Answer:
Part A)
[tex]390=(15+x)(13+x)[/tex]
Part B)
Approximately 18.77 feet long by 20.77 feet wide.
Step-by-step explanation:
Currently, the patio is 13 feet long by 15 feet wide. Therefore, the area right now is:
[tex]A=13(15)=195\text{ feet}^2[/tex]
We will increase the length and width of the patio by the same amount such that the new area is double the previous amount.
Part 1)
The previous area is 195. Therefore, we would like to the new area to be twice of that. Hence, the new area is:
[tex]A=2(195)=390[/tex]
We will increase the length and the width by the same amount. Let’s call this amount x. Then by the area formula (A=bh), we can write:
[tex]390=(15+x)(13+x)[/tex]
390 represents the doubled area. (15+x) is the width after the increase x, and (13+x) is the length after the same x increment.
Part 2)
So, we will solve for x. First, expand:
[tex]390=195+15x+13x+x^2[/tex]
Simplify:
[tex]x^2+28x+195=390[/tex]
Subtract 390 from both sides:
[tex]x^2+28x-195=0[/tex]
This is a quadratic. Hence, we can use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Our a=1, b=28, and c=-195. Hence:
[tex]x=\frac{-28\pm\sqrt{(28)^2-4(1)(-195)}}{2(1)}[/tex]
Evaluate:
[tex]x=\frac{-28\pm\sqrt{1564}}{2}[/tex]
Simplify the square root:
[tex]\sqrt{1564}=\sqrt{4}\cdot\sqrt{391}=2\sqrt{391}[/tex]
Hence:
[tex]x=\frac{-28\pm2\sqrt{391}}{2}\\[/tex]
Simplify:
[tex]x=-14+\sqrt{391} \text{ or } -14-\sqrt{391}[/tex]
Approximate:
[tex]x\approx5.77\text{ or } x\approx-33.77[/tex]
In this case, we can reject the negative solution.
Hence, the value of x is 5.77.
This means that we should increase the our length and width by 5.77.
Hence, the new length will be 13+5.77 or about 18.77.
And our new width will be 15+5.77 or about 20.77.
So, the new dimensions is approximately 18.77 by 20.77
Which number line best shows how to solve -8 - (-6)? (5 points)
Question 3 options:
1)
2)
3)
4)
Question 4 (5 points)
Answer:
its 3 solve -6
Step-by-step explanation:
Answer:
Where are the pictures
Step-by-step explanation:
I need help with this asap
10b^4+3b^4-11
what is the area of the rectangle
Answer:
54
Step-by-step explanation:
Width times height equals area so 9x6=54
Please answer correctly !!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answer:
x= 6 y=40
Step-by-step explanation:
Which of the following metals needs roman numerals?
copper
zinc
sodium
Answer:
Copper, and Zinc
Step-by-step explanation:
This is because Copper and Zinc are the only elements listed on the modern day Periodic Table of Elements.
Feel free to give brainliest.
Have an outstanding day!
2x^2-5x-10=4x-5 solve algebraically
Answer:
by factoring the answer is - x=1/2, 5
Step-by-step explanation:
hope it helps:))
Answer:
x=-½
x=5
Step-by-step explanation:
2x²-5x-10=4x-5
2x²-5x-10-4x+5=0
2x²-9x-5=0
2x²+x-10x-5=0
x(2x+1)-5(2x+1)=0
(2x+1)(x-5)=0
2x+1=0
2x=-1
x=-1/2
x-5=0
x=5
so if fingernails grow about 0.1 millimeters each day how much do nails grow in 30 days?
Answer:
3.47 mm
Step-by-step explanation:
Please help me I need this to be absolutely correct thanks!
Answer:
Step-by-step explanation:
I can't really graph it for you, but I will show you how to.
-x is the value on the horizontal axis, which are 1,2,3,4,6
if you replace x for 1, which is
y= -4(1) + 3
y= -1
so you can graph that point (1,-1)
you can replace x with other numbers on the horizontal axis.
