Mathematics College

Use any method to solve the equation. If necessary, round to the nearest hundredth.

x^2 + x − 30 = 0

A. –5, 6

B. 10, –12

C. 5, –6

D. 5. 5, –5.5


Answers

Answer 1

Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.

In the method, we will split 30, in such factors, which when added or subtracted gives us 1,  and when multiplied gives us -30.

So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.

Now, the equation will be written as -

x² - 5x + 6x - 30 = 0

Taking common, we get

x(x - 5) +6(x-5) = 0

(x-5)(x+6) = 0

So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6

Thus, the correct option is C). x = 5 and -6

Related Questions

21 ÷ 7 + 20 • 100 • 2 – 3

PLEASE SOLVE

Answers

Do the multiplication and division first. 

21 / 7 = 3

20 * 100 * 2 = 4000.

Now for the addition and subtraction. The 3 and - 3 cancel each other out. 

3 + 4000 - 3 = 4000
The first step for solving this expression is to divide 21 by 7.
3 + 20 × 100 × 2 - 3
Eliminate the opposites in the expression.
20 × 100 × 2
Multiply 20 by 100.
2000 × 2
Lastly,, multiply the two numbers together to get your final answer.
4000
Let me know if you have any further questions.
:)

50 POINTS...Which equation would best help solve the following problem? Tania releases a javelin 1.6 meters above the ground with an initial vertical velocity of 25 meters per second. How long will it take the javelin to hit the ground?

Answers

Let [tex]x(t)[/tex] be the vertical position of the javelin at time [tex]t[/tex]. Once it's thrown in the air, the only force acting on it is gravity, so the javelin would be subjected to a constant downward acceleration of approx. 9.8 meters per second per second. So

[tex]x''(t)=-9.8[/tex]

Integrating once with respect to [tex]t[/tex], we get

[tex]x'(t)=-9.8t+C_1[/tex]

where [tex]x'(t)[/tex] is the velocity of the javelin. We're told that [tex]x'(0)=25[/tex], so

[tex]25=-9.8\cdot0+C_1\implies C_1=25[/tex]

Integrating again with respect to [tex]x[/tex] to get

[tex]x(t)=-4.9t^2+25t+C_2[/tex]

and we know the javelin was initially thrown 1.6 meters above the ground, or [tex]x(0)=1.6[/tex], so we get

[tex]1.6=-4.9\cdot0^2+25\cdot0+C_2\implies C_2=1.6[/tex]

So the javelin's position at any time [tex]t[/tex] is given by

[tex]x(t)=-4.9t^2+25t+1.6[/tex]

It will hit ground when [tex]x(t)=0[/tex]. Solve this however you want; you'll find that this will happen at about [tex]t=5.165[/tex] seconds after the javelin has been thrown.
im doing the same quiz anyone know number 1 with the base of a traingle or something

What is the Least common denominator for -3/x -6/8x^2

Answers

Assuming your second fraction is -6/(8x^2), the denominator of the second fraction already includes the first denominator as a factor, so it is the lowest common denominator.

The Least Common Denominator is 8x^2 for the fractions as written.

_____
You can reduce the second fraction to -3/(4x^2), which would make the Least Common Denominator be 4x^2.

Find the surface area of the part of the surface z = x y that lies within the cylinder

Answers


A surface area, r radius, and h height

A=2πr²+2πrh

xy should be like a rectangle so x is r and y is h

A=2πx²+2πxy

Which describes the difference between the graph of f(x) = 2x3 - 8x + 3 and g(x) = x3 - 4x?
A) The graph of g(x) is obtained by shifting f(x) up 3 units and stretching vertically by a factor of 2.
B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.
C) The graph of g(x) is obtained by shifting f(x) right 3 units and compressing vertically by a factor of 2.
D) The graph of f(x) is obtained by shifting g(x) right 3 units and compressing vertically by a factor of 2.

Answers

The difference between the graph of f(x)=2x^3-8x+3 and g(x)=x^3-4x will be described as follows:
The graph of f(x)=2x^3-8x+3 is the first one
The graph of g(x)=x^3-4x is the second one
From the two graphs we see that:

B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.

B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.

John made $20 for 2 hours of work. Sally made $50 for 4 hours of work. How do John and Sally's hourly pay rate compare?

