The width of the pool is 10 feet.
What is area of rectangle?The area of rectangle is product of length and breadth.
Let the width be x.
length = 24 + 2x. and breadth = 12 + 2x
We know, area= 1408 ft².
(12 + 2x)(24 + 2x) = 1408
12*24 + 12*2x + 24*2x + (2x)² = 1408
288 + 72x + 4x² = 1408
4x² + 72x + 288 - 1408 = 0
4x² + 72x - 1120 = 0
x² + 18x - 280 = 0
x² - 10x + 28x - 280 = 0
x(x - 10) + 28(x - 10) = 0
(x - 10)(x + 28) = 0
So, x=10, -28.
Hence, the width be 10 feet.
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The inverse of the function f(x) =
f(x) = x + 10 is shown.
h(x) = 2x-0
What is the missing value?
0 1
05
O 10
O 20
Answer: 20
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]
Divide.round to the nearest tenth .16÷.03220
Answer:
5.0
Step-by-step explanation:
0.16÷0.03220=4.9689
=5.0
find y please help meeee :)
Answer:
the interior angle of a triangle = 180- 89 ( forming linear pair)
= 91°
y = 91 + 23
Y = 114° ( sum of interior angle of a triangle ls equal to its outer angle)
Answer:
114
Step-by-step explanation:
Angle A + 89 = 180 (Sum ofAngles in a straight line)
Angle A = 180 - 89 = 91
Angle B + Angle A + 23 = 180 (Sum of angles in a triangle)
Angle B + 91 + 23 = 180
Angle B = 180 - 114 = 66
Angle B + y = 180 (Sum of angles in a straight line)
66 + y = 180
y = 180 - 66 = 114
Refer to the attached picture.
Brad wants to buy flowers for his friend
with $33. The daisies are $1 each and
the roses are $2 each. He buys 3 more daisies than roses.
how much did the roses cost?
Answer:
20
Step-by-step explanation:
Answer:
20$ For the Roses
Step-by-step explanation:
Think about it like this. For each daisy (1$), the price is double for roses (2$).
Brad has a limit of 33$. And he bought 3 more daisies than roses.
If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.
(10 Daisies = 10$) + (10 Roses = 20$) = 30$
30$ + (3 Daisies = 3$) = 33$
PLEASE ITS DUE TODAY
Complete the table for the given rule
Rule: Y = 4x
X | Y
5
3
4
Answer:
Answers are 20, 12 and 16
Step-by-step explanation:
Y=4x
for x = 5
y=4(5)
y=20
for x = 3
y=4(3)
y=12
for x = 4
y=4(4)
y=16
Answer:
X I Y
5 20
3 12
4 16
Step-by-step explanation:
since y=4 multiplied by x
so, 5x4=20
3x4=12
4x4=16
226,710 - 724,435 =
How to work this out without calculator
Let E be the event where the sum of two rolled dice is greater than or equal to 7. List the outcomes in Ec.
Answer:
(1, 1) (1, 2) (1, 3) (1,4)
(1,5) (2,1) (2,2) (2,3)
(2,4) (3,1) (3,2) (3,3)
(4,1) (4,2) (5,1)
Step-by-step explanation:
An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.
What is an event?An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.
Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.
(1, 6)
(2, 6)
(3, 6)
(4, 6)
(5, 6)
(6, 6)
(2, 5)
(3, 5)
(4, 5)
(5, 5)
(6, 5)
(3, 4)
(4, 4)
(5, 4)
(6, 4)
(4, 3)
(5, 3)
(6, 3)
(5, 2)
(6, 2)
(6, 1)
Hence, the number of possible outcomes that Event E has is 21.
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Write an expression that contains atleast two terms and is in simplest form
Answer: x-1
Step-by-step explanation:
Given the graph of the pre-image and image, identify the correct
coordinate transformation.
The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]
help Which statement describes the pattern shown?
*
1 point
Captionless Image
A. Each figure has 3 fewer squares than the one before it.
B. Each figure has 6 fewer squares than the one before it.
C. Each figure has 3 more squares than the one before it.
D. Each figure has 6 more squares than the one before it.
A pattern is a recurring arrangement of numbers, forms, colours, and so on.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
As per the pattern, Each figure has 3 more squares than the one before it.
Hence, the correct option is C.
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Can anyone help me solve this? Please and thank you!
It's the sum of a geometric sequence.
Let's rewrite it a bit:
[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]
And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]
Now let's calculate the initial sum:
[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]
Lines l and m are parallel and intersect transversal p, as shown in the diagram below.
What is the value of n?
A 6
B 10
C 20
D 24
Cai drove 189 miles in 7 hours. If he continued at the same rate, how far would he
travel in 12 hours?
If 22% of high school students say they eat out 3 times a week, how many students of the 2346 students who attend WHS would you expect eat out 3 times a week?
Answer:
516 students eat out 3 times a week
Step-by-step explanation:
22% of 2346 is 516.12 and a person can't be a decimal so it's 516
22 x 2346 = 51612
and 51612÷100 = 516.12
We would expect about 516 WHS students to eat out 3 time
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that 22% of high school students say they eat out 3 times a week
We need to find the number of students of the 2346 students who attend WHS would you expect eat out 3 times a week
We can start by using the proportion:
(22/100) = (x/2346)
where x is the number of students we would expect to eat out 3 times a week.
