One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 1 unit wide.
10
5
The rectangle that is shaded has an area of 18 square units.
The framed rectangle is represented by the darkened area, while the frame is shown in white.
The frame's known width is two units, and both the rectangle and the frame have the following dimensions:
width = 7 units
length = 10 units
Now, if we remove the frame, each measure will lose 2*2 units, or 4 units (because for each measure we have the frame in both sides).
As a result, the measurements for the shaded rectangle are as follows:
width = 7 units - 4 units = 3 units
length = 10 units - 4 units = 6 units.
And since the product of a rectangle's width and length determines its area, we may calculate:
A = (3 units)*(6 units) = 18 square units.
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16. The formula A = r² can be used to find the area of a circle. Solve the equation for r.
a. r=A-2n
b. r = √A - T
C. r=
d.)r =
A
A
211
What is the selling price if cost is $18.00 and the mark up is 70% ??
show your work
The selling price if cost is $18.00 and the mark up is 70% is $30.60
What is mark up?
The mark up means profit earned as percentage of the cost price, whereas margin means the profit is a percentage of the selling price, in other words, the profit element to add to the cost price to derive the selling price in this case is 70% of the cost price of $18.00
profit(mark up)=70%*$18.00
profit(mark up)=$12.60
selling price=cost price+ profit(mark up)
selling price=$18.00+$12.60
selling price=$30.60
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Rob and Lila try to simplify 18 x 42 + (9 – 3)2. Rob simplifies the expression and gets 360. Lila simplifies it and gets 324. Which student is correct? What error did the other student make?
The result of the expression, 18 x 4² + (9 – 3)² after simplification is 324.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.
Simplifying the expression
The given expression is 18 x 4² + (9 – 3)²
Using the BODMAS rule, we get,
= 18 x 4² + (6)²
= 18 × 16 + 36
= 288 + 36
= 324
Lila estimated it right.
The mistake that Rob might have made would be that he must have not solved (9 – 3)² the right way and gained the wrong answer.
Hence, the result of the expression, 18 x 4² + (9 – 3)² after simplification is 324.
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14. Which expression shows the sum of 30 and 45 as the product of th and a sum of two numbers with no common factor? A) 5(6 + 9) B 15(2+3) C 15(15 +45) D 90(2+3)
Coordinates: (-4, 4), (5, -1)
midpoint:
slope:
distance:
Answer:
Step-by-step explanation:
Compute the midpoint of the line segment with endpoints:
p_1 = (-4, 4) and p_2 = (5, -1)
The midpoint between (x_1, y_1) and (x_2, y_2) is their componentwise average:
((x_1 + x_2)/2, (y_1 + y_2)/2)
Substitute (x_1, y_1) = (-4, 4) and (x_2, y_2) = (5, -1):
= ((-4 + 5)/2, (4 - 1)/2)
-4 + 5 = 1:
= (1/2, (4 - 1)/2)
4 - 1 = 3:
Answer: = (1/2, 3/2)
QUICK IM TIMED PLS HELP
Re arrange equation to make x the subject
X-3=4y
Answer:
Re arrange equation to make x the subject
X-3=4y
-3 will be moved to the other side of equal sign
in doing so, its sign will be be switched
so
x=4y+3
Absolute value of 2 is
Step-by-step explanation:
|2|=2
Hope this helps !!!!
Answer:
The absolute value is 2
Step-by-step explanation:
The absolute value is defined by how far a value is from zero and it is represented by a / /
/2/ = 2
If the end behavior is decreasing to the left ,what might be true about the function
Answer:
As the input gets smaller, the output gets smaller.
Step-by-step explanation:
- A certain forest covers an area of 30 square kilome-
ters. In 2018, the number of pine trees in this
particular forest was 75,000. In 2019, the number
of pine trees had decreased so that there was an
average of 2,000 pine trees per square kilometer in
the forest. What was the total percent decrease in
the number of pine trees in this forest from 2018 to
2019?
E. 20%
F.24%
G. 25%
H. 30%
Answer:
E
Step-by-step explanation:
2018 : 75 000 pines
2019 : 2000 pines / km^2 * 30 km^2 = 60 000 pines
(75 000 - 60 000) / 75 000 = .2 or 20 %
-6 + (-2)? What does it meanrnjrhdbr
adding a negative is the same as subtracting a positive
the expression -6+ (-2) is the same as -6-2 which is -8
If m is one sixth of n and p is five less than m, write a p as a function of n
p = (n - 30)/ 6 as a function of n.
