Mathematics College

solving radical equations
check for extraneous solutions
[tex] \sqrt{2x + 30} = x + 3[/tex]

Answers

Answer 1
I don’t know this question
Answer 2
[tex]\bf \sqrt{2x+30}=x+3\impliedby \textit{we'll squares both sides} \\\\\\ (\sqrt{2x+30})^2=(x+3)^2\implies 2x+30=x^2+6x+9 \\\\\\ 0=x^2+4x-21\implies 0=(x+7)(x-3)\implies x= \begin{cases} -7\\ 3 \end{cases}[/tex]

I don't see  an extraneous value there, -7 checks out well if you plug it in the original equation, and so does 3.

Related Questions

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week. ©

Answers

Answer:

2.28%

Step-by-step explanation:

Let X be the  number of books borrowed from a library each week

Given that X is normal with mean = 190 and std dev = 30

Thus Z score would be

Z=[tex]\frac{x-190}{30}[/tex]

Required probability or chance = P(X>250)

=P([tex]z>\frac{250-190}{30}[/tex]

=P(Z>2)

=0.5-0.4772

=0.0228

=2.28%

Answer:

2.5 for plato

Step-by-step explanation:

#platolivesmatter

When changes in one variable are usually accompanied by changes in the same direction in another variable?

Answers

when change in one variable is accompanied by the change of another variable in the same direction, they are directly proportional to each other, and it is usually represented by the general equation, y = kx where k is a constant.

The goal of an optimization problem is to find the maximum or minimum value of the

Answers

to complete your statement: function. optimization is a very useful tool in calculus to calculate extremi of functions

An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.

The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.

Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.

What happens to the force of gravity between two maser if they are moved father apart A. It increases. B. It decreases. C. It stays the same D. It fluctuates. ( Question two ) Earths path around the sun is ____. A elliptical. B circular. C . random. D. Triangular. (Question three). The asteroid belt separates what ? A. Sun and stars B. Earth in moon C. Inner and outer planets D. Milky Way from other galaxies ( Questikn four ) the tilt of the earth its axis causes ____. A. Day in night. B. The seasons. C. A year D. A month umm it right will mark brilliant

Answers

It decreases. Elliptical. Maybe c for the third question.
B. The seasons.

can someone help me with number 4

Answers

Let m = the number of member tickets.
Let n = number of nonmember tickets.
Let c = total cost

m number of member tickets cost 10m.
n number of nonmember tickets cost 24n.

The total cost is the sum of the two expressions.

c = 10m + 24n

Now we replace m w2 and n with 4, and we evaluate the expression.

c = 10m + 24n

c = 10(2) + 24(4)

c = 20 + 96

c = 116

Answer: The total cost is $116

Mr. lee drove his car 297.6 miles while using 16 gallons of gas . How many miles does he get to the gallon ?

Answers

18.6 mpg is the answer. hope it helped

Select two rations that are equivalent to 3: 12.

Answers

1 over 4 and 2 over 8. I just multiplied both sides of the ration to get this answer.

Brody calculated the area of a square to be16/36 square foot. Which shows the side length of the square?

Answers

s^2 = 16/36 ft^2
s = √(16/36 ft^2) = 4/6 ft

The side length of the square is 2/3 ft, or 8 inches.

bob started mowing at 9:55 am .It took him 25 minutes to mow the front yard and 45 minutes to mow back yard.at what did bob finish mowing?

Answers

Knowing that an hour has 60 minutes, add 25 minutes to 9:55 to get 10:20. Another way to think of this is by adding 25 to 55 to the base of 60. Assuming that he only had to mow the front and back yard, add 45 minutes to 10:20 to get your final answer.
The final answer should be: 11:05 am.
11:05 is the correct answer

A farmer wants to build a rectangular garden 10ft long and 6ft wide. How many feet of fencing should he buy?

