According to the scale factor, When the scale is changed to 20 feet to 1 unit, then the drawing would be exactly the same shape, here only each side would have half the original drawing units.
Scale factor:
The ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller) is known as scale factor.
Given,
This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft.
Here we need to find the reason for the scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment
Here we know that the actual apartment has a perimeter of 160 ft.
And we have to draw another scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment to the drawing.
So, as per the given details, the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is calculated as,
=> 160 / 16 = 10 feet on a side.
Therefore, 10 feet in real life plots to 1 unit on the drawing
Therefore, if we change the scale to 20 feet to 1 unit , then the drawing would be exactly the same shape, only each side would have half the original drawing units.
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A package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents. How many unique keys will result from the distribution
Using the multiplication, 192 unique keys will result from the distribution.
In the given question we have to find the number of unique keys will result from the distribution.
As given that a package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents.
So 1 package have 12 electrical locks with a unique key.
Package delivered to 16 job site.
We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.
So total keys=12×16
Total keys=192
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Select the correct answer. The equations y = 1 2 x + 1 and y = 2 x + 4 are graphed on the coordinate grid. A nonlinear function starting from the line (minus 2, 0), and (0, 2) another line intercepts the x and y-axis (minus 2, 0), and (0, 1) How many real solutions does the equation 2 x + 4 = 1 2 x + 1 have? A. 0 B. 1 C. 2 D. cannot be determined from the graph
These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
What are the types of solutions in a system of equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given are two equations y = 12x + 1 and y = 2x + 4.
Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
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A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
Find all points of intersection of the graphs of the polynomials. f(x)=(x+5)(x-5) and g(x)=(x+1)(x-3)
Answer:
1 intersection point at (11,96)
Step-by-step explanation:
Comment
The best way to solve this is to start with a graph. Then you can work out the actual intersection points.
The graph shows that there is only 1 intersect point. Let's try and find it.
Givens
y = (x - 5)(x + 5) = x^2 - 25
y = (x +1)(x - 3) = x^2 -2x - 3
If the intersect points are what you want, then the y value for both equations must be equal.
Solution
x^2 - 25 = x^2 - 2x - 3 Subtract x^2 from both sides
x^2 - x^2 - 25 = x^2 - 2x - 3 Combine
- 25 = - 2x - 3 Add 3 to both sides
-25+3 = -2x - 3 + 3 Combine
-22 = - 2x Divide by - 2
-22/-2 = x
x = 11
y = x^2 - 25
y = 11^2 - 25
y = 121 - 25
y = 96
An applicant receives a job offer from two different companies. Offer A is a starting salary of $55,000 and 5% increase for 5 years. Offer B is a starting salary of
$56,000 and an increase of $2,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation lor A, that represents the total salary received after
n years. Justity your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total: salary received
after n years. Justity your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after years? Show all necessary math work. (4 points)
After 5 years, Offer A will offer a higher total salary.
What is arithmetic mean?The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.
Given
a) that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:
b) Offer A -> Arithmetic
=>55000 x 1.05 ^ 5 = X
=>55000 x 1.2762 = X
70,195.48 = X
Offer B -> Geometric
=>56000 + (5 x 2000) = X
=>56000 + 10000 = X
66,000 = X
c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.
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Simplify: (A + C)(AD + AD) + AC + C
Answer:
It looks just fine! Well done!
It looks just fine! Well done!A bit more simply,
It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C
Step-by-step explanation:
Hope this helped
Two students share 8 markers equally enter the numerical expressions in he box that models the situation
Answer: 8÷2 or 8/2 and also just in case, the answer is 4
Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.
Hope this helps!
solve 5x+y=24x+y=4 use the linear combination method
Answer:
(x,y)=(0,4)
Step-by-step explanation:
write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)
-3/2t+1/3=2/4
Answer??
