Answer:
400
Step-by-step explanation:
Yumiko has a rectangular-shaped patio. She wants to double the area of the patio by increasing the length and the width by the same amount.
The length is 14 and the width is 10.
a. Write a function, in factored form, to calculate the number of feet Yumiko would need to add to the length and width.
b. What are the dimensions of the patio, rounded to the nearest hundredth feet?
I am not very good with completing the square and would like to understand it better. Any help would be very appreciated!
Answer:
For a rectangle of length L and width W, the area is:
A = L*W
In this case, we start with:
L = 14ft
W = 10ft
Then the initial area is:
A = 14ft*10ft = 140ft^2
a) Now she wants to increase the same amount in each measure, then the new measures will be:
L = 14ft + x
W = 10ft + x
Now we want this new area to be twice the one that we got before, then the equation will be:
(14ft + x)*(10ft + x) = 2*140ft^2 = 280ft^2.
b) Let's solve the equation:
(14ft + x)*(10ft + x) = 280ft^2
First lets distribute the multiplication:
140ft + x*10ft + 14ft*x + x^2 = 280ft
Now let's group terms with the same power of x.
x^2 + (10ft + 14ft)*x + 140ft - 280ft = 0.
x^2 + 24ft*x - 140ft = 0.
Now we need to solve this quadratic equation, here we must use the Bhaskara equation for quadratic equations, and we will get two solutions for x.
[tex]x = \frac{-24ft +- \sqrt{(24ft)^2 - 4*140ft*1} }{2*1} = \frac{-24ft +- 33.7ft}{2}[/tex]
Then the two solutions are:
x = (-24ft - 33.7ft)/2 = -28.9 ft
This solution is negative, so it does not make sense and we can discard it.
x = (-24ft + 33.7ft)/2 = 4.85ft
This is positive, so we can use this.
Now we can find the new length and width:
L = 14ft + 4.85ft = 18.85ft
W = 10ft + 4.85ft = 14.85ft
-3 = 1 3/5 + m .
what is m
Answer:
m = -4 3/5 or -4.6
Step-by-step explanation:
First, we need to isolate the variable, m. We subtract 1 3/5 on both sides of the equation, and then we should get -4 3/5 = m.
hope this helped !! :D
Is (2, 2) a solution to this system of equations? 3x + 7y = 20 7x + y = 16
Answer: Yes they both pass through the point
What is the value of A when we rewrite 4^x+3-4^x as A times 4^x
This looks simple I belive the answer would be 35 because 4^x + 31^x = 35^x
slove this for me please
Answer:
-10
Step-by-step explanation:
divide both sides by -4
simplify to v+8=-2
subtract 8 from both sides
v=-10
2/7x + 1/5x = 34 x= what?
Answer:
70
Step-by-step explanation:
[tex]\frac{2}{7}x +\frac{1}{5}x=34[/tex]
We need to combine like terms but since they are fractions we first need to find a common denominator. The common multiple of 5 and 7 is 35 so we need to multiply 7 by 5 and 5 by 7, but we have to do the same to the numerator too.
[tex]\frac{2*5}{7*5} +\frac{1*7}{5*7}[/tex]
[tex]\frac{10}{35}x+\frac{7}{35} x=34[/tex]
Combine like terms
[tex]\frac{17}{35}x=34[/tex]
Divide 34 by [tex]\frac{17}{35}[/tex]
[tex]\frac{34}{1} *\frac{35}{17} =\frac{1190}{17} =70[/tex]
x2 + 6 x+8 = 0
What is the factors
Answer:
Step-by-step explanation:
What is the area of this figure?
9 m
7 m
6 m
2 m
5 m
6 m
3 m
5 m
Write your answers using decimals, if necessary.
The total area of the composite figure made up of triangle, rectangle and square is; 106 m²
What is the Area of the Composite Figure?The area of the Triangle is;
A_t = (1/2) * (6 + 4) * 9
A_t = 45 m²
Area of Square;
A_s = 5 * 5
A_s = 25 m²
Area of Rectangle is;
A_r = 6 * 6
A_r = 36 m²
Total Area = 45 m² + 25 m² + 36 m²
Total Area = 106 m²
Read more about Area of Composite Figure at; https://brainly.com/question/10254615
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Michael travels 172 miles in 4 hours. Find the unit rate.
Answer:
43.5
Step-by-step explanation:
its a geo match to the ? type thing
HELP ME PLS THIS IS URGENT ASAP PLS HELP ILL BRAINLISTTT
Answer:
1.) h • g4 • h = 4g•2h
2.) c • 4 • a •b = ab•4c
3.) (40)/(11•a)= (a•11)/40
4.) (20)/(4•x)= (x•4)/20
Step-by-step explanation:
Think of it as adding and flipping :)
A race is 20 miles long . There is water station every 1 1/4 miles along the race route. How many water stations are needed for this race ?
Answer:
16
Step-by-step explanation:
just divide 20 by 1 1/4
i need help on this problem im stuck on it
Answer:2.8
or
2.83333
Step-by-step explanation:
Given : A table is given to us . The table is ,
[tex]\begin{tabular}{|c|c|}\cline{1-2} \bf Day of week & \bf Minutes Spend \\\cline{1-2} Sunday & 23 \\\cline{1-2} Monday & 38 \\\cline{1-2} Tuesday & 42 \\\cline{1-2} Wednesday & 17 \\\cline{1-2} Thursday & 29 \\\cline{1-2} Friday & 10 \\\cline{1-2} Saturday & 11 \\\cline{1-2} \end{tabular}[/tex]
To Find : The total hours spend by Marisol on reading .
Solution : Total hours spend on reading will be equal to the sum of time taken by him each day on reading .
So , total time of reading will be ;
= (23 + 38 + 42 + 17 + 29 + 10 + 11) min
= 170 min .
= 120min + 50min .
= 2 hours 50mim .
[tex]\boxed{\red{\bf Correct\:option - [d]}}[/tex]
What is the distance between (8, -3)and (4,−7)?
Answer:
+4sqrt(2)
Step-by-step explanation:
Note that the horizontal distance is 8 - 4, or 4 (which is the "run") and that the vertical distance is -3 - (-7), or 4 (which is the "rise"). Applying the Pythagorean Theorem, we get:
distance = length of hypotenuse = +sqrt(4^2 + 4^2) = +4sqrt(2)
At a local fitness center members pay an 8$ membership fee and $3 for each aerobics class nonmembers pay $5 for each aerobics class for what number of aerobics classes will the cost for members and nonmembers be the same
Answer:
4 aerobics classes
Step-by-step explanation:
8 + 3x = 5x
8 = 2x
4 = x
Can somebody explain and give examples on questions like
What is divisible by this number ?
Answer:
more than one digits.
Step-by-step explanation:
There are some simple divisibility rules to check this: A number is divisible by 2 if its last digit is 2, 4, 6, 8 or 0 (the number is then called even) A number is divisible by 3 if its sum of digits is divisible by 3. A number is divisible by 4 if the number consisting of its last two digits is divisible by 4
7y + 2x − 10y + 3x^2 − 10x.
Answer:
67
Step-by-step explanation:
Answer:
3x² - 8x - 3y
0.3 km are in how many miles?
Answer:
There are 0.186411 miles in 0.3 km.
The 2 Johnson children are playing a game. The
game has 10 cards that are passed out. Each child
gets the same number of cards. How many cards
does each child get?
Answer:
each child gets 5 cards
Step-by-step explanation:
just do 10/2 and you get 5
Answer:
5 cards
Step-by-step explanation:
10 divided by 2 is 5
John is trying to solve for y, but he made a mistake. Where did John mess up? What did he do wrong? Step 1: 2 - 3(y- 1) = 6 Step 2: -1(y- 1) = 6 Step 3: -y+1= 6 Step 4: -y = 5 Step 5: y = -5 Step 2; he combined the 2 and -3 before he distributed O Step 3; he did not distribute the -1 correctly Step 2; he did not combine the 2 & -3 correctly. Step 4; he should have added the 1 to 6, not subtracted it Step 3; he should have added 1 to both sides.
