Mathematics College

Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.
Please show all your work! (30 points)

Answers

Answer 1
2x² = 7x + 6

Subtract both terms so that we can get 0 on one side. 

2x² - 7x - 6 = 0

Find what factors of - 12 (2 * - 6) add up to be - 7. It's - 4 and - 3. 

2x² - 4x - 3x - 6 = 0
2x(x - 2) - 3(x - 2) = 0
(x - 2)(2x - 3) = 0

Now set each equal to 0.

x - 2 = 0
x = 2

2x - 3 = 0
2x = 3
x = 3/2

x = 3/2, 2
Answer 2
the quadratic formula can be aplied as follows:
for [tex]ax^2+bx+c=0[/tex], [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]


given [tex]2x^2=7x+6[/tex]
we need to get it into [tex]ax^2+bx+c=0[/tex] form

minus (7x+6) from both sides
[tex]2x^2-7x-6=0[/tex]
now, a=2, b=-7 c=-6
subsitute
[tex]x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-6)}}{2(2)}[/tex]
[tex]x=\frac{7 \pm \sqrt{49+48}}{4}[/tex]
[tex]x=\frac{7 \pm \sqrt{97}}{4}[/tex]

so [tex]x=\frac{7 + \sqrt{97}}{4}[/tex] or [tex]x=\frac{7 - \sqrt{97}}{4}[/tex]

Related Questions

what is a factor of 4x^2+36x+72

Answers

Clearly, 4 is a factor of all terms. Beyond that, a graph suggests that (x+3) and (x+6) are also factors.

[tex]4x^{2}+36x+72=4(x+3)(x+6)[/tex]

write a number sentence to compare 7.17 and 7.170

Answers

Both of these values are the same, so the number sentence would state:

7.17 = 7.170

You can place any number of zeros to the very end on the right side (when there is a decimal point) without changing the value of the number.

7.1700000 = 7.17 also

Answer:

They are equal

Step-by-step explanation:

A car dealer buys a new car for $24,500. The dealer then marks the car's price up 27%
What is the selling price of the car?

Answers

the new price of the car is $31,115

hope this helped. please mark as brainliest!

Which expression is equivalent to [log9+1/2logx+log(x^3+4)]-log6

Answers

You probably looking to write the given expression as a single logarithm.

Remember the follwing rules:

log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)

Based on these rules, we can write the above expression as a single logarithm, as shown below:

[tex]log(9)+ \frac{1}{2}log(x)+log( x^{3}+4)-log(6) \\ \\ =log(9)+ log(x)^{ \frac{1}{2} } +log( x^{3}+4)-log(6) \\ \\ =log( \frac{9 \sqrt{x}( x^{3}+4) }{6} ) \\ \\ =log( \frac{3 \sqrt{x}( x^{3}+4) }{2} )[/tex]

Answer:

A.) log 3 sqrt x(x^3+4)/2

For a popular Broadway musical, theater box office all $356 apiece 275, tickets and $60 apiece, and 369 tickets and $45 apiece. How much money did the box office ticket Take in?

Answers

Answer: $ 61,585

Explanation:

Since the question is incomplete and confusing, here I rephrase it:

A theater box office sold:

     356 tickets at $80 apiece,
     275 tickets at $60 apiece, and
     369 tickets at $45 apiece.

How much money did the box office take in?

The problem is solved by multiplying the number of tickets at each price and adding all the partial sums:

This is: 

356 tickets × $80 / ticket = $28,480
275 tickets × $ 60 / ticket = $16,500
369 tickets × $45 / ticket = $16,605

Sum = $28,840 + $ 22,000 + $ 16,605 = $ 61,585
Answer: $ 61,585
If this is what your question means, then;

1. 356 tickets at $80 apiece2. 275 tickets at $60 apiece3. 369 tickets at $45 apiece
Just multiply the number of tickets per class to its corresponding price:356 tickets * $80 / ticket = $28,480275 tickets * $ 60 / ticket = $16,500369 tickets * $45 / ticket = $16,605
Total = $28,840 + $ 22,000 + $ 16,605
Total = $ 61,585
The total earnings is $ 61,585

Which logarithmic graph can be used to approximate the value of y in the equation 3y = 7?

