Answer:
Step-by-step explanation:
[tex]u.v=|u||v| cos \theta\\(8)(9)+(7)(7)=\sqrt{8^2+7^2 } \sqrt{9^2+7^2} cos \theta\\72+49=\sqrt{64+49} \sqrt{81+49}~ cos ~\theta\\121=\sqrt{113} \sqrt{130} ~cos~\theta\\cos~\theta=\frac{121}{\sqrt{113} \sqrt{130} } \\\theta=cos^{-1} (\frac{121}{\sqrt{113}\sqrt{130} } )\approx 3.3^\circ[/tex]
whats 2+2-1+4x4-12-7
Answer:
is the answer 0
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
2+2-1+4x4-12-7
4-1+4x4-12-7
3+4+4x4-12-7
7+4x4-12-7
11x4-12-7
44-12-7
32-7
25
hope help :) .^.
what is 0.3% of 3.9*10^18
Answer:
1.17e+16
hope this helps! (if right pls mark brainy) thanks!
A school is selling tickets to a choral performance. On the first day, the school sold 6 adult tickets and 6 child tickets for $102. The school took in $96 on the second day selling 12 adult tickets and 3 child tickets. How much does each ticket cost ?
Answer:
adult $5
child $12
Step-by-step explanation:
make the adult as x and child as y.
this will makes 6x + 6y = 102
12x + 3y = 96
solve it and the answer comes out.
A rectangular tank with a square base, an open top, and a volume of 6912ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
The dimensions of the tank that minimize the surface area are a square base of 24 ft × 24 ft and a height of 12 ft.
To minimize the surface area, we need to minimize the sum of the areas of the five sides of the tank. Let's denote the side length of the square base as x and the height of the tank as h.
Given that the volume V = 6912 ft³, and for a rectangular tank, the volume is V = base area × height = x² × h.
So, we have x² × h = 6912.
To minimize the surface area, we differentiate the surface area formula with respect to x, set it equal to zero, and solve for x.
The surface area A = x² + 4xh.
Differentiating A with respect to x, we get [tex]\frac{dA}{dx}[/tex] = 2x + 4h.
Setting [tex]\frac{dA}{dx}[/tex] = 0 gives us 2x + 4h = 0, so x = -2h.
Since x cannot be negative, we ignore this solution.
Now, using x² × h = 6912, we can solve for h:
h = [tex]\frac{6912}{x^{2} }[/tex]
Substituting x = -2h:
[tex]\[ h = \frac{6912}{(-2h)^2} = \frac{6912}{4h^2} = \frac{1728}{h^2} \][/tex]
Solving for h:
[tex]h^3 = \frac{1728}{h^2}\\h^5 = 1728\\h = \sqrt[5]{1728} = 12[/tex]
Now, substituting h = 12 back into x² × h = 6912:
[tex]x^2 \times 12 = 6912\\x^2 = \frac{6912}{12} = 576\\x = \sqrt{576} = 24[/tex]
my question is that is 22.7 degrees colder than 96.5 degrees?
Answer:
73.8 degrees because 96.5-22.7=73.8
Step-by-step explanation:
2) radius = 5 yd find the circumference of each circle
Answer:
23
Step-by-step explanation:
Answer:
31.42 yards
Step-by-step explanation:
The formula for the circumference is pi multiplied by the diameter.
To work this out you would first multiply 5 by 2, which would be 10 yards. This is because the radius is half of the diameter. Then you would multiply pi by 10, which would be 31.416.
radius=[tex]\frac{1}{2}[/tex] of diameter
Circumference=[tex]\pi d[/tex]
1) Multiply 5 by 2.
[tex]5*2=10[/tex]
2) Multiply pi by 10.
[tex]\pi *10=31.416[/tex]
3) Round to 2 decimal places.
[tex]31.42[/tex]
You need to compute the a 90% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.5? (Use 9.2 as an estimate of the population standard deviation from prior studies.)
Answer:
The sample size required is 102.
