Suppose that a family wants to increase the size of the garden which is currently 16 feet long and 8 feet wide without changing the basic shape of the garden. That is, the family wants to ensure that the length of the garden remains twice the width (see figure).
1. Write an equation for the area of the new garden.
2. Write an equation that calculates how much more area the new garden will have as compared to the current garden. Simplify the equation into a quadratic equation in standard form.
3. Using the equation from Exercise 2, determine what effect increasing the width of the garden by two feet will have on the length of the garden and the total area of the garden.
4. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be 160 square feet larger than its original area.
5. Using the equation from Exercise 2 and factoring, determine how much the width of the garden will need to be increased in order for the garden area to be four times its original area.
Answers
Answer:
See below
Step-by-step explanation:
Sides of the garden
16 feet and 8 feetNew dimensions of the garden
16 + 2x and 8 + x1. The area of the new garden
(16 + 2x)(8 + x) = 2x^2 + 32x + 1282. The difference in area
2x^2 + 32x + 128 - 16*8 = 2x^2 + 32x3. x= 2 effect on the area
2*2^2 + 32*2 = 8 + 64 =72 ft²4. Area difference = 160
2x^2 + 32x = 160x^2 + 16x - 80 = 0Solving we get positive root of 4 ft5. Area difference = 4 times
2x^2 + 32x = 128*32x^2 + 32x - 384 = 0x^2 + 16x - 192= 0Solving we get positive root of 8 ftRelated Questions
PLEASE HELP ME ASAP! ILL GIVE BRAINLEST
Answers
Answer:6(-4)
Step-by-step explanation:
Answer:
4(-6), 6(-4), 12(-2)
Step-by-step explanation:
Hi there!
A negative number times a positive number is a negative number. So, since -4 x 6 has one negative number, you can think of it as 4 x 6 and then add a minus sign after multiplying, so -4 x 6 is -24.
In multiplication, no matter which way the equation goes, the answer will always be the same ( 5 x 3 is the same as 3 x 5). Therefore, we are looking for another equation that will also equal -24.
4(-6) is the same because it is still one number that is a negative, and it still equals -24.
6(-4) is the same as well, it's just we're putting the parentheses around the -4 this time.
12 x 2 is 24, so 12(-2) is negative 24 (-24)
I hope this explanation helped you! I'd appreciate if you gave me Brainliest, rated my answer and gave it a Thanks! Have a great day!
Quincy needs 322 yards of ribbon to decorate quilts for a craft fair. The ribbon comes in rolls of 15 yards. Alice needs twice as many yards of ribbon as Quincy. How many rolls of ribbon does Alice need? Explain your answer.
Answers
Answer:
The answer is 35
What is the difference between -3 and -12?
O-15
O 15
O -9
O 9
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What is the angle relationship? Meaning, what is the angle for this?
I’ll give brainliest to whoever answers right! :)
Answers
Answer:
Easy. Alternate interior angle.
Step-by-step explanation:
9) Mrs. Jones spends $12.35 per day on her
lunch If she buys lunch 15 days this month, how
much will she spend on lunch?
Answers
Answer:
Step-by-step explanation:
Since she buys lunch for 15 days you do 12.35 times 15 which is $185.25
Answer:
$185.25
Step-by-step explanation:
just multiply 12.35 x 15
hope this helps!! <3
The formula for the density of a bacteria population is \dfrac NA A N start fraction, N, divided by, A, end fraction where there's an average of NNN bacteria in an area size AAA. Guang and Orion are doing an experiment in school for which they need to measure the density of a bacteria population after a certain solution has been introduced. Guang reports a density of 450045004500 bacteria per square centimeter and Orion reports a density of 505050 bacteria per square millimeter. Which one reports a higher density? Choose 1 answer:
Answers
Answer:
Guang reports a higher density of 4.5 × 10⁷ bacteria/m²
Step-by-step explanation:
Since Guang reports a density of 4500 bacteria per square centimeter and Orion reports a density of 50 bacteria per square millimeter, we convert both densities into bacteria per square meter to compare their values.
