A recreational area is formed by a rectangular shaped pool and a cement patio surrounding the pool. the pool has a length of 3x-3 meters and a width of 2x+7 meters. The patio extends x meters around to pool, on all sides of the pool. Write a polynomial expression that gives the total area of the recreational area.
The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.
The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.
The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:
20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35
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What is the probability of picking a month at random that starts with the letter “J”
Answer:
A 1 in 4 chance or a probability of 0.25
Step-by-step explanation:
There is only 3 months that start with J and 12 months in a year so simplify 3/12 you get 1/4 or 0.25
2. Solve for x. Show your work.
45x 4 = 642x+12
The value of x for the equation 4(5x - 4) = 64( 2x + 12) is x = -7.25
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
4(5x - 4) = 64(2x + 12)
20x - 16 = 128x + 768
20x - 128x = 768 + 16
-108x = 784
x = -7.25
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( NO LINKS ) If x=7, is this equation true? 7 + 9x > 73 *
A. Yes
B. No
Answer:
[tex]\huge\mathfrak\red{Answer} \\ \\ 7 + 9x > 73 \\ \\ x = 7 \: \: \: \: \: \: given \\ \\ 7 + (9 \times 7) > 73 \\ \\ 7 + 63 > 73 \\ \\ 70 > 73 \\ \\ but \: 70 \: is \: not \: grater \: \: than73 \\ \\ so \: this \: equation \: is \: not \: true \\ \\ \huge\mathfrak\purple{Answer = no} \\ \\ \small\mathfrak\red{hope \: it \: helps...}[/tex]
There are 3 red chips and 5 white chips in a bag. If 2 chips are drawn, without replacement, what is the probability that both chips will be white?
Answer: 5/14
Step-by-step explanation:
5 white / 8 total
4 white / 7 total
5/8 * 4/7 = 20/56 = 5/14
how fast are you going if you run 12 kilometers in 2 hours
Answer:
3.73 miles per hour
Step-by-step explanation:
12 Kilometers is 7.46 miles.
7.46/2 = 3.73 Miles per hour
In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
not Maths. If 5 students did not like both, how many students liked both subjects?(WITH FULL PROCESS)
What is 90 divided by 1/3 as a fraction?
Answer:
270/1
Step-by-step explanation:
Here is 90 divided by 1/3 displayed mathematically in colors:
90 ÷ 1/3
The numbers in 90 divided by 1/3 are labeled below:
90 = whole number
1 = numerator
3 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
90x3/1 = 270/1
Answer: 270/1
Step-by-step explanation:
90/1*1/3 you have to do the reciprocal so it turns to 90/1*3/1= 270/1
PLEASE HELP ME WITH THESE!!!
9514 1404 393
Answer:
∠4 = 120°∠5 = 80°Step-by-step explanation:
Angle 5 is the third angle of the triangle whose other two angles are 45° and 55°. So, its measure is ...
∠5 = 180° -45° -55°
∠5 = 80°
__
This figure cannot be solved for angle 4 unless we assume the horizontal lines are parallel. Using the angle numbers as vertex designators, angle 245 and the one marked 45° are alternate interior angles, so are congruent. Angle 4 is vertical with the angle that is the sum of angle 245 and 75°, so we have ...
∠4 = 75° +45°
∠4 = 120°
An item costs $380 before tax and the sales tax is $15.20 find the sales tax rate write your answer as a percentage
please explain step by step in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answer:
x=120°
y=70°
Step-by-step explanation:
solution,
y=70°(alternate angles)
x=120°(corresponding angles)
Help me plz help me hep
Answer:
square root of 819 or 28.6
Step-by-step explanation:
I need help with this
Answer:
p = 0.11 (rounded to 2 DP)
p = 0.111 (rounded to 3DP)
Step-by-step explanation:
p = 0.48³
p = 0.110592
Rounded to 2 DP
p = 0.11
Rounded to 3DP
p = 0.111
1. What is the volume of this prism?
A.36
B.63
C.16
D.54
Answer:D
Step-by-step explanation:
simplify the radical of 200 squared
Answer:
The answer is 10√2.
Step-by-step explanation:
67. The line contains the point (4,0) and is parallel
to the line defined by 3x = 2y.
Answer:
[tex]y=\frac{3}{2} x-6[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form:[tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines will always have the same slope but different y-intercepts.1) Determine the slope of the parallel line
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.
[tex]3x = 2y[/tex]
Switch the sides
[tex]2y=3x[/tex]
Divide both sides by 2 to isolate y
[tex]\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x[/tex]
Now that this equation is in slope-intercept form, we can easily identify that [tex]\frac{3}{2}[/tex] is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope [tex]\frac{3}{2}[/tex] . Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{3}{2} x+b[/tex]
2) Determine the y-intercept
[tex]y=\frac{3}{2} x+b[/tex]
Plug in the given point, (4,0)
[tex]0=\frac{3}{2} (4)+b\\0=6+b[/tex]
Subtract both sides by 6
[tex]0-6=6+b-6\\-6=b[/tex]
Therefore, -6 is the y-intercept of the line. Plug this into [tex]y=\frac{3}{2} x+b[/tex] as b:
[tex]y=\frac{3}{2} x-6[/tex]
I hope this helps!
help pls the question is in the picture
Answer:
[tex]\neq \neq \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \geq x^{2} x^{2} \sqrt{x} \frac{x}{y} x_{123} x_{123}[/tex]
Step-by-step explanation:
yeah
Can y’all help me on question 18?!
Answer:
B
Step-by-step explanation:
16 - 7 = 9
Answer:
m=7
Step-by-step explanation:
Pls need help!!!! Giving brainliest to the person that gives me the right awnser
Answer:
you only have the answer choices not the question itself
could you please attach the question so i can help?
