Answer:
50.91
Step-by-step explanation:
Write a proportion:
1 kg / 2.2 lb = x kg / 112 lb
Cross multiply:
2.2 x = 112
Divide:
x = 50.91
50.91 kg equals 112 pounds.
What is the slope of the line passing through (1, 2) and (3, 8)?
slope = 1/17
slope = 1/3
slope = 3
slope = 7
Answer:
Option C is correct.
Step-by-step explanation:
Points given are
(1,2) and (3,8)
The formula used for slope is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
x₁ = 1, x₂=3, y₁=2 and y₂=8
[tex]m=\frac{8-2}{3-1}\\m=\frac{6}{2}\\m=3[/tex]
So, slope =3
Option C is correct.
Answer:
The slope of the line passing through (1,2) and (3,8) is 3.
Step-by-step explanation:
Slope formula is y2-y1/x2-x1
y2=8
y1=2
x2=3
x1=1
8-2/3-1
8-2=6
3-1=2
6/2=3
Jagdish is 3 years younger than Resham and Rajesh is 5 years older than Jagdish. If the product of present age of Resham and Rajesh is 960.How old is Jagdish?
Answer:
Jagdish is 27 years old
Step-by-step explanation:
Jagdish=x
Resham=x+3
Rajesh=x+5
(x+3)(x+5) = 960
x²+8x+15=960
x²+8x=945
x²+8x-945=0
now factor this to solve
(x-27)=0 (x+35)=0
which means
x=27 and x=-35
obviously, we cannot have negative ages so we use x=27
so, Jagdish=27
Resham=30
Rajesh=32
and we can check this by doing 30x32 which does equal 960 so it is correct
The age of Jagdish for the condition is 27 years.
What are quadratic equations?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
Given Jagdish is 3 years younger than Resham
and Rajesh is 5 years older than Jagdish
let age of Jagdish be x
Resham = x + 3
Rajesh = x + 5
according to conditions,
(x + 3)(x + 5) = 960
x² + 8x + 15 = 960
x² + 8x = 945
x² + 8x- 945=0
now factor this to solve
(x - 27)(x + 35) = 0
(x - 27) = 0, (x + 35) = 0
which means
x=27 and x=-35
obviously, we cannot have negative ages so we use x = 27
Therefore, the age of Jagdish is 27 years.
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which inequality represents all values of x for which the quotient below is defined?√8x^2 divided by √2x
Answer:
The function is defined when x > 0
Step-by-step explanation:
Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.
We know the function is undefined when the denominator is equal to zero. [tex]\sqrt{2x}[/tex] is equal to zero when x=0.
We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary. . [tex]8x^{2}[/tex] will always be positive, but [tex]2x[/tex] is negative when x < 0.
So the function is undefined when x = 0, and when x < 0.
Therefore it is defined when x > 0
Does the equation represent a direct variation? If so, find the constant variation. 3y=5x+4
Answer:
No.
Step-by-step explanation:
Direction variation is of the form y = kx.
This is not direct variation.
The equation 3y = 5x + 4 does not represent a direct variation because it includes a constant term '+4'. A direct variation would only have the form y = kx without any added or subtracted constants.
The equation 3y=5x+4 represents a direct variation, and if so, to find the constant of variation. A direct variation is when one variable is a constant multiple of another, expressed in the form y = kx, where k is the constant of variation. In this case, the equation 3y = 5x + 4 is not a direct variation because of the additional constant term '+4'. For it to be a direct variation, y must be alone on one side of the equation, and there should be no constant term added or subtracted with the term that is a multiple of x.
To be a direct variation, the equation needs to have the form y = kx. In the practice equation y + 7 = 3x, if we solve for y, we get y = 3x - 7 which still would not be a direct variation because of the -7. The other example equation 4y = 8 is not in the form of direct variation either since it has no variable x in it; it represents a horizontal line where y is a constant.
What is the solution of (4x-16)1/2=36^
Answer:
Answer is x=328 .
Step-by-step explanation:
solution= (4x-16)^1/2=36
squaring both sides we get
4x-16=129
4x=1296+16
x=(1296+16)/4
x=328 .
Answer:
x = 328
Step-by-step explanation:
The given equation is
[tex](4x-16)^{\frac{1}{2}}=36[/tex]
We need to find the solution of the given equation.
Taking square on both sides.
