A = (-3, 1) and B = (4,7)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{7-1}{4-(-3)}=\frac{6}{7}[/tex][tex]y=\frac{6}{7}x+b[/tex]Now, for b, using point B
[tex](7)=\frac{6}{7}(4)+b[/tex][tex]b=7-\frac{6}{7}(4)\rightarrow b=\frac{25}{7}[/tex][tex]y=\frac{6}{7}x+\frac{25}{7}[/tex](Solve the problem & round to four decimal places as needed.)
SOLUTION
Given:
[tex]ln0.0664=-2.7121[/tex]Final answer:
-2.7121
When you convert 0.0045 to scientific notation, the exponent will be
positive.
Or
negative.
i need help with my homework PLEASEMCHECK WORK WHEN FINISHED
Given:
The population of a town increases by 9 % annually.
The current population is 4,500.
Required:
We need to find the equation that gives the population of the town.
Explanation:
The population can be found by the following equation.
[tex]Th\text{e population =4500+9 \% of 4500}[/tex]Let now be the current population of the town =4500.
Let Next be the population of the town.
The population can be found by the following equation.
[tex]Next\text{ =Now+9\% of Now.}[/tex][tex]Next\text{ =Now+}\frac{9}{100}\times\text{Now.}[/tex]Take the common term now out.
[tex]Next\text{ =Now\lparen1+}\frac{9}{100})[/tex][tex]Use\text{ }\frac{9}{100}=0.09.[/tex][tex]Next\text{ =Now\lparen1+0.09})[/tex][tex]Next\text{ =Now\lparen1.09})[/tex][tex]Next\text{ =Now}\times\text{1.09}[/tex]Final answer:
[tex]Next\text{ =Now}\times\text{1.09}[/tex](8x+6)=mL(blank)
8x+6) =
8x=
x=
the L is an angle
The value of the unknown angle is as follows;
∠ = 62 degreesHow to find the unknown angle?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle 4 can be found as follows:
∠4 = 8x + 6 (alternate angles)
Hence,
8x + 6 + 118 = 180(sum of angles on a straight line)
8x = 180 - 118 - 6
8x = 56
divide both sides by 8
x = 56 / 8
x = 7
Therefore,
∠4 = 8(7) + 6 = 56 + 6 = 62 degrees
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The formula to calculate the gravitational force between two objects is F_g=\frac{GM_1M_2}{r^2},F
g
=
r
2
GM
1
M
2
, where M_1M
1
and M_2M
2
are the masses of the objects, GG is the gravitational constant and rr is the distance between the objects. Solve for M_2M
2
in terms of F_g,F
g
, G,G, M_1M
1
and r.r.
The expression for M in terms of other variables is M = Fr^2/Gm
Subject of formulaThe variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own.
In order to make one of the the variables the subject of the formula, we place rewrite the expression in a different form.
Given the formula to calculate the gravitational force between two objects as;
Fg = GMm/r^2
We are to make M the subject of the formula in terms of other variables.
F = GMm/r^2
Cross multiply
Fr^2 = GMm
Divide both sides by Gm
Fr^2/Gm = GMm/Gm
Fr^2/Gm = M
Swap
M = Fr^2/Gm
This gives the expression for the variable M.
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you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]Find the measures of the numbered angles in rhombus DEFG. I just need someone to shown me how to find each of the numbered angles
Step 1
Properties of a Rhombus
Below are some important facts about the rhombus angles:
Rhombus has four interior angles.
The sum of interior angles of a rhombus add up to 360 degrees.
The opposite angles of a rhombus are equal to each other.
The adjacent angles are supplementary.
In a rhombus, diagonals bisect each other at right angles.
The diagonals of a rhombus bisect these angles.
Step 2
From the figure
Angle DGF = Angle DEF = 118
Step 3
Since adjacent angles are supplementary, that is add to 180 degrees
[tex]\begin{gathered} \angle\text{DGF + }\angle GFE\text{ = 180} \\ 118\text{ + }\angle GFE\text{ = 180} \\ \angle GFE\text{ = 180 - 118} \\ \angle GFE\text{ = 62} \end{gathered}[/tex]Step 4
The diagonals of a rhombus bisect these angles
[tex]\begin{gathered} \angle3\text{ = }\angle4\text{ = }\frac{62}{2}\text{ = 31} \\ \angle3\text{ = }\angle4\text{ = 31} \end{gathered}[/tex]Step 5
The opposite angles of a rhombus are equal to each other.
