Answer:
4x2+216x-684x
Step-by-step explanation:
solnA) The dimensions of the table are in inches
Let
x=the thickness of the border
we know that the table and the border must have an area of 3,276 square feet
convert the dimensions of the table to feet
remember that; 1ft =12in
36in=3ft
72in=6ft
i.e; 3,276 = (6+12x)*(3+2x)
solve for x
3276=6×3+ 6×2x +2x×3+ 4x²
3276=18+12x+6x+4x²
4x²+18x+18-3276=0
4x²+18x-3258
solnB) The dimensions of the table are in feet
Let
x=the thickness of the border
we know that the table and the border must have an area of 3,276 square feet
i.e 3,276 = ()×()
solve for x
3,276 = 72×36 + 72×2x + 2x×36 + 4x²
3,276 = 2,592 + 144x + 72x + 4x²
4x² + 216x + 2,592 + 3276 = 0
4x²+216× - 684= 0
therefore; the quadratic equation can be used to determine the thickness of the border =
4x² + 216x - 684 = 0
Need help with question 2 ASAP PLS anything is appreciated:)
Answer:
D
Step-by-step explanation:
It is D because the coordinate (1,1) isn't equals to (2,4); (3,27); or (4,24). It is not constant and you cannot make a linear function/equation out of it.
A compressed air tank carried by scuba divers has a volume of 8.00 L and a pressure of 141 atm at 22.0°C. What is the volume (in liters) of air in the tank at STP?
A) 993 L
B) 1,044 L
C) 1,224 L
D) 1,280 L
Answer:
Volume of air in the tank =1,044 Liter
Step-by-step explanation:
Given:
Tank volume = 8 Liter
Pressure = 141 atm
Temperature = 22°C = 273° + 20° = 295° K
Find:
Volume of air in the tank = ?
Computation:
[tex]\frac{Pressure\times Tank\ volume}{Tempreture} =\frac{Pressure\times Air\ volume}{Tempreture}\\\\\frac{141\times 8}{295} =\frac{1\times Air\ volume}{273.15}\\\\\frac{1,128}{295} =\frac{Air\ volume}{273.15}\\\\Air\ volume=1,044.45[/tex]
Volume of air in the tank =1,044 Liter
Answer:
1,044 Liter
Step-by-step explanation:
the perimeter of an equilateral triangle is 150cm. If the length of the altitude of the triangle is x√3cm, what is the value of x?
Answer:
X = 25
Step-by-step explanation:
To solve this question, we'll first of all find determine the side length of the triangle from the perimeter.
Perimeter of an equilaterial triangle = 3 * s
S = side length
Perimeter = 150cm
150 = 3s
S = 150 / 3
S = 50cm
The side lengths are 50cm each since they are all equal.
To find x,
We have to divide the triangle equally into two different part.
Check the first attachment for better illustration on how the equilaterial triangle is.
Check the second attachment for better illustration on the triangle when its divided into a right angle triangle.
From the right angle triangle, we can use pythagorean theorem to solve for x
a² = b² + c²
a = 50cm
b = 25cm
c = x√(3)
50² = [x√(3)]² + 25²
2500 = x² * 3 + 625
2500 - 625 = 3x²
1875 = 3x²
X² = 1875 / 3
X² = 625
X = √(625)
X = 25
f(x)=x^2. What is g(x)
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Having the line moving to the right we know that it has to be in parentheses. And
Determine the equation for the line of best fit to represent the data.
scatter plot with points going up from about zero comma negative 3 to the right to about 7 comma zero
y equals three sevenths times x minus 3
y equals negative three sevenths times x minus 3
y equals seven thirds times x minus 3
y equals three sevenths times x plus 3
Answer:
A) y equals three sevenths times x minus 3
God has a plan for everyone!!
Suppose that the amount of algae in a pond doubles every 3 hours. If the pond initially contains 50 pounds of algae, how much algae will be in the pond after 8 hours.In this exponential situation, what would the y-intercept be? CHOICES:
(0,3)
(0,2)
(0,50)
(0,8)
Answer:
After 8 hour there will be 317.64 pounds of algae.
y-intercept: (0, 50)
Step-by-step explanation:
At time = 0 hours, there are 50 pounds of algae, after 3 hour there will be 100 pounds of algae, after 6 hour there will be 200 pounds of algae, and so on.
