Answer:
a) Similar
b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)
c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)
Step-by-step explanation:
Given:
Rectangle 1 has length = x
Rectangle 1 has width = y
Rectangle 2 has length = kx
Rectangle 2 has width = ky
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Perimeter of Rectangle = 2*(Length + Width)
Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y
Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky
= k(2x+2y)
= k(Perimeter of Rectangle 1)
Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.
Area of Rectangle = Length * width
Area of Rectangle 1 = x * y
Area of Rectangle 2 = kx*ky
= k^2 (xy)
= k^2 (Area of rectangle 1)
Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.
Final answer:
Rectangles 1 and 2 are similar due to proportional dimensions. The perimeter of Rectangle 2 is proven to be k times the perimeter of Rectangle 1 by factoring out the scale factor. Similarly, the area of Rectangle 2 is k² times the area of Rectangle 1, as shown by multiplying the scaled dimensions.
Explanation:
(a) Yes, Rectangle 1 and Rectangle 2 are similar because the sides of Rectangle 2 are proportional to the sides of Rectangle 1. This means that the two rectangles have the same shape but different sizes, which is the definition of similarity in geometry.
(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, consider the perimeter of Rectangle 1, which is 2x + 2y. When each dimension is multiplied by k, the new length is kx and the new width is ky, so the perimeter of Rectangle 2 is 2(kx) + 2(ky) = 2kx + 2ky. Factoring out the common factor of k gives k(2x + 2y), which is k times the perimeter of Rectangle 1.
(c) For the area of Rectangle 2, the area of Rectangle 1 is xy. After scaling by k, the new dimensions of Rectangle 2 are kx and ky, so its area is (kx)(ky) = k²(xy), which shows that the area of Rectangle 2 is k² times the area of Rectangle 1.
Graph the line y=-1/5x-2
Answer:
Can't really show a graph but I'll explain how to:
Step-by-step explanation:
Plot the point (0,-2) since -2 is the y=intercept. After, just count-down 1 unit and count 5 units to the right. I hoped this helped!
A kitchen drawer has a Volume 1,125 cubic inches. The drawer is 15 inches long and 5 inches deep. What is the width of the drawer? Please show work so I can understand
Answer:
The width of the drawer is [tex]15\ in[/tex]
Step-by-step explanation:
we know that
The volume of the drawer is equal to
[tex]V=LWH[/tex]
we have
[tex]L=15\ in[/tex]
[tex]H=5\ in[/tex] -----> the deep of the drawer
[tex]V=1,125\ in^{3}[/tex]
substitute the given values in the formula and solve for W
[tex]1,125=(15)(W)(5)[/tex]
[tex]1,125=(75)(W)[/tex]
[tex]W=1,125/(75)[/tex]
[tex]W=15\ in[/tex]
HELP PLEASE!!
What is the value of 18^2?
A) 36
B) 324
C) 360
D) 9
18² is the same as saying 18 * 18, which is 324
State if each angle is an inscribed angle. If it is, name the angles and the intercepted arc.
Answer:
Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST
Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY
Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ
Part 4) The figure does not show an inscribed angle
Step-by-step explanation:
Part 1) The figure shown a inscribed angle
The inscribed angle is the angle ∠TRS
The intercept arc is the arc LST
Remember that
The inscribed angle measures half that of the arc comprising
so
∠TRS=(1/2)[arc LST]
Part 2) The figure shown a inscribed angle
The inscribed angle is the angle ∠YWX
The intercept arc is the minor arc XY
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YWX=(1/2)[minor arc XY]
Part 3) The figure shown a inscribed angle
The inscribed angle is the angle ∠YXZ
The intercept arc is the arc YBZ
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YXZ=(1/2)[arc YBZ]
Part 4) The figure does not show an inscribed angle
The figure shown a interior angle ∠BAC
Find the volume of the rectangular prism
To find the volume of a rectangular prism, we use the formula
Volume = length × width × height.
Since the rectangular prism has a length of 4 m, a width of 2 m, and a height of 1 m we can plug this information into the formula.
(4 m) (2 m) (1 m)
4 m × 2 m = 8 m
8 m × 1 m = 8 m³
Therefore, the volume of the rectangular prism is 8 m³.
Answer:
8
Step-by-step explanation:
L=Length
W=Width
H=Height
L=4
W=2
H=1
4 x 2 x 1
4 x 2 = 8
8 x 1 = 8
Rearranging to check my work:
1 x 4 x 2
1 x 4 = 4
4 x 2 = 8
I was right.
Hope this answers your question.
If the number of bacteria in a colony doubles every 25 hours and there is currently a population of 10,000 bacteria, what will the population be 75 hours from now
Answer:
The population of 75 hours from now would be 40,000.
Step-by-step explanation:
The reason for this is because your initial number is 10,000 and when 25 hours pass by, your population would be 20,000. Another 25 hours pass by, and then your population would be 40,000. If you multiply 25 by 3, you will notice 75 hours have just passed, so your answer would be 40,000.
The population of a bacterial colony that doubles every 25 hours will increase exponentially. In this case, starting from a population of 10,000 bacteria, after 75 hours, we will have 80,000 bacteria. This demonstrates the concept of exponential growth commonly seen in bacteria.
Explanation:The population of a bacterial colony that doubles every 25 hours follows an exponential growth model. This process is where the increasing rate is proportional to the current scope, leading to continued growth. If we start with a colony of 10,000, after 25 hours, we will have 20,000 bacteria. After another 25 hours, this will double again to 40,000. And after a final 25 hours, we double the number again to 80,000.
Here are the calculations:
After 25 hours, the number of bacteria doubles, so the population is 10,000 * 2 = 20,000 bacteriaAfter another 25 hours (50 hours total), the number of bacteria doubles again, so we have 20,000 * 2 = 40,000 bacteriaAfter the final 25 hours (75 hours total), the number of bacteria doubles once more, so we end up with 40,000 * 2 = 80,000 bacteriaThis demonstrates the concept of exponential growth commonly seen in the bacteria populations. The growth rate increases over time due to the characteristic of bacteria to divide and reproduce, leading to a rapid increase in their numbers.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
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what value of x makes this equation true? justify your solution.
6x + 12 = -6x + 12
Answer
0
Solution
6x+6x=12-12
12x=0
X=0
A limited edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. What equation can be used to find the vale, y, after x years?
Answer:
y=3.11x
Step-by-step explanation:
Not sure if it's correct. But my reasoning behind it is that 23.81-20.70=3.11 which means every year the cost goes up by $3.11
What is the equation parallel to y= -1/5x + 3 and goes through the point (7,4)? Please show steps.
Answer:
Step-by-step explanation:
If it's parallel, that means it has the same slope: -1/5.
Use point-slope form to write the equation:
y - 4 = -1/5 (x - 7)
If you wish to write in point-intercept form:
y - 4 = -1/5 x + 7/5
y = -1/5 x + 27/5
If two lines are parallel, it means that they will have the same gradient:
And remember, the equation of a line is y = mx +c
-----------------------------------
So we know that the equation of the parallel line is:
y = - [tex]\frac{1}{5}[/tex]x + c through point (7, 4)
All we need to do now is to work out what c is
Note: at point (7, 4) x = 7 , and y = 4.