Step-by-step explanation:
The (1 - α)% confidence interval for population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
Given:
σ = 9.2
(1 - α)% = 90%
MOE = 1.5
The critical value of z for 90% confidence level is:
[tex]z_{0.10/2}=1.645[/tex]
*Use a z-table.
Compute the value of n as follows:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]
[tex]=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102[/tex]
Thus, the sample size required is 102.
To calculate the sample size for a 90% confidence interval with a 1.5 margin of error using a known standard deviation of 9.2, you would need a sample size of approximately 101.
90% Confidence Interval Sample Size Calculation
To determine the required sample size for a 90% confidence interval with a maximum margin of error of 1.5, and a known population standard deviation of 9.2, you can use the following formula:
n = (Z*σ/E)^2
Here, 'n' is the sample size, 'Z' is the Z-score corresponding to the desired confidence level, 'σ' is the population standard deviation, and 'E' is the maximum margin of error. For a 90% confidence level, the Z-score is approximately 1.645 (since 5% is in each tail of the normal distribution). Plugging in the values we have:
n = (1.645 * 9.2 / 1.5)^2
The calculation yields:
n = (15.074 / 1.5)^2
n = (10.049)^2
n = 101.0
Therefore, you would need a sample size of approximately 101 to ensure the sample mean does not deviate from the population mean by more than 1.5 with a 90% confidence interval.
For a sample of 100 men, the median weight is 155 lbs., the first quartile is 150 lbs., and the third quartile is 162 lbs. Select all of the answers that create a true statement. Approximately 25 men in the sample weigh
Answer:
Refer below.
Step-by-step explanation:
True statements for Approximately 25 men in the sample weigh are:
More than 150 lbs.
More than 162 lbs.
Between 150 and 155 lbs.
Between 155 and 162 lbs.
Based on the experimental data, approximately 25 men in this sample weigh:
More than 150 lbs.More than 162 lbs.Between 150 and 155 lbs.Between 155 and 162 lbs.What is a boxplot?A boxplot simply refers to a type of chart that can be used for the graphical representation of the five-number summary of any data set, especially based on skewness, locality, and spread.
Additionally, the five-number summary of a data comprises the following:
MinimumFirst quartileMedianThird quartileMaximumIn this scenario, the true statement is that approximately 25 men in this sample would weigh:
More than 150 lbs.More than 162 lbs.Between 150 and 155 lbs.Between 155 and 162 lbs.Read more on boxplots here: https://brainly.com/question/14277132
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Find the value of x (no labels)
Answer:
x=31
Step-by-step explanation:
The interior angles of a triangle must add to 180 degrees, so
81+68+x=180
Add on the left
149+x=180
Now, solve for x by getting it by itself. To do this, subtract 149 from both sides
149-149+x=180-149
x=31
Which are simplified forms of the expression sec^2 theta sin 2theta? Select all that apply.
There are two answers.
a) 2 cot theta
b) 2-sec^2 theta
c) 2 tan theta
d) sec^2 theta-1
e) (sin2 theta) / (cos^2 theta)
Answer:
2 tan theta & sin2theta/cos^2theta
Step-by-step explanation:
Final answer:
The simplified forms of the expression sec^2(theta) sin(2theta) are 2 tan(theta) and sec^2(theta) - 1. These correspond to answer choices (c) and (d) respectively, by utilizing trigonometric identities to simplify the expression.
Explanation:
To find the simplified forms of the expression sec^2(theta) sin(2theta), we can use trigonometric identities. The identity for sin(2theta) is 2sin(theta)cos(theta). Since sec(theta) is the reciprocal of cos(theta), we can write sec^2(theta) as 1/cos^2(theta).
Therefore, the expression becomes:
sec^2(theta) sin(2theta) = (1/cos^2(theta)) * (2sin(theta)cos(theta))
We can simplify this further by canceling one cos(theta) from the numerator and denominator, which yields:
2sin(theta)/cos(theta)
Simplified, this is equal to 2 tan(theta), since tan(theta) = sin(theta)/cos(theta).
