Mathematics College

x = 2, y = -1
14
2. x = 0, y = 2.5
1.665
3. x = -1, y = -3
0.44
4. x = 0.5, y =
9.17
5. x = , y =
-1
6. x = √2, y = √2
-11.25

Answers

Answer 1

Answer:

b

Step-by-step explanation:

Related Questions

Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?

Answers

Let f=amount invested at 4% and e=amount invested at 8%

0.04f+.08e=800

However, e=2f so the above equation becomes:

0.04f+0.08(2f)=800

0.04f+0.16f=800

0.2f=800

f=$4000, since e=2f

e=$8000

So Susan invested $4000 at 4% and $8000 at 8%.

Final answer:

To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.

Explanation:

Susan has invested $x at 4% interest rate and $2x at 8% interest rate.

Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.

Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.

If p is a positive integer,then p(p+1)(p-1) is always divisible by?

Answers

I am not quite sure what the choices are, but the answer to that problem is:

If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.

The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.

For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.

And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.

Answer: From the choices, select the even number

Final answer:

If p is a positive integer, p(p+1)(p-1) is always divisible by 3.

Explanation:

If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.

This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.

If f(x)=2x^2sqrt(x-2), complete the following statement f(6)

Answers

f(x) = 2x^2 + 5sqrt (x - 2)....when x = 6
f(6) = 2(6^2) + 5 sqrt (6 - 2)
f(6) = 2(36) + 5 sqrt 4
f(6) = 72 + 5 * 2
f(6) = 72 + 10
f(6) = 82

The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]  is 82

How to determine the function value?

The function is given as:

[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]

Substitute 6 for x

[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]

Evaluate the difference

[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]

Evaluate the exponents

f(6)=2 * 36 + 5 * 2

Evaluate the sum of products

f(6) = 82

Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]  is 82

Read more about functions at:

https://brainly.com/question/13136492

#SPJ2

The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8

Answers

Since x and y are inversely proportional:

xy = c, where c is a constant

when y = 40 and x = 5 -> c = 40*5 = 200

So xy = 200

Then, when x = 8, y = 200/8 = 25

Answer: 64

Step-by-step explanation:

i put it into math-way

In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?

Answers

1 lb = 16 oz

5.92 / 16 = 0.37 per oz.....37 cents per oz

Answer:

$,37 dollars per ounce of strawberries

Step-by-step explanation:

We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:

5,92/16= ,37

SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.

When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75

Answers

The books were bought for $40 - $7 - $3.25 = $29.75

$29.75 divided by 5 books is $5.95, answer A.
40 - 5b - 3.25 = 7
36.75 - 5b = 7
-5b = 7 - 36.75
-5b = - 29.75
b = -29.75 / -5
b = 5.95 <=== 5.95 per book

PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2

Answers

[tex]y= ax^{2} -8x-3[/tex]

1.

the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.

the point x=2 is the midpoint of the roots [tex]x_1[/tex] and [tex]x_2[/tex]. 

so 
[tex] \frac{x_1+x_2}{2}=2 [/tex]
[tex]x_1+x_2=4[/tex]

Remark: in the x-axis, if c is the midpoint of a and b, then [tex]c= \frac{a+b}{2} [/tex]


2.
since [tex]x_1[/tex] and [tex]x_2[/tex] are roots 

[tex]a(x_1)^{2} -8(x_1)-3=0[/tex] and [tex]a(x_2)^{2} -8(x_2)-3=0[/tex]

3.
equalizing:

[tex]a(x_1)^{2} -8(x_1)-3=a(x_2)^{2} -8(x_2)-3[/tex]

[tex]a(x_1)^{2} -8(x_1)=a(x_2)^{2} -8(x_2)[/tex]

[tex]a(x_1)^{2}-a(x_2)^{2} =8(x_1) -8(x_2)[/tex]

in the left side factorize a, in the left side factorize 8:

[tex]a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)[/tex]

in the right side use the difference of squares formula:

[tex]a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)[/tex]

simplify by [tex](x_1 -x_2)[/tex]

[tex]a(x_1 +x_2) =8[/tex]

substitute [tex](x_1 +x_2)[/tex] with 4:

[tex]a*4 =8[/tex]

a=2


Answer: C)2

Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)

Answers

1 kg = 2.25 pounds

5*2.25 = 11.25 pounds

11.25/5 = 2.25 bags

 so you would need 3 bags

1 kg = 2.25 lbs....so 5 kg = (5 * 2.25) = 11.25 lbs

at 5 lbs per bag.....2 full bags + 1.25 lbs in the other bag...so it would be 3 bags with 1 bag partially full or 2 bags, leaving out 1.25 lbs

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.