Michael bakes a soft pretzel and a loaf of bread. Use the system of equations to find c, the amount of flour, in cups, needed for the soft pretzel, and b, the amount of flour, in cups, needed for the loaf of bread. Show your work.
b = 24c
(1/4)b + 4c = 5/4
The amount of flour needed for soft pretzel is c = 1/8 and the amount of flour needed for the loaf of bread is b = 3.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given system of equations,
b = 24 c and
[tex]\frac{1}{4}[/tex] b + 4c = [tex]\frac{5}{4}[/tex]
Substitute b = 24 c in the second equation.
[tex]\frac{1}{4}[/tex] (24 c) + 4c = [tex]\frac{5}{4}[/tex]
6c + 4c = [tex]\frac{5}{4}[/tex]
10 c = [tex]\frac{5}{4}[/tex]
c = [tex]\frac{5}{4}[/tex] × [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{8}[/tex]
b = 24c = 24 / 8 = 3
Hence c = 1/8 and b = 3 in cups.
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what is the surface area of a cube with a side length of 3/4 inch? Use the expression 6s squared, where s is the side length of the cube.
Answer:
The volume of a cube is the side length cubed.
V = s x s x s where s is the length of the side = s x s^2 = 6s^2 so s must be 6.
The side length is 6 ,
Therefore the surface area is 6 times the area of each side = 6 x 6^2 = 6 x 36
= 108 square units
Pls help fractions pls and sm else
Answer:
Step-by-step explanation:
(49/72)-(13/14)
-125/504
Ashley and Saskia each think of a number.
1 less than Ashley's number is equal to 3 lots of Saskia's number.
4 lots of Ashley's number added to Saskia's number is 95.
Using the information above, write and solve two simultaneous equations to work out Ashley's and Saskia's numbers.
Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.
How to work out Ashley's and Saskia's numbers?In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent Ashley's number.Let the variable y represent Saskia's number.Translating the word problem into an algebraic equation, we have the following:
x - 1 = 3y .....equation 1.
4x + y = 95 .......equation 2.
Making x the subject of formula in equation 1, we have:
x = 3y + 1 .......equation 3.
Substituting equation 3 into equation 2, we have:
4(3y + 1) + y = 95
12y + 4 + y = 95
13y = 95 - 4
13y = 91
y = 91/13
y = 7.
For the value of x, we have:
x = 3y + 1
x = 3(7) + 1
x = 21 + 1
x =22.
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Determine which two numbers come next in the sequence 5,5,10,15,25, __, __
The two numbers that come next in the sequence 5,5,10,15,25, are 40 and 65.
How can the two numbers that come next in the sequence be calculated?To calculate this , You can figure it out by taking the first number, which is 5. However, since the previous number is 0, the sum is 5, and you proceed in the same manner.
5 + 5 = 10
(5 + 10) = 15
(10 + 15) = 25
(15 + 25) = 40
(25 + 40) = 65
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Theorem 6.1A states that if a quadrilateral is a Parallelogram, then it’s opposite sides are
Answer:
congruent
Step-by-step explanation:
The function h(t) = - 16t2 + 48t + 160 can be used to model the height, in feet, of an object t
seconds after it is launched from the top of a building that is 160 feet tall.
Two other forms of the function are:
h(t) = -16(t - 5)(t+2)
h(t) = -16(t-1.5)2 +196
Which value of the function represents the maximum height of the object?
A h(0)
B. h(1.5)
C. h(2)
D. h(5)
Answer:
answer is c because you have to put in the 2 and get -16
The axis of the sphere below is 12 units in length. What is the surface area of
the sphere?
A. 256 units2
B. 72 units
C. 144 units2
D. Cannot be determined
The surface area of the sphere is 144π square units.
What is a sphere?"A sphere is a three-dimensional figure (solid figure), which is made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere".
For the given situation,
The axis of the sphere = 12 units
The axis is the diameter of the sphere.
The radius of the sphere, r = d/2
⇒ [tex]r=\frac{12}{2}[/tex]
⇒ [tex]r=6 units[/tex]
The formula for the surface area of the sphere, A = [tex]4\pi r^{2}[/tex]
[tex]A = 4\pi( 6)^{2} \\[/tex]
⇒ [tex]A=144\pi[/tex]
Hence we can conclude that the surface area of the sphere is 144π square units.
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A sporting goods factory produced 13,234 tennis balls per month.How many tennis balls does it produce during 12 months?
Answer:
158,808 !
Step-by-step explanation:
13,234 × m (months)
13,234 × 12
= 158,808
Shana wants to buy a music player. She has $100 cash.
Can Shana afford an $89 unit plus HST? Yes or No?
Provide an estimate or a calculation to support your answer=
What is the original price of the most expensive item
Shana can buy for $100?
21. Find the volume of the water in the container in liters. (1 liter = 1000 cm3)
The volume of the water is
____ liters.
Answer:
volume of water in the container
30×10×8
2400cm³=2400ml=2.4liters
( since water is filled up to a height of 8 cm )
Solution :[tex] \large\boxed{ \mathrm{volume = l \times b \times h}} [/tex]
[tex]30 \times 10 \times 8[/tex][tex]\mathrm{2400 \: cm {}^{3} }[/tex]_____________________________
Since, 1000 cm³ = 1 litre
[tex]\mathrm{1 \: cm {}^{3} = \dfrac{1}{1000} }l[/tex][tex]\mathrm{2400 \: cm {}^{3} = \dfrac{1}{1000} \times 2400 } \: l[/tex][tex]\mathrm{2400 \: cm {}^{3} =2.4 \: \: litres} [/tex]_____________________________
[tex]\mathrm{ \#TeeNForeveR}[/tex]