Using another trigonometric identity, sec^2(theta) = 1 + tan^2(theta), we can also express the original expression as:
sec^2(theta) - 1 which simplifies to tan^2(theta).
This means that the correct answers from the provided choices are (c) and (d).
Why do you think it might be useful to rearrange formulas before solving for one of the variables? (Relate your answer to the Celsius and Fahrenheit formulas and examples.)
Answer:
It makes the solution of the equation easier
Step-by-step explanation:
Here we have the formula relating Celsius and Fahrenheit given as follows;
[tex]C = \frac{5\times (F - 32)}{9}[/tex]
From the above Celsius to Fahrenheit equation, we have that to solve for F we rearrange the formula as follows
[tex]C =\frac{5F}{9} - \frac{32\times 5}{9}[/tex]
Which is the same as
[tex]C =\frac{5F}{9} - 17\frac{7}{9}[/tex]
It is then seen that rearranging the equation between Celsius and Fahrenheit makes it easier to solve for either °C or °F.
Answer:
It’s easier to find the solution to a variable when that variable is by itself on one side of the equal sign. Rearranging formulas before substituting values for each variable makes calculations more straightforward. With this approach, we only need to perform operations such as multiplication, division, addition, and subtraction on one side of the equal sign, and we simplify instead of solving by using the properties of equality.
Step-by-step explanation:
In the past, joe got paid $229,390 annually. Since switching to a new career he has been making 10% less. How much does Joe make now.
Answer:
The answer is $206,451
Step-by-step explanation
This scenario is asking to subtract 19 percent away from 229,390 .
Step one : Divide 229,390 by 10 ( take away the zero behind the 9 )
Step 2 : Subtract 22,939 from 229,390 since we know ten percent of 229,390 is 22,939 = 206451
Answer:
Joe makes $206,451 annually
Step-by-step explanation:
229,390 divided by 10 = 22,939
Then Subtract 22,939 from 229,390 = 206,451
Watch help video
A bag contains 8 red marbles, 5 blue marbles and 7 green marbles. If three marbles
are drawn out of the bag, what is the probability, to the nearest 100oth, that all three
marbles drawn will be green?
Answer: There’s a .35 % chance that the marble will be green. When drawing all 3, the chance is .04%
Step-by-step explanation:
Consider a population variable measured in square-feet. The population standard deviation is 15 square-feet. How many observations do we need in our sample in order to be able estimate a 95% confidence interval with only 2.5 square-feet for error margin?
Given Information:
standard deviation = σ = 15 ft²
Confidence interval = 95%
Margin of error = 2.5 ft²
Required Information:
Sample size = n = ?
Answer:
Sample size = n ≈ 139
Step-by-step explanation:
The required number of observations can be found using ,
Me = z(σ/√n)
Where Me is the margin of error, z is the corresponding z-score of 95% confidence interval, σ is the standard deviation and n is the required sample size.
Rearrange the above equation to find the required number of sample size
√n = σz/Me
n = (σz/Me)²
For 95% confidence level, z-score = 1.96
n = (15*1.96/2.5)²
n = 138.29
since the sample size can't be in fraction so,
n ≈ 139
Therefore, a sample size of 139 would be needed.
When Mai turned 21, she invested $2000 in an individual Retirement Account that has grown at a rate of 10% compounded annually. If the account continues to grow at that rate, what will be its value when Mai turns 65?
Final answer:
When Mai turns 65, the value of her individual Retirement Account will be $61,917.28.
Explanation:
To calculate the future value of an investment with compound interest, we can use the formula:
FV = P(1+r)^n
Where FV is the future value, P is the principal amount (initial investment), r is the interest rate (as a decimal), and n is the number of compounding periods.
In this case, Mai invested $2000 and the interest rate is 10% compounded annually.
So, when Mai turns 65, the number of compounding periods would be 65 - 21 = 44 years.
Plugging in the values into the formula:
FV = $2000(1+0.10)^44 = $61,917.28
Therefore, the value of Mai's individual Retirement Account when she turns 65 will be $61,917.28.