Answers

John make 20 dollars an hour because 20/2 is 10 nd sally makes 12.50 dollars an hour because 50/4 is 12.50

Answer:

sally makes more

Step-by-step explanation:

john makes 20 per 2 hours

20/2= 10

sally makes 50$ per 4 hours

50/4= 12.5

so Sally makes more

the / is division

Hugo is a veterinarian. He knows the following information about his 41 patrons: 20 patrons in total do not have a dog. 17 patrons in total have a cat. 7 patrons have neither a dog nor a cat. Can you help Hugo organize the results into a two-way frequency table?

Answers

Answer:

4,17,13,7

Step-by-step explanation:

i got it right :)

Final answer:

To assist Hugo in organizing patron pet ownership into a two-way frequency table, calculations were made to determine the number of patrons with both a dog and a cat, leading to a complete frequency table illustrating pet ownership among 41 patrons.

Explanation:

Hugo, the veterinarian, is attempting to organize patron pet ownership information into a two-way frequency table. First, let's establish the total number of patrons which is 41. Since 20 patrons do not have a dog, it implies that 41 - 20 = 21 patrons have a dog. Of the 41 patrons, we know that 17 have a cat. Also, 7 patrons have neither a dog nor a cat. To create the two-way frequency table, we need to figure out how many patrons have both a dog and a cat.

To find the number of patrons with both pets, we add the number of patrons without pets to those with dogs and then subtract from the total number of patrons, which gives us 41 - 20 + 7 = 28. However, since this number includes all dog owners, we need to subtract those who only have dogs and no cats, which gives us 28 - (41 - 17) = 28 - 24 = 4 patrons with both a dog and a cat.

With these calculations, we can now fill out the two-way frequency table:

Patron\PetDogNo DogTotalCat41317No Cat17724Total212041

Note: The sum of the numbers for dog owners and non-dog owners must equal the total number of patrons, and the same applies for cat ownership.

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Hey can you please help me out posted picture

Answers

We have for this case:
 For each language we have:
 Number of people who speak Spanish:
 Spanish = 8 + 4 = 12
 Number of people who speak Chinese:
 Chinese = 5 + 6 = 11
 Number of people who speak both languages:
 Both = 3 + 2 = 5
 Adding we have:
 12 + 11 + 5 = 28
 Answer:
 28
 option A
Number of employees who speak only Spanish = 8
Number of employees who speak only Chinese = 6
Number of employees who speak Spanish and Russian = 4
Number of employees who speak Spanish and Chinese = 3
Number of employees who speak all three languages = 2
Number of employees who speak Chinese and Russian = 5

The number of employees who speak Spanish or Chinese or both will be the sum of all above values. The sum is = 28

Thus the correct answer is option A

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Answers

Find the horizontal or oblique asymptote of f(x) = negative 3 x squared plus 7 x plus 1, all over x minus 2

Finding the horizontal and oblique asymptote of
f(x)= (-3x^2+7x+1)/(x-2)

Solution:

For Horizontal Asymptote:
Line y=L is a horizontal asymptote of the function y=f(x), if either limx→∞f(x)=Llimx→∞f(x)=L or limx→−∞f(x)=Llimx→−∞f(x)=L, and LL is finite.

Calulate limits:

limx→∞(1x−2(−3x2+7x+1))=−∞

limx→−∞(1x−2(−3x2+7x+1))=∞

Thus, there are no horizontal asymptotes.

For Oblique Asymptote:

Do polynomial long division (−3x2+7x+1)/(x-2)=−3x+1+3/(x−2)

The rational term approaches 0 as the variable approaches infinity.

Thus, the slant asymptote is y=−3x+1y=−3x+1.


Determine the mean ,median,modes ,IQR,and rage for the data 3,8,6,6,4,6,9,9,12

Answers

Mean:

Add all the numbers:

3 + 8 + 6 + 6 +4 + 6 + 9 + 9 + 12 = 63

There are 9 numbers.

63 / 9 = 7

Mean = 7

Median:

Order all the numbers:

3, 4, 6, 6, 6, 8, 9, 9, 12

The median is 6.

Mode:

The number that appears the most is 6.

The mode is 6.

Inter-Quartile Range :

Median of 2nd part = 9

Median of 1st part = 5

Subtract:

9 - 5 = 4

The IQR is 4.

Range:

The highest number is 12. The lowest is 3

Subtract:

12 - 3 = 9

The range is 9.