[tex]\angle1\text{ = }\angle\text{ 2 = 31}[/tex]Final answer
[tex]\angle\text{1 = }\angle\text{ 2 = }\angle\text{ 3 = }\angle4\text{ = 31}[/tex]y-intercept of y=3/2|x-2|
Answer:
Combine [tex]\frac{3}{2 }[/tex] and | x - 2 |
[tex]y\frac{3|x-2|}{2}[/tex]
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, specify any restrictions on the variable.a²-3a-4/a² + 5a + 4Rational expression in lowest terms:Variable restrictions for the original expression: a
Factorize both quadratic polynomials, as shown below
[tex]\begin{gathered} a^2-3a-4=0 \\ \Rightarrow a=\frac{3\pm\sqrt{9+16}}{2}=\frac{3\pm\sqrt{25}}{2}=\frac{3\pm5}{2}\Rightarrow a=-1,4 \\ \Rightarrow a^2-3a-4=(a+1)(a-4) \\ \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} a^2+5a+4=0 \\ \Rightarrow a=\frac{-5\pm\sqrt{25-16}}{2}=\frac{-5\pm3}{2}\Rightarrow a=-1,-4 \\ \Rightarrow a^2+5a+4=(a+1)(a+4) \end{gathered}[/tex]Thus,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{(a+1)(a-4)}{(a+1)(a+4)}[/tex]Therefore, since the denominator cannot be equal to zero.
The variable restrictions for the original expression are a≠-1,-4Then, provided that a is different than -1,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{x-4}{x+4}[/tex]The rational expression in the lowest terms is (x-4)/(x+4)Factor completely. (3.2² - 12x)(x2 – 2x + 1) =
We will have the following:
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
Given,
Belinda wants to invest $1,000.
The Table is:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Now, According to the question:
When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.
For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:
1690/1300 = 1.3 = 1300/1000
Part A :
(Option 1) can be represented by exponential function.
(Option 2) can be represented by a linear function.
Part B:
For Option 1:
To find the value of the investment f(n), in dollars, after n years.
The generic form of an exponential function is ...
f(n) = a·b^n
Now, Amount after 1 year = 1100
Principle (P) is = 1000
Using the formula :
A = P[tex](1+r)^n[/tex]
1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]
1.10 = 1 + r
r = 0.10
Amount after t years can be given by :
A = 1000(1.10)^t
For Option 2,
The generic form of an exponential function is ...
f(n) = a·n + b
Rate of change (m) = (1100 - 1000) / 1 = 100
Amount after t years can be given by
A = 1000 + 100 x t .
Part C:
Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727
Investment in (2): $3000
Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
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i have to find is they similar or not. help im lost
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
Rewrite the following equation in slope-intercept form.
10x − 10y = –1 ?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x + 1/10
Step-by-step explanation:
Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?
slope intercept form: y = mx + b so you are solving for y:
10x − 10y = –1
subtract 10x from both sides:
10x − 10y – 10x = –1 – 10x
-10y = –1 – 10x
divide all terms by -10:
-10y/(-10) = –1/(-10) – 10x/(-10)
y = 1/10 + x
rearrange for slope intercept form: y = mx + b
y = x + 1/10
Answer:
[tex]y=x+\dfrac{1}{10}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]10x-10y=-1[/tex]
To write the given equation in slope-intercept form, perform algebraic operations to isolate y.
Add 10y to both sides of the equation:
[tex]\implies 10x-10y+10y=10y-1[/tex]
[tex]\implies 10x=10y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies 10x+1=10y-1+1[/tex]
[tex]\implies 10x+1=10y[/tex]
[tex]\implies 10y=10x+1[/tex]
Divide both sides of the equation by 10:
[tex]\implies \dfrac{10y}{10}=\dfrac{10x+1}{10}[/tex]
[tex]\implies \dfrac{10y}{10}=\dfrac{10x}{10}+\dfrac{1}{10}[/tex]
[tex]\implies y=x+\dfrac{1}{10}[/tex]
Therefore, the given equation in slope-intercept form is:
[tex]\boxed{y=x+\dfrac{1}{10}}[/tex]
If the LM follows the reference trajectory, what is the reference velocity vref (t) ?