Answers

He should buy 32 feet of fencing. I got 32 by just finding the perimeter or in other words adding 10+10+6+6 which equal 32. You would NOT do area or 10×6 because that would include that land within the fenced area and who wants 60 feet of fencing that you can't put anything in?

Good luck, hope that helped.

The enrollment in college a may be modeled by y = 0.051x + 0.470, and the enrollment in college b may be modeled by y = –0.041x + 1.850, where x is the number of years since 1990 and y is the enrollment in thousands. when will the two colleges have the same enrollment and what is that enrollment?

Answers

The first equation represents the enrollments of college A
The second equation represents the enrollments of college B
if you let two equation equal to each other, you can understand them as the enrollments of college A and college B at "x" year.

0.051x + 0.470 = -0.041x + 1.850
0.051x + 0.041x = 1.850 - 0.470
0.092x = 1.38
x = 1.38/0.092 = 15 years from 1990, 1990 + 15 = 2005 
both equations represents the enrollments, but for specific the year of 2005, they have the same enrollments. You can either plug 2005 in the first or second equation, the answer will come out the same.
y = 0.051(2005) + 0.470 = 102.745 thousands of enrollments. It's awkward to say it this way, you can multiply 102.745 by 1000.
==> 102.725 * 1000 = 102725 enrollements 
===================================================================
The year of 2005 college A and college B both have the same enrollments of 102725.  

In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.

What is Two Variable linear Equation?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Here, given relation between enrollment year and total number of enrollment

y = 0.051x + 0.470 ..............(i)

y = -0.041x + 1.850 ................(ii)

On comapring eq. (i) and eq. (ii), we get

0.051x + 0.470 = -0.041x + 1.850

0.051x + 0.041x = 1.850 - 0.470

0.092x = 1.380

x = 1.380 / 0.092

x = 15

put the value of x in equation (i), we get

y = 1235

Thus, In year 2005, both the colleges have same enrollments and the total number of enrollments are 1235 students.

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Pietro buys 20 candy bars for $6 he plans to sell all 20 candy bars in 1 day he need to make a profit of $10 per day to meet his fundraising goal how much must he charge for each candy bar?

Answers

He would have to charge 80 cents per candy bar!

what is the x intercept of the equation that passes through (1,-6) and is perpendicular to y=1/3x +1

Answers

[tex]\bf y=\stackrel{slope}{\cfrac{1}{3}}x+1\impliedby \textit{slope of this line, so a perpendicular will be} \\\\\\ \textit{perpendicular, negative-reciprocal slope for}\quad \cfrac{1}{3}\\\\ negative\implies -\cfrac{1}{ 3}\qquad reciprocal\implies - \cfrac{ 3}{1}\implies -3\\\\ -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~1 &,& -6~) \end{array}[/tex]

[tex]\bf slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-6)=-3(x-1) \\\\\\ y+6=-3x+3\implies 0+6=-3x+3\implies 3=-3x\implies \cfrac{3}{-3}=x \\\\\\ -1=x\qquad \qquad \qquad \qquad \qquad \qquad \qquad (~-1~,~0~)[/tex]

The sales tax in mike's state is 6%. mike bought a jetta having a sales tax of $820. what was the cost of the vehicle? round to the nearest dollar.

Answers

$13, 666.67
because you would do 820 divided by 0.06 and you get 13,666.6667 which you round to 13,666.67

"If you share 7 apples equally with 3 people, then there are 2 1/3

Answers

APPLES TO EACH PERSON (if that was a fill in the blank)

Answer:

Part A

"If you share 7 apples equally with 3 people, then there are  

2  1/ 3  ..."

First, complete the sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem.

Step-by-step explanation:

here is the full question just say answer by commenting

Which expression is an equivalent expression of 12x + 10 + 4y? 2(6x + 2y + 6) 3(4x + y + 10) 2(6x + 4y + 8) 2(6x + 5 + 2y)

Answers

12x + 10 + 4y is equivalent to
2(6x + 5 + 2y).