Answer:
t = 1/9
Step-by-step explanation:
Combine multiplied terms into a single fraction
-3/2 (t) + 1/3 = 2/4
3t/2+ 1/3 = 2/4
Find common denominator
3 x 3t/6 + 2/6 = 2/4
Combine fractions with common denominator
3 x 3t/6 + 2/6 = 2/4
3x3t + 2
/ 6= 2/4
Multiply the numbers
9t+2
/6 = 2/4
Divide the numbers
9t+2 divided by 6 is 1/2
Multiply all terms by the same value to eliminate fraction denominators
6 x 9t+2 divided by 6 = 6 x 1/2
Cancel multiplied terms that are in the denominator
9t+2=3
Subtract 2 from both sides
9t+2-2=3-2
Simplify
9t=1
Divide both sides by the same factor
9t/9+=1/9
Simplify
t= 1/9
Write an slope equation form of the equation of the line through the given points
through: (0, -3) and (-5, 4)
The slope equation form is :
m = - 7/5
Slope Solution
To calculate the slope use the slope formula.
m = (y2- y1)/(x2- x1)
Where (x1,y1) and (x2,y2) are 2 coordinate points.
Here the 2 points are (0,-3) and (-5,4)
let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)
m = (4 - (-3))/((-5) - 0)
m = 7/((-5) )
m = - 7/5
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HW1.
The vertices of a triangle ABC are A(2, 1), B(-2, 3) and C(4, 5). Find the equation of the median through the
vertex A
A
Assume D be the midpoint of BC
Answer:
y = -3x +7
Step-by-step explanation:
You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).
Midpoint of BCThe median will go through the midpoint of the segment opposite vertex A. That midpoint is ...
D = (B +C)/2
D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)
SlopeThe slope of the line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Then the slope of AD is ...
m = (4 -1)/(1 -2) = 3/-1 = -3
Point-slope equationThe point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
The equation of the line with slope -3 through point A(2, 1) is ...
y -1 = -3(x -2) . . . . . equation of the median line
This can be simplified to slope-intercept form:
y = -3x +6 +1 . . . . . eliminate parentheses, add 1
y = -3x +7 . . . . . slope-intercept equation of the median line
Find the area of the given figure
Answer:
you multiply the numbers to find the area so W*H with times hight so the answer would be 6,250
About 65% of American teenagers wear orthodontal corrective devices..
In Heritage High School, there are about 1,800 teenagers. How many of them would you expect to have corrective devices?
Answer:
1170 teenagers would have corrective devices
Step-by-step explanation:
hope this helps :)
Bianka makes an error when she tries to write an expression equivalent to 12+15×3 minus Y -10 Y what is the error
The error that Bianka made in the algebraic expression is that; when 15 was distributed it should be '45 - 15y' rather than '45 + 15y'
How to simplify algebraic expressions?An algebraic expression is defined as an expression that is made up of variables and constants, as well as algebraic operations such as multiplication, addition, division, subtraction, etc.
Now, the steps that Bianka took to solve the algebraic expression are;
12 + 15(3 - y) - 10y
12 + 45 + 15y - 10y
57 + 5y
Now, the first step according to the rule PEMDAS is to expand the bracket and when positive and negative are multiplied, the sign is negative and as such step 2 should have been 12 + 45 - 15y - 10y.
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help please, the question in the picture
The probability of either A or B is 0.48 and the probability neither A nor B would be 0.52
What is Probability?Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event
probability A will occur pr(A) = 0.39, probability A will not occur pr(A') = 1 - 0.39 = 0.61,
Probability B will occur pr(B) = 0.42, probability B will not occur, pr(B') = 1 - 0.42 = 0.58
For mutually exclusive events if A will occur it means that B will not occur
So, probability either A or B is
= pr(A) x pr(B') + pr(B) x Pr(A')
= 0.39 x 0.58 + 0.42 x 0.61
= 0.4824 and to 2 decimal places the answer becomes 0.48
The probability neither A nor B is equal to 1 - 0.48 = 0.52
In conclusion the probability Either A or B will occur is 0.48 and the probability neither A nor B is 0.52
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Josie is a student in a fifth-grade inclusion class. She has a specific learning disability in mathematics and has difficulty solving word problems. As soon as she finishes reading a problem, she begins doing computations; additionally, she seems to think that all problems have whole-number answers. One of the annual goals in her IEP is related to learning the process of solving word problems: "Josie will be able to solve grade-appropriate word problems independently 85 percent of the time, using a systematic and logical process.
