Answer:
easy
Step-by-step explanation:
How to solve a system of equations by elimination.
Write both equations in standard form.
Make the coefficients of one variable opposites.
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
What is 3 x 10 to the power of 4 multiplied by 5 x 10 to the power of 2.
Answer:
2,025,000,000
Step-by-step explanation:
(3×10)⁴×(5×10)
8810000×2500
2,025000,000
The line y=kx+4 goes through the point (2,-2)
Find the value of k.
Answer:
k= -3
Step-by-step explanation:
Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.
y = kx+4
-2 = k(2)+4
To get k by itself, we first have to subtract the 4 from both sides.
-2-4 = k(2)+4-4
-6 = k(2)
Then, we can divide each side by the 2 to get our answer.
-6/2 = k(2)/2
k = -3
Answer:
k=-3
Step-by-step explanation:
Answer this fraction based Question. I will make you brainliest and provide you 50 points.
6/7 of people are not having a disease, the whole is 1 so the difference is:
1 - 6/7 = 7/7 - 6/7 = 1/7 of the totalPart ii2/3 of those having a disease is:
1/7*2/3 = 2/21 of the totalPart iii15 people are the 1/7 fraction of total people referred to quarantine.
The total number is:
15 : 1/7 = 15 * 7 = 105 peoplePart iv3/5 of 105 people are male, that is:
3/5*105 = 63 peopleNumber of female is:
105 - 63 = 42 peopleAnswer:
[tex]\sf (i) \quad \dfrac{1}{7}[/tex]
[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]
[tex]\sf (iii) \quad 315\:people[/tex]
[tex]\sf (iv) \quad 126\: females[/tex]
Step-by-step explanation:
Part (i)If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:
[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]
Therefore, 1/7 of people in quarantine have the disease.
Part (ii)We are told that 2/3 of the people who have the disease come from abroad. Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:
[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]
Therefore, the fraction of diseased people who have come from abroad is 2/21.
Part (iii)We are told that 15 people who have the disease do not come from abroad. So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad. Remember that 1/7 of the total people have the disease.
[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]
Therefore, 1/21 of the total number of people have the disease and do not come from abroad.
Therefore, 15 people are equal to 1/21 of the total number of people:
[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]
Therefore, the total number of people in quarantine is 315.
Part (iv)If 3/5 of the total are male, then 2/5 must be female.
[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]
Therefore, 126 females are in quarantine.
Graph = 2/3x
Please graph the graph right and answer the ones that apply
1. Yes, the equation represent the proportionality relationship.
2. Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
3.Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
Given a picture in that we can see a graph and 3 option.
We have to check weather that 3 option satisfy the equation and what are they.
Given equation [tex]y=\frac{2}{3}x[/tex]
1st option: Is the equation represent the proportionality relationship.
Yes, the equation represent the proportionality relationship.
If we see the proportionality rule that is
The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.
A proportionate relationship exists if an equation in a different form can be rewritten as shown above.
Here, the equation is in the form of y=kx.
Therefore, Yes, the equation represent the proportionality relationship.
2nd option: the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
The amount of change in y for a change of one unit in x is the unit rate of change of y with respect to x.
The slope is [tex]\frac{2}{3}[/tex].
Therefore, Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].
3rd option: The slope of the line is [tex]\frac{2}{3}[/tex]
Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
It is possible to simplify the equation of the slope to the form
y=mx+b, where m is the slope of the line and b is constant.
y is the dependent variable and x is the independent variable.
By the equation [tex]y=\frac{2}{3}x[/tex]
Therefore, Yes, The slope of the line is [tex]\frac{2}{3}[/tex]
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4/3 times 6/5 in simplest form
Answer:
8/5 or 1 3/5
Step-by-step explanation:
Answer:
Exact form: 8/5
Mixed Number form: 1 3/5
Step-by-step explanation:
First, let's cancel the common factor of 3
4/3 * 6/5
4 * (3*2/5)
4 * 2/5
Next, lets combine 4 and 2/5
4*2/5
8/5
We can finish this off by simplifying 8/5
8/5 = 1 3/5
Simplify the radical √20
Evaluate 11,000,000,000 ÷ 100, write your answer in exponent form.
An investment account eaming 3.85% simple interest cas $67 50 in 3 years. How much was invested? Give your answer rounded to whole cents.
The amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.
Let the principal amount that is invested be equal to x.
So, we get that:
P = x
Now, the time period t = 3 years.
Simple interest rate = r = 3.85 %
Amount after 3 years = A = $ 6750
A = P + ( P × r × t / 100)
6750 = x + ( x × 3.85 × 3 / 100)
6750 = x + 0.1155 x
6750 = 1.1155 x
x = 6750 / 1.1155
x = 6051.098
Therefore, we get that, the amount that was invested at the start of the 3 years that is the principal amount will be equal to $ 6051.098.