Which equation can be used to solve for x, the increase in side length of the square in inches?

x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0

Answers

Let x be the "enlargement value" of each side :
 Then the enlarged side becomes (x+4) and the square = (x+4)²
The final area should be (x+4)² = 81
Let's expand:
x²+ 8x + 16 = 81
x² + 8x + 16 - 81 = 0
x² + 8x - 65 = 0

Answer:

[tex]x^2+8x-65=0[/tex]

Step-by-step explanation:

Side length of square = 4 inches

Let x be the increase in length

So, New length = x+4

Area of square = [tex]Side^2[/tex]

Area of enlarged square = [tex](x+4)^2[/tex]

Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]

Area of enlarged square = [tex]x^2+16+8x[/tex]

We are given that The final area needs to be 81 square inches.

So,  [tex]x^2+16+8x=81[/tex]

[tex]x^2+16+8x-81=0[/tex]

[tex]x^2+8x-65=0[/tex]

So, Option C is true

Hence  equation can be used to solve for x, the increase in side length of the square in inches is  [tex]x^2+8x-65=0[/tex]

The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?

Answers

In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:

t = (x – u) / s

where,

x = the sample score = 60

u = sample score mean = 82

s = standard deviation = 11

Substituting all given values into the equation:

t = (60 – 82) / 11

t = - 2

 

Based from the standard proportion distribution tables for z, this corresponds to:

P = 0.0228

This means that 2.28% of the students failed the exam or equivalent to:

failed students = (0.0228) * 85 = 1.938

approximately 2 students failed the exam

Answer:

2 students failed the exam

Step-by-step explanation:


If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?

Answers

Reflection in the y-axis.
g(x) = f(-x); -x has been substituted in for x.

Poisson suppose you have 5 cakes made ready to sell. what is the probability that you will sell out?

Answers

From question given, the selling of the cake is assumed to be a Poisson process.

Assume further that the mean number of cakes sold per day is lambda.

Let k=5 = number of cakes sold during the day, then the Poisson pmf (probability mass distribution) is given by
P(k)=lambda^k*e^(-lambda)/k!
or
P(5)=lambda^5*e^(-lambda)/5!
=lambda^5*e^(-lambda)/120

If the average number of cakes sold is 4 per day, then
P(5)=4^5*e^(-4)/120
=0.156 is the probability of selling exactly 5 cakes.

The probability of selling 5 cakes or more (i.e. the sixth and subsequent customers will be told to come back the next day) is then
P(k>=5)=1-(P(k=0)+P(k=1)+P(k=2)+P(k=3)+P(k=4)
=1-(0.018316+0.073263+0.146525+0.195367+0.195367)
=0.371163
(for  mean number of cakes sold per day = 4 )

Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?

Answers

check the picture. 

line l is the orange line, intersecting the positive x-axis and the positive y axis. 

The angle with measure ∅ is the angle made by the line and the positive x-axis. It is the obtuse (>90° angle) shown in the picture.

the slope of the line l is tan∅


A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?

Answers

if both crews work together, let's say the finish the job in "t" hours.

so.. in 1 hour, they have done 1/t of the whole work.

now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.

the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.

now, let's add their rates for 1 hour worth, to see what we get.

[tex]\bf \begin{array}{clclcllll} \cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\ \uparrow &&\uparrow &&\uparrow &&\\ new\ crew&&experienced&&total\\ rate/hr&&rate/hr&&work/hr \end{array}\\\\ -------------------------------\\\\ \textit{let's multiply both sides by \underline{12t}, to toss away the denominators} \\\\\\ t+2t=12[/tex]

and pretty sure you know how much that is.

The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898

Answers

Final answer:

The probability that the mean leg length is less than 20 cm is practically 0.

Explanation:

To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.

We can standardize the sample mean using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample size

Substituting the given values:

z = (20 - 43.7) / (4.2 / sqrt(9))

z = -23.7 / (4.2 / 3)

z = -23.7 / 1.4

z ≈ -16.93

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.

The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?

Answers

8.03 oz at the start- 5.26 oz eaten= 2.77 oz left

Final answer: 2.77 oz

What is the next number in the series? 71 62 53 44 35 ?

Answers

This is an arithmetic sequence with a common difference of -9, so the next term will be 35-9=26.
If you examine your sequence closely, you can notice that the number in the tens place is decreasing by 1 as the number in the ones place is increasing by 1.
To further prove this;
71 --> 62.
-10 and + 1.
62 --> 53.
-10 and +1
and so on.

However, if that's a little too complicated, there's an alternate method.
All you have to do is subtract 9 from the current number.
To further prove this;
71 - 9 = 62
62 - 9 = 53
53 - 9 = 44
and so on.

So, let's subtract 9 from our most current number, 35.
35 - 9 = 26.

The upcoming number in your sequence is 26.

I hope this helps!

Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?

Answers

so he climbed the first 1000ft in 1000/x hours then

the rate of the 5000ft is "10 feet per hour less than twice the first rate", so hmm twice the first rate is 2x, 10 less than that is 2x - 10.

so, the 5000ft were climbed in 5000/(2x-10)

the number of hours it lasted climbing? well, simply add them up.