To solve for x, we can cross-multiply:
100x = 22 × 2346
100x = 51612
Divide both sides by 100
x = 516.12
Hence, we would expect about 516 WHS students to eat out 3 time
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Plato trigonometry is crazy
Answer:
The answer is A. 21
i hope this can help you! :)
Answer:
a)21
-step explanation:
determine weather y varies directly with x. if so, find the constant variation and write the equation
Answer:
Yes, k = 1/3 and y = 1/3x
Step-by-step explanation:
[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]
[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]
[tex]\text{This implies that,}[/tex]
[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]
The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]
The price of a cup of coffee was 2.40 yesterday. Today, the price rose to
2.75. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
≈ 14.6%
Step-by-step explanation:
percentage increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
increase = 2.75 - 2.40 = 0.35 , then
percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )
Question 6b
6b of 6
The width of a rectangle is 15 centimeters less than its length. If the area of the
rectangle is 100 square centimeters, find the length and the width using the formula
A = lw.
O Length = 25 centimeters and Width = 10 centimeters
○ Length = 20 centimeters and Width = 5 centimeters
O Length = 115 centimeters and Width = 100 centimeters
○ Length = 5 centimeters and Width = 20 centimeters
Answer:
○ Length = 20 centimeters and Width = 5 centimeters
Step-by-step explanation:
Let the length = L
Then the width is L - 15
A = lw
100 = L(L - 15)
L² - 15L - 100 = 0
(L - 20)(L + 5) = 0
L - 20 = 0 or L + 5 = 0
L = 20 or L = -5
Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.
L = 20
width = L - 15 = 20 - 15 = 5
Answer: ○ Length = 20 centimeters and Width = 5 centimeters
hi i really need help with this it is due tonight
Answer:
[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]
What error did Lucia make?
Answer:
See below
Step-by-step explanation:
She combined 3x and - 9x incorrectly
she should have gotten - 6 x not - 12 x
what is the volume of this complex figure
The volume of the given figure is 210 cubic in..
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in., breadth=4 in. and height=12 in.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another
cuboid=4×4×12=192 cubic in.
The volume of the given figure=18+192=210 cubic in.
Therefore, the volume of the given figure is 210 cubic in.
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if angle X is an acute angle with tan X = 8/7, what is the value of sec X?
Answer: [tex]\frac{\sqrt{113}}{7}[/tex]
Step-by-step explanation:
As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.
Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],
[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]
What is the equation of a circle with center (8, 6) and radius 5?
The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].
f(x)=x2 what is g(x)
Answer:
-x^2-2
Step-by-step explanation:
So by looking at the two curves it appears that g(x) is simply a reflection of f(x) over the x-axis and then shifted 2 units down. So to reflect the parabola you simply make the x^2 negative to get -x^2 and then to go 2 units down you subtract 2 from the -x^2. This gives you the equation
[tex]g(x)=-x^2-2[/tex]
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second. The height h of the object after t seconds is given by the quadratic equation h= -16t^2 + 128t + 144. After how many seconds will the ball pass the top of the building
The time for the ball to pass the top of the building is determined as 4 s.
Time of motion of the ballThe time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.
h = -16t² + 128t + 144
v = dh/dt
v = -32t + 128
at maximum height, v = 0
0 = -32t + 128
32t = 128
t = 128/32
t = 4 s
Thus, the time for the ball to pass the top of the building is determined as 4 s.
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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
An object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
When the ball pass the top of the building, h = 144 foot
Plug h = 144 foot in h= -16t² + 128t + 144
144 = -16t² + 128t + 144
[tex]\rm -16t^2+128t=0[/tex]
t = 0 or t = 8 seconds
At t = 0, initially, the ball was thrown upward.
At t = 8 seconds, the ball passes the top of the building
Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144-foot building with an initial velocity of 128 feet per second.
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I don’t get this question
Simplify 4.5:9.9:8.1
Please help
Answer:
5:11:9
Step-by-step explanation:
Change the decimal to fractions
45/10:99/10:81/10
Multiply through by the Lowest Common Factor 10
10×45/10:10×99/10:10×81/10
Which makes it
45:99:81
They have a common factor which is 9, so divide through by 9
45/9:99/9:81/9
Your answer is
5:11:9
Hope it helps
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 3 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 63 ?
Answer:
43
Step-by-step explanation:
63-3/3=20 63-20
Answer:
mark has 18
don has 45
Step-by-step explanation:
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, -1][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
What is the value of y?
Answer:
Step-by-step explanation:
I can give you the meaning of Y
Y is the vertical value in a pair of coordinates. In other words how far up or down the point is. The Y coordinate is always written second in an ordered pair of coordinates (x,y) when used. A example from the internet is:
Which expression is equivalent to (15²)(15^-7)?
A 15^-21
B -15^4
C 1/15^4
D 1/15^-4
Answer:
there is no answer
Step-by-step explanation:
If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.
but there is no answer equal to this.
The equivalent expression will be;
⇒ 15⁻⁵
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (15²) × (15⁻⁷)
Now,
Since, The expression is,
⇒ (15²) × (15⁻⁷)
Hence, We solve as;
⇒ (15²) × (15⁻⁷)
⇒ 15²⁻⁷
⇒ 15⁻⁵
⇒ 1 / 15⁵
Thus, The equivalent expression is,
⇒ 15⁻⁵
⇒ 1 / 15⁵
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