Complete the equation describing how x and y are related
When x=0 we get y=1
1 = 3(0) + ?
1 = ?
Answer: 1
Answer:
1
Step-by-step explanation:
This equation is written in slope intercept form, which is y=mx+b
This is where m is the slope, and b is the y intercept. What we need to find here, is the y intercept.
The y intercept is what y equals when x is 0.
Based on the table, we know that y is 1, when x is 0.
Therefore, the equation completed, would be y=3x+1
I NEED HELP ON THIS SO BAD I WILL GIVE CROWN FOR ANSWER
Edwin fills 15 test tubes with a solution. Each test tube contains 150 milliliters of solution.
How many liters of solution in all is there in the test tubes?
2.25 L
22.5 L
225 L
2,250 L
The number of liters of solution in all is there in the test tubes is 2.25L, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Edwin fills 15 test tubes with a solution.
Each test tube contains 150 milliliters of solution.
Now,
The solution in all the tubes=150ml x 15
=2250ml
To convert it in liters
=2250/1000
=2.250L
Therefore, by algebra the answer will be 2.250L.
More about the Algebra link is given below.
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Suppose you go to a company that pays 0.03 for the first day, 0.06 for the second day, 0.12 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 29 days ? Total Income = 16106127.33 Correct
Answer:
The total income after 29 days is $16,106,127.33
Step-by-step explanation:
This is a geometric progression with the first element being 0.03 and the ratio is 2. So if we want to know the total income after 29 days we can use the formula for the sum of elements in a series of that kind, this is given by:
sum(29 elements) = [(first element)*(1 - r^(29))]/(1 - r)
sum(29 elements) = [0.03*(1 - 2^(29))]/(-1)
sum(29 elements) =(0.03*(-536870911))/(-1)
sum(29 elements) = -16106127.33/(-1) = 16106127.33
The total income after 29 days is $16,106,127.33
A cone fits inside a square pyramid as shown For every
cross section the ratio of the area of the circle to the area
the area of the square the
Since the area of the circle is
volume of the cone equals
of the square is more
I the volume of the pyramid
Cross section
the volume of the pyramid or 3 (2+m) or .arn
the volume of the pyramid or (en en) or zarah
the volume of the pyramid or ( 20 ) or tren
Answer:
C is the answer
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Mom put plums and apples onto a plate. The ratio of the number of plums to the number of apples was 3:2. How many fruit did mom put on the plate, if after Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples?
Answer:
30 fruits
Step-by-step explanation:
Let
x ----> number of plums on the plate
y ----> number of apples on the plate
we know that
The ratio of the number of plums to the number of apples was 3:2
so
[tex]\frac{x}{y} =\frac{3}{2}[/tex]
[tex]x=1.5y[/tex] ----> equation A
After Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples
so
[tex]x-6=y[/tex] ----> equation B
substitute equation A in equation B
[tex]1.5y-6=y[/tex]
solve for y
[tex]1.5y-y=6\\0.5y=6\\y=12[/tex]
Find the value of x
[tex]x=1.5(12)=18[/tex]
therefore
Mon put on the table
[tex]x+y=18+12=30\ fruits[/tex]
Answer:
30
Step-by-step explanation:
evaluate using tables square root of 0.792
Answer:
0.28142
Explanation
First change 0.792 into standard form
To evaluate the square root of 0.792 using tables, you would typically refer to a set of pre-calculated square root values in the form of a table. These tables were commonly used before calculators and computers became widely available.
To begin the evaluation process, you would follow these steps:
**Step 1: Locate the closest square values**
First locate the two perfect square values that surround 0.792. If you have a comprehensive table, you may find an exact value, but often you'll need to interpolate between two values.
**Step 2: Interpolation**
If 0.792 is not a value directly found in the table, you use interpolation. Let's assume that your table shows that the square root of 0.784 (which is \( 0.28² \)) is 0.28, and the square root of 0.81 (which is \( 0.9² \)) is 0.9. Your value, 0.792, lies between these two.
