The width of the lake on the scale drawing is 30 cm.
Based on the given conditions, formulate 1500*2/100
Cross out the common factor: 15*2 = 30
Get the result as 30 cm
An object is enlarged in a scale drawing. An expansion increases or decreases the size of an object by multiplying each of its lengths by a scale factor. Typically, a ratio is used to describe the scale of a drawing. a representation of a real thing with correct sizes that have been scaled back or blown up slightly (called the scale). The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.
Hence, the width of the lake on the scale drawing is 30 cm.
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Given the functions f(x) = 3x - 21 and g(x) = 3x+21 , show that the function f(x)-g(x) is a constant for all the values of x .
-42 is the constant for all values of x. If the given the functions f(x) = 3x - 21 and g(x) = 3x+21
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Given an arbitrary number x, lets calculate,
⇒ f(x) - g(x)
= 3x - 21 - (3x+21)
= 3x - 3x -21 -21
= 0 - 42
= -42
and thus -42 is the constant for all values of x.
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Tyler wrote the equation x=\frac{y}{65}x= 65 y , with x representing the time traveled, in hours, and y representing the distance traveled, in miles. Explain why Tyler's equation matches the story.
It should be noted that Tyler writing the equation x = y/65 is correct and matches the information.
How to illustrate the information?It should be noted that speed is calculated as:
= Distance / Time
In this case, the car is going 65 miles per hour down the highway
x = the time traveled, in hours
y = the distance traveled,
Therefore, time = Distance / Speed
Therefore, Tyler wrote the equation x = y/65, this is correct and matches the information.
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A car is going 65 miles per hour down the highway. Tyler wrote the equation x = y/65, with x representing the time traveled, in hours, and y representing the distance traveled, in miles. Explain why Tyler's equation matches the story.
PLEASE HELP Finding the initial amount and rate of change given a table for a linear function
As time passes, the amount of money in the account increases.
The amount in the account increases by $45.
The amount of money in the account when he started depositing is $197.
What is the rate of change of the linear function?A linear function is a function that has one independent variable and one dependent variable. A linear function increases at a constant rate over a period of time. When drawn on a graph, a linear function is usually a straight line.
The form of linear functions is:
y = a + mx
Where:
a = constant / slope m = y-intercept y = dependent variableLooking at the given table, it can be seen that as time passes, the amount of money increases.
Rate of increase = (change in the amount of money) / change in the months
(557 - 467) / (8 - 6)
= 90 / 2
= $45
Amount in the account at the beginning = account balance at 6 months - (rate of increase x 6)
467 - (6 x 45)
467 - 270 = $197
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Find the area of the polygon with the given vertices A(3,7), B(5,7), C(3,-7), D(5,-7)
The area of the given polygon which is a rectangle is; 28 sq. units
What is the area of the polygon with vertices?We are given the coordinates of the polygon as;
A(3,7)
B(5,7)
C(3,-7)
D(5,-7)
Now, by close inspection of the coordinates, we can tell that this polygon is a rectangle. Thus, we can deduce that;
AB = 5 - 3 = 2
CD = 5 - 3 = 2
BC = 7 + 7 = 14
AD = 7 + 7 = 14
Formula for area of a rectangle is;
A = Length * Width
A = 14 * 2
A = 28 sq. units
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b. What are the vertex, focus, and directrix of the parabola with equation y= x² / 4} ?
The vertex, focus and directrix of the parabola y = x²/4 are:
v = (0,0)f = (0, 1)d = -1What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
In this case we have an expression given by:
y = x²/4
We must find the canonical equation:
(y - 0)² = 1/4 (x - 0)²
(x - 0)² = 4 (y - 0)²
has the form
(x - h)² = 4p(y - k)
This means that the vertex of this parabola is
v = (h, k)
v = (0,0)
To know the focus we must know the value of "p".
4p = 4
p = 1
f = (0, 1)
Directrixd = -1
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Cynthia, Moses and John are to share $27,000 in the ratio 2:3:5 respectively. how much will each of them receive
Answer: Cynthia will receive $5,400, Moses will receive $8,100, John will receive $13,500
Step-by-step explanation:
First, we will see how many "portions" the money is broken up into.