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A couch went on a 19% off sale. the sale price is given $972. what was the original price of the couch?
Answer: $1200
Step-by-step explanation:
The equation to find out the price of the couch on sale is:
972=x*0.81
(0.81 is the same as 81% or 100% - 19%)
Then this equation can be arrange to figure out x
972=x*0.81
972/0.81=x
x=1200
Answer:
$1200
Step-by-step explanation:
Given the following question:
A couch when on a 19% discount
The new price of the couch was 972 dollars
We are trying to find the original price of the couch. To find that answer we are going to use the formula to calculate the percentage.
19% of 1200
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{19\times1200}{100}[/tex]
[tex]19\times1200=22800[/tex]
[tex]22800\div100=228[/tex]
Now check our answer by subtracting 228 from our original price 1200:
[tex]1200-228=972[/tex]
[tex]=972[/tex]
Our original price is "$1200."
Hope this helps.
Triangle `CDA` is the image of Triangle `ABC` after a `180°` rotation about the midpoint of segment `AC`. Triangle `ECB` is the image of Triangle `ABC` after a `180°` rotation about the midpoint of segment `BC`.
ABCD and ABEC are parallelograms becayse a parallelogram can be divided into congruent triangles of different orientations
How to explain why ABCD and ABEC are parallelograms?The pre-image of the rotations are given as:
Triangle ABCTriangle ABCThe image of the rotations are given as:
Triangle CDATriangle ECBNotice that the triangles ABC and CDA have a common line segment AC, while the triangles ABC and ECB have a common line segment CB
The above is true, because the triangle is rotated by 180 degrees through its own midpoint
When the images of the rotations are viewed as a single shape, the view of the shape is a parallelogram
Because a parallelogram can be divided into congruent triangles of different orientations, then ABCD and ABEC are parallelograms
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Complete question
Triangle CDA is the image of triangle ABC after a 180º rotation around the midpoint of segment AC. Triangle ECB is the image of triangle ABC after a 180º rotation around the midpoint of segment BC.
Explain why ABCD and ABEC are parallelograms.
See attachment for image
Explain that to me will you?
The values of x satisfying the condition of the quadratic function (f o g)(x) = 17 is; (2, 4)
How to solve quadratic equations?
We are given the functions;
f(x) = 2x - 3
g(x) = x² - 6x + 18
Thus;
(f o g)(x) = 2(x² - 6x + 18) - 3
= 2x² - 12x + 36 - 3
= 2x² - 12x + 33
Now, we want to find the value of x when (f o g)(x) = 17. Thus;
2x² - 12x + 33 = 17
2x² - 12x + 16 = 0
Factorizing this gives us;
(2x - 8)(x - 2) = 0
Thus;
2x - 8 = 0 or x - 2 = 0
x = 4 or 2
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Please answer following question in picture
1. The line passing through (-14,-9) and (7,9) has the equation:
y = 6/7x + 3/2
2.The line passing through (0,-3) and (0,15) has the equation:
since the slope is undefined, hence equation of the line is not formed.
3.The line passing through (-24,-16) and (-8,-6) has the equation:
y = 5/8x - 1
4.The line passing through (-8,-12) and (12,13) has the equation:
y = 5/4x - 2.
Given we have the pair of points, through which we need to determine the equation of the line:
1. (-14,-9) and (7,9)
first we need to find the slope
(-14,-9) = (x₁,y₁)
(7,9) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 9-(-9)/7-(-14)
= 18/21
m= 6/7
Use the slope and one of the points to find the y-intercept b:
(7,9) and m= 6/7
substitute in y=mx+b
9=6/7(7) + b
b = 9/6
b= 3/2
now substitute m=6/7 and b= 3/2 in slope intercept form.
y = 6/7x + 3/2
2. (0,-3) and (0,15)
first we need to find the slope
(0,-3) = (x₁,y₁)
(0,15) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 15-(-3)/0-0
= undefined
hence we can't frame the equation of the line.
3. (-24,-16) and (-8,-6)
first we need to find the slope
(-24,-16) = (x₁,y₁)
(-8,-6) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= -6-(-16)/-8-(-24)
= -6+16/-8+24
= 10/16
m= 5/8
Use the slope and one of the points to find the y-intercept b:
(-8,-6) and m= 5/8
substitute in y=mx+b
-6=5/8(-8) + b
b = -1
now substitute m=5/8 and b= -1 in slope intercept form.
y = 5/8x - 1
4. (-8,-12) and (12,13)
first we need to find the slope
(-8,-12) = (x₁,y₁)
(12,13) = (x₂,y₂)
m= y₂₋y₁/x₂₋x₁
= 13-(-12)/12-(-8)
= 25/12+8
= 25/20
m= 5/4
Use the slope and one of the points to find the y-intercept b:
(12,13) and m= 5/4
substitute in y=mx+b
13=5/4(12) + b
b = -2
now substitute m=5/4 and b= -2 in slope intercept form.
y = 5/4x - 2.
hence we get the acquired results.