Answer:
Step-by-step explanation:
Solving word problems is always hard. even w/o any learning challenges. I'm kind of good at word problems but what I notice is that people have ways to ask word problem questions that can be very much about their own thought process, not really about the math. Often it matters who is asking the word problem more than what the question is about for understanding the problem. I don't think Josie will stand a chance with some peoples questions, like she'll solve it .01% of the time. Not 85% of the time. Just my perspective. :)
find 5 consecutive odd integers if the sum of the first 3 integers more than the sum of the last 2
The five consecutive odd integers are 11, 13, 15, 17 and 19.
What are odd integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Odd numbers are whole numbers that cannot be divided exactly into pairs.
Therefore, odd integers are integers that cannot be divided exactly into pairs.
Hence, let's find five consecutive odd integers if the sum of the first three integer is 3 more than the sum of the last 2.
let
the first odd integer = x
x + x + 2 + x + 4 = x + 6 + x + 8 + 3
3x + 6 = 2x + 17
3x - 2x = 17 - 6
x = 11
Therefore, the consecutive odd integers are 11, 13, 15, 17 and 19.
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The distance covered by a car traveling at a constant speed is directly proportional to the
time spent traveling. If the car goes 75 miles in 2.5 hours, how far will it go in 7 hours?
Answer:75/5 = x/7
Step-by-step explanation:
Complete this equation and you will end up with the answer 105
Find the distance between the point (6,7) and the line y = 6x + 7 (rounded to the nearest hundreth).
A) 2.42
B) 5.92
C) 5.84
D) 1.38
Answer:
5.92
Step-by-step explanation:
Line in standard form
-6x + y - 7 = 0
distance = |-6 * 6 + 1 * 7 - 7|/([tex]\sqrt{(-6^2)+ 1^2)}[/tex]
|-36 +7 - 7| = √37
|-36|/√37
36/√37
5.918363 = 5.92
WHAT IS THE NAME OF THIS FORMULA????
Answer:
Estimation and Confidence Intervals
Step-by-step explanation:
Just found it on a math website basically.
1.Glenda wants to glue glitter over a piece of felt shaped like a parallelogram with a height of 52 in. and a base of 58 in.
If the glitter costs $1.10 per ft², how much will it cost to cover the felt?
2.The shape of a patio is trapezoidal with a height of 10 ft. and bases of 19 ft. and 13 ft.
What is the cost of outdoor carpeting to cover the patio if the carpeting costs $1.50 per ft².?
The cost of covering the felt with glitter is $3,317.60.
The cost of the outdoor carpeting to cover the patio is $240.
What are the costs?The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area = base x height
52 x 58 = 3,016 in²
Cost of covering the felt = cost of the glitter per feet are of the felt
$1.10 x 3,016 = $3,317.60
A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
Area of a trapezoid = 1/2 x (19 + 13) x 10
Area of a trapezoid = 1/2 x 32 x 10 = 160 ft²
Cost of the outdoor carpeting =cost per square feet x area of the patio
$1.50 x 160 = $240
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Another equation question?
The equation to represent the total number of students taking the yoga classes is s = 13c.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of students = s
Let the number of classes = c
Therefore the total students will be:
s = 13 × c
s = 13c
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I need help with this please help me
Answer:
Step-by-step explanation:
Hi, Danna, these are tough to figure out...
so, first check to see if the 3 known angles add up to 180°, they don't I checked, so, it tells us that the one angle 96° up at the top, does not include ∠2 , which is good, b/c we now know 2 of the angles in that inner triangle.. and we know that a triangle adds up to 180° , so just find that last angle... the one opposite to ∠1 .... nice, if we get the ∠1' angle we can then also figure out ∠1
180-96-30=54
∠1' =54°
so ∠1= 180-54 =126°
we now know ∠1
use that , and that the next smaller triangle also adds up to 180
to find ∠2
∠2= 180-28-126=26°
∠1=126°
∠2 = 26°
:) it's tough to think all of that through. don't worry. just keep working these , they will get easier.