Here we need to find the value of p in terms of n.
From the question, we have two equation
The first equation is:
m = 1/6n .......(1)
The second equation is:
p = m - 5.......(2)
From equations 1 and 2 we have to find the value of p in term of n.
So by putting the value of m in the second equation we have:
p = 1/6n - 5
= (n - 30)/6
Therefore we get the value of p as (n -30)/6 in terms of n.
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Find the population variance ad standard deviation
6,12,20,24,28
The population variance ad standard deviation are 64 and 8 respectively.
The variance for a population is calculated by the below steps :
1) First find the mean (the average).
2) Subtracting the mean from each number in the data set and then squaring the result. The results are squared to make the negatives value positive
3) Averaging the squared differences.
Here, the data set of population is given as :
population difference difference²
6 -12 144
12 -6 36
20 2 4
24 6 36
28 10 100
₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋
∑ 90 ∑ 320
Now, the average population will be :
∑ 90/5 = 18
Now finding the variance σ² using the formula :
σ² = ∑(x- x')²/N
σ² = 320/5
σ² = 64
Now, the standard deviation σ will be :
standard deviation = √σ²
standard deviation = √64
standard deviation = 8
Therefore, the population variance ad standard deviation are 64 and 8 respectively.
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Which point is part of the intersection of planes ACD and MHG?
A point that is part of the intersection of planes ACD and MHG is: Point B.
How to Find the Points of Intersection of Planes?A plane has at least three points that lie on it. When two planes intersect, they do so at some certain points. This means that two intersecting planes share some points in common alone the line of their intersection.
In the diagram given, plane ACD and plane MHG intersect along line BA. This means that both planes share points A and B in common.
Therefore, we can state that a point that is part of the intersection of planes ACD and MHG is: Point B.
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PLEASE HELP!
Anand is driving on a long road trip. He currently has 10 gallons of gas in hi
car. Each hour that he drives, his car uses up 2 gallons of gas. How much ga
would be in the tank after driving for 2 hours? How much gas would be left
after t hours?
gas left after 2 hours
gas left after t hours
Answer:
8 gallons left.......
Step-by-step explanation:
10 - 2 = 8
Model this expression on a number line
A nation can produce two products: tanks and autos. The table below is the nation's production possibilities schedule.
Production Possibilities
Product
Tanks
The total opportunity cost of three unit(s) of tanks is
A
0
1000
B
1
950
C
2
850
D
3
650
E
4
350
F
5
0
Using the it's formula, the total opportunity cost of three unit(s) of tanks is of 350 autos.
What is the opportunity cost formula?The opportunity cost formula is given by:
C = F - A.
In which:
F is the best return.A is the actual return.For this problem, we have that:
When no tanks are produced, 1000 autos can be produced, hence F = 1000.When 3 tanks are produced, 650 autos can be produced, hence F = 650.Thus:
F = 1000 - 650 = 350.
The total opportunity cost of three unit(s) of tanks is of 350 autos.
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What the slope of the line on the graph please help me
Answer: Slope = 7/6
Step-by-step explanation:
Which of the following is equivalent to sum from n equals 1 to infinity of 12 times quantity negative five eighths end quantity to the power of n question mark
-60/13
60/13
−20
20
The sum to infinity of the sequence is 96/13
Sum to infinity of a geometric sequenceGiven the nth term of a geometric sequence expressed as:
Tn = Σ12(-5/8)^n
The sum to infinity of the sequence is expressed as;
S∞ = a/1-r
where
a is the first term = 12
r is the common ratio = -5/8
Substitute
S∞ = 12/1-(-5/8)
S∞ = 12/1+5/8
S∞ = 12/(13/8)
S∞ =12 *8/13
S∞ = 96/13
Hence the sum to infinity of the sequence is 96/13
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refer to the image please!!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Value of g (x) is -2, when :
[tex]\qquad \sf \dashrightarrow \: - 2.5 < x \leqslant - 1.5[/tex]
And since -2 lies in this range of x,
[tex]\qquad \sf \dashrightarrow \:g( - 2) = - 2[/tex]
Value of x is -1, when :
[tex]\qquad \sf \dashrightarrow \: - 1.5 < x \leqslant - 0.5[/tex]
And -0.5 falls in this range, hence
[tex]\qquad \sf \dashrightarrow \:g( - 0.5 ) = - 1[/tex]
Next, The value of x is 0 when :
[tex]\qquad \sf \dashrightarrow \: - 0.5 < x < 0.5 [/tex]
But, it isnt equal to 0.5, since there is open interval at both extremes.
