Miss fernandez built two rectangular gardens the length of garden a is 2 feet longer than twice its width the list of garden b is 1 foot less than the width of garden a the length of garden b is 2.5 times its width the two gardens have the same perimeter what are the dimensions of the gardens

Answers

Answer 1

For garden A, let width = w, length = L
For garden B, let width = x, length = y

So we are given the following:
L = 2+2w
x = w - 1
y = 2.5x
2w+2L = 2x+2y ------> w+L = x+y

Ok lets do some substituting into the perimeter equation
[tex]w + (2+2w) = (w-1) + 2.5(w-1)[/tex]
adding like terms...
0.5w = 5.5
w = 11

This means that:
L = 2+2(11) = 24

x = 11-1 = 10
y = 2.5x = 2.5(10) = 25

Final solution:
Garden A is 11 by 24
Garden B is 10 by 25

Related Questions

To travel 105 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 64 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.

Answers

Let t=time Doreen travels; let r=rate of Doreen

RATE * TIME = DIST.
Sue | r+13 t-3 105
Doreen | r t 64

Now solve the system:
(r+13)(t-3)=105
r*t=64

[tex]r= \frac{64}{t} \\ \\(\frac{64}{t} +13)(t-3)=105 \\ \\64- \frac{192} {t}+13t-39-105=0 \\ \\13t- \frac{192} {t}-80=0 \\ \\ 13t^2-80t-192=0 \\ \\t_{1,2}= \frac{80\pm \sqrt{(-80)^2-4\times13(-192)} }{2\times13}= \frac{80\pm128}{26} \\ \\t=\frac{80+128}{26} =8 \\ \\r=\frac{64}{t} =\frac{64}{8} =8[/tex]

Doreen: rate = 8 mph, time = 8 hours
Sue: rate = 21 mph, time = 5 hours

1. A local pizzeria sold 65 pizzas yesterday.
(a) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning.

(b) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work.

Answers

65 + 0.20(65) = 65 + 13 = 78..they would have to sell 78 to get the bonus

(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday

Answer: 1) Pizzeria must sell 78 pizzas for receiving the bonus.

2) The number of pizzas sold is decreased by Approximately 7.69 %.

Step-by-step explanation:

1) The number of pizza sold yesterday = 65,

The target for receiving the bonus = 20% more than the number of pizza sold yesterday

= 20% more than 65,

= 65 + 20% of 65 ( 1% = 0.01 ⇒ 20% = 0.2 )

= 65 + 0.2 × 65

= 65 + 13 = 78.

Hence, they must sell 78 pizzas for receiving the bonus.

2) If the actual number of pizza sold today = 60

⇒ Total reduction in the number of pizza = 65 - 60

= 5

Thus, the percentage decrease in the number of pizza

[tex]=\frac{\text{Total reduction}}{\text{The number of pizza sold yesterday}}\times 100[/tex]

[tex]=\frac{5}{65}\times 100[/tex]

[tex]=\frac{500}{65}=7.69230769\approx 7.69\%[/tex]

10m - p = -n for m please help, I need help

Answers

10m-p=-n
10m-p+p=-n+p
10m=p-n devide by 10
m=(p-n)/10

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?

−5x − 7 < −22 and −5x − 7 ≥ −3
−5x − 7 > −22 and −5x − 7 ≥ −3
−5x > −22 and −7 ≥ −3
−5x − 7 < −22 and −5x − 7 ≤ −3