2:3:5 can become 2 + 3 + 5 = 10
Next, we will see how much money each "portion" is worth using division.
$27,000 / 10 = 2,700
Finally, we will multiply to see how much each person will receive.
2:3:5
2 * $2,700 = $5,400 [Cynthia]
3 * $2,700 = $8,100 [Moses]
5 * $2,700 = $13,500 [John]
Answer:
Cynthia's money = $5,400
Moses' money = $8,100
John's money = $13,500
Step-by-step explanation:
The full ratii of the money will be 2+3+5 = 10
Cynthia's ratio = 2 × $27,000
10
= 2 × 2,700
= $5400
Moses' ratio = 3 × $27,000
10
= 3 × 2,700
= $8100
John's ratio = 5 × $27,000
10
= 5 × 2,700
= $13,500
3. Which of the following points lie on plane R? Select all that apply.
A.C B.I C.F D.E
Answer:
dnenejnejehdhsbshsbsjsnsksknsosbs
(5x²)³ + 16y/4y When x=2 and y=3
Answer:
8004
Step-by-step explanation:
8000+4
= 8004
Answer: [tex]=2\circ \:3[/tex]
Step-by-step explanation:
[tex]\mathrm{For}\:\frac{\left(5x^2\right)^3+16y}{4y,\:x}\circ \:y\:\mathrm{substitute}\:\frac{\left(5x^2\right)^3+16y}{4y,\:x}\:\mathrm{\:with\:}\:2,\:y\:\mathrm{\:with\:}\:3[/tex]
[tex]=2\circ \:3[/tex]
Solve each equation. Check each solution.1/4x - 3/4 = 7/x
The soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.
According to the given question.
We have an equation 1/4x - 3/4 = 7/x.
As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Therefore, the solution of the equation 1/4x - 3/4 = 7/x is given by
1/4x - 3/4 = 7/x
⇒ 1/4x - 7/x -3/4 = 0
⇒ 1- 28/4x = 3/4
⇒ 27/4x = 3/4
⇒ 27 = (3/4)(4x)
⇒ 27 = 3x
⇒ 27/3 = x
⇒ x = 9
Hence, the soultion of the given equation 1/4x - 3/4 = 7/x for x is 9.
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What is the slope of the line represented by the function 3 x-2 y=-12 ?
The slope of the line 3x - 2y = -12 is 3/2 .
The equation of a straight line can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 3x - 2y = -12 .
To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1. So now we will rearrange the given equation as,
3x - 2y = -12
⇒ 2y = 3x + 12
Now on dividing this equation by 2 on both sides, we will get
⇒ y = (3/2)x + 6 equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 3/2.
Intercept = c = 6
The slope of the line 3x - 2y = -12 is 3/2 .
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What is the range of g(x) = -1/2|x-6| + 1?
-
OA. (-00, 1]
OB. [1,00)
OC. [6,00)
OD. (-∞, ∞)
The range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].
We are given a function:
g(x) = - 1 / 2 | x - 6 | + 1
We need to find the range of the function.
Now, we can see that the tip of the function will be formed when | x - 6 | = 0
x - 6 = 0
x = 6
For x = 6, we have the value of g(x) as
g(x) = - 1 / 2 | 6 - 6 | + 1
g(x) = 0 + 1
g(x) = 1
Also, since - 1 / 2 is negative, the function will have range from negative infinity to 1.
So, the range of the function will become:
( - ∞, 1]
Therefore, the range of the function g(x) = - 1 / 2 | x - 6 | + 1 is ( - ∞, 1].
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What is 12/24 in simplest form
Answer:
Step-by-step explanation:
1/2
Solve for x: -2x -4 > 8
A) x < - 6
B) x > - 6
C) x < - 2
D) x > - 2
Answer:
x < -2
Step-by-step explanation:
-2x + 4 > 8
-4 -4
-2x > 4
divide both sides by -2
x < -2
Because we divided by a negative number, the sign gets flipped. So, the answer is x < -2
Hope this helps!