This is because
2(6x + 5 + 2y) =
2 * 6x + 2 * 5 + 2 * 2y =
12x + 10 + 4y
12x + 10 + 4y= 2(6x + 5 + 2y)

Multiply it out
=2(6x + 5 + 2y)
distribute 2 to every term in parentheses
=(2*6x) + (2*5) + (2*2y)
=12x + 10 + 4y

ANSWER: Last choice 2(6x + 5 + 2y)

Hope this helps! :)

Form a seven-letter word by mixing up the letters in the word FIXTURE.
How many ways can you do this if no vowel is isolated between two consonants?

Answers

There are 4 consonants and 3 vowels. If the vowels can't be isolated between two consonants then the vowels would have to be right next to each other. Let's consider the vowels as a group so that they can be arranged in 3!=6 ways and the consonants 4!=24 ways. So:
6x24=144ways

You have the main rule: no vowel is isolated between two consonants.

The word FIXTURE consists of 4 consonants and 3 vowels.

There are such possible cases:

1. Formed word begins with three vowels and ends with 4 consonants.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

2.  Formed word begins with two vowels and ends with one vowel (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).

The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]

4. Formed word begins with with 4 consonants and ends with 3 vowels.

The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]

5. In total 144+144+144+144=576 different words.

someone help me on this question please

Answers

The proportion
  peanuts : raisins : chocolate chips = 4 : 6 : 2
tells you that peanuts make up
  4/(4+6+2) = 1/3
of the total quantity of the mix.

The quantity of peanuts required is (1/3)*(48 ounces) = 16 ounces (or 1 pound).

_____
In the 48 ounces of mix, 1 part = 4 ounces.

the dimensions of a porch are 16 feet long by 12 feet wide use the scale 1 inch=4 feet what is the width and length in inches

Answers

Hi there!

Since the scale is 1 in = 4 ft, we divide both the length and width by 4 to get the new length and width with the scale factor applied. 

16 / 4 = 4
12 / 4 = 3

So, the
length = 4
width = 3

Hope this helps!


Find the value of x. The diagram is not to scale.

A. x=70
B. None of these
C. x=20
D. x=16

Answers

My best guess would be B. None of these
For this case, the first thing to do is to observe that we are in the presence of an isosceles triangle.
 We then have two equal sides:
 RS = ST
 Thus,
 Angle R = Angle T
 Then, we have the following equation:
 5x = 180- (5x-20)
 From here, we clear the value of x:
 5x = -5x + 180 + 20
 10x = 200
 x = 200/10
 x = 20
 Answer:
 the value of x is: 
 C. x = 20

Solve the inequality and graph its solution: 2t + 1 > 9 or –18 > 5t – 3

Answers

Final answer:

To solve the inequality and graph its solution, solve the two separate inequalities: 2t + 1 > 9 and -18 > 5t - 3. The solution is t > 4 or t < -3.6. Graph the solution by plotting the points 4 and -3.6 on a number line, and shading the area to the right of 4 and the left of -3.6.

Explanation:

To solve the inequality and graph its solution, we need to solve the two separate inequalities:

1) 2t + 1 > 9

2) -18 > 5t - 3

For the first inequality, we can subtract 1 from both sides and divide by 2 to obtain t > 4.

For the second inequality, we can add 3 to both sides and divide by 5 to obtain t < -3.6.

Thus, the solution to the original inequality is t > 4 or t < -3.6.

To graph the solution, we would plot the points 4 and -3.6 on a number line, and shade the area to the right of 4 and the left of -3.6.

Final answer:

To solve the inequalities 2t + 1 > 9 and –18 > 5t – 3, we must solve each separately, and since it's an 'or' inequality, we combine the solution sets. The solutions are t > 4 and t < -3. Graphically, these solutions represent non-overlapping shaded regions on a number line.

Explanation:

To solve the inequality 2t + 1 > 9 or –18 > 5t – 3, we need to consider them separately as each inequality represents a different solution set.

For the first inequality:

Subtract 1 from both sides to obtain 2t > 8.Divide by 2 to isolate t, yielding t > 4.