Hope this helps
does anyone know the square root of my heart because it needs some adding rn...
sorry for that really bad dad pick up line heh
Answer:
lol
Step-by-step explanation:
Learning Task
It took Althea 40 minutes
to walk 27mile to her
Int's apartment after
hool because she
Srgot her keys and
noone was home yet.
Nhat was her speed in
miles per hour?
Answer:
40.3miles/hr
Step-by-step explanation:
Given parameters:
Time taken = 40min
Distance covered = 27mile
Unknown:
Speed in miles per hour = ?
Solution:
Speed is the distance divided by the time;
Speed = [tex]\frac{distance }{time}[/tex]
convert the time to hrs;
60min = 1hr
40min = [tex]\frac{40}{60}[/tex] = 0.67hr
Insert the parameters and solve;
Speed = [tex]\frac{27}{0.67}[/tex] = 40.3miles/hr
Jane wants to share her pizza with two friends.she wants to make sure they all get the same how should she cut the pizza
Answer:
She would cut the pizzas into 3rds.
Answer:
Depending on how big the pizza is I guess.
If it's three people, Jane can either...
Cut the pizza into 6 slices, 2 for everyone
Cut the pizza into 12 slices, 4 for everyone
Basically into thirds lol
Hope this helped :)
2.83333333333 simplify
Answer: So the answer is 2.83
Step-by-step explanation: This is a terminating decimal number, so if I round up to the nearest trillionth place it will be 2.83. Just only give me a thanks and 5-star rate. :)
During a regular respiratory cycle, the volume of air in liters in the human lungs can be described by the function V(t) = 0.173t +0.15t^2 - 0.035t^3 where t is the time in seconds. Estimate the time in seconds from the beginning of this respiratory cycle for the lungs to fill to their maximum volume of air. a. about 3.4 seconds b. about 4.4 seconds c. about 5.4 seconds d. about 10.4 seconds
Answer:
A. about 3.4 secondsStep-by-step explanation:
Given the volume of air in liters in the human lungs described by the function V(t) = 0.173t +0.15t^2 - 0.035t^3 where t is the time in seconds,
The beginning of this respiratory cycle for the lungs to fill to their maximum volume of air occurs when dV/dt = 0
dV/dt = 0.173 + 0.3t - 3(0.035)t²
dV/dt = 0.173 + 0.3t - 0.105t²
Since dV/dt = 0
0.173 + 0.3t - 0.105t² = 0
multiply through by -1
-0.173 - 0.3t + 0.105t² = 0
0.105t² -0.3t-0.173 = 0
Factorize;
t = 0.3±√0.3²+4(0.105(0.173))/2(0.105)
t = 0.3±√0.09+0.07266/0.21
t = 0.3±√0.16266/0.21
t = 0.30±0.4033/0.21
t = 0.7033/0.21
t = 3.349secs
t ≈ 3.4secs
Hence it will take about 3.4secs for the lungs to fill to their maximum volume of air
you want new picture frames that cost $12 each shipping is a $8 per order if you buy 15 frames what is the cost of the oder
Answer:
it would be $300 because it is $12 per frame so u would multiply 12*15 and get 180 then with $8 shipping u multiply 8*15 and get $120 then add 120+180 to get $300
Step-by-step explanation:
hope this helped:)
what is the length of the missing leg?
Answer:
it's 5
Step-by-step explanation:
you should use pythagoras theorem
Answer:
b = 5
Step-by-step explanation:
a^2 + 12^2 = 13^2
a^2 + 144 = 169
-144 -144
[tex]\sqrt{a^2}[/tex] = [tex]\sqrt{25}[/tex]
a = 5
[tex]a^2 + b^2 = c^2[/tex] pythagoream theory
Henry's soccer team is trying to raise $864 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $12 for the breakfast. How many people need to attend their breakfast in order to raise $864?
Answer:
Step-by-step explanation:
12/864 = 71 r4
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
864 ÷ 12 = 72
The number of people needed to attend their breakfast in order to raise $864 is 72 people.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
56÷ 4 is an expression.
We have,
Henry's soccer team is trying to raise $864 to travel to a tournament in Florida, so they decided to host a pancake breakfast.
Each person must pay $12 for the breakfast.
The number of people needed to attend their breakfast in order to raise $864.