Surds please answer this question
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{1+\frac{1}{\sqrt{3} } }=\\\\\frac{1}{\frac{1*\sqrt{3} +1}{\sqrt{3} } } =\\\\\frac{1*\sqrt{3} }{\sqrt{3}+1 }=\\\\\frac{(\sqrt{3})(\sqrt{3}-1) }{(\sqrt{3}+1)(\sqrt{3}-1) }=\\\\\frac{(\sqrt{3})(\sqrt{3})-(1)(\sqrt{3}) }{(\sqrt{3})^2-1^2 } =\\\\\frac{3-\sqrt{3} }{3-1} =\\\\\frac{3-\sqrt{3} }{2}[/tex]
Find a new function g(x) transformed from f(x)=-x-2 such that g(x) is perpendicular to f(x) .
The new function is g(x) =-1(1/-x) +2.
The transformation of function f(x) to function g(x) is given by g(x)=A f(Bx+ H)+K. where the constant A scales the function vertically. (A negative A reflects the function about the x-axis B scales the function horizontally. (A negative B reflects the function on the y-axis.) H shifts the function horizontally, and K shifts the function vertically.
Convert f(x) to g(x)
where the conversion is g(x)=f(x)+2.
A perpendicular line has negative reciprocal slopes, so for g(x) to be perpendicular to f(x), we need to get the negative reciprocal of -x, which is -1(1/-x)
So, f(x)=-x-2 ; m = -1
From the above information, we get g(x) as follows.
g(x) =-1(1/-x) +2
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PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
Answer: x = - 2
Step-by-step explanation:
3 ( x + 4 ) + 3 =9
multiply into the brackets
3x + 12 + 3 = 9
3x = 9 - 12 -3
3x = -6
x = -6/3
x = - 2
What f-value did you get for the interaction? report it to two decimal places (e.g. 12.34)
The F-value for the interaction is [tex]3.42[/tex]. It is determined by the interaction of gender and race.
What is F-value?
The calculation of the F-value is used on statistics in analysis of variance which is denoted as ANOVA. The calculated value is determined from the ratio of explained variance to unexplained variance. When the F-values in an ANOVA is higher that means the variance is higher in the sample.
The F-statistic value is also used in the regression analysis to calculate the mean between the population. It also depends on the null hypothesis and when the null hypothesis is true. That means the F-value is always close to one most of the time. It is named as F-value after Sir Ronald Fisher. The variance is the dispersion of the value.
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Simplify each sum or difference. State any restrictions on the variables.
1/2x + 1 / 2x
The simplification of each sum or difference of the given expression [tex]\frac{1}{2x} +\frac{1}{2x}[/tex] is equal to 1/x. Restriction on the variables is given by x≠ 0.
As given in the question,
Given expression is [tex]\frac{1}{2x} +\frac{1}{2x}[/tex]
Simplify the given expression by taking the least common multiple,
[tex]\frac{1}{2x} +\frac{1}{2x}\\\\= \frac{1+1}{2x}\\ \\= \frac{2}{2x}\\ \\= \frac{1}{x}[/tex]
Restriction on the variables is given by x≠ 0.
Therefore, the simplification of each sum or difference of the given expression [tex]\frac{1}{2x} +\frac{1}{2x}[/tex] is equal to 1/x. Restriction on the variables is given by x≠ 0.
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Solve for the missing part of the proportion. 1327 = ?324
Answer:
156
Step-by-step explanation:
1. cross multiply
2. Divide both sides
i hope i helped
Camille buys a cruise ticket during the sale. If the original price was $516, how much does Camille pay? 75% OFF!
Answer:
129
Step-by-step explanation:
75% of 516 is 387 so we just need to subtract 387 from 516. The answer will be 129. Please mark as brainiest
Physical science
If you throw a frisbee at 15 m/s, and it takes 12 seconds to land. How far did the frisbee travel?
Answer:
The answer is it travels 180 meters.
Step-by-step explanation:
To get the answer of how many meters the frisbee traveled in 12 seconds, all you have to do is multiply the number of meters the frisbee can do in 1 second by the number of seconds it traveled. The equation would be 15 x 12 = ? which would equal 180. That is how I got the answer that the frisbee traveled 180 meters in 12 seconds.