For the second inequality:

Add 3 to both sides to get –15 > 5t.Divide by 5, which flips the inequality because we are dividing by a positive number, resulting in t < –3.

We interpret these results as two separate conditions:

t > 4: This suggests that t is any value greater than 4.t < –3: This suggests that t is any value less than -3.

Since the original statement uses 'or', the solution set includes all the values that satisfy either inequality. Therefore, graphically, we would show these on a number line with a shaded region to the right of 4 and another shaded region to the left of -3. The areas do not overlap because there are no t values that can simultaneously be greater than 4 and less than -3.

The gift shop at Manatee mall was having a clearance sale everything was marked down 30% off the original price of a manatee that was $18 what is the clearance price

Answers

The manatee is 12.60$ for the clearance price. 

Derive the equation of the parabola with the focus
is (-7,5) and the directrix of y=-11

Answers

so, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \boxed{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=-7\\ k=-3\\ p=8 \end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2 \\\\\\ 32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2 \\\\\\ y=\cfrac{1}{32}(x+7)^2-3[/tex]

Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take rich and Michelle to meet?

Answers

Answer:

  2 7/27 hours, about 2 hours 15 minutes, 33 seconds

Step-by-step explanation:

You want to know how long it takes for Rich and Michelle to meet if they start 305 miles apart and are driving toward each other. Rich is driving 70 mph, and Michelle is driving 65 mph.

Closing speed

The speed at which they are moving toward each other is ...

  70 mph + 65 mph = 135 mph

Meeting time

That means they will reduce their separation distance to zero after ...

  time = distance / speed

  time = (305 mi)/(135 mi/h) = 2 7/27 h

It will take 2 7/27 hours, about 2.26 hours, for Rich and Michelle to meet.

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Find the equation of the line that has these features: slope, m=-6/5 passes through the point (-5,10)

Answers

we know that

the equation of the line is 
y-y1=m(x-x1)
then
m=-6/5 passes through the point (-5,10)
y-10=(-6/5)*(x+5)-------> y-10=(-6x/5)-6------------> y=(-6x/5)+4---------> y=-1.2x+4

see the attached figure

the answer is
y=-1.2x+4

Fawn plants 2/3 of the garden with vegetables. Her son plants the remainder of the garden. He decides to use 1/2 of his space to plant flowers and in the rest he plants herbs. What fraction of the entire garden is planted in flowers?

Answers

1/6th because he used half of a whole part. You just multiply the fraction by 2 and count how many parts are flowers in the whole garden afterward :) 

Drawing it out helps too! Good luck!

Find the equation of the tangent plane to the surface z=e−x/17ln(y) at the point (3,3,0.920883)

Answers

i dont know i will tell you when i find out

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price.

a stereo with a cash price of $1,200 at $119.00 per month for 12 months

Answers

Answer:

(a) $1428

(b) $228

(c) 11 months

Step-by-step explanation:

(a) Total installment price = 119 × 12 = $ 1428

(b) The carrying charges = amount paid - cash price

                                   = 1428 - 1200 = $ 228

(c) No. of needed to save the money = 1200 ÷ 119 = 10.08 ≈ 11 months


Answer:    A=1428.00

                 B=228.00

                 C=11

A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm

Answers

Try this option:

[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]

answer: B

B)    3 cm

Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]

Vcone =

1

3

πr2h

36π =

1

3

π(6)2h

36π = 12πh

h = 3

Thus, the height is 3 cm.

Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.

Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?

Answers

3.30*1.2=3.96
$3.96 will be the new price of gas

The price of the gas is $3.96.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Gas prices in Cook-County are at $3.30 per gallon.

If a market scientist predicts a 20% increase in the price of gas in the coming month,

that means,

100 + 20% = 120% increase = 1.2 in decimals.

The price of gas,

= 3.30 + 3.30 x 1.2

= 3.96

Therefore, the new price is $3.96.

To learn more about the percentage;

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