To solve this problem, let us recall that the formula for Area of a rectangle is:
A = l * w
Where,
l = length of one side = 4 ft
w = width of one side = 1 ft
Therefore the original area is:
Ao = 4 ft * 1 ft
Ao = 4 ft^2
Since each border would be increased by x, therefore the new l and w would be:
l = 4 + 2x
w = 1 + 2x
The new area becomes:
A = (4 + 2x) (1 + 2x)
The difference of the two would be the area of the remaining scarf:
A – Ao = 6 square ft
(4 + 2x) (1 + 2x) – 4 = 6 ---> 1
(4 + 2x) (1 + 2x) = 10 ---> 2
The equation to use can be equation 1 or equation 2.
Indicate a general rule for the nth term of this sequence. 12m, 15m, 18m, 21m, 24m,...
a. = 3mn + 9m
b. = -3mn - 9m
c. = -3mn + 9m
d. = 3mn - 9m
How do you simplify the square root of 27?
If 4 less than a number is less than 4 and greater than -3, find the number.
What is the number of degrees in the measure of each exterior angle of a regular polygon of 18 sides?
LAW ENFORCEMENT: A police accident investigator can use the formula S=25L‾‾‾√S=25L to estimate the speed s of a car in miles per hour based on the length l in feet of the skid marks it left. How fast was a car traveling that left skid marks 109 feet long?
A city's current population is 1,000,000 people. It is growing at a rate of 3.5% per year. The equation P=1,000,000(1.035)^x models the city's population growth where x is the number of years from the current year. In approximately how many years will the pooulation be 1,400,000? Round to nearest tenth
In which one of the above figures is AB = AC?
A. Figure B
B. Figure C
C. Figure A
D. Figure D
Answer: The answer is (D). the image is attached.
Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.
In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.
In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.
In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.
In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.
We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
So, we have AB ≅ AC.
Thus, (D) is the correct option.
Using the Degree minute second method to describe an angle, one degree of angle measurement can be divided into how many minutes?
HELP PLEASE ASAP !!!! 80 POINTS !!!!!!!
There are 975 birds in an aviary. Each month, the number of birds decreases by 7%. There are 350 trees in the aviary. Each month, 7 trees are removed.
Part A: Write functions to represent the number of birds and the number of trees in the aviary throughout the months. (4 points)
Part B: How many birds are in the aviary after 12 months? How many trees are in the aviary after the same number of months? (2 points)
Part C: After approximately how many months is the number of birds and the number of trees the same? Justify your answer mathematically. (4 points)
Part A
months = m
since birds decrease by 7%, there will be 93% left. 93% = 0.93
birds: 975 x 0.93^m
trees: 350 - 7m
Part B
birds: 975 x 0.93^12 = 408
trees: 350-7(12) = 266
Part C
350 - 7m = 0.93^m(975)
We have intersection points at approximately 22.21 and 44.4781. round off to whole numbers, we have 22 and 44 months.
The tile pattern shown was used in Pompeii for paving. If the diagonals of each rhombus are 2 inches & 3 inches, what area makes up each cube in the pattern?
Name the binomial you can multiply by (x + 9) to get the product x 2 + 5x – 36. A. 4 – x B. x + 6 C. x – 4 D. x – 6
In which section of the number line is √32?
sqrt(32) = 5.66
so it is in section B
Answer:
section B.
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Q and R are independent events. If P(Q)= 1/8 and P(R)=2/5 find P(Q and R).
The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.
Explanation:The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.
That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.
Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.
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The estimated measurements of the objects are shown below.
-length of a grain of salt: 0.0002 centimeters
-width of a key ring: 0.02 centimeters
Find the measurements written in standard notation to the estimated measurements in scientific notation.
The standard notation 0.0002 cm becomes 2 × 10^-4 and 0.02 cm becomes 2 × 10^-2, both in scientific notation.
Explanation:The standard notation for 0.0002 centimeters is 2 × 10^-4 in scientific notation. Meanwhile, the standard notation for 0.02 centimeters is 2 × 10^-2 in scientific notation.
You arrive at these translations by recognizing that the number 0.0002 means you've moved the decimal point four units to the right from 2 (thus raising 10, the base, to -4), and 0.02 represents moving the decimal point two units to the right from 2 (thus raising 10 to the -2).
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Someone pls help me!! and thank you if you do !
Use a translation rule to describe the translation of X that is 1 units to the left and 6 units up.
A.
T < -1, 6> (x)
B.
T < -1, -6> (x)
C.
T < 1, 6> (x)
D.
T < 1, -6> (x)
Answer:
C. < 1,6 > (x)
Step-by-step explanation:
We know that,
Translation is the transformation that shifts the image in any direction.
The general form of horizontal translation of f(x) to f(x±k) and vertical translation of f(x) to f(x)±k where k is any constant.
Now, as the given function 'X' is translated 1 unit to the left i.e. translated horizontally by 1 unit i.e. X+1.
Also, the function is translated 6 units up i.e. translated vertically by 6 units i.e. X+6.
Hence, the solution is < 1,6 >(x).
How were the numbers 1 10 100 and 1000 written by romans?
Which of the following is a solution to the inequality y < –2x + 3?
A. (1,1)
B. (3,0)
C. (-3,10)
D. (0,0)
Please select the best answer from the choices provided
y < -2x +3
A. (1, 1) → x = 1, y = 1
substitute:
1 < -2(1) + 3
1 < 1 FALSE
B. (3, 0) → x = 3, y = 0
substitute
0 < -2(3) +3
0 < -3 FALSE
C. (-3, 10) → x = -3, y = 10
substitute
10 < -2(-3) +3
10 < 9 FALSE
D. (0, 0) → x = 0, y = 0
substitute
0 < -2(0) + 3
0 < 3 CORRECT
Answer: D. (0, 0)
A file that is 256 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Use allfour operations only once without parentheses to write an expression that has a value of 100 only using 3's
There are a lot of ways to write an expression using only 3 to get an answer of 100. Some examples are:
1st example:
3 / 3 + 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
= 1 + 99
= 100
2nd example:
3 / 3 + 3 * 3 * 3 * 3 + 3 * 3 * 3 – 3 * 3
1 + 81 + 27 – 9 = 100
A game spinner is divided into 5 equal sections numbered 1 to 5. How many outcomes are in the sample space for 4 spins of this spinner? a. 625 b. 125 c. 20 d. 500
The correct option is a. 625.
The total number of outcomes in 4 spins of the spinner can be found by multiplying the number of outcomes in one spin by itself 4 times, resulting in 625 outcomes.
The sample space for 4 spins of the spinner can be calculated by raising the number of outcomes in one spin to the power of the number of spins.
In this case, as there are 5 outcomes on the spinner, the total number of outcomes in 4 spins would be 5^4 = 625.
Therefore, the correct option is a. 625.
Grace is half her father joseph's age. in 10 years grace will be three-fifths joseph's age. ten years ago, grace was one third joseph's age. how old are grace and joseph now
After setting up a system of equations based on the given age relationships and solving for both Grace and Joseph, we deduce that Grace is 20 years old and Joseph is 40 years old currently.
Let's denote Grace's current age as G and Joseph's current age as J. According to the problem, Grace is half of Joseph's age, so we have the first equation:
G = 0.5 * J
In 10 years, Grace will be three-fifths of Joseph's age, giving us the second equation:
G + 10 = (3/5) * (J + 10)
Ten years ago, Grace was one-third of Joseph's age, which gives us the third equation:
G - 10 = (1/3) * (J - 10)
We now have a system of three equations with two variables. We can solve this system to find the current ages of Grace and Joseph. After solving for G and J, we find that Grace is 20 years old and Joseph is 40 years old.
The scatter plot shows the test scores of a group of students who surfed the Internet for different amounts of time in a day.
What will most likely happen to the test scores of students if the number of hours they surf the Internet increases?
Test scores will decrease because the graph shows a negative association.
Test scores will increase because the graph shows a positive association.
Test scores will increase because the graph shows a negative association.
Test scores will decrease because the graph shows a positive association.
Answer: The correct answer is "Test scores will increase because the graph shows a negative association."
Step-by-step explanation: Negative association is decreasing and positive is increasing but in this case we flip it to get our answer.
The impact of time spent surfing the internet on students' test scores depends on whether the association represented on the scatter plot is positive or negative. In a positive association, scores increase with increased internet time, while in a negative association, scores decrease.
Explanation:Based on the question, it seems there is a relationship between the time spent surfing the Internet and students' test scores which is represented by a scatter plot. The association between these variables can be either positive, negative, or no association. A positive association means as the hours of surfing the internet increase, the test scores also increase. A negative association implies that as the hours of surfing the internet increase, the test scores decrease.
However, the question didn't provide the information about whether the scatter plot shows a positive or a negative association between these two variables, which is crucial to determine what happens to the test scores as internet surfing time increases.
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In ΔABC shown below, point A is at (0, 0), point B is at (x2, 0), point C is at (x1, y1), point D is at x sub 1 over 2, y sub 1 over 2, and point E is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: Triangle ABC is shown. Point D lies on segment AC and point E lies on segment BC. A segment is drawn between points D and E. Point A is at the origin. Prove that segment DE is parallel to segment AB.
Segment AB has slope 0. Segment DE, with midpoints of AC and BC, also has slope 0. Thus, DE is parallel to AB.
To prove that segment DE is parallel to segment AB, we need to show that the slopes of both segments are equal.
The slope of segment AB, denoted as [tex]\( m_{AB} \)[/tex], can be calculated using the coordinates of points A and B:
[tex]\[ m_{AB} = \frac{{y_B - y_A}}{{x_B - x_A}} \][/tex]
Given that point A is at (0, 0) and point B is at [tex]\((x_2, 0)\)[/tex], the slope [tex]\( m_{AB} \)[/tex] is:
[tex]\[ m_{AB} = \frac{{0 - 0}}{{x_2 - 0}} = 0 \][/tex]
Now, let's find the coordinates of points D and E.
Point D lies on segment AC, so it is at the midpoint of segment AC. Therefore, the coordinates of point D, denoted as [tex]\((x_{D}, y_{D})\)[/tex], are the average of the coordinates of points A and C:
[tex]\[ x_{D} = \frac{{x_1 + 0}}{2} = \frac{{x_1}}{2} \][/tex]
[tex]\[ y_{D} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Similarly, point E lies on segment BC, so it is at the midpoint of segment BC. Therefore, the coordinates of point E, denoted as [tex]\((x_{E}, y_{E})\)[/tex], are the average of the coordinates of points B and C:
[tex]\[ x_{E} = \frac{{x_1 + x_2}}{2} \][/tex]
[tex]\[ y_{E} = \frac{{y_1 + 0}}{2} = \frac{{y_1}}{2} \][/tex]
Now, let's calculate the slope of segment DE, denoted as [tex]\( m_{DE} \)[/tex]:
[tex]\[ m_{DE} = \frac{{y_{E} - y_{D}}}{{x_{E} - x_{D}}} \][/tex]
Substituting the coordinates of points D and E:
[tex]\[ m_{DE} = \frac{{\frac{{y_1}}{2} - \frac{{y_1}}{2}}}{{\frac{{x_1 + x_2}}{2} - \frac{{x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = \frac{0}{{\frac{{x_1 + x_2 - x_1}}{2}}} \][/tex]
[tex]\[ m_{DE} = 0 \][/tex]
Since the slopes of segments AB and DE are both equal to 0, we can conclude that segment DE is parallel to segment AB.
2[18-(5+9)÷7]
show how you did it
Based on the chart, which would be considered the dependant variable?
Answer:
u didn't provide a chart but the dependent variable is the y axis, or the vertical line
Step-by-step explanation:
It's always the y axis (the vertical line)
Help thank you :((((((((((((((((((
What is 35 minus 3 times 8
If the area of a rectangle is 16 then the length is 4 and the width is 4 what is the counterexample
I just need the answers for this.im really confused