Answer:
B. 10 ftStep-by-step explanation:
Let the width of the pool deck be x.
Dimensions of the pool are 12 + 2x and 24 + 2x.Total area is 1408 ft².We have equation:
(12 + 2x)(24 + 2x) = 140812*24 + 12*2x + 24*2x + (2x)² = 1408288 + 72x + 4x² = 14084x² + 72x + 288 - 1408 = 04x² + 72x - 1120 = 0x² + 18x - 280 = 0x² - 10x + 28x - 280 = 0x(x - 10) + 28(x - 10) = 0(x - 10)(x + 28) = 01)
x - 10 = 0x = 102)
x + 28 = 0x = - 28 (discarded as negative)Correct choice is B
The width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
Here, we have to find the width of the pool deck, we need to calculate the total area occupied by the pool and the deck and then find the value of x that makes the total area equal to 1,408 square feet.
First, let's calculate the area of the pool.
The pool is 12 feet by 24 feet:
Area of the pool = Length × Width
Area of the pool = 12 ft × 24 ft
Area of the pool = 288 ft²
Now, we want to add the deck around the pool.
The length and width of the entire area (pool + deck) will be (12 + 2x) feet and (24 + 2x) feet, respectively, because we add x feet to both sides of the pool.
Area of the entire area (pool + deck) = (12 + 2x) ft × (24 + 2x) ft
We want this area to equal 1,408 square feet:
(12 + 2x) ft × (24 + 2x) ft = 1,408 ft²
Now, we can solve for x:
(12 + 2x) × (24 + 2x) = 1,408
Expand the equation:
288 + 48x + 24x + 4x² = 1,408
Combine like terms:
4x² + 72x - 1,120 = 0
Now, let's solve this quadratic equation for x.
We can either factor it or use the quadratic formula:
Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
where a = 4, b = 72, and c = -1,120.
x = (-(72) ± √(72² - 4 * 4 * -1,120)) / 2 * 4
x = (-72 ± √(5,184 + 17,920)) / 8
x = (-72 ± √23,104) / 8
x = (-72 ± 152) / 8
Now, we have two possible solutions:
x = (-72 + 152) / 8
x = 80 / 8
x = 10
x = (-72 - 152) / 8
x = -224 / 8
x = -28
Since we are interested in a positive width for the deck, the width of the pool deck is 10 feet (x = 10).
So, the answer is option B: 10 ft.
To learn more on Area click:
brainly.com/question/20693059
#SPJ3
Mathe help #2 lots of points help please
Medians bisect eachother at centroid in ratio 2:1
ZS=XS=80SU is perpendicular bisector
UY=UZ
So
YZ=2(66)=132Apply Pythagorean theorem
[tex]\\ \tt\hookrightarrow VY^2=XS^2-VS^2=80^2-48^2=6400-2304=4096\implies VY=64[/tex]
Answer:
XS = 80
YZ= 132
VY = 64
Step-by-step explanation:
Firstly, SU is a perpendicular bisector
so, UV= UZ and YZ = 2(66) = 132
Each median bisect each other at centre with the ratio 2 : 1
therefore ZS = 80 = XS
now , by using P.G.T
VY² = XS²-VS²
=> 80²-48²
=> 6400-2304
=> 4096
=> √4096
=> 64
VY = 64
Help Me what is 2,267,742,732,288 in scientific notation for 20 pts
Answer:
2.267742732288 × 1012
Step-by-step explanation:
Can somebody explain how I do this?
Answer:
You carry the 1 bring the 2 then divide by 3 multiply by 4 times the 2nd power then gimme those points.
Step-by-step explanation:
i have no vlue
qiulian and tammy have 2400 cards. tammy has twice as many cards as qualian.how many cards must tammy gaive qiulian so that tey have a the same number of card?
Tammy must give Qiulian 800 cards, so that they have the same number of card.
Let Qiulian's card be Q.Let Tammy's card be T.Given the following data:
Total cards, T = 2400 cards.How to solve the word problem.Translating the word problem into an algebraic expression, we have;
Qiulian and Tammy have 2400 cards:
[tex]Q+T=2400[/tex] .....equation 1.
Tammy has twice as many cards as Qiulian:
[tex]T=2Q[/tex] .....equation 2.
To determine the amount of card that Tammy must give Qiulian so that they have the same number of card:
Substituting eqn. 2 into eqn. 1, we have:
[tex]Q+2Q=2400\\\\3Q=2400\\\\Q=\frac{2400}{3}[/tex]
Q = 800 cards.
For Tammy:
[tex]T =2Q\\\\T=2\times 800[/tex]
T = 1600 cards.
Therefore, Tammy must give Qiulian 800 cards, so that they have the same number of card.