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Find the coordinates of the point
7/10 of the way from A to B.
The coordinates of the point
7/10 of the way from A to B are
Answer:
(4,-4)
is the way from AtoB
find the value for x
(x+63)
(4x)
Answer:
x = 21
Step-by-step explanation:
You are given expressions (x+63)° and (4x)° for alternate interior angles at a transversal crossing parallel lines. You want to know the value of x.
Alternate interior anglesWhere a transversal crosses parallel lines, alternate interior angles are congruent. That means ...
(4x)° = (x +63)°
3x = 63 . . . . . . . . divide by °, subtract x
x = 21 . . . . . . . . . divide by the coefficient of x
A computer screen has a length of
16 inches and a width of 10 inches. What
is the area of the screen to the nearest
square centimeter?
The area of the screen to the nearest square centimeter is 0.103 m².
Given, that the length of the computer screen is = 16 inches
width of the computer screen = 10 inches
we know that 1 inch = 0.0254 m
Width = 10 inches = 10 × 0.0254 m
= 0.254 m
Length = 16 inches = 16 × 0.0254 m
= 0.4064 m
By definition,
Area = length × width
= 0.254 × 0.4064 m²
= 0.103 m²
hence we get the area of the computer screen as 0.103 m²
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Compute using long division 342÷23
Answer:
342 ÷ 23 = 14.869565217 or 14 r 20
Check step-by-step explanation below for 2 methods to solve.
14.869565217 method right below
14 r 20 method at the bottom in bold and underlined
Hope this helps :)
Step-by-step explanation:
divisor
↓ ? <------ quotient
23 | 342 <------ dividend
remainder = r (the number that the divisor can't go into.
1) 23 goes into 34 one time, so we write the one on top.
1
23 | 342
2) 23 • 1 = 23 so then we subtract 23 from 34 and get 11.
1
23 | 342
- 23
1 1
3) Now we carry down the 2 and get 112.
1
23 | 342
- 23 ↓
1 1 2
4) 23 goes into 112 four times, so we write the four on top.
1 4
23 | 342
- 23 ↓
1 1 2
5) 23 • 14 = 92 so we subtract 92 from 112 and get 20.
1 4
23 | 342
- 23 ↓
1 1 2
- 92
20
6) 23 can't go into 20 so we add a decinal and a zero to 342 (dividend) and add a decimal to 14 too.
1 4.
23 | 342.0
- 23 ↓
1 1 2
- 92
20
7) Repeat the same steps again (Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor (if greater use it if less than take the next number). Then divide it by the divisor and write the answer on top as the quotient. Subtract the result from the digit and write the difference below. Bring down the next digit of the dividend (if present). Repeat the same process.)
1 4.8
23 | 342.0
- 23 ↓↓
1 1 2
- 92
200
- 1 84
16
8) Keep repeating and then we get 14.8695652174
*However, if the directions say to not continue and add the decimal and zero then we must put a remainer (r).*
1 4 r 20
23 | 342
- 23 ↓
1 1 2
- 92
20
find the distance AC on the number line below
Answer:
6
Step-by-step explanation:
c is on -3 and A is on 3 -3 to 3 would be 6
Find the lengths of UV and ST and determine whether they are congruent.
Hint: Congruent line segments have the same length.
Answer:
-2, S, U, V. that was a good question.
Step-by-step explanation:
Thanks. You are known.
PLEASE HELP! I will mark you Brainly and rate well!
Fuel Usage.
The slope can be used to represent the average rate of change, or how much one quantity changes, on average, relative to the change in another quantity. An example of a slope that changes in real-life involves units of measure such as beats per minute or kilowatts per hour.
Over a 45-day period, the amount of propane in a tank that stores propane for heating a home decrease from 500 gallons to 344 gallons.
1. Use a graph or the slope formula to show the average rate of change in the amount of propane used over the 45-day period.
2. Show all work.
3. Explain what your solution represents in the context of the situation.
Answer: this is not answer but it will help u with whoever does answer it
Step-by-step explanation:
we see here, slope is another version of finding the average rate of change. Average rate of change is finding the difference between the dependent variable (y-term) divided by the difference in the independent variable (x-term). Slope and average rate of change is exactly the same thing
Find an equation of the line that passes through the points
(
5
,
9
)
and
(
−
2
,
1
)
. You do not need to simplify.
The total area of Wisconsin
is 65,498 square miles. Of that, about
80% is land area. About how many
square miles of Wisconsin is not land
area?