So, for Guang 4500 bacteria/cm² = 4500 bacteria/cm² × 10⁴ cm²/1 m² = 4500 × 10⁴ bacteria/m² = 4.5 × 10⁷ bacteria/m²
For Orion 50 bacteria/cm² = 50 bacteria/cm² × 10⁴ cm²/1 m² = 50 × 10⁴ bacteria/m² = 5 × 10⁵ bacteria/m²
Since 4.5 × 10⁷ bacteria/m² > 5 × 10⁵ bacteria/m², Guang reports a higher density of 4.5 × 10⁷ bacteria/m²
Answer:
B.) orion reports a higher desity than guang
Step-by-step explanation:
We found that Guang's reported density is 45 bacteria/ millimeter^2, while orion's reported density is 50 bacteria/ millimeter^2.
SIMPLIFY THIS EXPRESSION:
2(z + 3) + 3(5 - 3z)
Answers
-7z+21
Hope this helps
I DONT UNDERSTAND HELLPPP
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Answer:
choice answer choice f
can you guys help, plz i dont understand it
Answers
Answer:
21x+6
Step-by-step explanation:
A taxi service charges you $1.50 plus $0.60 per minute for a trip to the airport. The distance to the airport is 10 miles, and the total charge is $13.50
How many minutes did the ride to the airport take?
Answers
Answer:
20 minutes
Step-by-step explanation:
The question can be shown like so, 1.5+0.6x
Since the total charge was 13.5, you can write an equation
13.5=1.5+0.6x
Simplify using property of subtraction
13.5 - 1.5= 1.5 - 1.5 + 0.6x
12 = 0.6x
Simplify using property of division
12/0.6= 0.6x/0.6
x=20
If <3=70°, then find the rest of the angles.
1.) m<1=
2.) m<2=
3.) m<4=
4.) m<5=
5.) m<6=
6.) m<7=
Answers
2. 70
3. 110
4. 110
5. 70
6. 70
write 2x X(5y-y)/2 in a simplified form
Answers
Answer:
I'm not sure if you included an extra x so I'm including two answers with the work.
The answers are 4 x^ 2 y and 4 x y.
Step-by-step explanation:
Answer:
The answer is 4xy
Step-by-step explanation:
Rewrite the division as a fraction.
[tex]\frac{2x⋅(5y-y) }{2}[/tex]
Cancel the common factor of 2.
x ⋅ (5y - y)
Subtract y from 5y.
x ⋅ (4y)
Rewrite using the commutative property of multiplication.
4xy
I hope this helps.
Kiara has $450 in the bank. After
buying groceries she has $398.72 left in
her account. Write and solve an
equation to determine how much she
spent at the grocery store.
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write an equation for each quadratic function whose graph is shown
Answers
Answer:
9. y=5[tex]x^{2}[/tex]
10. y=2/3[tex]x^{2}[/tex]
11. y=1/10[tex]x^{2}[/tex]
12. y=-1/4[tex]x^{2}[/tex]
Step-by-step explanation:
9. Use vertex form (y=a(x-h)^2+k) and insert the vertex (0,0) as (h, k).
y=a(x-0)^2 +0
Substitute the x and y values for the given point on the graph, (-1, 5)
5=a(-1-0)^2+0
Solve for a.
5=a(-1)^2
5=a
Substitute a in vertex form and solve for general form (ax^2 +bx+c)
y=5[tex]x^{2}[/tex]
Use this method to find the rest of the equations.
solve for the indicated variable. e=f-g for g
Answers
Answer:
g = f - e
Step-by-step explanation:
f - g = e
- g = e - f
g. = f - e
Which exponent is missing for the given expression ?
Answers
If two quantities vary directly, which must be true of a graph showing the relationship between them? Select all that apply.
A) The graph is a curve.
B) The points on the graph are connected.
C) The graph increases from left to right.
D) The points of the graph form a straight line.
E) The points of the graph must include the origin.
