Below are some power of ten:
[tex]10^3=1000\\10^2=100\\10^1=10\\10^0 =1\\10^{-1}=\frac{1}{10} =\frac{1}{10^1} \\10^{-2}=\frac{1}{100} =\frac{1}{10^2}[/tex]
When you go from an exponent to the one below it, you divide by the base. For example, to go from [tex]10^3[/tex] to [tex]10^2[/tex], you divide by ten. This is the same principle used to find the values of negative exponents. [tex]10^0[/tex] is [tex]10^1[/tex] divided by 10, so [tex]10^{-1}[/tex] should be [tex]10^0[/tex] divided by ten. [tex]10^0[/tex] is 1, making the value of [tex]10^{-1}[/tex] as [tex]\frac{1}{10}[/tex]. When you divide by ten, you multiply by [tex]\frac{1}{10}[/tex], this effect makes the exponent stack on the bottom and correspond to the magnitude of the power.
For this specific example, we can write:
[tex]2x^{-2}[/tex]
We are raising x to the power of negative 2, so we can say it is the same as [tex]\frac{1}{x^2}[/tex]. We are also multiplying by 2, so that's how we get [tex]\frac{2}{x^2}[/tex]
If you need more of a visual, here are the powers of x:
[tex]x^2\\x^1=\frac{x^2}{x} \\x^0=\frac{x^1}{x}=1 \\x^{-1}=\frac{1}{x} \\x^{-2}=\frac{x^{-1}}{x}=\frac{1}{x*x}=\frac{1}{x^2}[/tex]
And we just multiply 2 times the value of [tex]x^{-2}[/tex].
Hope this helps.
A room has a length of 12 metres and width of 5 metres. What is the area of the room?
Working out please
Answer:
60 sq.mStep-by-step explanation:
Given,
Length of the room = 12m
Width of the room = 5m
Therefore,
Area of the room = l × w
= 12m × 5m
= 60 sq.m (Ans)
What is the value of sece given the diagram below?
What is the value of sece?
Answer:
[tex]\sec \upsilon = -\sqrt{5}[/tex]
Step-by-step explanation:
Given a point in rectangular form and by definition of trigonometric relations, we know that the secant associated to the vector is:
[tex]\sec \upsilon = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex] (1)
If we know that [tex]x = -3[/tex] and [tex]y = 6[/tex], then the secant of the vector is:
[tex]\sec \upsilon = \frac{\sqrt{(-3)^{2}+6^{2}}}{(-3)}[/tex]
[tex]\sec \upsilon = -\sqrt{5}[/tex]
Answer:
a
Step-by-step explanation:
just took the test
[tex]5y( y + 3) - 2(y - 2) = 20[/tex]
Answer:
[tex]y = \frac{ - 13 - \sqrt{489} }{10} [/tex]
Answer:
Step-by-step explanation:
5y^2+15y-2y+4=20
5y^2-13y+4=20
5y^2-13y+4-20=0
5y^2-13y-16=0
This equation is in standard form: ax^2+bx+c=0. Substitute 5 for a, 13 for b, and −16 for c in the quadratic formula.
Help ASAP
Jack lives 210 miles from Cleveland, where he wants to visit. He has already traveled 125 miles on the bus and then took the train the rest of the way. How many miles were traveled on the train?
Answer:
85 miles
Step-by-step explanation:
He needed to travel a total of 210 miles
He had already traveled 125 miles on bus
And he traveled the rest of the length on the train
If we want to find the distance he traveled on train we simply subtract total distance by distance traveled on bus
So distance traveled on train = 210 - 125 = 85
So he traveled a total of 85 miles on train
Find the missing segment
Answer:
The unknown side is 140
Step-by-step explanation:
Let the unknown side be x
Using ratios
90 90+36
------ = -----------
x x+56
90 126
------ = -----------
x x+56
Using cross products
90(x+56) = 126x
Distribute
90x+5040 = 126x
Subtract 90x
5040 = 36x
Divide by 36
140 =x
In this triangle, what is the value of x?
Enter your answer,
rounded to the nearest tenth, in the box.
Answer:
x = 75.7 cm
Step-by-step explanation:
sin = opp/hyp
sin63 = x/85
multiply both sides by 85
85 * sin63 = x
Use calculator
75.735554556011268 = x
Rounded
x = 75.7 cm
find the equation of Best fit for the data in the table
Answer:
The equation of the line is [tex]y = 2\cdot x + 3[/tex].
Step-by-step explanation:
The data of the table represents a line, also known as a linear function or a first order polynomial if and only if the following property is satisfied:
[tex]\frac{y_{i+1}-y_{i}}{x_{i+1}-x_{i}} = m, m \in \mathbb{R}[/tex] (1)
Now we proceed to check if the table represents a line instead of another kind of function:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{7-5}{2-1} = 2[/tex]
[tex]\frac{y_{3}-y_{2}}{x_{3}-x_{2}} = \frac{9-7}{3-2} = 2[/tex]
[tex]\frac{y_{4}-y_{3}}{x_{4}-x_{3}} = \frac{13-9}{5-3} = 2[/tex]
[tex]\frac{y_{5}-y_{4}}{x_{5}-x_{4}} = \frac{15-13}{6-5} = 2[/tex]
Hence, the data represents a line. From Geometry we know that the equation of the line can be obtained by knowing two distinct points. The formula of the line is described below:
[tex]y = m\cdot x + b[/tex] (2)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]m[/tex] - Slope.