Answer:
Explanation:
how do you calculate the volume of water in a lake? given is the area of the lake at 1.35 km2 and its depth is 4.0 m
Given
Area of lake = 1.35 square km
Depth = 4.0m
Find
Volume of water in a lake
Explanation
Volume of water in a lake is given by
[tex]area\times depth[/tex]first we have to make the units same
as we know 1 square km = 1000000
so , 1.35 square km = 1.35 * 1000000= 1350000 square meter
so , volume of water in a lake =
[tex]\begin{gathered} volume=1350000\times4 \\ volume=5400000\text{ }cubic\text{ meter} \end{gathered}[/tex]Final Answer
Therefore , the volume of water in a lake is 5400000 cubic meter
Fill in the blanks to find other expressions for 8%a. __ for every 100, b. __for every 50, c. 1 for every __, d. 0.5 for every __. 150
Using ratios, the sentences regarding a percentage of 8% are given as follows:
a. 8 for every 100.
b. 4 for every 50.
c. 1 for every 12.5.
d. 0.5 for every 6.25.
Ratio between two amountsThe ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
One example of ratio is a percentage, as a percentage of x% is equivalent to the ratio of x to 100, that is:
r = x/100.
Hence a percentage of 8% is equivalent to the following ratio:
r = 8/100.
That is, 8 for every 8.
Ratios are fractions, and they can be simplified, dividing both the numerator and the denominator by the same amount, as is the case in this problem:
r = 4/50 (simplifying by 2, four for every 50).r = 1/12.5 (simplifying by 4, one for every 12.5).r = 0.5/6.25 (simplifying by 2, 0.5 for every 6.25).More can be learned about ratios at https://brainly.com/question/2328454
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The semi annual compound interest of a sum of money in 1 year and 2years are Rs400 and Rs441 respectively.Find the annual compound interest for 2years
Answer:
Step-by-step explanation
Correct option is A)
C.I. for the third year = Rs. 1,452.
C.I. for the second year = Rs. 1,320
∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.
Rate of interest =
1,320
132×100
=10%.
Let the original money be Rs. P.
Amount after 2 year − amount after one year =C.I. for second year.
P(1+
100
10
)
2
−P(1+
100
10
)=1,320
P[(
100
110
)
2
−
100
110
]=1,320
⇒P[(
10
11
)
2
−
10
11
]=1,320⇒P(
100
121
−
10
11
)= Rs. 1,320
⇒P×
100
11
=Rs.1,320⇒P=
11
1,320×100
= Rs. 12,000
∴ Rate of interest =10%
and Original sum of money = Rs. 12,000
A rectangular room is twice as long as it is wide, and its perimeter is 60 meters. Find the dimensions of the
room.
The length is __
meters and the width is __
meters.
Answer: 20, 10
Step-by-step explanation:
Let the width be w. Then, the length is 2w. Substituting into the formula for the perimeter of a rectangle,
[tex]2(w+2w)=60\\\\w+2w=30\\\\3w=30\\\\w=10\\\\\implies 2w=2(10)=20[/tex]
you get a student loan from the educational assistance Foundation to pay for your educational expenses as you earn your associate's degree you will be allowed 10 years to pay the loan back find the simple interest on the loan if you borrow $3,600 at 8 percent
Simple interest = PRT/100
where p = $3600
R=8
T=10
Substituting into the formula;
S.I = $3600 x 8 x 10 /100
=$36 x 8 x 10
=$2880
Check each answer to see whether the students evaluated the expression correctly. If the answer is incorrect cross out the answer and write the correct answer. 8(x+2)when x= 68(6+2) = 48 +2 = 50
The answer is not correct. There is a mistake applying the distributive property.