F) The points must all form equivalent ratios.
Answers
Answer:
Step-by-step explanation: D. F. And
E
, as graphe
7. Which point would not be on a graph of the equation y = 3.5x ?
(1) (6,21)
(3) (3,9.5)
(2) (0,0)
(4) (1,3.5)
which point would not be on a graph of the equation y=3.5x
Answers
Pls help! I will mark brainliest!!!
Answers
Answer:
The answer should be -1 degree
Step-by-step explanation:
Combine all temperatures then divide by amount added together in this case five
Which graph best represents the function y = - 1/2 (x +4)?
Answers
Answer:
y=-1/2x-2
Step-by-step explanation:
simplify the expression to get the equation in slope intercept form, and find the graph that fits it
A Turtle traveled 1/10 mile in 1/2 hour. What was the turtle’s rate in miles per hour?
A.1/20
B.1/12
C.1/6
D.1/5
Answers
1/10 / 1/2= 2/10
Then simplify it by 2, it becomes D.1/5
Complete the statements using the drop-down menus. The line perpendicular to the y-axis through the point (–4, –2) is . The slope of this line is .
Answers
Answer:
Y=-2, 0
Step-by-step explanation:
EDG 2020
Answer:
1. y= -2
2. 0
Step-by-step explanation:
Correct on Edg 2020
Chris purchases a living room furniture set for $4,345 from Halloran Gallery. She has a one-year, no interest, no money down, deferred payment
plan. She does have to make a $15 monthly payment for the first 11 months.
a. What is the sum of these monthly payments?
b. How much must Chris pay in the last month of this plan?
Answers
Answer:
a) $165
b) $4180
Step-by-step explanation:
15×11=165
4,345-165=4180
a) The sum of these monthly payments is $165
b) Chris pay in the last month of this plan is $4180
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units?
For example
Ram spends 36 Rs. for a dozen (12) bananas. 12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Price for furniture set = $4,345
a) The sum of these monthly payments
=15×11
=$165
b) Chris pay in the last month of this plan
=4,345-165
= $4180
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
Please help me it would mean a lot.
Answers
Answer:
60
Step-by-step explanation:
119-59 = 60
x + 2y = 23
A.(15,-4)
B.(-15,4)
C.(15,4)
Answers
Answer:
23
Step-by-step explanation:
232323
3
3
3
3
23
23
3
this isnt correct btw
Booster club sell tickets to Saturday's basketball tournament admission with student ID was two dollars per person regular admission is five dollars the booster club sold 120 student tickets and 50 regular tickets how much money did the booster club click show all the work necessary to justify your answer
Answers
Answer:
170 Tickets were sold and 490$ was made
Step-by-step explanation:
to find how many tickets were sold add 120 + 50 to get 170
For how much they made Multiply 120 X 2 to get 240
Then, Multiply 5 x 50 to get 250
Add 240 + 250 and your answer will be 490$
Point D is on line segment CE.Given DE = 2 + 10, CD = 6, and CE = 3x,
determine the numerical length of DE.
Answers
Answer:
18
Step-by-step explanation:
There are selveral ways of doing this
1. add all the numbers together so 2+10+6=18
or
2. 3x= (2+10) +6
(12)+6
18
3x=18
/3. /3
x=6
then 3(6)
therefore equalling 18 as well
Write an equation of a line that has a slope of 1/2 and has a point at (2, 5).
Answers
y-5 = 1/2 ( x-2)
y -5 = 1/2x -1
y = 1/2x + 4
Find the area of the shaded region.
Round to the nearest tenth.
Answers
Answer:
(Assuming they are both right triangles)
214.5 sq ft
Step-by-step explanation:
Area of a right triangle= leg×leg / 2
25×25 / 2 = 312.5
14×14 / 2 = 98
312.5-98= 214.5
If you do this whole page you get brainlessly and 5 rating and a thanks
Answers
Answer: A then 0.700 .7 .70
Step-by-step explanation:
Part B. is 0.7 and 0.70
I hope this helps:)