[tex]((4x-16)^{\frac{1}{2}})^2=(36)^2[/tex]
[tex](4x-16)^{\frac{2}{2}}=1296[/tex]
[tex]4x-16=1296[/tex]
Add 16 on both sides.
[tex]4x-16+16=1296+16[/tex]
[tex]4x=1312[/tex]
Divide both sides by 4.
[tex]x=\dfrac{1312}{4}[/tex]
[tex]x=328[/tex]
Therefore, the value of x is 328.
Which of the following equations is equivalent to 1/4x - 1/2y = 8?
(A) 2x - 4y = 8
(B) 2x - 4y = 64
(C) 4x - 2y = 64
Answer:C
Step-by-step explanation:4x _2y =64 because 8×8= 64
For this case we must find an equation equivalent to:
[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]
We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:
[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]
We multiply by 4 on both sides of the equation:
[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]
Multiplying by 2 on both sides of the equation:
[tex]2x = 64 + 4y\\2x-4y = 64[/tex]
Answer:
Option B
19.) Here's the data (sorted) of the ages of 91 women who won the Oscar for Best Actress in a Leading Role:
21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81
Give the five number summary.
Final answer:
The five number summary for the ages of best actress Oscar winners is composed of the minimum (21), first quartile (Q1 - 30), median (Q2 - 33), third quartile (Q3 - 41), and maximum (81) values.
Explanation:
The first step to finding the five number summary is to identify the minimum, first quartile (Q1), median (second quartile Q2), third quartile (Q3), and the maximum from the sorted dataset of best actress Oscar winners.
Minimum: The smallest number in the dataset is 21.
Q1: The first quartile is the median of the first half of the data. Since we have an odd number of data points (91), we split the data into two parts of 45 values each. The first quartile is the median of the first 45 ages, which is the 23rd data point in the sorted list when counting from the smallest age. In our case, Q1 is 30.
Median (Q2): The median is the middle value, which is the 46th data point for our 91 data points. The median is also the age of 33.
Q3: The third quartile is the median of the second half of the data. The third quartile is the 68th data point, which is the age of 41.
Maximum: The largest age in the dataset is 81.
Therefore, the five number summary of the ages of best actress Oscar winners is 21, 30, 33, 41, and 81.
Select the correct answer.
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
OA. Q(1, 11)
OB. R(2, 4)
OC. S(4, -4)
OD. T(9, -2)
Answer:
b
Step-by-step explanation:
any set times the radius will give you the answer
Determine if the relation represented in table form represents y as a function of x.
Answer:
Yes, it is a function.
Step-by-step explanation:
Since each x-value is used only once, the relation is a function.
Yes, The relation represented in table is a function.
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The table is,
x | 5 10 15
y | 3 8 8
Now,
Clearly, Each inputs having one output in the table as;
⇒ f (5) = 3
⇒ f (10) = 8
⇒ f (15) = 8
So, The table represent the function.
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Two similar triangles are shown.
Triangle MNO was dilated, then _______ to create Triangle YHO.
rotated
reflected
translated
dilated
Answer:
rotated
Step-by-step explanation:
The triangle MNO has already been dilated and therefore, the answers were left to 3: rotated, reflected and translated. Triangle YHQ is not an image of triangle MNO. Thus, leaving only 2 choices: rotated and translated. If triangle MNO was translated, triangle YHQ was supposed to be in the same position as triangle MNO is and leaving only 1 option which is rotated.
Answer:
rotated
Step-by-step explanation:
the correct answer is rotated
when triangle Δ M N O was dilated to create Triangle Δ Y H Q
we can clearly see that the length of the sides of the triangle is increased and from the figure we can clearly see that the largest side is rotated.
marked angle is also rotated.
so, we can clearly say that to make Triangle Δ Y H Q triangle Δ M N O is dilated and rotated.
Two angles are complementary, and Angle A is 6° more than Angle B. What is the measure of Angle A?
6°
42°
45°
48°
Complementary angle add up to 90 degrees.
Angle A = x + 6
Angle B = x
They both add up to 90.
x + 6 + x = 90
2x + 6 = 90
2x = 90 - 6
2x = 84
x = 84/2
x = 42
Angle A = x + 6
Angle A = 42 + 6
Angle A = 48 degrees
can someone help me solve this step by step? tyyyy
Answer:
x=4/7
Step-by-step explanation:
6 - 2/3(x+5) = 4x
First I want to clear the fraction so I will multiply everything by 3
3*6 -3* 2/3(x+5) = 3*4x
18 - 2(x+5) =12x
Distribute
18 - 2x-10 =12x
Combine like terms
8 -2x = 12x
Add 2x to each side
8 -2x+2x =12x+2x
8 = 14x
Divide each side by 14
8/14 =14x/14
8/14=x
Divide top and bottom by 2
4/7=x
Consider the equation and its solution.
8(x-2)=64
8x-16=64
8x=80
x=10
Which property is used in the last step to find that X=10?
A. distributive property
B. addition property of equality
C. subtraction property of equality
D. division property of equality
Answer:
D. division property of equalityStep-by-step explanation:
[tex]8(x-2)=64\qquad\text{distributive property}\\8x-(8)(2)=64\\8x-16=64\qquad\text{add 16 to both sides}\\8x-16+16=64+16\qquad\text{addition property of equality}\\8x=80\qquad\text{divide both sides by 8}\\\dfrac{8x}{8}=\dfrac{80}{8}\qquad\text{division property of equality}\\x=10[/tex]
Answer:
ANSWER WOULD BE D . division property of equality
Step-by-step explanation:
Took the test the math is quite simple
X^-2+4x^-1+3=0 solve by making appropriate substitution
ANSWER
[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]
EXPLANATION
The given equation is:
[tex] {x}^{ - 2} + 4 {x}^{ - 1} + 3 = 0[/tex]
Recall that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
[tex] \frac{1}{ {x}^{2} } + \frac{4}{x} + 3 = 0[/tex]
Or
[tex] {( \frac{1}{x} )}^{2} + 4( \frac{1}{x} ) + 3 = 0[/tex]
Let
[tex]u = \frac{1}{x} [/tex]
Our equation then becomes:
[tex] {u}^{2} + 4u + 3 = 0[/tex]
The factors of 3 that add up to 4 are:
[tex] {u}^{2} + 3u + u + 3[/tex]
[tex]u(u + 3) + 1(u + 3) = 0[/tex]
[tex](u + 1)(u + 3) = 0[/tex]
[tex]u + 1 = 0 \: or \: u + 3 = 0[/tex]
[tex]u = - 1 \: or \: u = - 3[/tex]
This implies that:
[tex] \frac{1}{x} = - 1 \: or \: \frac{1}{x} = - 3[/tex]
[tex]x = - 1 \: or \: x = - \frac{1}{ 3} [/tex]
If L is the line having x -intercept of -1 and y -intercept of 3, complete the equation of L .
y = -x + 3
y = -3x + 3
y = 3x + 3
Answer:
y = 3x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3)
m = [tex]\frac{3-0}{0+1}[/tex] = 3
We are given the y- intercept, that is c = 3
y = 3x + 3 ← equation of line
What is the location of the point on the number line that is 2/9 of the way from A=5 to B=23
Answer:
9 is (2/9) of the way from A = 5 to B = 23.
Step-by-step explanation:
Note that there are 23-5, or 18, units separating 5 and 23.
2/9 of that distance is (2/9)(18), or 4.
Adding 4 to 5, we get 9.
9 is (2/9) of the way from A = 5 to B = 23.
If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.
Answer:
9
Step-by-step explanation:
The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9
What is the average rate of change for this function for the interval from x = 2
to x = 4?
Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 2, 4 ]
From the table
f(b) = f(4) = 16
f(a) = f(2) = 4, hence
average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The average rate of change for a function is calculated using the change in y-values divided by the change in x-values.
Explanation:The average rate of change for a function is the change in the y-values (output) divided by the change in the x-values (input) over a given interval. To calculate the average rate of change for the function from x = 2 to x = 4, we need to find the change in y-values and the change in x-values for this interval.
Let's assume the function is f(x). We can calculate the average rate of change using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
Replace f(4) and f(2) with the corresponding y-values for x = 4 and x = 2, respectively, to get the final result.
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Pleaseeeeeeee helppppp ASAP help....
Answer:
42.5 %
Step-by-step explanation:
You would multiply the probability of the couple having a girl and the test predicting it’s a girl.
0.85 x 0.5= 0.425 = 42.5%
Over Thanksgiving break, the Heywards collected 980 cans for a food drive. The Ballards collected 200 fewer cans than the Heywards. How many cans did the Ballards collect?
Answer:
1180 cans
Step-by-step explanation:
Heywards collected = 980 cans
Ballards collected 200 fewer cans than Heywards.
Total cans collected by Ballard = ?
Therefore the sum of Heywards collected cans and Ballards fewer cans will give us the total cans collected by Ballard.
=980+200
=1180
Ballard collected 1180 cans....
Complete these ordered pairs for this equation. (0, ), (-2, ), (4, ) y=2x
Answer:
Part 1) The ordered pair is (0,0)
Part 2) The ordered pair is (-2,-4)
Part 3) The ordered pair is (4,8)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have a direct variation
[tex]y=2x[/tex]
Complete the ordered pairs
Part 1) we have (0,?)
For x=0
Substitute in the equation and solve for y
[tex]y=2(0)=0[/tex]
therefore
The ordered pair is (0,0)
Part 2) we have (-2,?)
For x=-2
Substitute in the equation and solve for y
[tex]y=2(-2)=-4[/tex]
therefore
The ordered pair is (-2,-4)
Part 3) we have (4,?)
For x=4
Substitute in the equation and solve for y
[tex]y=2(4)=8[/tex]
therefore
The ordered pair is (4,8)
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.
A x= -1.1
B x= -2.2
C x= 0
D x=-10
E x= 10
Answer:
C x= 0 greater than
E x= 10 greater than
Step-by-step explanation:
4(2 – x) > –2x – 3(4x + 1)
Distribute
8 –4x > –2x – 12x -3
Combine like terms
8 –4x > – 14x -3
Add 14x to each side
8 –4x+14x > – 14x+14x -3
8 +10x > -3
Subtract 8 from each side
8-8+10x>-3-8
10x > -11
Divide each side by 10
10x/10 >-11/10
x >-1.1
Any number greater than -1.1 is a solution
A x= -1.1 not greater than
B x= -2.2 not greater than
C x= 0 greater than
D x=-10 not greater than
E x= 10 greater than
Answer:
C & E
Step-by-step explanation:
Need help QUICK! Given triangle ABC, which equation could be used to find the measure of angle B?
Plz look at pic for answers
Answer:
second option
Step-by-step explanation:
We are going to use the acronym:
"Soh Cah Toa".
Why? It tells us the right-triangle definitions of sine, cosine, and tangent.
sine is opposite over hypotenuse.
cosine is adjacent over hypotenuse.
tangent is opposite over adjacent.
So looking at our triangle with respect to B tells us that 3 is the opposite measurement and 6 is the adjacent. No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].
So let's look at cos(B).
[tex]\cos(B)=\frac{6}{3\sqrt{5}}[/tex]
We need to rationalize the denominator by multiplying top and bottom by sqrt(5):
[tex]\cos(B)=\frac{6\sqrt{5}}{3(5)}=\frac{2\sqrt{5}}{5}[/tex]
So now looking at sin(B).
[tex]\sin(B)=\frac{3}{3\sqrt{5}}[/tex]
We have to rationalize again by multiplying top and bottom by sqrt(5):
[tex]\sin(B)=\frac{3\sqrt{5}}{3(5)}=\frac{\sqrt{5}}{5}[/tex].
So looking at our triangle with respect to A tells us that 3 is the adjacent measurement and 6 is the opposite. No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].
We don't have to use any trigonometric ratios with A.
Answer:
2 Square 5/ 5
Step-by-step explanation:
I got it right on the test
What is the range of the exponential function shown below?
f(x) = 9.27
A: y<0
B:y>0
C: all numbers are real except 9
D: all real numbers
Answer:
Option B [tex]y> 0[/tex]
Step-by-step explanation:
we have
[tex]f(x)=9(2^{x})[/tex]
This is a exponential function of the form
[tex]y=a(b^{x})[/tex]
where
a is the initial value
b is the base
r is the rate
b=1+r
In this problem
a=9
b=2
r=2-1=1=100%
The domain for x is the interval ------> (-∞,∞)
All real real numbers
The range is the interval -----> (0,∞)
[tex]y> 0[/tex]
All real numbers greater than zero
see the attached figure to better understand the problem
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 51 squares? (Assume that each grain of wheat weighs 1/7000 pound. Remember that 1 ton equals 2000 lbs.)
Answer:
Step-by-step explanation:
The number of grains of wheat on the n(th) square is 2^(n-1), or 2 to
the power of n-1. This is because the first square has 2^0 = 1 grain,
the second has 2^1 = 2, and the n(th) square has twice as many as the
previous. Thus the total number of grains of wheat is
S = 1 + 2 + 4 + 8 + ... + 2^63.
Since this is a geometric sequence with common ratio 2, the sum is
2^64 - 1
S = -------- = 2^64 - 1 = 18446744073709551615.
2 - 1
What is the range of the function f(x) = -|X - 4| + 5?
19 A. (-0,5)
B. (-09. 5)
C. (-5. infinity)
D. (5 .infinity)
Answer:
Range = (-∞, 5)
Step-by-step explanation:
This is the absolute value function with transformation.
The parent function is f(x) = |x|
This function has a "negative" in front, so it makes it reflect about x axis
The -4 after x makes horizontal translation of 4 units right
the +5 at the end makes the function translate 5 units UP
The graph is shown in the attached picture.
Looking at the graph, we can clearly see the range. The range is the allowed y-values. Hence, we can see that the range is -infinity to 5
answer is not properly given, so i can't choose from the options, but the answer is -∞, 5 to 5
Is the spinner below , what is the probability of lading on 2 ? Help me !!!!
Answer: C
Step-by-step explanation:
Probability: the outcome you want (2) over the total number of outcomes (6).
Probability= 2/6= 1/3.
The probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a spinner shown in the picture.
Total number of outcomes = 6
{1, 2, 3, 4, 5, 6}
Total number of favorable outcomes = 1
{2}
P(landing on 2) = 1/6
Thus, the probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.
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What is the measure of angle RST?
Options
A) 15°
B) 75°
C) 105°
D) 165°
The measurement of angle RST is 105
Answer:
Option C). 105°
Step-by-step explanation:
From the figure we can see a cyclic quadrilateral QRST
To find the measure of <RST
From the figure we can see that, angle RST is an obtuse angle.
The measure of angle RST is nearer to a right angle that is nearer to 90°
From the options we get the measure of angle RST = 105°
What is the area of the trapezoid
O 120in
O 140in
O 91in
O 182in
Answer:
A = 91 in²Step-by-step explanation:
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdor h[/tex]
b₁, b₂ - bases
h - height
We have b₁ = 20in, b₂ = 6in and h = 7in.
Substitute:
[tex]A=\dfrac{20+6}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)=91\ in^2[/tex]
can u help me wit A, B, C, and D
And can you explain which statement would have the largest answer on the four choices
Answer:
D is 36080
Step-by-step explanation:
D is the largest since A is 3.608, B is 360.8, C is 36.08
When dividing, the smaller decimal points will be larger, but if you multiple, the numbers shrink.
For Sophia’s graduation party, several tables of the same width will be arranged end to end to form a serving table with a total area of 75 ft 2 . The total length of the tables will be two more than three times the width. Find the length and width of the serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth
Answer:
The length is 16.1 ft and the width is 4.7 ft
Step-by-step explanation:
Let
x -----> the total length of the tables
y -----> the width of the tables
we know that
The area is equal to
[tex]A=xy[/tex]
[tex]A=75\ ft^{2}[/tex]
so
[tex]75=xy[/tex] -----> equation A
[tex]x=3y+2[/tex] -----> equation B
substitute equation B in equation A
[tex]75=(3y+2)y[/tex]
[tex]3y^{2} +2y-75=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=4.7\ ft[/tex]
Find the value of x
[tex]x=3(4.7)+2=16.1\ ft[/tex]
therefore
The length is 16.1 ft and the width is 4.7 ft
Answer:
The length and width of the serving table is 16.1 ft and 4.7 ft respectively.
Step-by-step explanation:
Consider the provided information.
Let the width of the table is x and length of the table is y.
The total length of the tables will be two more than three times the width.
This can be written as:
y = 2+3x
The area of the table is 75 ²ft
The area of rectangle is:
length × width = Area
Substitute width = x and length = 2+3x in above formula.
(x)(2+3x) = 75
2x+3x²-75 = 0
3x²+2x-75 = 0
The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute a=3, b=2 and c=-75 in above formula.
[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]
[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]
[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]
[tex]x_{1}=\frac{-2+30.07}{6}[/tex]
Ignore the negative value of x as width should be a positive number.
[tex]x=4.7\ ft[/tex]
Now substitute the value of x in y = 2+3x.
y = 2+3(4.7)
y = 16.1 ft
Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.