Answers

we have that
3^y = 7
applying log both members
log(3^y)=log 7
y*log 3=log 7
y=log 7/log 3

using the logarithmic graph of y=log x

I graphically determine the values ​​for x = 3 and x = 7

see the attached figure

for x=3
log 3=0.48

for x=7
log 7=0.85

therefore
y=log 7/log 3-----> y=0.85/0.48-----> y=1.77

the answer is
the approximate value of y is 1.77

Find the area of the parallelogram with vertices at (−2,3),(−2,3), (6,14),(6,14), (−14,1),(−14,1), and (−6,12).(−6,12).

Answers

C is your answer your welcome

When no more than 110 units are​ produced, the cost of producing y units is given by​ c(x). ​c(x)equals0.2 x cubed minus 24 x squared plus 1524 x plus 31 comma 272 how many units should be produced in order to have the lowest possible average​ cost?

Answers

Given that the cost of production is modeled by:
c(x)=0.2x^3-24x^2+1524x+31272
for lowest average cost, we calculate c'(x)=0
thus:
From c(x), we shall have:
c'(x)=0.6x^2-48x+1524
solving for x we get:
x=40+/- 30.6594i
but since we are looking for a definite number of units, we shall do away with the complex part such that we shall remain with:
x=40 units
hence the minimum number of units will be 40 units

What value of y makes the equation true?

Answers

Hi there!

First, we'll need to solve the equation for y. In order to solve for y, we can use our properties. The property we can use in order to solve for y is the subtraction property. Using this property, we can subtract 2.9 from each side. This gives us the value of y as 8.1. Therefore, the answer is A - 8.1.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. what is the probability that washing dishes tonight will take me between 11 and 13 minutes?

Answers

12 min 12 min 12 min 12 min

hey can you please help me posted picture of question

Answers

For this case we have the following function transformation:
 Horizontal translations:
 Suppose that h> 0:
 To graph y = f (x + h), move the graph of h units to the left.
 Answer:
 option B
Addition of a number to x as is done in F(x+6) results in a shift towards left direction of the original function. Since G(x) = F(x+6) , G(x) is obtained by moving F(x) 6 units to left.

So, G(x) is F(x) shifted 6 units to the left.

Thus, the correct answer is option B

Find the relative rate of change of the function f(x)=150-0.08x^2

Answers

Relative change of a function is given by it's first derivative:
The relative rate of change will be given by:
f(x)=150-0.08x^2
the first derivative is given by:
f'(x)=-0.16x
thus the answer is:
f'(x)=-0.16x

Explain how you can use a model to find 4x 3/8

Answers

4 rectangles split it on 8 part then shade 3 of the 8 parts, them count every rectangle shades and add the all together, you will get 12/8, is the same if you multiply 4*3/8 you will get 12/8 simplified is 1/2!

hey can you please help me posted picture of question

Answers

Option B is the correct answer.

The solution is listed below:

[tex]3 x^{2} +27 \\ \\ =3( x^{2} +9) \\ \\ =3( x^{2} +3^{2}) \\ \\ =3( x^{2} -(3i)^{2}) \\ \\ =3(x-3i)(x+3i) \\ \\ =(3x-9i)(x+3i) [/tex]

hey can you please help me posted picture of question

Answers

To remove the the complex number from the denominator we multiply and divide the entire expression with the conjugate of denominator.

The conjugate of 1 - 4i is 1 + 4i

So, we can write:

[tex] \frac{2+i}{1-4i}* \frac{1+4i}{1+4i} \\ \\ = \frac{2+8i+i-4}{1+16} \\ \\ =\frac{-2+9i}{17} \\ \\ = \frac{-2}{17} + \frac{9i}{17} [/tex]

So, the correct answer is option B

What is the standard form of the equation of a circle given by x^2 + y^2 - 18x + 8y + 5 = 0

Answers

Completing the square:


x^2 - 18x + y^2 + 8y                       = -5
x^2-18x +81 - 81 + y^2 + 8y + 16 - 16 = -5.

Then, (x-9)^2 + (y+4)^2 = -5 + 81 + 16 = 92

Then the desired equation is (x-9)^2 + (y+4)^2 = 92.

Answer:

x-9,y+4,92

Step-by-step explanation:

Use right triangle DCB to find the trig values for angle D.

sinD =

cosD =

tanD =

Answers

sin D= opp./hyp. = 35/37
cos D= adj./hyp. = 12/37
tan D= opp./ adj. = 35/12

Answer: sinD = 0. 9459

cosD =0. 3243 tanD=2. 917

Step-by-step explanation:

From the figure above;

opposite = 35

adjacent = 12

hypotenuse = 37

sin D = opposite/hypotenuse

sinD = 35/37 = 0. 9459

cosD = adjacent/hypotenuse

= 12/37 = 0. 3243

tanD = adjacent/opposite

= 35/12 = 2. 9167

Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the measure of each part?

