A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).
Pls Show Work
Answer:
Width of Pathway; 2 meters
Step-by-step explanation:
To determine the width of the pathway we can tell that the length of the ends ( in meters ) is distributed among the two other ends of the garden so that the width ⇒
Increase length on one side * 2, if increased length / width ⇒ x, 2x
From this we can formulate an equation based on the lengths of the garden, as the increased lengths represents the side lengths of the total area ( walkway + garden );
( 12 + 2x )( 6 + 2x ) = 160 ⇒ Expand,
72 + 36x + 4x^2 = 160 ⇒ Subtract 160 on either side,
4x^2 + 36x - 88 = 0 ⇒ Factor,
4 * ( x - 2 ) * ( x + 11 ) = 0 ⇒ Use Zero Factor Principle,
x = 2, and x = - 11;
Now the width can only be a positive value, thus;
Solution; Width ⇒ 2 meters
Randy bought 5 candy bars for $6.00. What is the cost per candy bar?
A. $0.83
B. $7.20
C. $1.14
D. $1.20
Answer:
The answer is D: $1.20.
Step-by-step explanation:
1. The overall cost is $6
2. There are 5 candy bars
3. Assuming of the bars cost the same, we can find out the cost per bar
4. To do that, we take our overall cost $6, and we divide it by 5
5. 6/5=1.20 which is why the answer is D: $1.20
Answer:
D.$1.20
Step-by-step explanation:
Find the 40th term of this arithmetic sequence 4,9,14,19
Answer:
199
Step-by-step explanation:
I believe it's 199. The interval is just 5.
Answer:
the answer is going to be more than 11111111111119 (this is the 26th term)
Step-by-step explanation:
The amount of people in a population can be determined by using the model y=1000(1.35)x. What is the growth rate?
A.
35%
B.
1.035%
C.
1.35%
D.
3.5%
Answer:
The growth rate is 35%
Step-by-step explanation:
We are given that the amount of people in a population can be determined by using the model :
[tex]y=1000(1.35)^x[/tex]
Formula of exponential growth : [tex]y=a(1+r)^t ----1[/tex]
Where y is the population in t years
a = Initial population
r = growth rate
The given equation can be written as [tex]y=1000(1+0.35)^x[/tex]
Om comparing it with 1
r = 0.35
So, Growth rate = 35%
Hence The growth rate is 35%
A runner won a 100-meter race with a time of 9.73 seconds.
How can you use place value to explain this time?
Answer:
You can move the place value over to explain
Step-by-step explanation:
Answer:
The runner is going exactly 10.2774922919 meters per second
Step-by-step explanation:
Using the ratio 100:9.73, we can simplify that to 10.2774922919:1
What is the range for this data set?
37 years
9 years
41 years
Answer:
30 years
Step-by-step explanation:
41 minus 11=
Factor the expression below.
x2 - 6x + 9
A.
(x + 3)(x + 3)
B.
3(x2 - 2x + 3)
OC. (x-3)(x-3)
OD.
(x - 3)(x + 3)
HELP
This is a perfect square trinomial in the form a^2 - 2ab + b^2 = (a-b)^2. In this case, a = x and b = -3.
Another way you can look at it is to ask yourself "what two numbers multiply to 9 (last term) and add to -6 (middle coefficient)?". Those two numbers are -3 and -3
-3 plus -3 = -6
-3 times -3 = 9
So this is why x^2-6x+9 = (x-3)(x-3)
We can expand (x-3)(x-3) back out to get x^2-6x+9 again using the FOIL rule, distributive property, or the box method.
Answer:
C. (x-3)(x-3)
Step-by-step explanation:
x² - 6x + 9 = 0
x² - 3x - 3x + 9 = 0
x(x - 3) - 3(x - 3) = 0
(x - 3) (x - 3) = 0
A tea set was bought for $ 328, if a discount of 12% is offered on the price. Find the price of the tea set.
288.64
this is the real answer the last one was a mistake
It takes a painter and his friend 8 hours to paint a room. If the painter was working alone, it would take him 12 hours less than if his friend was working alone. How long does it take the painter to paint the room by himself?
Answer:
1 room-8hr (with friend)
alone- -12hr
friend working alone- x-12
Here is the base for you
hope this helps
Step-by-step explanation:
A class goes to a science museum. There is an exhibit which has a giant sphere that shows different weather patterns. The surface area of the sphere is 24,316.16 ft. What is the radius of the sphere? Use 3.14 for pi.