I hope I helped!
find the midpoint of the two points (8, -2) and (4, 6)
Answer:
(6, 2)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\\textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Defined points:
[tex](x_1,y_1)=(8,-2)[/tex][tex](x_2,y_2)=(4,6)[/tex]Substitute the defined points into the formula:
[tex]\textsf{Midpoint}=\left(\dfrac{4+8}{2},\dfrac{6-2}{2}\right)=(6,2)[/tex]
Therefore, the midpoint of the two given points is (6, 2).
Negative Net Worth is defined as:
Answer:
something
Step-by-step explanation:
onther something
12 kilowatt hours in 3 days (kilowatt hours per year).
Step-by-step explanation:
Given that
12 kilowatt/hours in 3 daysTo find
kilowatt/hours per yearSo, according to the question
we have,
12 kilowatt/hours power in 3 daysWe have to find the value in kilowatt / hours power for per year basis
So, We know
Days in one year = 365
power in 3 days = 12 kilowatt/hours
For calculate power in single day, we have to divide power in 3 days by 3.
So power in a single day = 12/3 kilowatt/hours
= 4 kilowatt/hours
Now we have to multiply days in one year with power in a single day
power for per year basis
= days in one year x power in a single day
Now, putting the all values,
= 365 x 4 kilowatt/hours.
= 1460 kilowatt/hours.
Answer:
So the total power will produced in single year is 1460 kilowatt/hours.To learn more about multiply and division, please click on the link:
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can you please help me with this?
(worth 12 points)
I also need the work shown
ty
Answer:
new position is 360 feet below sea level.
Step-by-step explanation:
see picture for reference.
In Chicago, the assessed value of a house is calculated by taking 60% of its current market value. The property tax is calculated by taking 3.9% of the assessment value. What would the property tax be on a house that has a market value of $420,000?
A. $9,828
B. $98,280
C. $982.80
D. $98.28
E. None Of The Above
The property tax be on a house that has a market value of $420,000 is A. $9,828
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Assessed value of a house = 60% of current market value
Property tax = 3.9% of the assessment value
Now the given market value of a house is $420,000
Assessed value of a house = 60% of $420,000
⇒ Assessed value of a house = 0.60 * $420,000
⇒ Assessed value of a house = $252,000
Thus, Property tax = 3.9% of $252,000
⇒ Property tax = 0.039 *$252,000
⇒ Property tax = $9,828
Thus, the property tax be on a house that has a market value of $420,000 is A. $9,828
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solve for x show all steps
What's the answer........................
Using the general recursive formula, he 25-th term in the arithmetic sequence is 29.7
How to find the value of a₂₅?Here we have an arithmetic sequence with the first term a₁ = 3.3 and the common difference is d = 1.1
Remember that the general arithmetic recursive formula is:
aₙ = a₁ + (n - 1)*d
This formula allows us to find the n-th term of the arithmetic sequence only using the first term and the common difference.
In this case, we just need to replace n by 25 and the values written above.
a₂₅ = 3.3 + (25 - 1)*1.1 = 29.7
We can conclude that the 25th term in the sequence is 29.7
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How do you find a 3 sided shape from a triangle?
Answer:
Identify angle C. It is the angle whose measure you know.
Identify a and b as the sides that are not across from angle C.
Substitute the values into the Law of Cosines.
Solve the equation for the missing side.
Step-by-step explanation:
For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles. If you know some of the angles and other side lengths, use the law of cosines or the law of sines.
Rs8000for3year3manthat6×1÷2%pur annum find simple intrest
Answer:
Simple Interest = Rs1560
Step-by-step explanation:
A = P (1 + rt)
A = final amount
P = initial principal balance = Rs8000
r = annual interest rate = [tex]6\frac{1}{2}[/tex]% = 0.065
t = time (in years) = 3 years
A = 8000*(1 +(0.065*3)) = 8000*(1+0.195) = 8000*(1.195) = 1560
Simple Interest (A) = Rs1560