**Step 3: Estimation**
Since \( 0.28² \) is 0.784 and \( 0.9² \) is 0.81, 0.792 is closer to 0.784 than 0.81. You would then estimate it to be closer to 0.28 than 0.9.
**Step 4: Fine-tuning**
Now, find the difference between the square roots and the differences between the squares:
- The difference between 0.28 and 0.9 is 0.62.
- The difference between 0.784 and 0.81 is 0.026.
Next, find out where 0.792 falls between 0.784 and 0.81 in proportion to the difference between the square roots.
- The difference between 0.792 and 0.784 is 0.008.
- To find the proportion of 0.008 to the total difference 0.026, you divide 0.008 by 0.026 to get approximately 0.308.
- Now, multiply this proportion by the difference between the square roots to refine your estimate: 0.62 * 0.308 ≈ 0.191.
**Step 5: Calculate your estimate**
Add this value to the lower square root to get an approximation of the square root of 0.792:
0.28 + 0.191 ≈ 0.471.
**Final Answer**
The square root of 0.792 is approximately 0.471 using interpolation with table values.
what is the precent decrease from $219.95 to $131.00
Let X={1,2,3}X={1,2,3}. Let P(X)P(X) be the set of all subsets of XX (i.e. Power set of XX). Let RR be a relation defined on P(X)P(X) by the following. For all sets AA and BB in P(X)P(X), ARBARB iff |A|=|B||A|=|B|. Is RR an equivalence relation?
Answer:
Yes
Step-by-step explanation:
For the equation to be equivalence then it must be
Reflexive, Symmetric and transitive
since |A|=|B|;
Every element in A is in B then R is reflexive
If f(1) = g(1), then g(1) = f(1), so R is symmetric.
If f(1) = g(1) and g(1) = h(1), then f(1) = h(1), so R is transitive.
R is reflexive, symmetric, and transitive,
thus R is an equivalence relation.
The city of Raleigh has 9000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 500 randomly selected registered voters was conducted. 217 said they'd vote for Brown, 242 said they'd vote for Feliz, and 41 were undecided.
Describe All citizens of Raleigh
A. All registered voters in Raleigh
B. All registered voters with telephones in Raleigh
C. The 500 voters surveyed
D. The 217 voters who said they'd vote for Brown
C. None of the abovethe sample for this survey.
Answer:
c
Step-by-step explanation:
plz mark me brainlesssss
For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x2?
The function [tex]k(x) = 2x^2[/tex] is which the average rate of change over the interval 1 < x < 5 greater than the average rate of change of g(x).
Given data:
The function is represented as [tex]g(x)=1.8x^2[/tex].
Now, the average rate of change of the function is S.
The value of [tex]S=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex].
The interval of the function is from 1 < x < 5.
So, for g(x), [tex]S=\frac{f(5)-f(1)}{5-1}[/tex].
The value of S = 10.8
For the function [tex]k(x) = 2x^2[/tex], the rate of change is:
[tex]S=\frac{k(5)-k(1)}{4}[/tex]
[tex]S=\frac{50-2}{4}[/tex]
So, the value of S = 12 and is greater than 10.8
Hence, the function is [tex]k(x) = 2x^2[/tex].
To learn more about rate of change of function, refer:
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The complete question is attached below:
For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x^2?
A.=f(x) = x^2
B.=g(x) = 1.2x^2
C.=h(x) = 1.5x^2
D.=k(x) = 2x^2
£399 is shared between Ann, Bill, Chloe and Dave.
The ratio of the amount Ann gets to the amount Bill gets 2 : 9
Chloe and Dave get 2.5 times the amount Ann gets.
Work out the amount of money that Bill gets.
Show your working out.
Answer:
Ann=£38
Bill=£171
Chloe=£95
Dave=£95
Step-by-step explanation:
By the information provided we can create an equation:
[tex]2x+9x+2*5x=399\\11x+10x=399\\21x=399\\x=19[/tex]
Now that we know x, we multiply it correspondingly.