Answers

The answer is: [A]: " −5x − 7 < −22 and −5x − 7 ≥ −3 "
______________________________________________
Explanation:
___________________________
We are the given the following compound inequality:
__________________
" −22 > −5x − 7 ≥ −3 "
__________________________
Consider Answer choice: [A]: −5x − 7 < −22 and −5x − 7 ≥ −3
____________________________________________
Do both of these given in "Answer choice [A]" hold true?
______________________________________
First, does: −5x − 7 < −22 hold true?
___________________________________
Yes, because, in the compound inequality given:
___________________________________
−22 > −5x − 7 ; which is another way of saying that:
__________________
−5x − 7 < −22 .
____________________
Second does: "−5x − 7 ≥ −3 " , hold true?
_____________________________
Yes, because, in the compound equality given,
________________
−5x − 7 ≥ −3 ; which explicitly tells us that it holds true.
_________________
Thus, "Answer choice: [A]: −5x − 7 < −22 and −5x − 7 ≥ −3 " is a correct answer.
___________________
There could be other correct answers, so let us examine the other answer choices:
____________________
Consider "Answer choice: [B]: −5x − 7 > −22 and −5x − 7 ≥ −3 ;
__________________________
Do EACH of these hold true in "Answer choice "B"?
_______________
First let's examine:
_________________
−5x − 7 > −22 ; Does this hold true?
_____________________
No! Because in the compound inequality given,
−5x − 7 < −22 ; so we already know that "Answer choice: [B]" is incorrect; and thus, it makes no difference whether the other part of "answer choice [B]" is correct or incorrect.
_______________________
Let us consider: "Answer choice: [C]: 5x > −22 and −7 ≥ −3" .
Do these hold true with respect to our given compound inequality?
____________________________________________________
No; since NEITHER one of of this 2 (two) components given are are part of our compound inequality given.
__________________________________________________
Furthermore, the particular component given: " −7 ≥ −3" does not make sense. "Negative 7" is not 'greater than or equal to' "Negative 3". -7 ≠ -3 . Additionally, "-7" is LESS THAN—not GREATER THAN—"-3".
_________________________________________________
Also, "−5x > −22" is NOT part of the compound inequality given. So, "Answer Choice: [C]: −5x > −22 and −7 ≥ −3" ; is INCORRECT.
___________________________________________________
Additional note: " −5x < −22" is NOT part of the compound inequality given, either.
____________________
The [incorrect] "Answer Choice: [C]: "−5x > −22 and −7 ≥ −3" ; can be somewhat deceptive.

The compound inequality given:
___________________________
" −22 > −5x − 7 ≥ −3 " ; should be viewed as:
_______________________________________
" −22 > (−5x − 7) ≥ −3 " ;
_____________________________________
and the term, "(−5x − 7)" should be treated as one separate term—just like the terms: "(-22)", and "(-3)".
_______________________________________________
Let us consider "Answer choice: [D]: −5x − 7 < −22 and −5x − 7 ≤ −3 " .
_______________________________________________
Start with: −5x − 7 < −22 . Does this hold true for our original compound inequality?
________________
Yes! (Since in our original compound inequality; "−22 > −5x − 7" ;
and this component of 'Answer choice: [D]' — "−5x − 7 < −22 "— is another way of saying that: "−22 > −5x − 7" (as denoted in our original compound inequality).
___________________
Now, we shall examine the second component of
'Answer choice: [D]' — "−5x − 7 ≤ −3 ".
_____________________
Does this hold true for our original compound inequality?
_______________________
No! This second component given in our 'Answer choice'—is:
"-5x − 7 ≤ −3" ; and in our original compound inequality:
_______________
"−5x − 7 ≥ −3 " !
________________________
As such, since one of the compounds in 'Answer choice: [D]' is incorrect;
_______________________________________________
Answer choice: [D]: "−5x − 7 < −22 and −5x − 7 ≤ −3" ; is incorrect.
______________________________________________________

Which one is the greater quantity 1/3 of a box of corn crinkles or 50% of a box of corn krinkles

Answers

1/3=0.3333333333333
50%=0.50

0.50>0.33333333333333
50%>1/3

50% is biger

50% is bigger because if you divide 1/3 it equals 0.333333 and it just keeps going. 50% equals 0.5

V-15=-27 what's they equation

Answers

v would be equal to -12

The given expression V-15=-27 gives the value of v = -12.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

And we know that a mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given expression is:

V-15=-27

To solve this equation:

Add 15 on both sides

v - 15 + 15 = - 27 + 15

v = -12

Hence,

The given expression gives the value of v = -12

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Which of the following recursive formulas represents the same geometric sequence as the formula an = 3 * 3n - 1?

A.an = 9 * an - 1
B.an = 3 * an - 1
C.an = 9 + an - 1
D.an = 3 + an - 1

Answers

The recursive formula that represents the same geometric sequence as [tex]$ a_n = 3 \times 3^{n-1} $[/tex] is option B: [tex]$ a_n = 3 \times a_{n-1} $.[/tex]

To find the recursive formula that represents the same geometric sequence as [tex]$ a_n = 3 \times 3^{n-1} $[/tex], we need to find a recursive formula that generates the same sequence.