Hope this helped☺☺
Mean=Average/add all the numbers and divide it by how many numbers there are

3+8+6+6+4+6+9+9+12

=63

63/9

=7 is your mean

Median=The middle number in a set of ordered numbers

first place all the numbers from least to greatest

3,4,6,6,6,8,9,9,12

The middle number of this set is 6 so 6 is your median

Mode is the most numbers repeated so if no numbers are repeated there is no mode

6 is repeated 3 times so 6 is your mode

Range: greatest number minus least number


12-3

=9 is your range

IQR=since the median is 6 we would split it and then minus it

so 3,4,6,6,6,8,9,9,12

It would be 9-5

=4is your IQR I am pretty sure that is correct!

^o^




What is the sum of the first 35 terms in the series 7 + 9 + 11 + ...?

a.

29

c.

1645

b.

1399

d.

1435

Answers

The answer is d 
Hope this helps :)
First find the 35th number in the series using the formula:
an = a1 + (n - 1)d
a1 = first number in the series
d = difference between successive number
n = number of terms
a35 = 7 + (35 - 1)2
a35 = 7 + (34)2 
a35  = 7 + 68 = 75.
Therefore, the 35th term is 75.
To find the sum of the first 35 numbers, use the formula:
Sn = n(a1 + an) / 2
Sn = 35(7 + 75) / 2
Sn = 2870 / 2 = 1,435.
Therefore, the sum of the first 35th term is 1,435.
The correct answer is D.

Find the absolute maximum of f(x,y) = e^(-x^2-y^2)(x^2+2y^2) on x^2 + y^2 < 2

Answers

[tex]f(x,y)=e^{-x^2-y^2}(x^2+y^2)[/tex]

Notice that converting to polar coordinates, setting
[tex]x=r\cos\theta[/tex]
[tex]y=r\sin\theta[/tex]
[tex]\implies r^2=x^2+y^2[/tex]

allows us to consider [tex]f(x,y)[/tex] as a function of one variable; let's call it [tex]F(r)[/tex], where

[tex]f(x,y)\equiv F(r)=re^{-r}[/tex]

Then

[tex]F'(r)=e^{-r}(1-r)=0\implies r=1[/tex]

We have [tex]F'(r)>0[/tex] for [tex]r<1[/tex], and [tex]F'(r)<0[/tex] for [tex]r>1[/tex], which means [tex]F[/tex] is increasing, then decreasing as [tex]r[/tex] exceeds 1. This suggests that extrema occur for [tex]f(x,y)[/tex] wherever [tex]r^2=x^2+y^2=1[/tex], i.e. along the intersection of the cylinder [tex]x^2+y^2=1[/tex] and [tex]f(x,y)[/tex].

Computing the second derivative of [tex]F(r)[/tex] and setting equal to 0 gives

[tex]F''(r)=-e^{-r}(2-r)=0\implies r=2[/tex]

as a possible point of inflection. We have [tex]F''(r)<0[/tex] for [tex]r<2[/tex], and namely when [tex]r=1[/tex], which means [tex]F(r)[/tex] is concave downward around this point. This confirms that [tex]r=1[/tex] is a site of a maximum. Along this path, we have a maximum value of [tex]F(1)=e^{-1}\approx0.368[/tex].

Next, to check for possible extrema along the border, we can parameterize [tex]f(x,y)[/tex] by [tex]x=\sqrt2\cos t[/tex] and [tex]y=\sqrt2\sin t[/tex], so that

[tex]x^2+y^2=(\sqrt2\cos t)^2+(\sqrt2\sin t)^2=2[/tex]

and we can think of [tex]f(x,y)[/tex] as a function a single variable, [tex]F(t)[/tex], where

[tex]F(t)=2e^{-2}\approx0.271[/tex]

In other words, [tex]f(x,y)[/tex] is constant along its boundary [tex]x^2+y^2=2[/tex], and this is smaller than the maximum we found before.

So to recap, the maximum value of [tex]f(x,y)[/tex] is [tex]\dfrac1e\approx0.368[/tex], which is attained along the surface above the circle [tex]x^2+y^2=1[/tex] in the [tex]x-y[/tex] plane.

At the deli Jennifer bought roasted turkey and provolone cheese. The turkey costs $6.35 per pound and the cheese costs $4.75 per pound. In total, she bought 3 pounds and the price was $17.13 How many pounds of each did she buy?

