A scale factor is a factor that can be used to either increase or decrease the size of a given figure. Therefore, the scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
Scale drawing is a type of drawing that requires the use of a factor to either enlarge or reduce the size of a given figure. The factor required is called a scale factor. It can be expressed as:
scale factor = [tex]\frac{length of side of image}{length of side of object}[/tex]
In the given question, the radius of the circle drawn is 3 inches, while that on the wall has a diameter of 4 feet.
Thus;
diameter of circle = 2 * 3
= 6 inches
But;
1 feet = 12 inches
So that;
x = 6 inches
⇒ x = [tex]\frac{6}{12}[/tex]
= [tex]\frac{1}{2}[/tex]
x = 0.5 feet
Thus, the diameter of the circle is 0.5 feet.
So that;
scale factor = [tex]\frac{0.5 feet}{4 feet}[/tex]
= 0.125
scale factor = [tex]\frac{1}{8}[/tex]
The scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
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The data set represents the number of hours that fifteen students walked during a two-week period.
6 6 7 8 8 8 9 10 10 12 13 14 15 16 30
The median is 10 hours, Q1 is 8, Q3 is 14, and the IQR is 6 hours. Are there any outliers in the data? Explain or show your reasoning.
please help
Answer:
Yes, 30 would be your outlier.
Step-by-step explanation:
The rest of the numbers are closer and 30 is far away from the rest.
ABCD is a quadrilateral. Select all the criteria that are sufficient to prove that ABCD is a parallelogram.
Line segment AB is congruent to line segment DC and Line segment is congruent to line segment BC.
Line segment AB is parallel to line segment DC
X is the midpoint of line segment AC and line segment BD
A parallelogram is a shape which has opposite sides to be equal and parallel. Therefore, the required properties that are sufficient for the prove are:
A. Line segment AB is congruent to line segment DC and Line segment AD is congruent to line segment BC.
B. Line segment AB is parallel to line segment DC.
Quadrilaterals are four sided shapes. Examples are square, rectangle, parallelogram, trapezium etc. These have different or distinguishing properties.
A parallelogram is a figure that has its opposite sides to be equal in length and which are also parallel. This properties can be used to answer the given question.
Thus, the appropriate criteria that are sufficient to prove that ABCD is a parallelogram are:
A. Line segment AB is congruent to line segment DC and Line segment AD is congruent to line segment BC.
B. Line segment AB is parallel to line segment DC.
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Select all that are solutions to the inequality below:
3x - 15 > 3
Answer:
solutions are all values greater than 6
Step-by-step explanation:
add 15 to each side to get:
3x > 18
divide each side by 3 to get:
x > 6
solutions are all values greater than 6
solve pls brainliest
Answer:
48.95
Step-by-step explanation:
{1, 2, 3, 4, 5, ..., 198, 199, 200}
How many members of the set shown above are multiples of 6 but not a multiple of 9?
(I need a faster way of doing this question. Not listing the factors of 6 and 9 one by one.)
Thank you so much. I will give brainliest!!!
Answer:
22
Step-by-step explanation:
The least common multiple of 6 and 9 is 18. Consider a group of 18 numbers, 1–18, for example. The multiples of 6 are 6, 12, and 18, of which two are not multiples of 9.
There are 11 groups of 18 numbers in 1–200, with 2 left over. That means there will be 11×2 = 22 numbers that are multiples of 6 but not 9.
__
200/18 = 11 remainder 2
What is the domain and range of the function below
The graph of f(x) = 2x + 3 is shown above. Which graph represents f-'(x)?
Answer:
May we assume "f-'(x)" means the fiurst derivative of f(x)? I'm not sure what f-'(x) sign means, if not that. The answer assume this is the first derivative. No graphs are shown, so I'll add one.
Step-by-step explanation:
f(x) = 2x + 3
f'(x) = 2
The graph would be a staight vertical line through x=2. The slope of the line f(x) = 2x + 3 is 2
PLEASE HELPPPPPPPPPPPPP
In a recent year, 34.7% of all registered doctors were female. If there were 48,900 female registered doctors that year, what was the total number of registered doctors?
ROUND YOUR ANSWER TO THE NEAREST WHOLE NUMBER
Answer:
140922
Step-by-step explanation:
48900/34.7 = 1409.2219
1409.2219 *100 = 140922.19
rounded - 140922
Alacrosse player throws a ball in the air from an initial height of 7 feet.