The formula [tex]$ a_n = 3 \times 3^{n-1} $[/tex] can be rewritten as:

[tex]\[ a_n = 3 \times 3^{n-1} = 3 \times 3^n \times 3^{-1} = 3 \times \left(3 \times 3^{n-1}\right) \][/tex]

This indicates that each term is 3 times the previous term. So, the recursive formula should involve multiplying the previous term by 3.

Let's examine the options:

A. [tex]$ a_n = 9 \times a_{n-1} $[/tex] - This represents multiplying the previous term by 9, not 3.

B. [tex]$ a_n = 3 \times a_{n-1} $[/tex] - This represents multiplying the previous term by 3, which matches the original sequence.

C. [tex]$ a_n = 9 + a_{n-1} $[/tex] - This represents adding 9 to the previous term, not multiplying it.

D. [tex]$ a_n = 3 + a_{n-1} $[/tex] - This represents adding 3 to the previous term, not multiplying it.

Therefore, the recursive formula that represents the same geometric sequence as [tex]$ a_n = 3 \times 3^{n-1} $[/tex] is option B: [tex]$ a_n = 3 \times a_{n-1} $.[/tex]

The leg of a right triangle is 2 units and the hypotenuse is 4 units. what is the length, in units, of the other leg of the triangle

Answers

the answer would be the square root of 12

Use you graph to estimate the value of x when y = 2. How would you work that out?

Answers

What the question is asking you to do is list what numbers x is equal to, whenever y is equal to 2

for example, if your equation was y=1/2x,

you would do this: 2=1/2x, then solve

2( 2=1/2x ) equals

4 = x

What is the equation for this slope question??

4.)The line whose slope is half as great as Its y-intercept. Their sum is 1.

Answers

I think the slope is 1/3 and the y-intercept is 2/3

Final answer:

We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.

Explanation:

The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.

Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.

So, the equation of the line is y = 1/3x + 2/3.

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What is the slope of this graph?

−1/3

3

1/3

−3

Answers

I'm assuming there is probably a graph that goes with this problem so here is all the info I can give you with the four choices: If it is -1/3, the line will go DOWN 1, over 3 (just count on the graph) If it is 3, the line will go UP 3, over 1 If it is 1/3, the line will go UP 1, over 3 And if it it -3, it will go DOWN 3, over 1 (If the slope is 3 or -3, it would be quite steep compared to a slope of 1/3 or -1/3) Hope that helps!

what times what equals 429

Answers

20.71 * 20.71 = 429

Your answer is 20.71
If you want more than it is 20.71231517

A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of 3?

Answers

There are 48 possible outcomes in this situation, and of those outcomes, the ones whose sums are a multiple of three are;
12, 21, 15, 51, 24, 42, 33, 18, 27, 36, 63, 45, 54, 48, 57, and 66. So, that is 16 out of 48 possibilities, or 16/48, which simplifies to 1/3. Written as a percent, the probability of getting numbers whose sum is a multiple of three is 33.33%.

Hope this is helpful! :)

To solve this problem, we have to find the multiples of 3 and then find the probability of selecting them. The probability of having a multiple of 3 is 1/3.

Probability of tossing a fair dice.

The probability of tossing a six-sided dice and a eight-sided dice.

When we toss them together, the maximum value will be

[tex]6 * 8 = 48[/tex]

The multiplies of 3 will be

Data;

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

The probability of having a multiple of 3 will be

[tex]P(multiple of 3) = \frac{16}{48} = \frac{1}{3}[/tex]

The probability of having a multiple of 3 is 1/3

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Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?
h and k cannot both equal zero
k and c have the same value
the value of a remains the same
h is equal to one half –b

Answers

"h and k cannot both equal zero" -- yes, it can. if the vertex of a parabola is at (0, 0), there's nothing incorrect/invalid about that!!

"k and c have the same value" -- k and c do not have the same value. "k" is the y-value of the vertex and c is the constant in your quadratic equation, and the constant is not necessarily the y-value.

"the value of a remains the same" -- this is true. the a's in your equations are the same values, because the a-value is the coefficient of the x-variable in both equations. y = a(x - h)^2 and y = ax^2 -- both of these have a applying to your x-variables.

"h is equal to one half -b" -- this isn't true. the formula for calculating the x value of the vertex (h is the x-value of the vertex) is h = (-b/2a). -b/2a is not the same as one half -b because this answer choice doesn't involve the a-value.