Next, Value of x is 1, when :
[tex]\qquad \sf \dashrightarrow \:0.5 \leqslant x < 1.5[/tex]
And since it also has the value 0.5 included in it,
[tex]\qquad \sf \dashrightarrow \:g(0.5) = 1[/tex]
PLS HELP PLS I DON'T WANT TO FAIL PLEASE HELP PLEASE 20 POINTS
Answer:
653209
Step-by-step explanation:
Because i did this already
if a piece of ribbon is 4 3/4 feet long, how long is it in inches?
Please HELP ME I need help on this final question
Two cyclists, 30 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as
the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
a. Write an equation using the information as it is given above that can be solved to answer this problem.
Use the variable r to represent the speed of the slower cyclist.
b. What is the speed of the faster cyclist?
mi/hr
The equation as r + 2 r = 30 miles / 2 hours and the speed of faster cyclist as 10 miles per hour.
We are given that:
The distance between the two cyclist = 30 miles.
Now let the speed of one cyclist be x miles / hour.
Speed of other cyclist = 2 x miles / hour.
Now, 2 hours later they meet.
Distance covered by 1st cyclist in 2 hours = 2 x
Distance covered by 2st cyclist in 2 hours = 4 x
Equation will be:
2 x + 4 x = 30 miles
6 x = 30 miles
x = 5 miles.
Equation for the cyclist in terms of r will be :
r + 2 r = 30 miles / 2 hours
Speed of faster cyclist = 10 miles per hour.
Therefore, we get the equation as r + 2 r = 30 miles / 2 hours and the speed of faster cyclist as 10 miles per hour.
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Given || m
m || n, find the value of x.
Answer:
x=142°
Step-by-step explanation:
hope it helps ⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄
Which angles in the picture are NOT adjacent?
A. ∠2 and ∠3
B. ∠3 and ∠4
C. ∠1 and ∠2
D. ∠1 and ∠3
Answer:
D. ∠1 and ∠3
Hope this helps!
Answer:
1 and 3 or also known as D
Step-by-step explanation:
i took the test and got it right
Jorge sells chairs for $230 after a markup of $80. Jorge's percent of markup based on the selling price is?
Jorge's percent of markup based on the selling price is 34.78%.
The Percent markup based on Selling Price is calculating using the formula
Percent Markup = ( Markup/Selling Price )*100
In the given question
The Selling Price of chair = $230
Markup = $80
Substituting the values of Selling price and Markup in the Percent markup formula,
We get ,
Percent Markup = (80/230) * 100
=0.3478
=34.78
Therefore , the percent markup based on the selling price is 34.78%.
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solve the equation secx=2 on interval[0,2pie)
The threes solutions to the given equation sec²x - secx = 2 are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]What exactly are equations?An equation is a statement composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To solve: sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
When we set t = sec x, we get the quadratic equation:
[tex]t^2-t-2=0[/tex]Which has the solutions: [tex]t_1=2 ; \quad t_2=-1[/tex]As a result, we must seek solutions to the equations:
[tex][1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;[/tex]
Therefore, the three solutions are:
[tex]x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ; \ x_3=\pi[/tex]Know more about equations here:
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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])
write the product using an exponet
(5.6)(5.6)(5.6)
Answer: [tex](5.6)^3[/tex]
This is the same as saying (5.6)^3
===============================================
Explanation:
The base is 5.6 and it is multiplied a total of 3 times. We use an exponent of 3 to condense things down. So [tex]5.6 * 5.6 * 5.6 = (5.6)^3[/tex]
Another example: [tex]2^4 = 2*2*2*2 = \text{four copies of '2' multiplied}[/tex]
Question 4
Tricia wants to install a decorative wall paper border around the top of the wall in he
master bedroom. The room measures 18ft by 14ft. How many feet of the border will
will she need?
Provide a numeric answer only. Do not include a unit of measure with your response
For the installation of a decorative wall paper Tricia will need 70 ft of the border to decorate the wall of her master bedroom.
The measures of the room is 18 ft by 14 ft.
So, the length of the room (l) = 18 ft
The width of the room(w) = 15 t
As we know that, perimeter of rectangle is 2(l×w).
We will get perimeter of he room = 2l × 2w
= 2(18) × 2(14)
= 70 ft.