Answer: sjsjsjdjffj
Step-by-step explanation:
To find the mileage, or how many miles a car can travel per gallon of gasoline, you can use the expression m/g, where m is the distance in miles and g is the number of gallons of gas used. Find the mileage in miles per gallon for a car that travels 585 miles on 18 gallons of gas? (Your answer does not need miles per gallon at the end.)
Answer:32.5
Step-by-step explanation:
585/18
Triangle A’B’C’ is the image of triangle ABC.
On a coordinate plane, triangle A B C has points negative 4, negative 1), (negative 5, negative 5), (negative 3, negative 4). Triangle A prime B prime C prime has points (3, 4), (4, 8), (2, 7).
Which transformations could have been used to create A’B’C’ ? Choose all that apply.
a 180Degrees rotation about the origin and then a translation 3 units up and 1 unit left
a translation 3 units up and 1 unit left and then a 180Degrees rotation about the origin
a 90Degrees clockwise rotation about the origin and then a reflection over the y-axis
a 90Degrees counterclockwise rotation about the origin and then a reflection over the x-axis
a translation 3 units down and 1 unit right and then a 180Degrees rotation about the origin
Answer:
Its the First and Last answer on Edg
Step-by-step explanation:
I took the test
What’s the answer to this??
Answer:
i think the letter d is the correct answer sorry if im wrong
Answer:85
Step-by-step explanation:
360-119-71=170
170÷2=85
I WILL GIVE YOU BRAINLIEST, AND 30 POINTS SO PLEASE HELP ME, IT'S URGENT!
Which input value produces the same output value for the
two functions on the graph?
x = -3
x= -2
x= -1
x = 3
Answer:
hmm
um i don't think I could solve this why not try ta scan math i
Jodi learned to sing a total of 4 pieces over the course of 2 weeks of voice lessons.
After 8 weeks of voice lessons, how many pieces will Jodi be able to sing in total?
Assume the relationship is directly proportional.
A: 16 pieces
B: 20 pieces
C: 15 pieces
D: 12 pieces
Answer:
A. 16 pieces
Step-by-step explanation:
If Jodi learned to sing a total of 4 pieces over the course of 2 weeks of voice lessons, after 8 weeks of voice lessons, Jodi be able to sing 16 pieces.
2 x 2 =4
8 x 2= 16
Therefore the answer is 16.
Hope this helps and I explained it well enough !
Have a nice day.
Complete the square y^2+3y+
Answer:
y^2+3y+9/4
Step-by-step explanation:
y^2+3y+
Take the coefficient of y
3
Divide by 2
3/2
Square it
(3/2)^2 = 9/4
Add it
y^2+3y+9/4
Please justify the answer
Answer:
The age of the car in years is the independent variable
The average miles is the dependent variable
Step-by-step explanation:
Typically, the age of the car will have an affect on the number of miles per gallon. However, the number of miles per gallon will not make it gain or lose more years, so the age is independent because it does not depend on another variable.
Hope this makes sense :)
please answer this and please provide explanation since I need to explain in homework thank you I really appreciate it
Answer:
27648inches÷64inches=432 tiles
Step-by-step explanation:tiles cost 3456
What is the probability that a randomly selected player is a boy on the Sunderland team?
Hint: Sunderland boy/grand total.
.384
.462
.615
.538
Answer:
7/30
Step-by-step explanation:
First we need to find the number of girls on the Newcastle team, which is the total number of girls minus the number of girls on the other team, giving us 20-6=14. This means the number of player total is 3+7+6+14 or 30 players. There are 7 Sunderland boys so we have 7/30
Write the following number in scientific notation:
0.0000487
Answer:
4.87 × 10-5
Step-by-step explanation:
Hopes this helps.
The answer is 4.87 x 10^-5
Which of the following is equivalent to the expression below?
(7 X + 8) + (15 - 7x)
OA. 7x+ 23
B. 14x + 23
23
D. 7
Step-by-step explanation:
7x + 8 + 15 - 7x
Solving like terms
23
Option C is the correct answer
Answer:
23
Step-by-step explanation:
Given
(7x + 8) + (15 - 7x) ← remove parenthesis
= 7x + 8 + 15 - 7x ← collect like terms
= 23
The area of a wetland is 10,000 acres. A biologist predicts that the area of the wetland will change according to the equation y equals 10000 left-parenthesis 0.65 right-parenthesis Superscript x Baseline, where y is the area of the wetland after x years. Based on the biologist's prediction, what will the area of the wetland be in 2 years?