The ball has an initial vertical velocity of 90 feet per second. Another player catches the ball when it is 3 feet
above the ground. How long is the ball in the air? Round your answer to the nearest hundredth.
Answer:
Modeling the situation with a quadratic equation, it is found that:
The maximum height of the ball is of 60.2 feet.
The ball hits the ground after 3.39 seconds.
Considering the gravity, the height of the ball, after t seconds, is given by the following quadratic equation.
In which:
is the initial velocity.
is the initial height.
In this problem:
Height of 8 feet, thus .
Initial velocity of 32 feet per second,
The equation is:
Which is a quadratic equation with .
The maximum height is the output of the vertex, which is:
Then, with the coefficients of this question:
The maximum height of the ball is of 60.2 feet.
It hits the ground at t for which , thus:
We want the positive value, so:
The ball hits the ground after 3.39 seconds.
A similar problem is given at brainly.com/question/24626341
Step-by-step explanation:
Can someone help me?
Answer:
CD = 32 units
Step-by-step explanation:
The midpoint divides the segment into congruent parts:
CM = MD
8(x -2) = 4(5x -16)
2(x -2) = 5x -16 . . . . . . divide by 4
2x -4 = 5x -16 . . . . . . . eliminate parentheses
12 = 3x . . . . . . . . . . . . . add 16-2x to both sides
4 = x . . . . . . . . . . . . . . . divide by 3
Then the segment measures are ...
CM = 8(x -2) = 8(4 -2) = 16
CD is twice that length. CD = 32 units.
_____
Additional comment
There are many ways to solve equations like this. The one usually recommended is to simplify it first. That generally means eliminating parentheses and collecting terms. Doing that would give ...
8x -16 = 20x -64
Since there is a common factor of 4 on both sides, we can divide by that, making the numbers smaller and eliminating one set of parentheses.
Of course, the properties of equality require that whatever operation you perform on one side of the equal sign must also be done on the other side. So "divide by 4" means "divide by 4 on each side of the equal sign."
There are 50 sheets of scrapbook paper in a pack, and 20% of them are striped. How many sheets of scrapbook paper are striped? Pick the model that represents the problem. How many sheets of scrapbook paper are striped?
Answer:
10 sheets of paper are striped
Step-by-step explanation: Make a proportional relationship.
20% as a fraction is 20/100
Make 50 into a fraction using a variable. For example, x/50
Cross multiply 20 and 50. That equals 1000.
Then divide 1000 by 100 and that equals 10. So 10 sheets of paper are striped.
Hope this helps!
Fill the gaps in the
a Die
x = -7
5x - 7 ?
Answer: -42
Step-by-step explanation:
If X = -7
Then:
= 5(-7) - 7
= -35 - 7
= -42
Hope it helps:)
At a local grocery store, 7 lb of squash cost $14.00
and 4 lb of tomatoes cost $10.00.
Answer:
1 LB of tomatoes is $2.50 and 1 LB of squash is $2.00
Step-by-step explanation:
Determine if the table represents a linear function, quadratic function, or exponential function.
That would be linear because its going at a constant rate of change
Write each number without exponent 6.453 x 10^-3
Answer:
.006453
Step-by-step explanation:
6.453 x 10^-3
Move the decimal 3 places to the left since the exponent is negative
006.453
.006453
- 3/4(12x+16)<9-5x Show your work
Answer:
x > -5.25
Step-by-step explanation:
A mobile phone company increases its monthly prices by 1.8% to 35.62. How much is the monthly price increase?
Answer:
0.62982 monthly price increase
Step-by-step explanation:
The length of the base of an isosceles triangle is x. The length of a leg is 5x -5. The perimeter of the triangle is 111. Find x
Answer:
x = 11
Step-by-step explanation:
Perimeter of a triangle = the sum of the three sides.
In an isosceles triangle there is a base and two equal legs
Perimeter = (x) + (5x - 5) = (5x - 5)
111 = 11x -10
111 + 10 = 11x
121 = 11x
[tex]\frac{121}{11} =\frac{11x}{11}[/tex]
x = 11
I need some help please
The length is 5 units.
2
For the following Arithmetic Sequence, find the explicit form, and then find a 40
11, 1,-9, -19, ...
a40 =
an=
Answer:
see explanation
Step-by-step explanation:
The explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 11 and d = a₂ - a₁ = 1 - 11 = - 10 , then
[tex]a_{n}[/tex] = 11 - 10(n - 1) = 11 - 10n + 10 = 21 - 10n ← explicit formula
Using the explicit formula to find a₄₀ , then
a₄₀ = 21 - 10(40) = 21 - 400 = - 379
Given the graph below, which of the following could be the quadratic equation?