Answers

She bought two pounds of turkey and one pound of cheese

Let the amounts of Turkey Jennifer bought be [tex] T [/tex] pounds and that of Cheese be [tex] C [/tex] pounds.

From the given information,

[tex] 6.35T+4.75C=17.13\\
T+C=3 [/tex]

Solving the above two equations together,

[tex] 6.35T+4.75(3-T)=17.13\\
(6.35-4.75)T+4.75*3=17.13\\
1.6T=2.88\\
T=\frac{2.88}{1.6}\\
T=1.8
[/tex]

Thus, Jennifer bought [tex] 1.8\;pounds [/tex] of Turkey and [tex] 3-1.8=1.2\;pounds [/tex] of Cheese.

When 415 junior college students were surveyed, 150 said they have a passport. constructa 95% confidence interval for the proportion of junior college students that have apassport. round to the nearest thousandth?

Answers

Solution:
The 95% confident interval will be estimated as follows:

sample proportion: 150/415=0.362

ME=1.96*[0.362*0.638/415]=0.0011
thus
95% CI
0.362-0.0011<p<0.362+0.0011

Answer:

[tex]0.362-0.045<p<0.362+0.045[/tex]

Step-by-step explanation:

It is given that When 415 junior college students were surveyed, 150 said they have a passport, then sample proportion will be:

Sample proportion=[tex]\frac{150}{415}=0.362[/tex]

Then, [tex]ME=1.96\sqrt{\frac{0.362{\times}0.638}{415}}[/tex]

=[tex]1.96\sqrt{\frac{0.230}{415}[/tex]

=[tex]1.96(0.023)[/tex]

=[tex]0.045[/tex]

Therefore, at 95% confidence interval, the proportion of junior college students that have a passport is:

[tex]0.362-0.045<p<0.362+0.045[/tex]

Use the word BULLDOG to answer the question. If the letters of this word are written on paper and then cut into squares with one letter per square, what is the probability of selecting a C or a Z?

Answers

There is a 0% chance of selecting either of those letters as they do not appear in the work BULLDOG. 

one more question please help me!!!

Answers

a = (9/6)*10 mm = 15 mm

b = (35/10)*6 mm = 21 mm

The ratio in parentheses is the ratio of corresponding sides in the respective rectangles, so is the scale factor. The unknown dimension is that scale factor applied to the corresponding known dimension.

The price C, in dollars per share, of a high-tech stock has fluctuated over a twelve-year period according to the equation C= 14 +12x – x2, where x is in years. The price C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = 2x + 30. For what values are the two stock prices the same?

Answers

For this case we have the following equations:
 C = 14 + 12x - x2
 C = 2x + 30
 Equating the equations we have:
 14 + 12x - x2 = 2x + 30
 Rewriting we have:
 -x2 + 10x - 16 = 0
 Solving the polynomial we have:
 x1 = 2
 x2 = 8
 Answer:
 the two stock prices are the same for:
 x1 = 2
 x2 = 8
Final answer:

The values for which the two stock prices are the same are approximately x ≈ -1.405 and x ≈ 11.405.

Explanation:

To find the values for which the two stock prices are the same, we need to set the equations for the prices equal to each other and solve for x.

Equation for the first stock: C = 14 + 12x - x^2

Equation for the second stock: C = 2x + 30

Setting the two equations equal: 14 + 12x - x^2 = 2x + 30

Rearranging the equation and combining like terms: x^2 - 10x - 16 = 0

Using the quadratic formula to solve for x: x = (-b ± sqrt(b^2 - 4ac))/(2a)

Plugging in the values: x = (-(-10) ± sqrt((-10)^2 - 4(1)(-16)))/(2(1))

Simplifying: x = (10 ± sqrt(100 + 64))/2

Calculating: x = (10 ± sqrt(164))/2

Approximate values: x ≈ (10 ± 12.81)/2

Therefore, the two stock prices are the same for x ≈ -1.405 and x ≈ 11.405.

Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. explain the steps that lana could take to determine the equation.