Answer:
4,225 acresStep-by-step explanation:
If a biologist predicts that the area of the wetland will change according to the equation [tex]y = 10,000(0.65)^{x}[/tex] where;
y is the area of the wetland after x years
In order to determine the area of the wetland in 2 years based on the biologist prediction, we will substitute the value of x = 2 into the modeled equation as shown;
[tex]y = 10,000(0.65)^{2}\\y = 10,000 * 0.4225\\y = 4225[/tex]
The area of the wetland in 2 years based on the biologist prediction will be 4225 acres
Answer:
4225
Step-by-step explanation:
I WILL GIVE YOU BRAINLIEST!!!!! The first side of a triangle is three times as long as the second side, and the third side is 50 cm shorter than the first side. Find all sides of the triangle if its perimeter is 370 cm. PLS HELP ME!!!!!!!
Answer:
The first side of the triangle = 180 cm
The second side of the triangle = 60 cm
The third side of the triangle =130 cm
Step-by-step explanation:
To solve this, we will follow the steps below;
First, re-write the question in a mathematical format and then solve;
let a=the first side of the triangle
b=the second side of the triangle and
c=the third side of the triangle
"The first side of a triangle is three times as long as the second side" can be re-write mathematically as:
a=3b ------------------------------------------------(1)
"the third side is 50 cm shorter than the first side" can be re-write as :
c=a-50-----------------------------------------------(2)
"perimeter is 370" can be re-write as:
a + b + c = 370 --------------------------------------(3)
from equation (2), make b subject of the formula; a= 3b
b=a/3 ------------------------------------(4)
substitute equation (2) and (4) into equation (3)
a + b + c = 370
a+[tex]\frac{a}{3}[/tex] + a-50 = 370
add 50 to both-side of the equation
a+[tex]\frac{a}{3}[/tex] + a-50 + 50= 370 + 50
a+[tex]\frac{a}{3}[/tex] + a= 420
[tex]\frac{3a + a + 3a}{3}[/tex] = 420
[tex]\frac{7a }{3}[/tex] = 420
multiply both-side of the equation by 3
[tex]\frac{7a }{3}[/tex] ×3= 420×3
7a = 1260
Divide both-side of the equation by 7
[tex]\frac{7a}{7}[/tex] = [tex]\frac{1260}{7}[/tex]
a= 180
from equation (4) b = a/3
b = 180/3 = 60
from equation (2) c= a- 50
c= 180 - 50
c= 130
a= 180 cm
b = 60 cm
c= 130 cm
Therefore,the first side of the triangle = 180 cm
the second side of the triangle = 60 cm
the third side of the triangle =130 cm
what is the triangular number of (546)
Answer:
Step-by-step
149331:
Answer:
149331
Step-by-step explanation:
hope its correct and it helps
-9x+2y=16
7x+2y=16
A8,1
B8,0
C8,-10
D0,8
i need help!!!
x+y=6
x=4
simplify the answer as much as possible
What is the factored form of 8x^24-27
Answer: 4.722
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The results of a survey indicate that the true proportion of households who recycle paper products
is likely in the interval (0.61,0.7).
What is the point estimate of the proportion of households who recycle paper?
Enter your answer, as a decimal, in the box.
Answer:
[tex] 0.61 \leq p \leq 0.70[/tex]
And for this case we can estimate the proportion of households who recycle paper is given by:
[tex] \hat p = \frac{Upper +Lower}{2}[/tex]
And replacing we got:
[tex] \hat p =\frac{0.7+0.61}{2}= 0.655[/tex]
And for this case the answer is 0.655 for the proportion of households who recycle paper
Step-by-step explanation:
For this case we know that the confidence interval for the proportion of interest is given by:
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And for this case the confidence interval is given:
[tex] 0.61 \leq p \leq 0.70[/tex]
And for this case we can estimate the proportion of households who recycle paper is given by:
[tex] \hat p = \frac{Upper +Lower}{2}[/tex]
And replacing we got:
[tex] \hat p =\frac{0.7+0.61}{2}= 0.655[/tex]
And for this case the answer is 0.655 for the proportion of households who recycle paper
Answer:
this answer is correct because i just took the test
Step-by-step explanation:
harold collected data on the daily high temperature in two cites over a period of one week . he analyzed the data and found the measures below . which statement is true based on these measures
Answer:
The temperature in Carlton was always cooler than in Borden.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