Answers

The angle of 1/4 of a circle is given by:
 (1/4) * (360) = 90 degrees
 We now look for the angle that results from dividing 1/4 of a circle into three equal parts.
 We have then:
 (1/3) * (90) = 30 degrees.
 Answer:
 the measure of each part is:
 30 degrees

The measure of the each part of the large circle is 90 degrees.

What is the measue of each part?

A circle is a bounded figure which points from its center to its circumference is equidistant. The sum of angles in a circle is 360 degrees.

Measure of the angle of each part = 1/4 x 360 = 90 degrees

To learn more about a circle, please check: https://brainly.com/question/14351152

Write the quotient as a mixed number. 33 ÷ 5 = 6 R2

Answers

A mixed number is a number with an integer and proper fraction.

33 / 5 = 6 R3 which is equal to 6 and 3/5

Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1

Answers

Graph B is the correct answer as of July 2018

The graph that shows a negative linear relationship that has a correlation coefficient, r, that is closer to -1 is: B. graph B.

What is a Negative Linear Relationship Graph?

A graph that shows a negative linear relationship has a trendline that slopes downwards from your left to the right.

The closer the data points are to each other along the trendline in a negative linear graph, the closer the correlation coefficient, r, is to -1.

Therefore, the graph that shows a negative linear relationship and has a correlation coefficient, r, that is closer to -1 is: B. graph B.

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A wheel spins at 300 revolutions per minute. What is the angular velocity of the wheel, in radians per second? Round the answer to the nearest hundredth.

Answers

Angular velocity = 300 revolutions per minute

1 revolution = 2π radians.

So, we can write:

Angular velocity = 300 x 2π radians per minute = 600π radians per minute

1 minute = 60 seconds.

So, 

Angular velocity = 600π radians per 60 seconds
⇒
Angular velocity = 10π radians per second
Angular velocity = 31.42 radians per second

Thus, rounding of to nearest hundredth, the angular velocity will be 31.42 radians per second. 

Answer:

31.42

Step-by-step explanation:

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

Answers

We have to find value of the house in 8 years so we will plug t=8 years in given equation.

[tex] y=150000(1.004)^{\left(12t\right)} [/tex]

[tex] y=150000(1.004)^{\left(12*8\right)} [/tex]

[tex] y=150000(1.004)^{96} [/tex]

[tex] y=150000(1.46702133432) [/tex]

[tex] y=220053.200148 [/tex]

Hence house will worth approx $220053.20 in 8 years.

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

Solution:

Equation of the appreciation of the value of house is given by:-

[tex]y=150000(1.004)^{12t}[/tex]

We need to find the worth of the house after 8 years

So, that means time, t=8

Let us plug t=8 in the equation [tex]y=150000(1.004)^{12t}[/tex]

So, we get,

[tex]y=150000(1.004)^{12*(8)}[/tex]

[tex]y=150000(1.004)^{96}[/tex]

[tex]y=150000(1.467021)[/tex]

y=150000*1.467021

y=220053.20

In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320


To choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot. Was the sample a biased sample?

Answers

The sample is biased because only 8th-grade students were polled and the choice of 8th grade students might not be the representative choice of other grades in the middle school.

Answer:

Yes, the sample was biased.

Step-by-step explanation:

We are told that to choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot.

We know that an unbiased sample is an accurate representation of the entire population and it can help us draw conclusions about the population.

For an unbiased sample each member of a population should equally likely to be chosen and the sample should be representative of the population as a whole.  

For an unbiased sampling for mascot students should be chosen randomly from each grade of the middle school.

Since all the students were polled from the same grade, so their choice can not represent the choices of all the students of the school, therefore, the sample was a biased sample.

six friends are going to buy a pizza. Their chices are to biu 2 medium 10-inch diameter pizzas for 7:00 each, or 1 large 14 inch diameter pizza for 15.00. Both prices include tax and tip. The friends agree that their best choice is the one that gives them the most pizza for their money. which is the best choice?

Answers

For this question, we want to find out the greatest amount of area of pizza for the least amount of money:

So we have two pizzas with a 10 in. diameter. Let us take one of those pizzas.

The formula for area of a circle is [tex] \pi r ^2[/tex]; So the area for one of these 10 in. pizzas would be [tex] \pi (5)^2[/tex] or 25[tex] \pi [/tex].

We have two of these pizzas, so the total area that we would get with $14 would be 25[tex] \pi [/tex]*2 or 50[tex] \pi [/tex].

For the second case, we have one pizza with a 14 in. diameter.

The area of this pizza will be [tex] \pi (7)^2[/tex] or 49[tex] \pi [/tex].

So for $15 we can buy 49[tex] \pi [/tex] worth of pizza.

The best deal would be to buy the two medium pizzas of 10 inch diameter, because for $14, you get 50[tex] \pi [/tex].

Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.

Answers

Just to be clear, the data are reported in the picture attached.

We set the difference in graffiti incidents between before (B) and after (A) as:
d = A - B
If the number of incidents has indeed reduced, then d will be negative.

In order to choose the hypothesis, we need to recall that the null hypothesis H₀ represents the statement that we want to prove wrong, while the alternative hypothesis H₁ represents the statement that we want to prove right.
Therefore, we want μd to be strictly negative (= 0 would mean that the number of incidents stayed constant).

Hence:
H₀ : μd  ≥ 0
H₁ : μd < 0  


Final answer:

The appropriate hypotheses to determine if graffiti incidents declined involve a null hypothesis where the mean difference is greater than or equal to zero and an alternative hypothesis where the mean difference is less than zero. The μd represents the mean difference in graffiti incidents before and after the institution of the community watch program.

Explanation:

The appropriate hypotheses to test whether the number of graffiti incidents declined in the suburban communities after the institution of a citizen community watch program are as follows:

H0: μd ≥ 0 (Null hypothesis: The mean difference in graffiti incidents before and after is greater than or equal to 0, indicating no decrease.)Ha: μd < 0 (Alternative hypothesis: The mean difference in graffiti incidents before and after is less than 0, indicating a decrease.)

Here, μd (mu-sub-d) represents the mean difference between the number of incidents before the program and after the program was implemented. To test these hypotheses, we would typically conduct a paired t-test if the samples are normally distributed or a Wilcoxon signed-rank test if the distribution is not normal.

Assuming μd is the mean difference in graffiti incidents before and after, the test will determine if there is statistically significant evidence to support that the community watch program resulted in a reduction of graffiti incidents.

PLZ HELP ASAP TANGENTS OF CIRCLES

Answers

First, we are given that the inscribed angle of arc CB which is angle D is equal to 65°. This is half of the measure of the arc which is equal to the measure of the central angle, ∠O. 
 
    m∠O = 2 (65°) = 130°

Also, the measure of the angles where the tangent lines and the radii meet are equal to 90°. The sum of the measures of the angle of a quadrilateral ACOB is equal to 360°. 

     m∠O + m∠C + m∠B + m∠A = 360°

Substituting the known values,
     130° + 90° + 90° + m∠A = 360°

The value of m∠A is equal to 50°.

Answer: 50°

require help with this question

Answers

a) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
  1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k

bi) Π₁ can be written using r = (x, y, z).
  Π₁ ⇒ 3x +2y +z = 4

bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
  Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
  Π₂ ⇒ 2x +3y -z = 5

c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.

A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.

hey can you please help me posted picture of question

Answers

im sure that it is A. i hope this helps you and you make a great grade on your test
Answer:
The solutions are: 1 + 6i and 1 - 6i

Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0

The given equation is:
x² - 2x + 37 = 0

By comparison:
a = 1
b = -2
c = 37

Now, to get the solutions of the equation, we will use the quadratic formula shown in the attached image.

By substitution in this formula, we would find that:
either x = [tex] \frac{2+ \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 + 6i[/tex]

or x = [tex] \frac{2- \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 - 6i[/tex]

Hope this helps :)

hey can you please help me posted picture of question

Answers

The parent function of the shown graph is option C
y = x³

Information about the age of participants in a robotics competition is below: A box plot titled "Age of Participants" and labeled "Age" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 31 on the number line. A line in the box is at 16. The whiskers end at 11 and 33. The middle 50% of the data is between what two numbers?

Answers

Final answer:

The middle 50% of the age of participants in the robotics competition falls between 13 and 31.

Explanation:

The box plot represents the age distribution of participants in a robotics competition. The box extends from the lower quartile (Q1) to the upper quartile (Q3), which in this case are 13 and 31, respectively. The line within the box represents the median, which is 16. The whiskers represent the range of the data, ending at 11 and 33.

To find the middle 50% of the data, we need to determine the values that lie between Q1 and Q3. Therefore, the middle 50% of the age of participants in the robotics competition falls between 13 and 31.

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