A 40-foot rope is cut into 2 pieces. Seven less than four times the length of the longer rope piece x is five times the length of the shorter piece, which is (40 − x) ft. Find the length of the longer rope piece x (in ft). (Enter an exact number.)
If a 40-foot rope is cut into 2 pieces. the length of the longer rope piece x is 23ft.
How to find the length?Seven less than 4 times = 4x-7
4x-7=5(40-x)
4x-7=200-5x
Collect like terms
9x=207
Divide both side by 9x
x = 207 /9
x=23 ft (longer part of the rope)
Shorter part of the rope
40-x where x is 23
40 -23
= 17ft
Therefore the longer part is 23ft.
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Need help with question
The required derivative of the given function g(z) = ln√(16- z² / 16+z²) is
[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]
What is the chain rule in differentiation?The outside-inside rule, the composite function rule, and the function of a function rule are all synonyms for this chain rule in differentiation. It is exclusively used to calculate the derivatives of composite functions.
The chain rule formula as shown below
d/dx ( f(g(x) ) = f' (g(x)) · g' (x)
The function is given in the question
g(z) = ln√(16- z² / 16+z²)
We have to differentiate g(z) = ln√(16- z² / 16+z²)
Differentiation with respect to z in the given function,
[tex]\frac{d}{dz}\left(\ln \left(\sqrt{\left(\left(\frac{16-z^2}{16+z^2}\right)\right)}\right)\right)[/tex]
We have to apply the chain rule of differentiation for finding derivatives,
[tex]\dfrac{1}{\sqrt{\dfrac{16-z^2}{16+z^2}}}\dfrac{d}{dz}\left(\sqrt{\dfrac{16-z^2}{16+z^2}}\right)[/tex]
[tex]-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]
Therefore, the required derivative of the given function g(z) = ln√(16- z² / 16+z²) is
[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]
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The top of an Iceberg is 67 ft above sea level, while the bottom is 283 ft below sea level. What is the distance between the top and the bottom
of the Iceberg?
The distance between the top and the bottom of the iceberg is 417 feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The top of an Iceberg is 67 ft above sea level, while the bottom is 283 ft below sea level.
We can draw as,
Top of an iceberg
|
|
| (67 feet)
|
Sea level
|
| (283 feet)
|
|
Bottom of the iceberg
The distance above the sea level = 67 feet
The distance below the sea level = -283 feet
( negative sign due to below-sea level
Now,
The distance between the top and the bottom of the iceberg.
= 67 - (-283)
= 67 + 283
= 417 feet
Thus,
The distance between the top and the bottom of the iceberg is 417 feet.
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Write an equation for a parabola with x-intercepts (-4,0) and (3,0) which passes through the point (2, -12).
Answer:
y = 2(x + 4)(x - 3)
Step-by-step explanation:
Knowing the x-intercepts, we can set up the equation:
y = (x + 4)(x - 3)
However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"
-12 = a(2 + 4)(2 - 3)
-12 = a(6)(-1)
-12 = -6a
2 = a
Now, we can write the equation for the parabola:
y = 2(x + 4)(x - 3)
Can someone please look in the photo and explain? Thanks so much I appreciate the help.
Answer:
25.12
Step-by-step explanation:
C = [tex]\pi[/tex]d The d is the diameter. This is the distance across the ha that goes through the middle of the circle.
C 3.14(8) The c stands for the circumference or the distance around the circle. We generally use 3.14 for [tex]\pi[/tex]
C= 25.12
Tom rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a facto
r of 21.
The probability of getting a total that is a factor of 21 is 2/9
Tom rolls 2 fair dice and adds the results from each
Total number of outcomes = 6 × 6
= 36
The probability = Number of favorable outcomes / Total number of outcomes
The factors of 21 = 1, 3, 7, 21
The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
Number of possible outcomes = 8
The probability = Number of favorable outcomes / Total number of outcomes
Substitute the values in the equation
= 8 / 36
= 2/9
Hence, the probability of getting a total that is a factor of 21 is 2/9
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Ed and Flo share money in
the ratio 3:5. Flo gets £40
more than Ed. How much
money was shared in total?
5x - 3x = 2x
2x = 40
x = 20
x * 8 = 160