Exponential growth is modeled by the following equation:
y = x0*(1 + r)^t
where x0 is the amount of algae at the beginning, r is the rate of change, and y is the amount of algae after t hours. Replacing with data:
100 = 50*(1 + r)^3
2 = (1 + r)^3
ln(2) = 3*ln(1 + r)
r = exp(ln(2)/3) - 1
r = 0.26
This result can be checked as follows
y = 50*(1 + 0.26)^6 = 200
After 8 hours:
y = 50*(1 + 0.26)^8 = 317.64
The y-intercept corresponds to t = 0
y = 50*(1 + 0.26)^0 = 50
I need some help with this answer please :)
Answer:
1/9 is my guess
Step-by-step explanation:
Bob Jones bought a new log cabin for $63,000 at 10% interest for 30 years. Prepare an amortization schedule for the first three periods.
What is the "unknown" in this problem that we need to find?
Answer:sorry i cant help but i dont see an unknown in this question please edit your answer so we can see something.Thank you.
Step-by-step explanation:
5)What will be the new position of the given point (7,4) after translation of
2 units left and 4 units up?
a) (5,8) b) (9,-8) c) (5,-8) d) (9,8)
Answer:
The correct answer is (5,8)
Step-by-step explanation:
HELP ME please :) Please
Answer:
If the question was to the first one I'm pretty sure the answer is a lot fewer people got sick I'm not sure but the second question but from what I could see of the bottom question burning fossil fuels driving cars and deforestation I know are may cause global warming I can't see the rest of it though and I'm not sure about ice cores
Step-by-step explanation:
The sum of the first 333 terms of a geometric series is 171171171 and the common ratio is \dfrac23
3
2
start fraction, 2, divided by, 3, end fraction.
What is the first term of the series?
Answer:
The first term of the series is 81
Step-by-step explanation:
The sum of the nth term of a geometric sequence is expressed as shown;
Sn = a(1-rⁿ)/1-r for r<1
a is the first term
r is the common ratio
n is the number of terms
Given Sn = 171
r = 2/3
n = 3
a =?
Substituting the values in the equation
171 = a(1-(2/3)³)/1-2/3
171 = a(1-8/27)/(1/3)
171 = a(19/27)/(1/3)
171 = a × 19/27 × 3/1
171 = a × 19/9
Cross multiplying
171×9 = 19a
1539 = 19a
a = 1539/19
a = 81
The first term is 81
Answer:
81
Step-by-step explanation:
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The triangles have the same shape, but not the same size.
B. The corresponding angles of the triangles are congruent.
C. The triangles have the same shape and size.
D. The corresponding sides of the triangles are congruent.
SUBM
Answer:
C. The triangles have the same shape and size.
B with C together also is accepted.
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Step-by-step explanation:
All the rest are wrong.
Assuming that the Earth is a sphere of radius 4000 miles, find the distance between the
following two cities whose latitudes are given. You may assume that these cities are on
the same basic longitude.
Cincinnati, Ohio (39° 8' 46" N) and Huntsville, Alabama (34° 43'41" N)
Answer:
308.44 miles
Step-by-step explanation:
Cincinnati, Ohio (39° 8' 46" N); and Huntsville, Alabama (34° 43'41" N)If the two locations are on the same basic longitude, then they are both on a great circle.
Distance along great circle [tex]=\dfrac{\theta}{360^\circ}X2\pi R[/tex]
Where:
[tex]\theta=$Angular difference\\R=Radius of the earth[/tex]
Since they are on the same polar axis (North), we subtract.
Angular Difference =39° 8' 46"-34° 43'41"=4°25'5"
Therefore:
[tex]Distance =\dfrac{4\°25'5''}{360^\circ}X2*4000*\pi \\=308.44 \:miles[/tex]
What is the length of line segment CD with endpoints (Negative 3 2) and (2, 2) as shown on the coordinate plane? On a coordinate plane, line C D goes from (negative 3, 2) to (2, 2). 2 units 3 units 4 units 5 units
Answer:
5 units
Step-by-step explanation:
im taking the test rn
NEED HELP ASAP
the angle of elevation from the far side of the pool to the top of the waterfall is 54 degrees and the distance is 230 ft. Find x
Answer:
(Use right triangle)
1) find the height of the waterfall (opposite side) to the nearest foot.
draw the triangle. distance from far side of the pool to the top of the waterfall is the hypotenuse given to be 230.
sinx = opp/hyp
sin54 = opp/230
opp = 230sin54
opp = approx 186 ft
2) find the width across the pool (adjacent side) to the nearest foot.
cosx = adj/hyp
cos54 = adj/230
adj = 230cos54
adj = approx 135 ft
Answer: 135 ft
The value of x is 135.2 feet.