Answer:
Step 4!!!
Step-by-step explanation:
What is the slope of the line through (3, 2) and (-3, 4)?
3.4)
(32)
1
2
14
A. -3
O B.
O D. 3
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 3, 4)
m = [tex]\frac{4-2}{-3-3}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex] → C
The slope of the line is -1/3 through the points(3, 2) and (-3, 4) which is correct option (C).
What is slope of line?Slope of line is defined as the angle of line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
From the given graph we can pick the points which can tell us about the nature of the line that slope of line is negative.
Given,
Points of line is (3, 2) and (-3, 4)
Let
x₁ = 3, y₁ = 2
x₂ = -3, y₂ = 4
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in formula
m = (4 - 2)/(-3 - 3)
m = 2/(-6)
m = -1/3
Hence, the slope of the line is -1/3
Learn more about Slope of Line here :
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The Duquesne Incline, a cable car railway, rises 400 feet over a horizontal distance of 685 feet on its ascent to an overlook of Pittsburgh, Pennsylvania. What is the slope of the incline?
Answer: 400/685, which simplifies to 80/137. Decimal is about 0.58.
Step-by-step explanation: To calculate the slope of an incline, all you have to do is put the rise over run. In other words, y/x. In this case, The Duquesne incline rises 400 feet while moving horizontally 685, which gives you both the x and the y.
Write the equation of the parabola in vertex form.
vertex (4,2), point (3,- 1)
f(x) =
Write the equation of the parabola in vertex form.
vertex (4,4), point (2,- 8)
f(x) =
Answer:
Step-by-step explanation:
poin
can someone explain to me how to do this
Answer:
x=45
Step-by-step explanation:
We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102. [tex]6y=108[/tex], which means that y=18. [tex]2\cdot(18)+6=36+6=42[/tex]. Since one line is a straight angle, it is 180 degrees we can do [tex]3x=180-45=135[/tex], so x=45.
Answer:
y = 18
x = 46
measures of the angles:
8y - 102 = 42
2y + 6 = 42
3x = 138
Step-by-step explanation:
So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is, they will have the same measure.
Using this we know that opposite angles have to be congruent:
so
(2y + 6) = (8y -102)
now there is an algebra equation that can be solved by inverse operations and simplifying
2y + 6 = 8y - 102
+102 +102
2y + 108 = 8y
-2y -2y
108 = 6y
/6 /6
18 = y
Also, remember that two adjacent angles that form a line will add up to 180,
so
3x + (2y + 6) = 180
*note: I could have also used (8y - 102) but I choose to use (2y + 6)
so now substitute in the value of y that was found
y = 18
3x + (2 * 18 + 6) = 180
simplify
3x + ( 36 + 6) = 180
3x + 42 = 180
now use inverse operations
3x + 42 = 180
-42 -42
3x = 138
/3 /3
x = 46
PLEASE ANSWER!! Quadrilateral PQRS is shown on the coordinate plane.
Answer:
i have no idea
dont spam "please answer" its not cool
PHOTO ADDED
NEED URGENT HELP
Answer:
A
Step-by-step explanation:
The product of Greg's height and 5 is 90
Answer:
450
Step-by-step explanation:
is the answer
Graph the inequality:
y < − abs(x−3)−2
Answer:
suck dic
Step-by-step explanation:
Translate this into an equation.
The product of Greg's height and 5 is 90.
use g to represent Greg's height.
Answer:
g times 5 equals 90
Step-by-step explanation:
Answer:
g5 = 90
Step-by-step explanation:
if Greg's height is and 5 is the product of 90 that means you have to multiply g and 5 together to equal 90.
Translate the algebraic expression below into a written expression.
Answer:
b is the anwer of youre question
Answer:
B
Step-by-step explanation:
the plus sign means sum so that leaves you with the first two choices already
c has an exponent of two so that would be called squared, and that leaves you with the second one