Answer:
the other 20%
Step-by-step explanation:
calculate 20% of 65498
Answer:
13,099.6 square miles
Step-by-step explanation:
80%*65,498=
80/100 * 65,498=
4/5 * 65,498=52,398.4 square miles of land area
65,498-52,398.4= ==> subtract the total area of Wisconsin by the total land area to get the total area that isn't land.
65,498.0-52,398.4=13,099.6 square miles of area that isn't land
USING TOOLS The table shows the numbers y (in thousands) of people in a city who regularly use sharable
electric scooters x weeks after the scooters are introduced.
Time, x Number of users, y
1, 1.5
4, 2.2
6, 2.4
10, 3.9
12, 5.5
15, 6.8
20, 12.3
24, 16.4
25, 17.6
1. Write function that models the data
2. Use the model to predict the number of users after 32 weeks
From the data given, we have that:
1. The linear regression equation is given by:y = 0.69684x - 1.43675.
2. 21 users during the 32th week.
How to find the equation of best fit using a calculator?To find the equation, we need to insert the points (x,y), given in a scatter plot or in a table, in the calculator. We also have to identify the type of data that models the situation, such as linear, quadratic or exponential.
For this problem, the data is increasing somewhat linearly, hence linear regression is used.
The points of the function, from the table, are given as follows:
(1, 1.5), (4, 2.2), (6, 2.4), (10, 3.9), (12, 5.5), (15, 6.8), (20, 12.3), (24, 16.4), (25, 17.6).
Hence the the linear equation that models the data is:
y = 0.69684x - 1.43675
The value during the 32th week is found when x = 32, hence:
y = 0.69684(32) - 1.43675 = 21 (rounded up, as the first decimal digit is greater than 0.5).
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Hey guys please help me with this thanks
Answer:
Step-by-step explanation:
boy just include the unit rate of mph and make the question solvable as easy as that, or you could use the example and change the mph
What is the place value of 5 in 62,506,300,782?
A. Hundred thousands
B. Ten thousands
C. Millions
D. Hundred millions
Write an absolute value inequality for the graph below.
Use x for your variable.
←++
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
An absolute value inequality for given graph is |x| ≤ 6
In this question, we have been given a graph of a number line.
We need to write an absolute value inequality for given graph.
From the given graph, we can observe that the value of x lies between -6 to 6.
i.e., -6 ≤ x ≤ 6
We know that, for a real number 'm', the absolute value function for m would be,
|±m| = m
So, -6 ≤ x ≤ 6
|x| ≤ 6, which is required inequality.
Therefore, an absolute value inequality for given graph is |x| ≤ 6
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Rewrite in simplest terms: (x +9y) — (9x -8y)
Answer:Your answer would be -8 x - 17 y
Step-by-step explanation: x - 9 x would be - 8 x
You would have to distribute the negative in the problem -(9 x- 8 y) which would make it -9 x +8 y and 9 y + 8 y is 17 y so there fore the answer is -8 x - 17 y
Do you know the muffin man?
i need this in a hour O_o
Answer:
x= 5/12,y=− 5/4
Step-by-step explanation:
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
6x−12y=24,4x+2y=8
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
6x−12y=24
Add 12y to both sides of the equation.
6x=12y+24
Divide both sides by 6.
x= 6/1 (12y+24)
Multiply 6
1 times 24+12y.
x=2y+4
Substitute 4+2y for x in the other equation, 4x+2y=8.
4(2y+4)+2y=8
Multiply 4 times 4+2y.
8y+16+2y=8
Add 8y to 2y.
10y+16=8
Subtract 16 from both sides of the equation.
10y=−8
Divide both sides by 10.
y=− 5/4
Substitute − 5/4 for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.
x=2(− 5/4 )+4
Multiply 2 times − 5/4 .
x=− 5/8 +4
Add 4 to − 5/8 .
x= 5/12
Identify and extend the pattern to find the next number in the sequence 3, 12, 48, 1 92
Answer:
768
Step-by-step explanation:
The numbers are multiplying by 4 each time, Therefore the next number will be 768.
These questions are about calculus, I would greatly appreciate your help on both questions! .
asap , please !
The 107th derivative of f(x) =cos(x) is sin(x).
What is derivative of a function?The derivative of y = f(x) function is the rate of change of y with respect to the independent variable x.
Derivative is represented by [tex]\frac{d}{dx}[/tex] and
First derivative to y is given by [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]
Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.
[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]
Given f(x) = cos(x)
Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]
The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]
Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]
[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]
Eighth derivative if cos(x) is cos(x)
and so on
Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x) is -sin(x)
The second, sixth, tenth.... derivative of f(x) =cos(x) is -cos(x)
The fourth , eighth , 12th,... derivative of f(x) =cos(x) is cos(x)
We can say that very multiple of fourth derivative of f(x) =cos(x) is cos(x)
We can write 107 as 104 + 3
As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)
[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]
Therefore, the 107th derivative of f(x) =cos(x) is sin(x).
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