A.
[tex]3(x + 2 {)}^{2} + 5[/tex]
B.
[tex] - {x}^{2} + 8x + 18[/tex]
C.
[tex] - 2(x - 3 {)}^{2} + 1[/tex]
D.
[tex] {x}^{2} - 8x + 18[/tex]
Needs to be answered quickly
Answer:
only D as the correct answer
Step-by-step explanation:
The correct quadratic could not be B or C, because the negative sign in each indicates that the parabola opens down, which is not what we see here.
A is not appropriate either, because of the (x + 2)^2; that + sign tells us that the vertex lies 2 units to the left of the y-axis.
This leaves only D as the correct answer.
Which represents the solution set of 5(x+5) <85?
X<12
Χ> 12
X< 16
Χ<16
Answer:
[tex]x<12[/tex]
Step-by-step explanation:
[tex]5(x+5)<85\\\\5x+25<85\\\\5x<60\\\\x<12[/tex]
Option A is correct, x<12 represents the solution set of 5(x+5) <85
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 5(x+5) <85
We have to find the solution set of the given inequality
Five times of x plus five less than eight five.
Apply distributive property
5x+25<85
Subtract 25 from both sides
5x<85-25
5x<60
Divide both sides by 5
x<12
Hence, option A is correct, x<12 represents the solution set of 5(x+5) <85
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Which of the following is a solution to the inequality below?
–4 +
10
m
< –68
10 points
Answer:
m < - 6.4
Step-by-step explanation:
- 4 + 10m < - 68 ( add 4 to both sides )
10m < - 64 ( divide both sides by 10 )
m < - 6.4
Answer:
m can be -9
Step-by-step explanation:
-4+10m < -68
10m < -64
m < -6.4
using this statement, m can be any value less than -6.4, such as -9.
9 4/5÷3 1/2 as a fraction
Answer:
As an improper fraction, the answer is 14/5, and as a mixed fraction, the answer is 2 4/5.
Step-by-step explanation:
Brainliest Please!Find the perimeter. Simplify your answer.
Answer:
2p -2
Step-by-step explanation:
To find the perimeter, add up all the lengths of each side of the rectangle.
Perimeter
= 2 +2 +p -3 +p -3
= 2 +2 -3 -3 +p +p
= -2 +2p
= 2p -2
What is an equation of the line that passes through the points (2, -7)(2,−7) and (2, -2)(2,−2)
Answer:
X = 2
Step-by-step explanation:
Slope: (- 7 - -2)/(2 - 2) = -5/0 = 0
The line is vertical (undefined
What is the slope-intercept form of the linear equation x + 4y = 12?
Quick please!!!!
Answer:
y=(12-x)/4
Step-by-step explanation:
subtract x on both sides, then divide by four
Answer:
Step-by-step explanation:
Slope intercept form: y = mx +b
x +4y = 12
4y = -x + 12
Divide the entire equation by 4
[tex]\dfrac{4y}{4}=\dfrac{-x}{4}+\dfrac{12}{4}\\\\\\y =\dfrac{-1}{4}x+3[/tex]
X = 4 + y
2x – 3y = 1
We know x = 4 + y (1)
So 2x - 3y = 1
<=> 2.(4 + y) - 3y = 1
<=> 8 + 2y - 3y = 1
<=> 8 - y = 1
<=> y = 8 - 1
<=> y = 7 (2)
move (2) to (1) : x = 7 + 4 = 11
ok done. Thank to me :>
Which is bigger 12 cm or 102 mm
On comparing the quantities 12 cm or 102 mm, 12 cm (120 mm) is greater than 102 mm.
To compare the sizes of 12 cm and 102 mm, both numbers should have the same unit.
Now, the conversion factor cm and mm is
1 cm = 10 mm
Then, using the conversion factor convert 12 cm to mm
12 cm = 12 x 10 mm
= 120 mm
Now, compare 120 mm and 102 mm which gives 120 mm is greater.
Thus, 12 cm is greater than 102 mm.
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confused can get some help plz
Answer:
Blue costs 2.875 or 2.88 if rounded, Red costs 3.875 or 3.88 if rounded
Step-by-step explanation: