A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.
A. Find the original perimeter and area of the garden
B. Find the perimeter and area of the garden with a 20% increase in each dimension.
C. By what percent will the perimeter increase? By what percent will the area increase?
D. Explain why the area and perimeter will not increase by the same percentage.
Answer:
w=12 ft
l= 20 ft
A.
P= 2(12+20)= 64 ft
A= 12*20= 240 ft²
B.
P=2(12*1.2+20*1.2)= 76.8 ft
A= 12*1.2*20*1.2= 345.6 ft²
C.
(76.8-64)/64*100%= 20%
(345.6- 240)/240*100%= 44%
D.
perimeter increase is linear function of one dimension increase
area increase is function of 2 dimensions increase
are the ratios 1:3 and 4:12 equivalent
Answer:
Yes.
Step-by-step explanation:
When you simplify the ratio of 4:12, dividing it by 4, you will get 1:3.
Answer:
Yes it is equivalent
Step-by-step explanation:
Yes because 1*4= 4
And 3*4=12
That is 1/3 is equivalent to 4/12
You can say that 1:3 is in proportion with 4:12
or 1:3::4:12
Find the area and perimeter of a square that has a side length of 4. Remember area is a length times width and perimeter is when you add all the sides together.
Answer:
Area= 16
Perimeter= 16
Answer:
A = l*w
P = 2l + 2w
A = 4*4 = 16
A = area
l = length
l = 4
w = width
w = 4
The area is equal to 16.
P = 2*4 + 2*4 = 16
P = perimeter
2l = 2*length
2l = 2*4
2w = 2*width
2w = 2*4
The perimeter is equal to 16.
It can be concluded both are equal to each other.
Hope this helps
Help please
What are the coordinates of the hole in the graph of the function?
f(x)=x2−3x−10/x−5
Enter your answer in the boxes.
Answer:
(5, 7)
Step-by-step explanation:
A hole is found in the graph of a rational function where numerator and denominator factors cancel each other.
The x-coordinate of the hole is the value of x that makes the factor zero. The y-coordinate of the hole is the value of the simplified function after the cancelled factors are removed. It is the limit of the function value as x approaches the hole location.
__
[tex]f(x)=\dfrac{x^2-3x-10}{x-5}=\dfrac{(x+2)(x-5)}{x-5}=x+2\qquad x\ne 5[/tex]
The hole is found at x = 5. The limit of the function value as x approaches 5 is 5+2 = 7. The coordinates of the hole are (5, 7).
que se necesita para que una magnitud vectorial esté completamente definida ?
Answer:
Dirección y magnitud
Espero que esto ayude.
Answer:
Dirección y magnitud
Step-by-step explanation:
A bottle of iron supplement has 45g of iron in 330ml of solution. How many grams of iron are in
100ml of solution?
Answer:
45 * 100 / 330 = amount in 100 ml of solution
13.6363636364 grams
Step-by-step explanation:
Simplify an Expression
Quick
Check
Simplify each expression involving signed numbers
-7-2=
12 + (-4)= |
-3(-6) = 1
18
Answer:
-10827is the answer for your question I think
Answer:
[tex]-9[/tex]
[tex]8[/tex]
[tex]18[/tex]
Step-by-step explanation:
[tex]-7-2=-9[/tex]
[tex]12+(-4)=8[/tex]
[tex]-3(-6)=18[/tex]
Kaleb looks at a tennis court and uses a geometric term to describe two lines that cross at a right angle. What term could use Kaleb use? A. Acute angle B. Parallel lines C. Perpendicular lines D. Straight angle
how do I solve: 8 – (m - 3) = 7 – 3m
Answer:
m=-2
Step-by-step explanation:
8-(m-3)=7-3m
8-1(m)-1(-3)=7-3m
8-m+3=7-3m
-m+3m+8+3=7-3m+3m
2m+8+3=7
2m+11=7
2m=-4
m=-2
Hope this helps!
Step-by-step explanation:
So, this is how you do it.
Which statement best describes the function below
Answer:
Option D. will be the answer.
Step-by-step explanation:
Given function is f(x) = 2x³ + 2x² - x
Table of input and output:
Input (x) -2 -1 0 1 2
Output (y) -6 1 0 3 22
Option (A).
From the graph attached,
It passes the vertical line test.
Option (B).
Since every input value gives a unique output value, it's not a many-to-one function.
Option (C).
It's a function.
Option (D).
It's a one-to-one function.
Answer: It is a many-to-one function.
Step-by-step explanation:
just did the test
Can someone help meee!
Answer:
X intercept = 4
Y intercept = -4
Step-by-step explanation:
X-intercept is when the graph crosses the X-axis or where the y is 0 for a X value. Here the (4,0) is where Y is 0 for a given x value and you see the graph crosses it on X-axis thus X intercept is 4.
Y-intercept is when the graph crosses the Y-axis or where the x is 0 for a Y value. Here the (0,-4) is where X is 0 for a given Y value and you see the graph crosses it on Y-axis thus Y intercept is -4.
Hey everyone! Please help me figure this out...
Answer:
See below
Step-by-step explanation:
0.82=82/100=82%
22%=22/100=0.22
3/4=0.75=75/100=75%
0.8=0.80=80/100=80%
Hope this helps!
Answer:
column 2: 41/50, 0.82, 82%
column 3: 11/50, 0.22, 22%
column 4: 3/4, 0.75, 75%
column 5: 4/5, 0.80, 80%
PLEASE HELP ME SHOW ME HOW U GOT YOUR ANSWER PLZ AND THANK U
Answer:
2/3
Step-by-step explanation:
There are 6 marbles in the jar
4 are not purple
P(not purple) = marbles that are not purple/ total marbles
= 4/6 = 2/3
Answer:
2/3
Step-by-step explanation:
since there are 6 total marbles and 4 of them are colors other than purple, there is a 4/6 chance of drawing a marble that is not purple which can be simplified to 2/3.
Can someone help me with math please?
Answer:
Multiply 60 by 2.5 centimetres
60×2.5=150
, 8 technicians can test 560 samples in 36 hours. How long
(in days) can 15 technicians'test 525 samples?
Answer:
0.75 days (im a bit unsure but i tried my best, hope this helps :) )
Step-by-step explanation:
If it takes 8 technicians 36 hours to test 560 samples, find how many technicians can test 525 samples.
8: 560
x: 525
x= 7.5 (which is considered 7)
Then, find how long it takes to sample 525 samples, when 560 are done in 36 hours;
560: 36
525: x
x= 33.75 (which is considered 34 hours)
The last step is to check how long 15 technicians take to sample 525 samples when 8 can do the same number in 34 hours. this is inverse proportion so dont forget to flip one numerator and denominator
8; 34
15; x
it will become
15:34
8: x
x= 18 hours
Divide by 24 for days hence 0.75 days
What is the diameter of the smallest circle that would enclose 2,000 pennies?
Answer:
Almost about 4500 mm
Step-by-step explanation:
Measure the pennies width and estimate. Multilpy by 2000 and there you go!
What is a rigid motion?
Answer:
Rigid motion is otherwise known as a rigid transformation and occurs when a point or object is moved, but the size and shape remain the same. This differs from non-rigid motion, like a dilation, where the size of the object can increase or decrease.
Step-by-step explanation:
What are the factors of 36xyz?
A. 36,x,y
B. 36x,y,z
C. x,y,z
D. 36,x,y and z
Answer:
ç
Step-by-step explanation:
the two-way table below shows the intended careers among the incoming class of first-year college students, divided by gender. If a student is chosen and random, what is the probability of the student is female who intends to be a research scientist?
Answer:
c. 2.2%
Step-by-step explanation:
The total number of all students in all fields, male and female is 4663.
There are 103 female research scientists.
p(female scientist) = 103/4663 = 0.022 = 2.2%
Rewrite the expression 24x - 12 using the distributive property
Answer:
12(2x-1)
Step-by-step explanation:
24x - 12
Factor out a 12 from each term
12*2x -12*1
12(2x-1)
Answer:
[tex]12(2x - 1)[/tex]
Step-by-step explanation:
[tex]24x - 12[/tex]
Factor out a 12 from each
[tex]24x - 12 \\ 12(2x - 1)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
How would you describe the curve?
the answer is C, the curve is a one to one function
Pls solve for x. (Pls show step by step explanation)
3(x-2)+7x=1/2(6x-2)
Answer:
x=5/7
Step-by-step explanation:
Distribute
3x-6+7x=3x-1
Combine Like Terms
10x-6=3x-1
7x-6=-1
7x=5
x=5/7
Answer:
[tex]x=5/7[/tex]
Step-by-step explanation:
[tex]3(x-2)+7x=1/2(6x-2)[/tex]
Use algebraic distribution.
[tex]3x-6+7x=3x-1[/tex]
Add like terms.
[tex]10x-6=3x-1[/tex]
Add [tex]-3x[/tex] and [tex]+6[/tex] on both sides of the equation.
[tex]10x-3x=-1+6[/tex]
Add and subtract.
[tex]7x=5[/tex]
Divide [tex]7[/tex] on both sides of the equation.
[tex]x=5/7[/tex]
The square of a number I see equal to two less than three times the number. What are two possible values of the number? A. 1,2 B. -1,2 C. 1,-2 D. -1,-2 E. 2,3
Answer:
Option A
Step-by-step explanation:
Let us take this number as x, translating this description of the equation into mathematical language;
[tex]x^2 = 3x - 2[/tex]
Now let us solve for x;
[tex]x^2 = 3x - 2,\\x^2+2=3x-2+2,\\x^2+2=3x,\\x^2+2-3x=3x-3x,\\x^2-3x+2=0,\\\\Factored = \left(x-1\right)\left(x-2\right)=0,\\Zero Factor Principle, \\x = 1, x = 2\\\\Solution - Option A[/tex]
* Note that for the the previous problem I solved, I set up a similar equation that had two values for the width, one negative and the other positive. Now the width could only be a positive number, so there was only one solution out of the two.
Please help! Correct answer only!
There are 10 cards in a hat, numbered 1 to 10. The game is to draw one card out of the hat. If the number you draw is even, you win $30. If the number you draw is odd, you win nothing. If you play the game, what is the expected payoff?
$___
Answer:
$15
Step-by-step explanation:
Since there are 10 cards and a total possible prize of 30 dollars, the probability for each one is 30/10=3 dollars. And since 5 out of the 10 are even, you can multiply the individual amount by 5 to get a total estimated payout of $15. Hope this helps!
(2x+3)²=125 find x
with full solution please
Answer:
x = ± ( 5√5 - 3 ) / 2
Step-by-step explanation:
We are given the equation ( 2x + 3 )² = 125;
[tex]( 2x + 3 )^{ 2 } = 125 - Take Square Root on Either Side,\\| 2x + 3 | = \sqrt{ 125 } - Simplify Square Root of 125,\\\\| 2x + 3 | = \sqrt{ 5 * 25 } - Simplify Further,\\| 2x + 3 | = 5\sqrt{ 5 } - Take | |,\\\\2x + 3 = 5\sqrt{ 5 } , and , 2x + 5 = - 5\sqrt{ 5 } - Algebra, \\2x = 5\sqrt{ 5 } - 3 , and , 2x = - 5\sqrt{ 5 } - 3 - Divide Either Side by 2\\\\x = ( 5\sqrt{ 5 } - 3 ) / 2, and , x = ( - 5\sqrt{ 5 } - 3 ) / 2\\Conclusion ; x = ( + / - 5\sqrt{ 5 } - 3 ) / 2[/tex]
Solution ; x = ± ( 5√5 - 3 ) / 2
4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
1. $14,310.40
2. $14,990.90
3. $15,290.70
4. $15,737.50
5. $16,935.80
Answer:
12590/80*100 = $15,737.50 4. Is your Answer
Step-by-step explanation:
12590 is 80% so simply divide by 80 and multiply by 100 to get the answer.
The point (2,9) lies on a circle and the center of the circle is at the point (2,1). What is the equation of this circle? A. (x - 2)2 - (y - 1)2 = 64 B. (x - 2)2 + (y - 1)2 = 64 C. (x + 2)2 + (y + 1)2 = 64 D. (x - 1)2 - (y - 2)2 = 8
Answer:
B:(x-2)^2+(y-1)^2=64
Step-by-step explanation:
center is (2,1), point is (2,9)
so the radius=9-1=8
(x-2)^2+(y-1)^2=64
PLEASE HELP ME WITH THIS! VERY IMPORTANT!!! SMART PEOPLE PLEASEEE
10+12+14+...+(2n)=90 n=?
Answer:
n=10
Step-by-step explanation:
The given equation is
[tex]10+12+14+...+2n=90[/tex] ...(1)
Let nth term is 2n.
We need to find the values of n.
It is clear that [tex]S_n=10+12+14+...+2n[/tex] is sum of A.P., whose first term is 10 and common difference is 2.
Sum of A.P. is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=10 and d=2 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(10)+(n-1)2][/tex]
[tex]10+12+14+...+2n=n[10+n-1][/tex]
[tex]10+12+14+...+2n=n[9+n][/tex] ...(2)
From (1) and (2), we get
[tex]n(9+n)=90[/tex]
[tex]n^2+9n-90=0[/tex]
Splitting middle term, we get
[tex]n^2+15n-6n-90=0[/tex]
[tex]n(n+15)-6(n+15)=0[/tex]
[tex](n+15)(n-6)=0[/tex]
[tex]n=-15,6[/tex]
Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.
Note: nth term and variable n both are different.
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=10+(6-1)2=10+10=20[/tex]
Sixth term is 20. So,
[tex]2n=20[/tex]
[tex]n=10[/tex]
Therefore, the value of n is 10.
Topic: Probability
Only complete question 9.
Answer:
see below
Step-by-step explanation:
a. H 1, H2 ,H3 T1 ,T2, H3
b 6 possible outcomes
c 2 outcomes for the coin ( h,T) 3 outcomes for the spinner
2*3 = 6