To understand more, check below explanation.
Angle of elevation:From given figure,
It is observed taht, a right angle triangle is formed in the given figure.
Angle of elevation = 54 degree
Hypotenuse = 230 feet
We have to find base i.e x
Apply cosine of angle,
[tex]cos (54)=\frac{x}{230}\\ \\x=230*cos(54)\\\\x=230*0.587\\\\x=135.2ft[/tex]
Hence, the value of x is 135.2 feet.
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An amusement park's cost for cotton candy is $1.50. The markup rate for cotton candy is
300%. What is the price of cotton candy at the park?
Answer:
The answer is $6
Hope this helps!
The price of cotton candy at the park is $6.00.
The markup rate of 300% means the price is increased by three times the cost. So, $1.50 * 3 = $4.50 is the markup cost. Adding the original cost to the markup cost gives $1.50 + $4.50 = $6.00.
Mandy paints four square walls that are ten feet on each side. Which expression represents the total square footage that Mandy painted?
4 × 10 squared
4 squared × 10
4 × 10 × 2
10 squared + 4
Answer:
i think its c
Step-by-step explanation:
Final answer:
The correct expression for the total square footage that Mandy painted is 4 × 10 squared, which totals 400 square feet when calculated.
Explanation:
The expression that represents the total square footage that Mandy painted when she paints four square walls that are ten feet on each side is 4 × 10 squared. To understand why, let us analyze a related problem where Marta has one square with a side length of 4 inches and another larger square with dimensions that are twice the first square, which means the side length of the larger square is 8 inches (4 inches × 2).
The area of a square is calculated by squaring its side length, so the smaller square has an area of 16 square inches (4 inches squared), and the larger square will have an area of 64 square inches (8 inches squared). This demonstrates that the area of the larger square is four times larger than the area of the smaller square, as the scale factor of the side lengths is squared to obtain the ratio of the areas.
Similarly, for Mandy's wall painting, each wall is 10 feet by 10 feet, so the area of one wall is 10 feet squared, which equals 100 square feet. Since there are four walls, the total area is 4 × 100 square feet, or 400 square feet in total. The correct expression for the total square footage Mandy painted is 4 × 10 squared.
Convert each measurement into another measurement unit. How many inches are in 5 ft?
Answer:
60 inches
Step-by-step explanation:
Multiply the length value by 12
Using the greatest common factor for the terms, how can you write 56 + 32 as a product?
A) 4(14 + 8)
B) 7(4 + 8)
C) 8(7 + 4)
D) 14(4 + 2)
PLZ HELP
Answer:
8(7+4) (C.)
Step-by-step explanation:
First find the biggest number thta can go into 56 and 32:
8!
Since C. is the only one that has an 8 out in the front, let's try that one:
[tex]8*7=56[/tex]
[tex]8*4=32[/tex]
So C. Is correct!
Study the following diagram, where points C and D lie on circle A.
Point B lies in the exterior of circle A.
Angle ACB and angle ADB are right angles.
The diagram as described in the problem, where segment B C equals negative 2 x plus 85 and segment B D equals 5 x minus 48.
What is the length of BC¯¯¯¯¯¯¯¯?
Enter the correct value.
Answer:
Triangle ACB = Triangle ADB
=> BC = BD
=> -2x+85 = 5x - 48
=> x = 133/7 = 19
=> BC = -2 x 19 + 85 = 47
If we are provided with the value of AC or CD, we can calculate the length of BC is 47
Let's first determine the lengths of segment BC and BD in terms of x using the given expressions:
BC (B C¯¯¯¯¯¯¯¯) = -2x + 85
BD (B D¯¯¯¯¯¯¯¯) = 5x - 48
Now, as ACB and ADB are right angles, we can utilize the property of perpendicular chords intersecting a circle to find the value of x. When two chords intersect inside a circle, the product of their segments is equal. Therefore, we can set up the following equation:
BC * BD = (AC * CD) [Property of perpendicular chords intersecting]
Substitute the values:
=> BC = BD
When we simplify this one, then we get,
-2x+85 = 5x - 48
Then the value of x is calculated as,
x = 133/7 = 19
BC = -2 (19) + 85 = 47
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On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = –4. The domain is all real numbers. The function is increasing over (–∞, –4). The function is negative over (–6, –2).