= 864 ÷ 12
= 864 / 12
= 72 people
We can cross-check.
Amount collected from 72 people.
= 12 x 72
= $864
Thus,
The number of people needed to attend their breakfast in order to raise $864 is 72 people.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
11. need help with this maths question
Answer:
Step-by-step explanation:
Use your calculator
first times the 9 five times (9x9x9x9x9) then time it by the 177147.
then put that value in the
[tex]\sqrt[3]{x}[/tex]
Lola runs at a constant speed of 3.4 meters per second for 1/2 hour.then she walks at a rate of 1.5 meters per second for 1/2.how far did Lola run and walk in 60 minutes?
Answer:
8,820m
Step-by-step explanation:
Let m be meters
We will have to find the amount of seconds in half an hour
60 * 30
= 1,800
Then we will multiply the meters she walks per second by 1,800
3.4m * 1,800
= 6,120m
1.5m * 1,800
= 2,700m
We add those two together to get the total walked in an hour
6,120m + 2,700m
= 8,820m
Consider these functions: f(x)=x+1, g(x)=2/x
Which polynomial is equivalent to (fog)(x)?
A.2/x+1
B.2x+2/x
C.2/x +1
D.2/x^2+x
Answer:
A.2/x+1 ............
The composite function f(g(x)) is 2/x + 1
Given the function
f(x)=x+1g(x)=2/xWe are to get the composite function (fog)(x)
This can be written as:
f(g(x)) = f(2/x)
f(2/x)= 2/x + 1
Hence the composite function f(g(x)) is 2/x + 1
Learn more on composite function here: https://brainly.com/question/10687170
A bit confused I need some help
Answer:
B
Step-by-step explanation:
Write a unit rate for the situation.
$12.50 for 5 ounces
$__ per ounce
Answer:
The correct answer is $2,50.
Step-by-step explanation:
The unit rate is what we use to determine the price of a single unit, when something is sold in a group, as in this case 5 ounces.
We have been told that $ 12.50 is the price for 5 ounces, but what we want to know is how much 1 ounce costs.
To determine this, what we must do is divide the total price by the quantity of ounces, in order to determine the unit price:
12.50 / 5 = 2.50
In this way we can verify that the unit price of 5 ounces is $ 2.50
What is the probability of drawing a king or a queen, given
that you have already drawn two kings and two queens and
have not replaced them?
(A) 12
1
(B) 26
(C) 13
2.
(D) 25
(E) 0.080
Answer:
D
Step-by-step explanation:
EVERYONE LISTEN PLZ!!!! there's this person named mariaivanovaloveyou
report her NOW! she's posting very gross stuff that isn't nice to see and she's trying to get u to see a website (copy and paste this and spread it for we can stop her)
Answer:
done
Step-by-step explanation:
the x- and Y negative coordinates have the same sign
Answer:
if the x and y coordinates that mean that number is the solution to whatever the question is.
Step-by-step explanation:
-3.8+5+2.7g=12 i neeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeed help
We first of all have to simplify this expression to be 2.7g+1.2=12 then subtract 1.2 to both sides and that = to 10.8 and then divide both sides by 2.7 and you will get 4 so,
G=4
Solve the quadratic by using the quadratic formula
X2-8x+17=0
which algebraic expression is a polynomial?
Answer:
wym?? where's the expressions or am i just dumb
Step-by-step explanation:
Answer:
what expression?
Step-by-step explanation:
Please answer this question please :)
Answer:
B
Step-by-step explanation:
A linear equation has the highest degree of 1.
In other words, there is only one x, and this x is to the first power.
Graphically, linear equations are lines.
Hence, the correct answer is B.
A is incorrect because it is the reciprocal of x, which is a rational function.
C and D are incorrect because the highest degree is 2, making them quadratics.
Answer:
B)
Step-by-step explanation:
A) Rational
B) Linear Equations
C) Quadratic Equations
D) Quadratic Equations
=== Terima Kasih ===
Bao is mixing flour and water to make dough. The graph show how much water he uses for different amounts of flour
Answer:
1/3 and 3
Step-by-step explanation:
due today, pleaseee helppp