For Ann -> 2*19=38
Bill -> 9*19= 171
Chloe and Dave have the exact same amount each (because they both have 2.5 times the amount Ann's money)
Chloe/ Dave -> 5*19=95 each.
an angle that measures 50° Turns through how many 1° angles
Answer:
50
Step-by-step explanation:
An angle that measures 50° Turns through 50 1° angles because 50 *1 = 50
1 degree * 50 turns = 50 degrees
write an equation of the line that passes through the origin that intersects the line y= 2x+1 to form a right angle
Answer:
y = [tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
To find a right angle we need to find the perpendicular line. The trick here is to do the flip of your slope and since there is no "that passes through the point (#, #) you're done after that. So the answer is
y = [tex]\frac{1}{2}[/tex]x+1
You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 1715cm3. Determine the dimensions of the bin that will minimize the surface area, where x is the length of each side of the base and y is the height of the box.
Answer:
x=15.08 cm
y=7.54 cm
Step-by-step explanation:
We are given that
Volume of box=1715 cubic cm
Side length of base=x
l=b=x
Height of box=h=y
Volume of box=lbh=x^2y
[tex]1715=x^2y[/tex]
[tex]y=\frac{1715}{x^2}[/tex]
Surface area of box=Area of bottom+area of four faces=[tex]x^2+4xy[/tex]
[tex]S=x^2+4x(\frac{1715}{x^2}=x^2+\frac{6860}{x}[/tex]
Differentiate w.r.t x
[tex]S'(x)=2x-\frac{6860}{x^2}[/tex]
[tex]S'(x)=0[/tex]
[tex]2x-\frac{6860}{x^2}=0[/tex]
[tex]2x=\frac{6860}{x^2}[/tex]
[tex]x^3=\frac{6860}{2}=3430[/tex]
[tex]x=(3430)^{\frac{1}{3})=15.08[/tex]
Again differentiate w.r.t x
[tex]S''(x)=2+\frac{13720}{x^3}[/tex]
Substitute x=15.08
[tex]S''(x)=2+\frac{13720}{(15.08)^3}>0[/tex]
Hence, the surface area is minimum at x=15.08 cm
[tex]y=\frac{1715}{(15.08)^2}=7.54 cm[/tex]
The dimensions of the bin that will minimize the surface area are:
Base side (x): 7.5cm
Height (y): 36.13cm
Let's express the surface area and volume of the box in terms of x and y:
Surface area (A):
A = 2x^2 + 4xy
Volume (V)V = x^2y
We are given that the volume of the box must be 1715cm3:
1715cm3 = x^2y
Solving for y, we get:
y = 1715/x^2
Now, we want to minimize the surface area (A) subject to the constraint that the volume (V) is 1715cm3. We can use Lagrange multipliers to solve this optimization problem.
L(x, y, λ) = A - λ(V - 1715)
L(x, y, λ) = 2x^2 + 4xy - λ(x^2y - 1715)
Taking partial derivatives of L with respect to x, y, and λ, we get:
∂L/∂x = 4x + 4y - 2λxy = 0
∂L/∂y = 4x - λx^2 = 0
∂L/∂λ = -x^2y + 1715 = 0
Substituting V = x^2y into the third partial derivative, we get:
∂L/∂λ = -V + 1715 = 0
Solving these equations simultaneously, we get:
x = 7.5
y = 36.13
What is the solution to the following equation x²+3x+7=0
Answer:
x =(3-√37)/2=-1.541
x =(3+√37)/2= 4.541
Step-by-step explanation:
to long to explain sorry but trust me
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Equation x² + 3x + 7 = 0
Let's solve this equation by two methods.
1) Completing the perfect square trinomial
x² + 3x = -7
x² + 3x + (3/2)² = -7 + (3/2)²
(x + 3/2)² = -7 + 9/4
(x + 3/2)² = -19/4
x + 3/2 = √-19/√4
x = -3/2 + √-19/2 It has imaginary solutions.
2.- Graph the equation
See the graph below.
In the graph we notice that the equation does not cross the x-axis so it does not have real solution.