So to work out c, we substitute in the values of x and y, and solve:
y = - [tex]\frac{1}{5}[/tex]x + c
4 = - [tex]\frac{1}{5}[/tex] * 7 + c
4 = -1.4 + c
5.4 = c
----------------------------------
Finally, we just put the value of c back into the original equation
y = - [tex]\frac{1}{5}[/tex]x + 5.4
------------------------------------------
Answer:
The equation of the a line parallel to y = - [tex]\frac{1}{5}[/tex]x + 3 through point (7,4)
is: y = - [tex]\frac{1}{5}[/tex]x + 5.4
What are the solutions to the system of equations? y=− x 2 +5x+6 −6x+y=6
(0,−1) and (6, 0)
(−1, 0) and (0, 6)
(0, 6) and (1, 2)
(−1, 0) and (6, 0)
Answer:
option B
(−1, 0) and (0, 6)
Step-by-step explanation:
Given in the question two equations,
Equation 1
y =−x² + 5x + 6
Equation 2
−6x + y = 6
plug value of y in second equation
−6x −x² + 5x + 6 = 6
-x² -6x + 5x +6 - 6 = 0
-x² - x + 0 = 0
-x² -x = 0
-x(x+1) = 0
x = 0
and
x = -1
plug value of x in second equation to find y
x = 0
−6(0) + y = 6
0 + y = 6
y = 6
and
x = -1
−6(-1) + y = 6
6 + y = 6
y = 0
Answer:
(−1, 0) and (0, 6)
Step-by-step explanation:
The given system of equations is
[tex]y=-x^2+5x+6[/tex]
and
[tex]-6x+y=6[/tex]
Solve for y in this second equation
[tex]y=6x+6[/tex]
We equate the two equations to get;
[tex]-x^2+5x+6=6x+6[/tex]
[tex]x^2+x=0[/tex]
[tex]x(x+1)=0[/tex]
x=0,x=-1
When x=0,
y=6(0)+6
y=6
When x=-1
y=6(-1)+6
y=0
Which sequences are arithmetic? Select three options.
Answer:
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Step-by-step explanation:
find the area. please show steps!
Answer:
96 in²
Step-by-step explanation:
The surface area of the square pyramid is the area of the square base plus the area of the four triangular faces. The slant length is the height of each triangle.
A = s² + 4 (½ sL)
A = s² + 2sL
Given s = 6 and L = 5:
A = (6)² + 2(6)(5)
A = 36 + 60
A = 96
The area that needs to be painted is 96 in².
Graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=x-6
The linear equation -3y=x-6 can be graphed using the slope-intercept form y = -1/3x + 2. By choosing different values for x and solving for y, we can find three points that solve the equation. Plotting these points on a graph and connecting them with a line represents the linear equation.
Explanation:The linear equation -3y=x-6 can be rewritten in slope-intercept form as y = -1/3x + 2. This form allows us to easily determine the slope and y-intercept of the equation. The slope is -1/3, which means for every increase of 1 in x, y decreases by 1/3. The y-intercept is 2, which indicates that the line crosses the y-axis at the point (0, 2).
To find three points that solve the equation, we can choose different values for x and substitute them into the equation to solve for y. Let's choose x = 0, x = 3, and x = -3. Plugging these values into the equation, we get y = 2, y = 1, and y = 3, respectively.
Therefore, the three points that solve the equation are (0, 2), (3, 1), and (-3, 3). When we plot these points on a graph, we can then connect them with a straight line to represent the linear equation.
I need help ASAP.... please help....
Answer:
(7x-1)(x-3)
Step-by-step explanation:
7x^2 - 22x + 3
The factors have to add to -22, but multiply to equal 3. But since the "a" value has a number on it, you have to use it too.
(7x +/- [n1]) ( x +/- [n2]) = 7x^2 - 22x + 3
Since the two numbers multiply to a positive value, they have to have the same sign. (7x-1) (x-3) works to produce the expression when it's foiled.
Answer:
(7x-1)(x-3)
Look in the photos. I hope this helps!
Let me know if you're unsure about anything! Thanks! :)
Joelle bought 20 lollipops and 6 bags of Doritos for a total cost of $8.20. She knows that each lollipop cost 25 cents and reasoned that two bags of chip must cost a little more than $1.00. Is this a reasonable guess? Why or why not?
I mean... I think it's a reasonable guess because not gonna lie- chips can get expensive. BUT- It doesn't really make sense because like, she bought so many lollipops. My brain isn't really functioning to do the math- but my best guess would beeeee... UNreasonble. I'm super super sorry if it's wrong. Math isn't my strong point, sorry. Have a nice day!
Answer:
no
Step-by-step explanation:
because 20×.25 = 5 so the lollipop cost $5.00 and then you only have 3.20 left over
11. Kara's credit card had a balance of $209.53 on July
1. On July 8, she made a payment of $50. On July
16, she made a charge of $20. On July 24, she
made another charge of $35 and did not use the
credit card the rest of the month. What was her
average daily balance?
$159.53
$179.53
$214.53
$190.18
$190.78
190.18 is the average balance
Answer:
The answer is $190.18
Step-by-step explanation:
When we calculate the average daily balance, we total the balance from each day in the billing cycle and divide the total by the number of days in the cycle. Here the billing cycle is given for July that has 31 days.
Lets calculate each days amount.
Opening balance from 1st July to 7th July = $209.53
So, it is a total of 7 days; amount is [tex]209.53\times7=1466.71[/tex]
On 8th July a payment of $50 is made making the amount
[tex]209.53-50=159.53[/tex]
So, from 8th July to 15th July (8 days), the balance was $159.53 making a total of [tex]159.53\times8=1276.24[/tex] dollars
On 16th July a charge of $20 was added, so from 16th July to 23 July (8 days), the amount became = [tex](159.53+20)\times8=1436.24[/tex] dollars
On 24th July additional charge of $35 was added and the period it remained same was till 31st July, making it 8 days.
So, amount is = [tex]214.53\times8=1716.24[/tex] dollars
Now adding all the charges we get;
[tex]1466.71+1276.24+1436.24+1716.24= 5895.43[/tex] dollars
Now we will divide this by 31 days to get the average daily balance.
[tex]\frac{5895.43}{31}=190.175[/tex] ≈ $190.18
A rectangular room is 8 feet long and 12 feet wide. How many tiles would be needed to cover the floor if the tiles are six inches by six inches?
Answer: 192
Step-by-step explanation: 6 inches times 2 is a foot. 12 times 2 is 24 tiles across the top times 8 rows. 24 times 8 is 192
16
Because 8x12=96 and 96/6= 16
What is the measure of B E
Answer:
8cm
Step-by-step explanation
In between AE and DE
Gracie baked 4 apple pies. She cuts the pies into halves and will give them to her neighbors. How many neighbors will get 1/2 of an Apple pie?
Answer:
8
Step-by-step explanation:
If you cut one apple pie in half, then you have two halves. Do the same with the other 3 pies and you will have 8 halves of the pie to give to neighbors.
Find the arc length of the semicircle?
Answer:
5(pi) (exactly) or 15.7 (approximately)
Step-by-step explanation:
The length of arc of an entire circle is the circumference of the circle.
The length of arc of a semicircle circle is half of the circumference of the circle.
C = pi * d
For a semicircle:
arc length = 0.5 * pi * d
arc length = 0.5 * pi * 10
arc length = 5(pi)
arc length = 15.7
$4386 + 25% of the amount over $31850 1) 3986 2) 426.25 3) 4650 4) 7750
Answer:
3.)
Step-by-step explanation:
PLEASE HELP!!!!
The table shows which color boys and girls from 8th grade picked as their favorite color
Answer:
It should be B I me
Step-by-step explanation:
To determine which percentage is higher, we need to calculate the percentage of boys who prefer green and the percentage of girls who prefer red.
Percentage of boys who prefer green:
Total number of boys = 2 + 4 + 4 + 5 = 15
Number of boys who prefer green = 5
Percentage of boys who prefer green = (5/15) x 100% = 33.33% (rounded to the nearest whole number, this is 33%)
Percentage of girls who prefer red:
Total number of girls = 4 + 3 + 1 + 3 = 11
Number of girls who prefer red = 4
Percentage of girls who prefer red = (4/11) x 100% = 36.36% (rounded to the nearest whole number, this is 36%)
Therefore, the percentage of girls who prefer red (36%) is higher than the percentage of boys who prefer green (33%).
The answer is B. At 36%, the percentage of girls who prefer red is higher.
Identify GCF and LCM (1)
Identify the GCF or LCM for each pair of numbers.
2205
3570
1100
1576
1100
1576
456
4680
456
4680
Choices to choose from
GCF = 24
GCF = 4
LCM = 433400
LCM = 74970
LCM = 88920
Answer:
2205
3570
LCM = 74970
1100
1576
GCF = 4
1100
1576
LCM = 433400
456
4680
GCF = 24
456
4680
LCM = 88920
Step-by-step explanation:
18837429928373829193
Kate sets a goal to walk 3 miles every day for a year. How many miles more or less than 1,000 miles will she walk in the year? A. 95 miles more B. 33 miles less C. 33 miles more D. 95 miles less
Answer:
95 miles more.
Step-by-step explanation:
There are 365 days in the normal year.
Walking 3 miles daily for a year thus comes to (3 miles/day)(365 days) =
1095 miles total per year. This is Answer A: 95 miles more than 1000 miles.
Answer:
95 miles
Step-by-step explanation:
Sharon suspects that her brother's penny is unfair. She flips it 50 times and heads comes up 40 times. Based on these trials, the probability that a flip of this coin comes up TAILS is A) 1/5 B) 4/5 C) 4/9 D (5/9)
The correct answer is B. 4/5. Hope this helps! : )
Answer:
1/5
Step-by-step explanation:
it said so in usa testprep and i hope this helps you! ^-^
line s passes through the points (2,7) and (6,1) line t passes through the point (5,2) and is perpendicular to line s what is the equation for line t
let's keep in mind that perpendicular lines have negative reciprocal slopes, hmmm what is the slope of line S anyway?
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-7}{6-2}\implies \cfrac{-6}{4}\implies -\cfrac{3}{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{2}{3}}}[/tex]
so, we're really looking for the equation of a line whose slope is 2/3 and runs through (5,2)
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{2})~\hspace{10em} slope = m\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=\cfrac{2}{3}(x-5)\implies y-2=\cfrac{2}{3}x-\cfrac{10}{3} \\\\\\ y=\cfrac{2}{3}x-\cfrac{10}{3}+2\implies y=\cfrac{2}{3}x-\cfrac{4}{3}[/tex]
Evaluate 1/3m-1-1/2n, when m=21 and n
=12
Answer:
0
Step-by-step explanation:
= 7 - 1- 6
= 6 - 6
=0
To evaluate the expression 1/3m - 1 - 1/2n with m=21 and n=12, you perform a series of arithmetic operations, resulting in an evaluated expression of 0.
Explanation:To evaluate the expression 1/3m - 1 - 1/2n when m=21 and n=12, we substitute the given values of m and n into the expression.
Firstly, calculate 1/3 of m: (1/3) × 21 = 7.Secondly, subtract 1 from the result of the first step: 7 - 1 = 6.Thirdly, calculate 1/2 of n: (1/2) × 12 = 6.Finally, subtract the result of the third step from the result of the second step: 6 - 6 = 0.A chef has 6 cups of berries and will use 2/3 cups of berries for each serving of fruit salad how many servings can be made
Answer:
6*2/3 = 12/3 = 4
Step-by-step explanation:
For this case we have a total of 6 cups of berries and per serving of salad we use [tex]\frac {2} {3}[/tex]of cups.
Let "x" be the variable that represents the portions of fruit salad that can be made, then, to find it we divide the number of cups of berries among the amount that is used for a portion:
[tex]x = \frac {6} {\frac {2} {3}} = \frac {6 * 3} {2 * 1} = \frac {18} {2} = 9[/tex]
Thus, 9 portions of salad can be prepared.
Answer:
9 portions
find the area of the shape
Answer:
A = 12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) * h where b1 and b2 are the lengths of the bases and h is the height
b1 = 7.5 and b2 = 2.5 and h = 2.5
A = 1/2( 7.5 + 2.5) * 2.5
A = 1/2(10) * 2.5
A = 12.5
2.5x2.5=6.25
7.5-2.5=5/2=2.5
(1/2)x2.5x2.5=3.125x2=6.25
6.25+6.25=12.5
The answer is: 12.5 units^2
Erica has a monthly budget of $300 to spend on all of her expenses. She uses 2/3 on rent, and 1/4 on food. How much money remains for her expenses
Answer: $25
Step-by-step explanation: 2/3 of $300 is $200. 1/4 of $300 is $75. The total money she used is $275. $300-$275= $25.
Answer:
$75
Step-by-step explanation:
2/3 of 300 is 200 which means $100 bucks is left and 1/4 on food is $25 so what is left over is $75