Quadratic equations can be expressed in standard form or in vertex form.

The true statement about [tex]\mathbf{y = ax^2 + bx + c}[/tex] and [tex]\mathbf{y = a(x - h)^2 + k}[/tex] is that: the value of a remains the same

The original expression is given as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

He wants to rewrite it as:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Expand the above equation

[tex]\mathbf{y = a(x - h)(x - h) + k}[/tex]

Open brackets

[tex]\mathbf{y = a(x^2 - hx - hx + h^2) + k}[/tex]

[tex]\mathbf{y = a(x^2 - 2hx + h^2) + k}[/tex]

Remove bracket

[tex]\mathbf{y = ax^2 - 2ahx + ah^2 + k}[/tex]

Compare the above equation to: [tex]\mathbf{y = ax^2 + bx + c}[/tex]

[tex]\mathbf{ax^2 = ax^2}[/tex]

[tex]\mathbf{-2ahx = bx}[/tex]

[tex]\mathbf{ah^2 + k = c}[/tex]

Analyzing the above equations

[tex]\mathbf{ax^2 = ax^2}[/tex]

Divide both sides by [tex]\mathbf{x^2}[/tex]

[tex]\mathbf{a = a}[/tex]

The above equation means that, the value of a remains unchanged.

Hence, option (c) is true

Answers

n is greater than or equal to 30 would be the condition that must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population.

Use the SAS Congruence Axiom to prove the ASA criterion ...?

Answers

Given the SAS, we can use the CPCPT (congruent parts of congruent triangles are congruent) and get the ASA.

A girl is 18 years old and her brother is a third of her age. When the girl is 36 what would be the age of the brother?

Answers

her brother is 6 yrs old

First we need to calculate how many years her brother has when she is 18. As text says he is:
18/3 = 6 years old

Now when she gains another 18 years (36-18=18) he will also gain those 18 years

When she is 36 he will have 6+18=24 years old

Answer is 24.

What is the equation in point slope form of the line that passes through the point (–1,–3) and has a slope of 4?

Answers

m=4

(-1, -3)
x1, y1

just plug the rest in

Answer:

The required equation is y + 3 = 4(x + 1)

Step-by-step explanation:

Since, the point slope form of a line passes through the point [tex](x_1, y_1)[/tex] having slope m is,

[tex]y-y_1 = m(x-x_1)[/tex]

Here,

[tex]x_1 = -1, y_1 = -3\text{ and }m = 4[/tex]

Hence, the equation of the line,

[tex]y+3 = 4(x+1)[/tex]

[tex]y = 4(x+1) - 3[/tex]

Kate ate 1 out of 4 of her orange. ben eat 2 out of 4 of his banana. did kate and ben eat 1 out of 4 add 2 out of 4 equal 3 out of 4 of their fruit? explain

Answers

no its 3 of 8 because you have to add the max fruit which is 8 and how many did they eat together which is 3

Estimate 24% of 33.

a) 17

b) 12

c) 2

d) 8

Answers

Just by estimating, I would estimate the answer to be d) 8.

24% is close to 25%, which is one fourth. One fourth of 33 is about 8.

Solve the following equation: 2x - 3 = 17.

a. 5
b. 7
c. 10
d. 12

Answers

I hope this helps you

2x=17+3

2x=20

x=10

I need help on this asap i'll give you so many points!!

Answers

So. The total of the interior angles of a triangle, are equal to 180°. So...add them together, and solve for X.

30x+60=180
30x=120
x=4

The distance adjacent to the smallest angle is the smallest.

Carrie=70°
Nayla=87°
Maria=23°

So...the distance across from Maria.

Carrie and Nayla are closest to each other.

how do I solve : COT pi/4 ...?

Answers

cot x = cos x / sin x
cot π/4 = cot 45° = cos 45° / sin 45°
We know that sin 45° and sin 45° have the same value:
cos 45° = sin 45° = √2 / 2;
cos 45° / sin 45° = √2/2 : √2/2 = 1
Answer:
cot π/4 = 1

During which two time intervals does the particle undergo equal displacement?