Answers

We have the following equation:
 3x + 2y = 15

 Step 1:
 Rewrite given equation:
 2y = 15 - 3x
 y = 15/2 - (3/2) x

 Step 2:
 Parallel lines have the same slope:
 y = mx + b
 m = -3 / 2
 y = (- 3/2) x + b

 Step 3:
 Find b, for this we evaluate the point (5, 2) in the equation:
 2 = (- 3/2) (5) + b
 2 = (- 15/2) + b
 2 + 15/2 = b
 19/2

 Step 4:
 The parallel line is:
 y = (- 3/2) x + 19/2

Costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $88 and a standard deviation of $24. what is the probability that one bill for veterinary services costs between $42 and $133?

Answers

 the probability that one bill for veterinary services costs between $42 and $133 will be given as follows
P(42<x<133) 
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
thus
when x=42:
z=(42-88)/24=-1.92
thus
P(x<42)=0.0281

when x=133
x=(133-88)/24=1.875
thus
P(x<133)=0.9699
Thus
P(42<x<133) 
=0.9699-0.0281
=0.9418

Answer: 0.9418
Final answer:

There is a 94.25% probability that a bill for veterinary services costs between $42 and $133 in this local animal hospital, based on calculating Z-scores for $42 and $133 and finding the difference between probabilities.

Explanation:

The question pertains to the concepts of statistics, specifically the normal distribution which often appear in situations describing natural phenomena and social behavior. To solve this, we need to calculate the Z-scores for both values given and then look those Z-scores up in a standard normal distribution table, or use a calculator or software that can do this.

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It's measured in terms of standard deviations from the mean.

If X is a random variable from a normal distribution with mean (µ) and standard deviation (σ), the Z-score is calculated by the formula Z = (X - µ)/σ.

For X =$42, Z1 = ($42 - $88)/$24 = -1.92 and for X=$133, Z2=($133-$88)/$24 = 1.88.

The probability that one bill for veterinary services costs between $42 and $133 equals the probability for Z values falling between -1.92 and 1.88. Refer to the standard normal distribution table or a calculator for the corresponding probabilities. The probability for Z1 equals approximately 0.0274, probability for Z2 equals approximately 0.9699. The required probability is then P(Z1

So, "there's a 94.25% chance that a bill for veterinary services costs between $42 and $133 in this local animal hospital".

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4.
Find the present value of the annuity.

Amount Per Payment: $4,725

Payment at End of Each: 6 months

Number of Years: 15

Interest Rate: 10%

Compounded: Semiannually


$72,634.83

$35,938.73

$32,242.03

$68,951.03

Answers

To solve this we are going to use the present value of annuity formula: [tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ][/tex]
where
[tex]PV[/tex] is the present value 
[tex]P[/tex] is the periodic payment 
[tex]r[/tex] is the interest rate in decimal form 
[tex]n[/tex] is the number of times the interest is compounded per year 
[tex]k[/tex] is the number of payments per year 
[tex]t[/tex] is the number of years 

We know from our problem that [tex]P=4725[/tex] and [tex]t=15[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the interest is compounded semiannually, it is compounded 2 times per year; therefore, [tex]n=2[/tex]. Similarly, since the payment is made at the end of each 6 months, it is made 2 times per year; therefore, [tex]k=2[/tex].
Lest replace the values in our formula:

[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{-kt} }{ \frac{r}{n} } ][/tex]
[tex]PV=4725[ \frac{1-(1+ \frac{0.1}{2})^{-(2)(15)} }{ \frac{0.1}{2} } ][/tex]
[tex]PV=72634.83[/tex]

We can conclude that the correct answer is $72,634.83

hey can you please help me posted picture of question

Answers

The correct answer  for the problem shown in the figure atttached is the last option (option D), which is shown below:

 D. (-3x+6i)(x+2i)
 It is impotant to know that if you want to verify that the option D. (-3x+6i)(x+2i) is the correct answer, you can apply the distributive property to (-3x+6i)(x+2i). 
 Therefore, when you apply the distributive property, you obtain that the result is:
 -3x²-12

 Which is correct

 Therefore, you can be sure that the correct answer is the option D. (-3x+6i)(x+2i).