Read more on word problems here: brainly.com/question/13170908
3 3/8 divided by 2 1/4 ILL GIVE BRAINLEIST
Answer:
I missed the part where that's my problem
Answer:
1 1/2
Step-by-step explanation:
Divide
3 and 3 over 83
3
8
÷ 2 and 1 over 42
1
4
= 108 over 72
108
72
One half of a number is subtracted from 25 the answer is 10. What is the number
Answer:
The answer is 30
Step-by-step explanation:
30÷2=15
25-15=10
Answer:
30
Step-by-step explanation:
25-30/2 = 25-15 = 10 Hope this helps!
75 POINTS
Provide the missing reasons for the proof.
Answer:
1. Given
2. definition of vertical angles
3. SAS triangle similarity theorem
Step-by-step explanation:
1. Given simply means the problem directly tells you it is true
2. Vertical angles are angles that share 2 lines and are congruent.
3. SAS triangle similarity theorem is the theorem that proves 2 triangles with a similar side, angle, and side (in that order) are similar.
Earning Commission
Sales Commision Rate Commission
$450
6%
?
The commission is ?
Answer:6%
Step-by-step explanation:
This is pretty much asking what the percentage is!
Remi plans on spending at most $75 at the mall. She wants to buy a $30 hoodie and some t-shirts that cost $9. Write and solve an inequality to find how many t-shirts Remi can purchase.
Please help! :(
Answer:
T-shirts= 5
Step-by-step explanation:
Remi plans on spending 75$ and she already bought a hoodie that cost $30.
x= how many hoodies you buy.
Inequality- $75= 30+75+x
Next- 75-30= $45
Finally- 45/9= 5 t-shirts that you can buy.
Hope that helped! :)
Ava cannot spend more than $100 on food for a party. The lemonade will cost $19 and she wants to spend the rest on pizza. Each pizza costs $7.
How many pizzas can she buy?
Enter your answer in the box.
___ pizzas
Answer and Step-by-step explanation:
So for this question, we need to create an equation. We will use one of the most common forms of equations of math, which would be the linear equation of y=mx+b. The only difference is, we need to change the = to a ≥ symbol, meaning greater than or equal to, because the 100 dollars needs to be more or equal to the amount spent. But we cannot solve this problem until we know where everything goes.
So, the 100 is all she can spend, so this is where the ≤ comes in handy. She can use less than or equal to the amount of 100 dollars for the food for this party. And because she started out with 19 dollars, that can be added into the problem. So far we have:
100 ≥ __x + 19.
Now we need to find what the missing part of the equation is. But first let's change the x to p in this equation so that it is easier to understand. The p stands for the amount of pizzas purchased. Each pizza costs 7 dollars, so the equation should look like this:
100 ≥ 7p + 19. Now we solve for p.
-19 - 19 Subtract 19 from both sides to cancel out the positive 19 (+ 19).
81 ≥ 7p Divide 7 into 81 to single out p.
7 7 So p = 81/7. But we can't have 81/7 of a pizza, so we convert this to a decimal then round. So: 11.57142857… is the decimal form.
Now we need to round, because that is way too big. So, we round to the nearest whole number. So we look at the placement behind it (The tenths placement in this situation). Because the placement behind it (5) is on the 5 - 9 scale, the placement before it gets rounded up.
So, Ava can buy 12 pizzas.
I hope that this helps.
Answer:
12
Step-by-step explanation:
I Took The Test
The solutions to a certain quadratic equation are x= -4 and X = 3. Write the equation in standard form below.
[blank] +x [blank] [blank] = 0
Answer:
x² + x - 12 = 0
Step-by-step explanation:
If x = -4 and x = 3 are solutions to a quadratic equation, then
(x + 4)(x - 3) = 0
Expand the brackets: x² - 3x + 4x - 12 = 0
Combine like terms: x² + x - 12 = 0
please help me ..............................................................................
Hiyaaa! I'm Nat and I'm gonna help you~♡
Thermo means heat! So. Thermosphere has to relate to hot and warm things.
Meso meaning middle,or intermediate.
,
Thermosphere = is very hot,satellites travel here,reached out into spaceMesosphere= Directly under the stratosphere,is very cold,acts has a barrierHope this helps!!
Brainliest?
-Nat
The table represents the number of medals won by each member of the Academic Bowl Team. What is the ratio of the number of medals won by Josephine to the total number of medals won by the team?
A) 1/13
B) 1/4
C) 1/3
D) 2/5
1. Ratio of medals won by Josephine to the total number won by the team: 1/13 (A)
2. Ratio of medals won by Jacob to medals won by Antonio: 2/1 (D)
What is Ratio?Ratio can be described as a quantitative relation that compares how many times a value is contained in another.