Answer:The axis of symmetry is x=-4
The domain is all real numbers
The function is negative over (-6,-2)
Step-by-step explanation:
Its right
The statement that described the graph should be
The axis of symmetry is x=-4
The domain is all real numbers
The function is negative over (-6,-2)
What is a parabola in the graph?A parabola refers to the U-shaped curve that should be drawn for a quadratic function. The graph of the parabola should be considered downward at the time when the value of a should be less than 0, a < 0.
So based on this, we can conlcude that the above 3 statements should be considered and the other statements should be incorrect.
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True or false: the Pythagorean theorem can be applied to every triangle
The Pythagorean theorem can only be applied to right triangles.
Explanation:The Pythagorean theorem can be applied to right triangles only.
It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, while the Pythagorean theorem cannot be applied to every triangle, it can be used to find the length of one side of a right triangle given the lengths of the other two sides.
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Howard wants to use multiplication to solve w=5 divided by 1/5 Which multiplication equation can Howard use?
A:5*1/5=w
B:1/5*5=w
C:5=1/5*w
Answer:
C.5=1/5*w
Step-by-step explanation:
W=5÷1/5
Multiply both sides by 1/5
(1/5)w=5÷1/5(1/5)
(1/5)w=5×5/1(1/5)
1/5*w=25/1 * 1/5
1/5*w=25/5
1/5*w=5
It can also be written as
5=1/5*w
Answer:
5 1/5 * w
Step-by-step explanation:
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On which of the following lines does the point (–3, –1) lie? y = −4x − 6 y = 3x + 9 y = −3x − 10 y = 5x − 1
Answer: [tex]y = -3x - 10[/tex]
Step-by-step explanation:
You can substitute the value "-3" for x and "-1" for y in each of the equations given. Whichever equation is correct when simplified is the line that the point (-3, -1) lies on:
[tex]-1 = -4(-3)-6\\\\-1=3(-3)+9\\\\-1=-3(-3)-10\\\\-1=5(-3)-1[/tex]
Simplifying the right side of each equation:
First equation: -1 = 6
Second equation: -1 = 0
Third equation: -1 = -1
Fourth equation: -1 = -16
The correct answer is "[tex]y = -3x - 10[/tex]".
solve for c 3c − 10 = 2c
Answer:
10 is your answer for c.
Step-by-step explanation:
Isolate the variable c. Note the equal sign, what you do to one side, you do to the other.
Subtract 3c from both sides:
3c (-3c) - 10 = 2c (-3c)
-10 = 2c - 3c
-10 = -c
Isolate the variable, c. Divide -1 from both sides:
(-c)/-1 = (-10)/-1
c = -10/-1
c = 10
c = 10 is your answer.
~
25% of what number is 30?
to find the 25% of 30
first 25/100=0.25
then we write 0.25 x 30=7.5
so the answer is 7.5 or 120
Answer:
The answer is 120
Can someone please find C for me
kenneth drove 177.55 miles in 3 7/20 hours. what was his average speed
Kenneth's average speed, we divide the total distance by the total time traveled. In this case, Keneth's average speed was approximately 52.91 miles per hour.
Kenneth's average speed, you can use the formula:
Average Speed = Total Distance/Total Time.
In this case, Kenneth drove 177.55 miles in 3 7/20 hours.
First, convert the mixed number time to an improper fraction:
3 7/20 = 67/20.
Now, substitute the values into the formula:
Average Speed = 177.55 / (67/20).
To divide by a fraction, multiply by its reciprocal:
Average Speed = 177.55 * (20/67).
Average Speed ≈ 52.91 miles per hour.
Therefore, Keneth's average speed was approximately 52.91 miles per hour.
Paul rolled a number cube. What is the probability he will roll a 5 or 6
Answer:
2/6, 33.33, or 33.33%
Step-by-step explanation:
6 total possible outcomes, and 2 in this scenario.
That's 2 over 6.
Hope this helps!
Answer:
2 chances divide by 6 sides = 0.333333 or 1/3 or 33% like the other person said.
Step-by-step explanation: