Answers
Answer:58?
Step-by-step explanation:
\((2x + 12)^{\circ} + 32^{\circ} = 90^{\circ}\\2x + 12^{\circ} + 32^{\circ} = 90^{\circ}\\2x = 90^{\circ} - 12^{\circ} - 32^{\circ}\\2x = 46^{\circ}\\x = 23^{\circ}\)
Related Questions
when conducting a hypothesis test concerning the population mean, and the population standard deviation is known, the value of the test statistic is calculated as
Answers
We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.
test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))
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$1.77. Lian weighs a bag of apples on the
Store's Scales. The scale shows that the appies
weigh 1.32 lb. How much do lian's apples
a grocery store, each pound of apples Costs
Cost? show your work.
Answers
Answer:
About $2.34
Step-by-step explanation:
If each pound of apples cost 1.77 and you have 1.32 pounds, you would multiply 1.77 by 1.32 to get 2.3364, but when rounded, 2.34.
Answer:
Step-by-step explanation:
1.77 answer 2.34
or somthing like that
Each individual result of a probability experiment is called a(n) a. complement b. event s
c. ample space
d. outcome
Answers
Each individual result of a probability experiment is called an "outcome" (d).
An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.
For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.
Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.
In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.
Thus, each individual result of a probability experiment is called an "outcome" (d).
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Given the following linear function sketch the graph of the function and find the domain and range.
\(f\left(x\right)\ =\ \frac{2}{7}x\-21)
Answers
A graph of the given linear function (y = 2x/7 - 2)is shown in the image attached below.
The domain of the given linear function is (-∞, ∞).
The range of the given linear function is (-∞, ∞).
How to determine the domain and range?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain = -∞ < x < ∞ or (-∞, ∞).
Range = -∞ < y < -∞ or (-∞, ∞).
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Complete Question:
Given the following linear function sketch the graph of the function and find the domain and range. y = 2x/7 - 2
Amazon Math Flow Questions • You have 30 associates who all work an 8 hour day, 5 days a week. 2 need to be indirect-they are not on the floor producing. Your direct rate is 150 units per hour but you have two 15 minute breaks during the day. How many units can your department produce in a 40 hour week? . If you need to produce an extra 10,000 units in a given week how many extra people will it require? Question: Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a... Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a total of 60 sandwiches. The deli wants an efficient way to increase the sandwich output using the same five workers and 10 hour shift (Don't Factor Break in) to produce 75 because of the 25% increase due to the expansion of the deli. What would you do to make the the process more efficient? Where each sandwich would take 8 minutes to make instead of 10 minutes. Please answer the question throughly.
Answers
Extra people required is 50.
Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Question 1 :
Number of associates = 30
Number of direct workers = 30 - 2 = 28
You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.
Direct rate = 150 units per hour
Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week
= 37.5 hours per week
Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units
28 people produce 5625 units in a week
Let x people produce 10,000 + 5625 = 15,625 units in a week
Using proportion,
28 : 5625 = x : 15,625
28 / 5625 = x / 15,625
x = (28 × 15,625) / 5625 = 77.78 ≈ 78
Extra people required = 78 - 28 = 50
Question 2 :
Number of sandwiches made in 10 minutes = 1
Number of sandwiches made in 10 hours = 60
5 workers are there. one worker makes 60/5 = 12 sandwiches
But Deli want number of sandwiches in 10 hours = 75
One worker should make 75/5 = 15 sandwiches instead of 12.
Number of sandwiches made in 8 minutes should be 1.
So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.
Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.
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Which expression is NOT equivalent to 3^5?
A. 3^7 – 3^2
B. 3^5×3^0
C. 3^1×3^4
D. 3^6÷3^1
Answers
Answer:
APart 1:
A.53 =53
B.3^5/3^-6 =177147
C.(1/4)^3 • (1/4)^2 = 1 /1024
D.(-7)^5/(-7)^7 = 1/49
Step-by-step explanation:
I tried my best for part 2 but i'm pretty sure it's not right. I think 1/1024 and 1/49 has a value between 0 and 1
How do I find x in an iregular hexigon
Answers
Answer:
It mostly depends on the question
Step-by-step explanation:
This function has a local minimum at x= with output value: And a local maximum at x=With output value:
Answers
minimum:10
output :509
maximum:5
output: 634
Explanation
Step 1
graph the function:
to do this, you need put values for x, and you will get a set of values for y, those formed pairs are the coordinates,
we can see, there are a minimun and a maximum
Step 2
find the minimum
To find the local minimum of any graph, you must first take the derivative of the graph equation, set it equal to zero and solve for
\(f(x)=2x^3-45x^2+300x+9\)a) derivate
\(\begin{gathered} f(x)=2x^3-45x^2+300x+9 \\ \end{gathered}\)To take the derivative of this equation, we must use the power rule
\(\begin{gathered} f(x)=2x^3-45x^2+300x+9 \\ f^{\prime}(x)=(2\cdot3)x^{(3-1)}-(45\cdot2)x^{2-1}+300x^{(1-1)}+9 \\ f^{\prime}(x)=6x^2-90x+300 \end{gathered}\)solve for x by applying the quadratic formula
\(ax^2+bx+c=0\rightarrow6x^2-90x+300=0\)\(\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{replace} \\ x=\frac{-(-90)\pm\sqrt[]{90^2-4\cdot6\cdot300}}{2\cdot6} \\ x=\frac{90\pm\sqrt[]{8100-7200}}{12} \\ x=\frac{90\pm\sqrt[]{900}}{12} \\ x=\frac{90\pm30}{12} \\ so \\ x_1=\frac{90+30}{12}=\frac{120}{12}=10 \\ x_2=\frac{90-30}{12}=\frac{60}{12}=5 \end{gathered}\)then, let's find the output when x=5
\(\begin{gathered} f(x)=2x^3-45x^2+300x+9 \\ f(5)=2\cdot5^3-45\cdot5^2+300\cdot5+9 \\ f(5)=250-1125+1500+9 \\ f(5)=634 \end{gathered}\)so,infelection point is (5,634)
Step 3
Now, the output when x=10
\(\begin{gathered} f(x)=2x^3-45x^2+300x+9 \\ f(10)=2\cdot10^3-45\cdot10^2+300\cdot10+9 \\ f(10)=2000-4500+3000+9 \\ f(10)=509 \end{gathered}\)inflection point (10,509)
Step 3
so, at x=5 and x=10 we have two inflection points, to know if those points are minimum we need to check the second derivate of the fucntion
\(\begin{gathered} f^{\prime}(x)=6x^2-90x+300 \\ f^{\prime^{\prime}}(x)=12x^{}-90 \end{gathered}\)now, check if f''(x) is greater than zero
a)at x=5
\(\begin{gathered} f^{\prime^{\prime}}(x)=12x^{}-90 \\ f^{\prime^{\prime}}(5)=12\cdot5^{}-90 \\ f^{\prime^{\prime}}(5)=60-90=-30 \\ f^{\prime^{\prime}}(5)=-30 \end{gathered}\)it is smaller than zero, it means (5,634) is a maximum
b)at x=10
\(\begin{gathered} f^{\prime^{}}^{\prime}(x)=12x^{}-90 \\ f^{\prime^{}\prime}(10)=12\cdot10-90 \\ f^{\prime^{}\prime}(10)=120-90 \\ f^{\prime^{}\prime}(10)=30 \end{gathered}\)it is greater than zero, it means (10,509) is a minimum
I hope this helps you
helpppp please find the area with explanation, answer and find the missing sides thank you!!
Answers
Shape 1- 42*42=1764
Shape 2- 42*70=2940
Then you add both together
1764+2940= 4,704
Why does the factor tree method for finding the LCM work?
Answers
The reason this method works is that the LCM is the smallest multiple that all the numbers have in common. When we break each number down into its prime factors, we are essentially finding all the factors that each number shares with the others.
What is the factor tree method for finding the LCM work?The factor tree method is a useful technique for finding the least common multiple (LCM) of two or more numbers.
The method works by breaking each number down into its prime factors, and then finding the product of all the unique factors raised to their maximum powers.
By taking the product of all the unique factors raised to their maximum powers, we are essentially finding the smallest multiple that includes all these shared factors.
For example, let's find the LCM of 12 and 18 using the factor tree method:
We start by breaking down 12 and 18 into their prime factors: \(12 = 2^2 \times 3\) and \(18 = 2 \times 3^2.\)
We then identify the unique factors and their maximum powers: \(2^2 \times 3^2.\)
Finally, we multiply the unique factors raised to their maximum powers: \(2^2 x 3^2 = 36.\)
So the LCM of 12 and \(18\) is \(36\) . This method works because 36 is the smallest multiple that includes all the shared factors of 12 and 18 (which are 2, 2, and 3).
Therefore, The reason this method works is because the LCM is the smallest multiple that all the numbers have in common. When we break each number down into its prime factors, we are essentially finding all the factors that each number shares with the others.
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PLEASE HELP GIVING 20 POINTS FOR BRAINLEST!!!(FIRST TO ANSWER)
what is f(5)
Answers
Answer:The F-5 is an agile, highly maneuverable, reliable supersonic fighter, combining advanced aerodynamic design, engine performance and low operating costs. ... The U.S. Navy operates the F-5 in its adversary squadrons to simulate enemy aircraft in aerial combat training exercises.
Translate the following statement into an algebraic expression: Use x for your variable. The sum of the square of a number and eleven times the number.
Answers
Step-by-step explanation:
Let x be the number.
Then the algebraic expression will be x^2 + 11x.
The algebraic expression in x will be : x² + 11x
Given,
Variable x,
The sum of the square of a number and eleven times the number.
Now,
Let the variable be x .
Square of variable : x²
Eleven times of the variable x : 11x
Now combine the term to get the algebraic expression,
Alegbraic expression : x² + 11x
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What is the value of x? Enter only the number in the box! Help Asap
Answers
Answer:
x = 5
Step-by-step explanation:
90 - 55 = 35
8x - 5 = 35
+5 +5
8x = 40
x = 5
write a function m-file that calculates the volume of a parallelepiped whose sides are determined by given vectors
Answers
The completed function m-file would look like this:
function volume = parallelepiped_volume(a,b,c)
% a,b,c are input vectors representing the sides of parallelepiped
ab_cross = cross(a,b);
volume = abs(dot(ab_cross,c));
end
To calculate the volume of a parallelepiped determined by given vectors, a function m-file can be created. The function will take in three input vectors representing the sides of the parallelepiped, and will output the calculated volume.
To calculate the volume of a parallelepiped, the cross product of two adjacent sides must be taken, and then the dot product of the result with the third side must be computed. The magnitude of the resulting vector will give the volume of the parallelepiped.
Here is the step-by-step explanation for the function m-file:
Define the function and input variables:
function volume = parallelepiped_volume(a,b,c)
% a,b,c are input vectors representing the sides of parallelepiped
Compute the cross product of vectors a and b:
ab_cross = cross(a,b)
Compute the dot product of ab_cross with vector c:
volume = abs(dot(ab_cross,c))
End the function with "end"
Therefore, the completed function m-file would look like this:
function volume = parallelepiped_volume(a,b,c)
% a,b,c are input vectors representing the sides of parallelepiped
ab_cross = cross(a,b);
volume = abs(dot(ab_cross,c));
end
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If another equation is graphed so that the system has no solution, which equation could that be?
y=-2(x-1/2)
y=-1/2(4x+2)
y=-x+1
y=-1/2x+2
Answers
Answer:
y=-2(×-1/2)
Step-by-step explanation:
...........
The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10. What test score is 0.8 standard deviations below the mean?
Answers
Given:
The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.
Required:
What test score is 0.8 standard deviations below the mean?
Explanation:
\(\begin{gathered} \text{ The standard deviation is 10. So, 0.8 standard deviation is } \\ 0.8\times10=8.\text{ So, }115-8=107\text{ is the score that is 0.8 standard deviation } \\ \text{ from the mean.} \end{gathered}\)Answer:
answered the question.
Water flows through a straight 10-cm-diameter pipe at a diameter reynolds number of 250,000. if the pipe roughness is 0.06 mm, what is the approximate moody friction factor?
Answers
It would be ideal to utilise a piece of software or an internet calculator created especially for calculating the Moody friction factor. This will produce a result that is more precise and effective.
How to find?
To find the approximate Moody friction factor, you can use the Colebrook equation, which relates the friction factor (f) to the Reynolds number (Re), pipe roughness (ε), and pipe diameter (D).
The equation is:
\(1 / sqrt(f) = -2 * log10((ε / (3.7 * D)) + (2.51 / (Re * sqrt(f))))\)
First, convert the pipe diameter from cm to meters by dividing by 100:
D = 10 cm / 100
= 0.1 m
Next, plug in the given values into the Colebrook equation and solve for the friction factor:
\(1 / sqrt(f) = -2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f))))\)
Rearrange the equation to solve for sqrt(f):
\(sqrt(f) = 1 / (-2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f)))))\)
Square both sides to solve for f:
\(f = (1 / (-2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f))))))^2\)
Using an iterative method or a calculator, you can approximate the value of f.
However, since the calculation involves an iterative process, it can be quite complex to solve manually.
Therefore, it would be best to use a software or online calculator specifically designed to solve for the Moody friction factor. This will give you a more accurate and efficient result.
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After performing the iterations, we find that the approximate Moody friction factor (f) is approximately 0.022.
The Moody friction factor is a dimensionless parameter used to describe the flow characteristics of fluid in a pipe. To determine the approximate Moody friction factor, you can use the Colebrook equation:
1/√f = -2log10((ε/D)/3.7 + 2.51/(Re√f))
Where:
f is the Moody friction factor,
ε is the pipe roughness,
D is the pipe diameter,
Re is the Reynolds number.
Given:
Pipe diameter (D) = 10 cm = 0.1 m,
Reynolds number (Re) = 250,000,
Pipe roughness (ε) = 0.06 mm = 0.00006 m.
Let's substitute these values into the Colebrook equation and solve for f:
1/√f = -2log10((0.00006/0.1)/3.7 + 2.51/(250,000√f))
Now, we need to solve this equation iteratively because the friction factor appears on both sides of the equation. We can use a numerical method called the Newton-Raphson method to solve for f.
Let's start by assuming an initial value for f, let's say f = 0.02. We'll use this initial value to calculate the left side of the equation:
1/√0.02
By substituting this into the right side of the equation, we can solve for the new value of f:
-2log10((0.00006/0.1)/3.7 + 2.51/(250,000√0.02))
We continue this iteration until we reach a convergence point, where the new value of f is very close to the previous value.
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Rational numbers can
be written in the form
a/b
where a and b
are integers and b :
0.
Answers
Answer:
4/2 45/63
Step-by-step explanation:
In a company the ratio of men to women i 3:2. 30% of the women are under the age of 30. What fraction of all people in the company are women under age of 30
Answers
6/50 fraction of all people in the company are women under age of 30 In a company where the ratio of men to women i 3:2.
In a company the ratio of men to women 3:2
30% of the women are under the age of 30.
suppose there are 500 people in the company
then 300 are men and 200 are women
30% of 200 = 200*30/100= 60 women are under 30
60/500= 6/50 women are under 30
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Every day, Luis buys 5 more baseball cards to add to his collection. If he had 25 baseball cards before making any purchases, how many will he have on day 20? Answer without units
Answers
Answer:
125
Step-by-step explanation:
Before he had 25 baseballs,
Everyday he buys 5 baseballs to add to his collection
If he he is adding 5 baseballs everyday he will end up having 125 baseballs
For any input, there is only
possible output
O Three
O Two
O One
O Zero
Answers
Answer:
I think it's one
Step-by-step explanation:
why?
any input needs at most one output
write down the multiplication tables for z/6zand z/7z. list the elements have multi- plicative inverses.
Answers
For Z/6Z and Z/7Z, the multiplication tables are 1-5 and 0 and 1-6 and 0 correspondingly. The elements 1, 2, 3, 4, 5 and 1, 3, 5, 6 respectively have multiplicative inverses.
The multiplication table is as follows for the group Z/6Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4\s5 * 1 = 5\s0 * 1 = 0
1, 2, 3, 4, and 5 are the elements with multiplicative inverses.
The multiplication table is as follows for the group Z/7Z:
1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4
5 * 1 = 5\s6 * 1 = 6\s0 * 1 = 0
1, 3, 5, and 6 are the elements with multiplicative inverses.
The group members in a group Z/NZ are the remainders after dividing the integers by N. For instance, the elements in Z/6Z are 0, 1, 2, 3, 4, and 5. The product of each element is shown in the multiplication table.by itself when multiplied. The multiplication table for Z/6Z is as follows: 0 * 1 = 0; 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 4, 5 * 1 = 5. 1, 2, 3, 4, and 5 are the elements with multiplicative inverses. The multiplication table is also the same for Z/7Z: 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 5, 6 * 1 = 6, 0 * 1 = 0. 1, 3, 5, and 6 are the elements with multiplicative inverses.
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What is equivalent to 5x+3
Answers
Answer : 5x+3
There are no like terms
PLEASE GIVE ME AS BRAINLIEST
What does x equal? log6 x = 4
A. 36
B. 216
C. 222
D. 1296
Answers
logb^y=x
please help me
ill give brainlyist
Answers
The constant of proportionality is calculated as:
Option D: 8.5
How to find the constant of proportionality?The constant of proportionality is defined as the constant value of the ratio between two proportional quantities.
Now, we are given a table of values and as such, we can find the constant of proportionality from the formula:
k = y/x
From the table, we have:
k = 25.50/3
k = 8.5
k = 42.5/5
k = 8.5
k = 59.50/7
k = 8.5
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for what points (x0,y0) does theorem a imply that this problem has a unique solution on some interval |x − x0| ≤ h?
Answers
The theorem that we are referring to is likely a theorem related to the existence and uniqueness of solutions to differential equations.
When we say that theorem a implies that the problem has a unique solution on some interval |x − x0| ≤ h, we mean that the conditions of the theorem guarantee the existence of a solution that is unique within that interval. The point (x0, y0) likely represents an initial condition that is necessary for solving the differential equation. It is possible that the theorem requires the function to be continuous and/or differentiable within the interval, and that the initial condition satisfies certain conditions as well. Essentially, the theorem provides us with a set of conditions that must be satisfied for there to be a unique solution to the differential equation within the given interval.
Theorem A implies that a unique solution exists for a problem on an interval |x-x0| ≤ h for the points (x0, y0) if the following conditions are met:
1. The given problem can be expressed as a first-order differential equation of the form dy/dx = f(x, y).
2. The functions f(x, y) and its partial derivative with respect to y, ∂f/∂y, are continuous in a rectangular region R, which includes the point (x0, y0).
3. The point (x0, y0) is within the specified interval |x-x0| ≤ h.
If these conditions are fulfilled, then Theorem A guarantees that the problem has a unique solution on the given interval |x-x0| ≤ h.
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How do you find the inverse of sin?
Answers
In a right-angle triangle, a sine function of an angle θ is equal to the opposite side to θ divided by hypotenuse.
Sin θ = Opposite side/Hypotenuse
How do you find the inverse of a trig function?y = f(x) → x in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.
The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say θ is the angle, then:
sin θ = (Opposite side to θ/Hypotenuse)
Or θ = Sin-1 (Opposite side to θ/Hypotenuse)
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during normal breathing, about 12% of the air in the lungs is replaced after one breath. write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 ml. approximately how much original air is left in the lungs after 5 breaths?
Answers
If the initial amount of air in the lungs is 500 ml. approximately then original air is left in the lungs after 5 breaths is 263.86 ml.
During normal breathing, about 12% of the air in the lungs is replaced after one breath,
initial amount of air in the lungs is 500 mL.
After 1 breath original air in lung = 500 - (12/100)500
= 500*(88/100)
= 500 (0.88)
After 2 breath original air in lung = 500 (0.88) - (12/100)500 (0.88)
= 500 (0.88) (1 - 12/100)
= 500 (0.88) (0.88)
= 500(0.88)²
After n breaths original air in lung = 500(0.88)ⁿ
original air is present after 5 breaths = 500(0.88)⁵
= 263.86 ml
Therefore, original air is left in the lungs after 5 breaths is 263.86 ml.
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Can someone please help?? I don’t understand this
Answers
Answer:
When y = 5; x = 2
Step-by-step explanation:
What we have to do here is to first go to the point y = 5 on the y-axis
Now, the next thing is to trace this to the plot
The tracing will meet the plot at a point
At this point, we can now drop a line to the x-axis
By this, we can get that at y = 5; then x = 2
Now, we want to check the validity from the linear equation given
That would be;
y = -x + 7
y = -2 + 7
y = 5
This holds according to the linear equation given
A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a piece of steel and will have a final area as close to 28 cm2 as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the frame must be 11 cm by 6 cm.Complete the equation that models the above situation, and find the width of the frame, x.The area of the steel frame can be modeled by the following equation.x2 +x - 28 = 0The width of the frame, x, rounded to the nearest hundredth, is approximatelycm.
Answers
The steel company is making flat rectangular frames. So,The width of the frame, x, rounded to the nearest hundredth, is approximately 4.38 cm.
To find the width of the frame, we need to solve the equation \(x^2 + x - 28 = 0\). This equation represents the area of the steel frame, which needs to be as close to \(28 cm^2\) as possible.
To solve the equation, we can use factoring or the quadratic formula. In this case, factoring the equation is not straightforward, so we'll use the quadratic formula:
\(x = (-b \pm \sqrt{(b^2 - 4ac)} ) / (2a)\)
For the given equation\(x^2 + x - 28 = 0\), we have \(a = 1\), \(b = 1\), and\(c = -28\). Substituting these values into the quadratic formula, we get:
\(x = (-1 \pm \sqrt{(1^2 - 4(1)(-28))}) / (2(1))\)
Simplifying the expression further:
\(x = (-1 \pm\sqrt{(1 + 112)}) / 2\)
\(x = (-1 \pm \sqrt{(1 + 112)}) / 2\)
The two possible solutions are obtained by taking the positive and negative square roots of 113 and dividing them by 2. Rounding to the nearest hundredth, we find that x is approximately 4.38 cm.
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