1. Ratio of medals won by Josephine to the total number won by the team:
Total won by the team = 26
Medals won by Josephine = 2
Ratio = 2:26 = 2/26
= 1/13 (A)
2. Ratio of medals won by Jacob to medals won by Antonio:
Jacob = 8
Antonio = 4
Ratio = 8:4 = 8/4
= 2/1 (D)
Learn more about ratios on:
https://brainly.com/question/13513438
8(2x – 10) = 28
What is the steps to complete?
Answer:
6.75
Step-by-step explanation:
first let's simplify whatever is inside the parantheses
8(2x-10)=28
8*2(x-5)=28
16(x-5)=28
now we divide both sides by 16 to get rid 16
x-5 = 28/16
now move -5 to the right side
x = 28/16 + 5
x = 28/16 + 80/16 = 108/16 = 6.75
Please help me simplify both of these.
Answer:
A is 3/y, B is 4y
Step-by-step explanation:
6h + 16 = 46
Evaluate the equation
Answer:
h=5
Step-by-step explanation:
Answer:
6h +16 =46
6h +16-16
6h =30 6h ÷6 =30÷6
h =5
bernice buys 5 VHS tapes. each VHS tape cost $9. if bernice receives a $2 discount on each vhs, what is the total amount of money she spends? write an expression that matches the words.
Answer: bernice buys 5 VHS tapes. each VHS tape cost $9. if bernice receives a $2 discount on each vhs, what is the total amount of money she spends? write an expression that matches the words.
the answer is $11
Step-by-step explanation: 9+2=11
Santino fires a paintball 3 meters from the ground such that the initial trajectory is perfectly horizontal. Assume the paintball does not hit anything in the ground is level. When will the paintball hit the ground?
A. About 3 seconds
B. About 0.78 seconds
C. About 0.52 seconds
D. About 1 second
Answer: B
How many solutions of linear equation of -x + y = -5
Answer:
infinite
Step-by-step explanation:
What visualization is most appropriate to see if there is an association between birth and death rates during a given time interval
Bar chart visualization should be used if there is an association between birth and death rates during a given time interval.
Bar chartA bar chart is a chart that is used to represent data using rectangular bars with heights proportional to the values that they represent. Bar charts can either be vertically or horizontally.
Bar graphs are usually used when comparing two or more different things as well as their respective changes over time.
Bar chart visualization should be used if there is an association between birth and death rates during a given time interval.
Find out more on Bar chart at: https://brainly.com/question/24741444
find the equation of the line tangent to the graph of f at (1,4), where f is given by f(x)=2x^3-3x^2+5
Answer:
[tex]y = 4[/tex]
Step-by-step explanation:
First, find the derivative of f:
[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ 2x^3 - 3x^2 + 5\right] \\ \\ & = 6x^2 - 6x \\ \\ & = 6x(x-1)\end{aligned}[/tex]
Find the instantaneous slope at x = 1:
[tex]\displaystyle \begin{aligned} f'(1) & = 6(1)((1)-1) \\ \\ &= 0 \end{aligned}[/tex]
From the point-slope form, find the equation of the line:
[tex]\displaystyle \begin{aligned}y - y_1 & = m(x-x_1) \\ \\ y - (4) & =(0)(x-(1)) \\ \\ y & = 4 \end{aligned}[/tex]
In conclusion, the equation of the tangent line is y = 4.
THIS IS DUE IN 5 MINUTES!!!!!!!!!!! I NEEED THIS ASAP! A 13 3/4 -inch candle burns down in 11 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
I HOPE THIS HELPSSSSSS
GOOD LUCKKKKKK :)
solve 2x +5y =-24 2x+ y =-8
Answer:
[tex]x=-2, y=-4[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}2 * \frac{-24 - 5y}{2}+ y= -8\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-24-4y=-8\end{array}\right][/tex]
[tex]x=\frac{-24-5(-4)}{2}[/tex]
[tex]x=-2, y=-4[/tex]
Answer:
[tex]{x,y} = {-2,-4}[/tex]
Step-by-step explanation:
[tex]2x + 5y = -24 \\ 2x + y = -8[/tex] <---------- Linear equations given
Graphic Representation of the Equations : PICTURE
[tex]5y + 2x = -24 \\ y + 2x = -8[/tex]
Solve by Substitution :
// Solve equation [2] for the variable y
[tex][2] y = -2x - 8[/tex]
// Plug this in for variable y in equation [1]
[tex][1] 2x + 5*(-2x-8) = -24\\ [1] -8x = 16[/tex]
/ Solve equation [1] for the variable x
[tex][1] 8x = - 16 [1] x = - 2[/tex]
// By now we know this much :
[tex]x = -2 \\ y = -2x-8[/tex]
// Use the x value to solve for y
[tex]y = -2(-2)-8 = -4[/tex]
Solution :
[tex]{x,y} = {-2,-4}[/tex]
In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of the L shaped figure is 258 ft²
Area
Area is the amount of space occupied by a two dimensional figure.