[tex]b[/tex] - y-Intercept.
If we know that [tex](x_{1}, y_{1}) = (1, 5)[/tex] and [tex](x_{2}, y_{2}) = (6, 15)[/tex], then we have the following system of linear equations:
[tex]m + b = 5[/tex] (1)
[tex]6\cdot m + b = 15[/tex] (2)
The solution of the system of linear equations is: [tex]m = 2[/tex], [tex]b = 3[/tex].
The equation of the line is [tex]y = 2\cdot x + 3[/tex].
express the ratio below in its simplest form 4 : 2 : 2
simplest form 4 : 2 : 2 is 2:1:1
parallel lines
EF and CD
perpendicular lines
GH and EF
neither parallel nor
perpendicular lines
AB and CD
Answer:
[tex]{ \tt{AB || CD}} \: \: they \: are \: parallel. \\ { \tt{AB \:and \: EF}} \: \: are \: perpendicular \\ { \tt{CD \: and \: EF}} \: \: are \: perpendicular \\ { \tt{GH \: is \: neither \: parallel \: nor \: perpendicular \: to \: any \: other \: line}}[/tex]
7 giờ bằng bao nhiêu giây?
Answer:
Step-by-step explanation:
25 200 giây
help me plss if you see this help i have a short time or this for will close
Answer:
Value of x will be 12.
Step-by-step explanation:
11. Find the area of each figure. Show all your calculations a. 3 cm 13 cm
Answer:
[tex]39[/tex]
Step-by-step explanation:
[tex]A=lw[/tex]
Area = length * width
[tex]A = 3 * 13[/tex]
[tex]A=39[/tex]
Hope this helps
I need this rn can someone pls help me
Answer:
[tex]V=2080m^3[/tex]
Step-by-step explanation:
The volume formula for triangular prism is [tex]V=\frac{1}{2}bhl[/tex]
[tex]V=\frac{1}{2}(26)(20)(8)[/tex]
[tex]V=\frac{1}{2}(4160)[/tex]
[tex]V=2080[/tex]
Hope this helps
Answer:
The answer is 2080m^3
Step-by-step explanation:
The formula for volume of a prism is 1/2 x length x width x height
Hope it helps :)
Help
Will give
Brainlist
Thank uuu
Answer:
first option is correct
Step-by-step explanation:
finding area for upper rectangle
length = 16 miles
breadth = (2x - 1) miles
area of rectangle = l*b
=16 *(2x - 1)
16*2x - 16*1
=32x - 16
finding area for another rectangle
length = (5x + 5) miles
breadth = 4 miles
area of rectangle = l*b
= (5x + 5) * 4
=5x*4 + 5*4
=20x + 20
area of the figure = area of upper rectangle + area of another rectangle
=32x - 16 + 20x + 20
= (52x + 4) sq mi
what is the solution of the system of liner equations -3x+4y=-18 2x-y=7
Answer:
(2, -3)
Step-by-step explanation:
YEAH
Answer:
x=2; y=-3
Step-by-step explanation:
A rectangle has a perimeter of `52` cm. Its width is `9` cm.
what is the length of the rectangle
Answer:
The length is 17 cm.
17+17+9+9 adds up to 52.
Country Day's scholarship fund receives a gift of $ 185000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 3.3 % interest, and stocks pay 7.5 % interest. Country day invests $ 20000 more in bonds than in CDs. If the annual income from the investments is $ 9560 , how much was invested in each vehicle?
Answer:
$65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.
Step-by-step explanation:
Since Country Day's scholarship fund receives a gift of $ 185000, and the money is invested in stocks, bonds, and CDs, and CDs pay 4.75% interest, bonds pay 3.3% interest, and stocks pay 7.5% interest, and Country day invests $ 20000 more in bonds than in CDs, if the annual income from the investments is $ 9560, to determine how much was invested in each vehicle, the following calculation must be performed:
55000 x 0.075 + 55000 x 0.0475 + 75000 x 0.033 = 9,212.5
57000 x 0.075 + 54000 x 0.0475 + 74000 x 0.033 = 9,282
65000 x 0.075 + 50000 x 0.0475 + 70000 x 0.033 = 9,560
Therefore, $ 65,000 was invested in stocks, $ 50,000 in CDs and $ 70,000 in bonds.
Write the slope-intercept form of the linear equation that has a slope of 3
and a y-intercept of -1.
Answer:
y = 3x - 1
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Use the following situation to answer the questions that follow: A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32t + 6.
Describe in detail (using formulas and/or specific steps needed) TWO ways to find the maximum height reached by the ball.
Answer:
1) find the verted of the parabols
[-b/2a, f(-b/2a)]
-32/-32 = 1 .... -16+32+6 = 22
2) take the derivative and set = to 0
-32t+32 = 0
t = 1 .....height = 22
Step-by-step explanation:
Công ty Hà Dũng chuyên sản xuất và kinh doanh máy điều hòa nhiệt độ. Hiện công ty đang tự chế tạo được tất cả các bộ phận của máy. Có nhà cung cấp bên ngoài đề nghị bán cho công ty một chi tiết của máy giá 20.000đ/cái. Để đánh giá đề nghị này công ty đã tập hợp các chi phí có liên quan đến 15.000 chi tiết như sau: (ĐVT : 1.000đồng) Khoản mục chi phí Tính cho 1 đơn vị Tính cho 15.000 đơn vị mỗi năm Chi phí NVL trực tiếp 6 90.000 Chi phí Nhân công trực tiếp 8 120.000 Biến phí sản xuất chung 1 15.000 Định phí SXC 5* 75.000 Chi phí chung phân bổ 10 150.000 Tổng cộng chi phí 30 450.000 • Định phí SXC có 40% là lương quản lý bộ phận, 60% là khấu hao TSCĐ ( không có giá trị tận dụng Yêu cầu : 1. Giả sử công ty không có phương án nào để sử dụng hết các thiết bị hiện tại đang dùng trong sản xuất của bộ phận trên. Vậy công ty có nên chấp nhận lời đề nghị của nhà cung cấp bên ngoài không ? Lập báo cáo so sánh thu nhập hai phương án
How do you solve this??
Answer:
[tex]a_n=-\frac{9}{4} +\frac{1}{4} *n; \ a_{45}=9.[/tex]
Step-by-step explanation:
1. the difference between two sequent term is: 2- 7/4=7/4 - 3/2 = 3/2 - 5/4=... = 1/4.
2. using the value of the calculated difference it is possible to make up the formula of the given sequence ('n' - the number of term):
[tex]a_n=-\frac{9}{4}+\frac{1}{4} n.[/tex]
3. for n=45:
[tex]a_{45}=-\frac{9}{4}+45*\frac{1}{4}=9.[/tex]
There are a total of 40 red, yellow or blue balls in a box. Each ball is marked with a number out of 1, 2, 3 and 4 on the side. The figure in the shaded area below each shows the number of balls in that category. For example, the number of red balls marked with the number "1" is 12. What is the minimum number of balls to be taken out of the box to ensure that you have at least one ball of each color and each marked number?
Answer:
9
Step-by-step explanation:
Question:
Minimum number of balls to ensure there is at least one ball of each colour marked with each number.
The quantity of distinct numbers are:
red: 4
Yellow 3
Blue 2
So the minimum number of balls to satisfy the given requirements is
4+3+2= 9
Please help. I completely forgot what to do ahh. If anyone knows, please let me know :(
A school raises £468 for their chosen charity by dressing up.Tge money raised is increased by 42% by holding a cake sale.The headtheacher makes up the total sum to £700.How much does the headteacher donate?
Answer:
35.44
Step-by-step explanation:
(1 +.42)*468 = 664.56
if you add 35.44 you would have 700
which of the following is the equation of a line in slope-intercept form for a line with slope = 1/2 and y intercept at (0,-4)?
Answer:
y = [tex]\frac{1}{2}[/tex] x - 4
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 )
Here m = [tex]\frac{1}{2}[/tex] and c = - 4 , then
y = [tex]\frac{1}{2}[/tex] x - 4 ← equation of line
What is the slope of the line with equation y−3=(x−2)?
A coordinate plane with a line passing through the points at (2, 3) and (4, 2).
–2
–negative StartFraction one-half EndFraction.
StartFraction one-half EndFraction
2
Answer:
B on edge 2021
Step-by-step explanation:
x
+
5
y
=
20
x
+
3
y
=
14
Answer:
A) x + 5y = 20
B) x + 3y = 14
Multiplying A) by -1
A) -x -5y = -20 then adding B)
B) x + 3y = 14
-2y = -6
y = 3
x = 5
Step-by-step explanation:
Cual es el volumen de un cubo de 6cm de lado
Answer:
Espero te sirva saludos
solve the system below by substitution. write the solution as a coordinate pair.
y = x + 3
y = - 1/2x + 9
PLEASE SHOW YOUR WORK!!!!!!
GIVING BRAINIEST TO WHOEVER ANSWERS THIS AND SHOWS THERE WORK!!!
Answer:
x = 4 y = 7
Step-by-step explanation:
x + 3 = -1/2x + 9
x = -1/2x + 6
3/2x = 6
x = 4
y = (4) + 3
y = 7
In how many ways can a committee of
3 boys and 2 girls be chosen from 6
boys and 4 girls?
(WAEC)
Answer:
This might be permutation promblem srry if im wrong.
P(6,3)=6x5x4=120
P(4,2)=4x3=12