The distributive property says:
[tex]a(b+c)=ab+ac[/tex]But in this case, the 8 only multiplies the 6, and not the 2. The correct procedure is:
[tex]8(6+2)=8\cdot6+8\cdot2=48+16=64[/tex]The correct answer is 64
What point in the feasible reign maximizes the objective function? constraints: x => 0 y => 0 y<= x - 4 x + y <= 6
Objective Function: C = 2x + y
The point in the feasible region maximizes the objective function is (5, 1)
How to determine the feasible region?The given parameters are
Objective function: C = 2x + y
Subject to (i.e. the constraints)
x >= 0, y >= 0
y <= x - 4, x + y <= 6
Represent y <= x - 4, x + y <= 6 as equations
y = x - 4 and x + y = 6
Substitute y = x - 4 in x + y = 6
So, we have
x + x - 4 = 6
Evaluate the like terms
2x = 10
This gives
x = 5
Substitute x = 5 in y = 6 - x
y = 6 - 5
Evaluate
y = 1
So, we have
(x, y)= (5, 1)
Hence, the coordinates is (5, 1)
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i need help on number 7. Please use 4 points
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
10 pts What is x and y intercept for the following equation? 8x + y = 12 A. x intercept = 0 y intercept = 4 B. x intercept = 12 y intercept = 0 C. x intercept = 4 y intercept = 6 D. x intercept = 3/4 y intercept = 12 OB ОА Oc
To find the x intercept of the equation make y=0 and solve for x.
[tex]\begin{gathered} 8x+y=12 \\ 8x=12 \\ x=\frac{12}{8} \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]The x intercept is 3/2
To find the y intercept, make x=0 and solve for y
[tex]\begin{gathered} 8x+y=12 \\ 8(0)+y=12 \\ y\text{=}12 \end{gathered}[/tex]The y intercept is 12.
you pull with 45nm on a torque wrench of 1m what's the tourqe at the end
The torque at the end is equal to 45 Nm.
What is torque?Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.
Mathematically, torque can be calculated by using this formula:
τ = Fd
Where:
τ represents the torque.F represents the force.d represents the perpendicular distance.In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.
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Can you help me figure this out
By using the fact that the interior angles of a triangle must add up to 180, we will see that the value of x is 15.
How to get the value of x?Here we have 3 expressions for the measures of the interior angles of a triangle.
Now, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write:
(8x - 7)° + (x + 7)° + (2x + 15)° = 180°
Ignoring the degrees and solving this for x, we get:
8x - 7 + x + 7 + 2x + 15 = 180
11x + 15 = 180
11x = 180 - 15 = 165
x = 165/11 =15
The value of x is 15.
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Zaria is making pipe cleaner flowers for
her friends. She has 215 pipe cleaners.
How many flowers can she make with 3
pipe cleaners in each?
[?] flowers and pipe cleaners leftover
I
Answer
Enter
We can get the answer by dividing 215 by 3
What is dividing?
One of the four fundamental arithmetic operations, or ways to combine numbers to create new ones, is division. The other operations are multiplication, addition, and subtraction. The process of counting the instances in which one integer is included into the others is the most fundamental definition of the division of two natural numbers. This amount need not be an integer. For instance, if twenty apples are divided equally among four people, everyone will get five of them.
We can get the answer by dividing 215 by 3
215/3 = 71.67
Hence, 71 flowers are made
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Which equation is the best approximation of the trend line
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
21.) Determine the distance between the points (-2, 3) and (4,9).A 142B 7146C 413D 6V222.) Infigure
The distance formula can be represented below
[tex]\begin{gathered} c^{}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} c=\sqrt[]{(4+2)^2+(9-3)^2} \\ c=\sqrt[]{(6)^2+(6)^2} \\ c=\sqrt[]{36+36} \\ c=\sqrt[]{72} \\ c=\sqrt[]{36\times2} \\ c=6\sqrt[]{2} \end{gathered}[/tex]The answer is D.
For the equation, complete the given table.
Answer:
Step-by-step explanation:
first row: 4
second: 2
third: 6
fourth: 9
plug in x for x in the equation/plug in y for y in the equation for whichever is given.
Identify the x intercept(s) from the graphType your answer using set notation {x,x} listing x values in order from least to greatest
The x-intercept is where the graph passes the x-axis.
The graph extends from {-5 ≤ x ≤ 3}
The x-intercept is {x = -1}.