The area of a rectangle is given by:
Area = length * breadth
From the diagram, the area is:
Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²
The area of the L shaped figure is 258 ft²
Find out more on Area at: https://brainly.com/question/25292087
Total Area = Area 1 + Area 2
Total Area = (18ft*9ft) + (21ft*8ft)
Total Area = 330ft²
I hope this helps!
8x18divided by (16divide8x3)
Answer:
It might be 96. I don't know
Step-by-step explanation:
Answer number 1 please.
[tex] \sf {a}^{2} = {13}^{2} - {5}^{2} [/tex]
Formula :
Base²= Hypotenuse² - Perpendicular ²
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a}^{2} = {13}^{2} - {5}^{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a}^{2} =169 - 25[/tex]
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a}^{2} =144[/tex]
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a} = \sqrt{144} [/tex]
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a} = \sqrt{12 \times 12} [/tex]
[tex] \\ \\ [/tex]
[tex] \hookrightarrow\sf {a} = 12[/tex]
Remember the a² in formula has nothing to do with the a we have to find. :)
[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]
[tex]\bold{\underline{ Given :-}}[/tex]
We have a right angled triangle whose two sides that is perpendicular and hypotenuse are 5 units and 12 units[tex]\bold{\underline{ Let's\: Begin:-}}[/tex]
According to the Pythagoras theorem, Pythagoras theorem states that the sum of squares of two small sides that is perpendicular height and base are equal to the square of longest side that is hypotenuseThat is,
[tex]\sf{\red{ ( Base)² + ( Perpendicular )² = ( Hypotenuse)²}}[/tex]
[tex]\sf{ ( a )² + ( b )² = ( c )²}[/tex]
Subsitute the required values,
[tex]\sf{ ( a )² + ( 5 )² = ( 13)²}[/tex]
[tex]\sf{ a² + 25 = 169}[/tex]
[tex]\sf{ a² = 169 - 25 }[/tex]
[tex]\sf{ a² = 144}[/tex]
[tex]\sf{ a = √144}[/tex]
[tex]\sf{ a = 12}[/tex]
[tex]\sf{\blue{ Hence,\: Length \:of \:a\: is \:12 units }}[/tex]
Find the measure of angle
Answer:
It can be any measure
Step-by-step explanati
PLZ HELP ILL MARK AS BRAINLEIST
Answer:
c
Step-by-step explanation:
A=2πrh+2πr2=2·π·3·20+2·π·32≈433.53979
Four eighth graders solve the equation
x
3
−
150
=
66.
x3−150=66. The table shows the students’ answers.
Which statement is true?
Student
1
1 is correct because
72
3
−
150
=
66.
723−150=66.Student 1 is correct because 72 cubed minus 150 is equal to 66 point
Student
2
2 is correct because
6
3
−
150
=
66.
63−150=66.Student 2 is correct because 6 cubed minus 150 is equal to 66 point
Student
3
3 is correct because
18
3
−
150
=
66.
183−150=66.Student 3 is correct because 18 cubed minus 150 is equal to 66 point
Student
4
4 is correct because
7
3
−
150
=
66.
73−150=66.Student 4 is correct because 7 cubed minus 150 is equal to 66 point
Answer:
Student 2 is correct because 6 cubed minus 150 is equal to 66
Step-by-step explanation:
[tex]x^3-150=66[/tex]
[tex]\implies x^3=66+150=216[/tex]
[tex]\implies x=\sqrt[3]{216} =6[/tex]
(-3x+5)(2x+4) in standard form step by step
Answer:
[tex]- 6 {x}^{2} -2x + 20[/tex]
[tex]( - 3x + 5)(2x + 4) \\ \\ = - 3x(2x + 4) + 5(2x + 4) \\ \\ = - 3x(2x) - 3x(4) + 5(2x) + 5(4) \\ \\ = - 6 {x}^{2} - { 12x} + {10x} + 20 \\ \\ = - 6 {x}^{2}-2x + 20[/tex]
Solution:
To simplify this expression, multiply the terms together....
(-3x + 5)(2x + 4)=> (-3x × 2x) + (-3x × 4) + (2x × 5) + (5 × 4)=> -6x² - 12x + 10x + 20=> -6x² - 2x + 20Hence, the simplified expression is -6x² - 2x + 20.
Hoped this helped!