2.
Find the amount of the annuity.

Amount of Each Deposit: $295

Deposited: Quarterly

Rate per Year: 10%

Number of Years: 6

Type of Annuity: Due


$9,671.28

$9,542.97

$10,076.54

$9,781.54

Answers

To solve this we are going to use the future value of annuity due formula: [tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
where
[tex]FV[/tex] is the future value [tex]P[/tex] is the periodic payment [tex]r[/tex] is the interest rate in decimal form [tex]n[/tex] is the number of times the interest is compounded per year [tex]k[/tex] is the number of payments per year [tex]t[/tex] is the number of years

We know for our problem that [tex]P=295[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
[tex]r= \frac{10}{100} [/tex]
[tex]r=0.1[/tex]
Since the payment is made quarterly, it is made 4 times per year; therefore, [tex]k=4[/tex].
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so [tex]n=4[/tex].
Lets replace those values in our formula:

[tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
[tex]FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ] [/tex]
[tex]FV=9781.54[/tex]

We can conclude that the amount of the annuity after 10 years is $9,781.54

what are the common factors of 24 and 48

Answers

The common factors of 24 and 48 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factors are the numbers that can be multiplied with another number, to equal the product stated. Common factors are the factors that both stated products have.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Finding all the shared factors, will give you a final answer of 1, 2, 3, 4, 6, 8, 12, and 24.

I hope this helps!

A line intersects the points (6, -12) and (15, -3). What is the slope intercept equation for this line?
y = 1x - [?]

Answers

Let's say that the unknown value here is c. Although we are given two points on the line, it is only necessary to use one as there is only one unknown value, so let's say we choose the point (6, -12) and substitute this into the equation:

-12 = 1(6) - c
-12 - 6 = -c
-18 = -c
c = 18

Thus the equation for the line is y = 1x - 18

If r = -6, s = -2, v = 10, and w = 3; then vs(r - s) ÷ 2 + rw =

Answers

vs(r - s) ÷ 2 + rw =

= (10)(-2)[-6 - (-2)] ÷ 2 + (-6)(3)

= -20(-4) ÷ 2 -18

= 80 ÷ 2 - 18

= 40 - 18

= 22

Write an expression that represents the difference of 32 and N multiplied by 10

Answers

(32-n)10________________
So, we first find the difference:
32-n
we multiply it by 10:
10(32-n)
If you want it to be distributed:
320 - 10n

Determine whether quantities vary directly or inversely and find the constant of variation.
A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

Answers

Divide 25/4 to figure out how many essays the teacher grades in 1 hour.

The time take him to grade 35 essays is, 5.6 hours.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A teacher grades 25 students essays in 4 hours.

And, To find the time take him to grade 35 essays.

Now, Let us assume that,

Time take him to grade 35 essays is, x

Hence, We get;

25 / 4 = 35 / x

Solve for x;

x = 35 × 4 / 25

x = 5.6 hours

Thus, the time take him to grade 35 essays is, 5.6 hours.

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Question part points submissions used use the gram-schmidt process to find an orthogonal basis for the column space of the matrix. (use the gram-schmidt process found here to calculate your answer. let xi be the ith column of the matrix.) 0 1 1 1 0 1 1 1 0

Answers

Assuming your unformatted string of numbers at the end is a 3x3 matrix, {(0, 1, 1), (2, - 1, 1), (1, 1, - 1)} is an orthogonal basis for its column space.

Solve by using the quadratic formula. 9x2 + 24x + 32 = 0

Answers

The quadratic formula is:

[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]

b =coefficient of x term = 24
a = coefficient of squared term = 9
c = constant term = 32

Using the values, we get:

[tex]x= \frac{-24+- \sqrt{576-4(9)(32)} }{2(9)} \\ \\ x= \frac{-24+- \sqrt{-576} }{18} \\ \\ x= \frac{-24+-24i}{18} \\ \\ x= \frac{-4+-4i}{3} \\ \\ x= \frac{-4+4i}{3}, x \frac{-4-4i}{2} [/tex]


The first step for solving this equation is to multiply the first two numbers together.
18 + 24x + 32 = 0
Add together 18 and 32.
50 + 24x = 0
Now move the constant to the right side of the equation and change its sign.
24x = -50
Lastly,, divide both sides of the equation by 24.
x = [tex]- \frac{25}{12} [/tex]
This means that the correct answer to your question is going to be x = [tex]- \frac{25}{12} [/tex] or x = [tex]-2 \frac{1}{12} [/tex] simplified.
Let me know if you have any further questions.
:)

If rain is falling at a rate of ¼ inch per hour, how much rain would you expect after 6 hours

Answers

1 hour = 1/4 inch 

6 hours = 1/4 x 6 = 6/4 = 1 1/2 inches

Answer: 1 1/2 inches
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