Choices:

a) AB & BC
b) AB & DE
c) BC & DE
d) CD & DF

Answers

It’s AB and DE so it would be b

Which of the pairs of angles are complementary

Answers

the third choice. complementary angles add up to 90 degees

Find the 9th term of the following geometric sequence: 1, –3, 9, –27. PLEASEEEEE HELP!!!!!!

A. –5,661
B. 7,241
C. –2,456
D. 6,561

Answers

find common ratio
1 times -3=-3
-3 times -3=9

an=a1(r^(n-1))
a1=first term
r=common ratio
n=which term

an=1(-3)^(n-1)

9th term
n=9
an=1(-3)^(9-1)
an=1(-3)^(8)
an=1(6561)
an=6561

answer is D

Tomas orders a meal the costs $7.89.lisa's meal costs $9.05. about how much is combined cost if their meals?

Answers

$7.89 rounded is about $8
$9.05 rounded is about $9
8 + 9 = 17

Their meals together costed about $17

Which equation could be used to solve the following system?

x+y=11
4x^2-3y^2=8

A. 4(y + 11)2 – 3y2 = 8

B. 4(11 – y)2 – 3y2 = 8

C. 4(y – 11)2 – 3y2 = 8

D. 4(–11y)2 – 3y2 = 8

Answers

I hope this helps you

x=11-y

4. (11-y)^2-3y^2=8

we have

[tex]x+y=11[/tex]

[tex]x=11-y[/tex] --------> equation A

[tex]4x^{2} -3y^{2}=8[/tex] ----> equation B

Substitute equation A in equation B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

therefore

the answer is the option B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

10 with a small 6 on top is

Answers

Do you mean [tex] 10^{6} [/tex]?

Are you asking what that equals or what the 6 means?

I'll just answer both lol

[tex] 10^{6} [/tex]=1,000,000

The 6 is an exponent by the way, if you needed to know that

10to the 6th power is 1000000

Which ordered pair is a solution to this equation?

(x + 3) y = 14

A. (3, 2)

B. (5, 2)

C. (11, 1)

D. (7, 2)

Answers

I hope this helps you

the answer would be C because (11+3)*1=14

Other Questions

write 3 different improper fractions that equal 4 2/3 Which of the following persons was assassinated in connection with the israeli-palestinian conflict? a. abu jihad b. anwar sadat c. rajiv gandhi d. indira gandhi different types of cells within an organism A are all the same B do not have any function C serve a different function D can survive on their own First Impressions As the moving truck pulled away from her new house, Cris commenced unpacking her things and breaking in her new accommodations, all the while contemplating her first day of school, which began tomorrow. Before moving, her dad had explained how crucial a good first impression could be and offered a recommendation. She had no idea if his absurd advice would work, but she was willing to give it a chance. The next morning, as Cris gathered her things to make it to the bus stop on time, she took one last glance at her reflection in the mirror. "Here goes nothing," she murmured before yelling goodbye to her parents as she raced out the front door. Cris arrived first at the bus stop, and while she frantically paced back and forth, she noticed another girl struggling to carry multiple bags. Cris decided on the spot to embrace her dad's advice and rushed over to the girl. "Let me help you with those!" she squelched in an outlandish cartoon voice, hoping to break the ice. "I'm Cris." "Huh . . . oh, thanks! I'm Aishah," she said with a stuttering giggle. "Why do you have so many bags?" "These are decorations for the upcoming school dance. Say, would you mind helping me get them set up?" Aishah asked suddenly. "Uh, sure!" exclaimed Cris at the unexpected offer. Cris was working through a set of problems during her midday Geometry class, when she noticed the boy next to her struggling on a practice problem that she, too, worked hard to solve. She could see his frustration beginning to bubble to the surface, so she took a deep breath, thought of the funniest character she could and asked, "Help with your problem, do you need?" "What? Oh, yes," the boy chuckled. "I'm usually quick with probability, but I don't understand geometry equations quite so easily." "Yeah, it gave me trouble too. Let me show you how I derived the answer." Cris began as she demonstrated the solution and explained it, this time without the absurd voice. "Thanks for the help. I'm Jackson, by the way." "Cris, nice to meet you." When Cris arrived home, she began thinking of all the new voices she could use to win over new friends. She began practicing a new one when her dad walked in and asked, "So, how was your day?" "Great! I'm helping Aishah with the school dance decorations, and I met Jackson by aiding him with a geometry equation. And they seemed to really like my first impressions! 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