Answer: The expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

Step-by-step explanation:

Since we have given that

Distance covered by mountaineer = 1000 feet

Speed at which he climbed = x feet per hour

Time taken by him would be

[tex]\dfrac{1000}{x}[/tex]

Additional distance covered by him = 5000 feet

Speed at which he climbed this time = 2x-10

So, Time taken is given by

[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]

Hence, the expression that represents the number of hours the mountaineer climbed is given by

[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]

A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?

Answers

7.6 so i would say 7 medium and 1 small or 8 medium apples

Answer:

7

Step-by-step explanation:

53 ℃ below zero degrees

Answers

your answer is -53 degrees celsius

hope this helps

find the equation of a line containing the given point and slope (10,5); m=9/20

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 10}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{9}{20} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{9}{20}(x-10)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-5=\cfrac{9}{20}x-\cfrac{9}{2}\implies y=\cfrac{9}{20}x-\cfrac{9}{2}+5\implies y=\cfrac{9}{2}x+\cfrac{1}{2}[/tex]

How do you solve this

Answers

1. reduce the fraction and subtract the exponents

(5x^7y^2)/2

What is the answer to this question?

Answers

*Hint: The formula to solve this is SA = 2bs + b^2

Now that you know the formula, plug in and solve.

SA = 2(5)(8) + (5)^2
SA = 80 + 25
SA = 105

Now that you see that the question is asking for the answer in yards, you convert feet into yards.

3 feet = 1 yard.

105 is divided by 3 and you get 35.

The answer is 35 square yards.

What is the integral of 1/x?

Answers

The indefinite integral is usually written as ln(x) if x>0, as u can see it's undefined for x = 0.

Final answer:

The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.

Explanation:

The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:

[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]

The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.

Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056

Answers

5,600 ml................

If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).

Answers

Answer:  The required value is

[tex](f-g)(x)=x^2+8.[/tex]

Step-by-step explanation: The given functions are:

[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]

We are given to find the value of [tex](f-g)(x).[/tex]

We know that, if s(x) and t(x) are any two functions of a variable x, then we have

[tex](s-t)(x)=s(x)-t(x).[/tex]

Therefore, we have

[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]

Thus, the required value is

[tex](f-g)(x)=x^2+8.[/tex]

Answer:

3x2 - 6   its the answer

Please help quick !!

Answers

1) sin(60 degrees)=0.86602540378 (Make sure your calculator is in degrees, not radians)
√3/2
√3=1.73205080757
1.73205080757/2
=0.866025404
1) IS CORRECT
Solve the rest using the same technique.

Hope this helps! A thanks/brainliest answer would be appreciated :)

Explain why we need more than one digit to express certain quantities

Answers

We need more than one digit to express certain quantities in order to record more precise values. The significant figure of a measured quantity refers to all the digits known with certainty and the first estimated digit. This will usually differ depending on the quality that is been measured.

Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°

Answers

Given |u| = 1 and a = 45, you can determine the component form of u.
[tex]u = \ \textless \ cos(45),sin(45)\ \textgreater \ [/tex]

In same way you can find component form of u+v
[tex]u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater \ [/tex]

By property of vector subtraction:
v = (u+v) - u

[tex]v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater \ [/tex]
[tex]v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater \ [/tex]

At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?

Answers

let's say in 2006, year 0, there were "I" amount of customers, and we dunno what "I" is.

now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]
Other Questions
The video says, If you cant study fish in the sea, set up an aquarium. Essentially, when you cant conduct a study in the real world, build a model. What are some of the benefits and drawbacks of this idea? what are the domain and range of the following functions? write your answer using inequality symbols if possible Julio has started his very own floral business. He sells centerpieces for $19.50 each. His fixed costs are $500 per month, and each centerpiece cost $8 to produce. What is your break-even point? a. Julio must sell approximately 18 centerpieces to break even. b. Julio must sell approximately 23 centerpieces to break even. c. Julio must sell approximately 44 centerpieces to break even. d. Julio must sell approximately 55 centerpieces to break even. Help me with the first question What is the medical term for the ventral fold of tissue that attaches the foreskin to the glans? Which of the following is a characteristic of early civilizations?a)written languageb)nomadic lifestylec)social equalityd)system of schools If the following fraction is reduced, what will be the exponent on the p? -5p^5q^4/ 8p^2q^2A. 5B.4C.3D.2 The absolute value function g(x) = |x + 7| 4 is translated 5 units right and 2 units up to become g(x). The quadratic function f(x), graphed below, is also moved 5 units right and 2 units up to become f(x). Which of these two transformed functions has a range of y 2 and what is the vertex of this transformed function?g(x) has a range of y 2 and its vertex is at (2, 2).g(x) has a range of y 2 and its vertex is at (2, 2).f(x) has a range of y 2 and its vertex is at (3, 2).f(x) has a range of y 2 and its vertex is at (7, 6). Stiff muscles only result from overworking them. T/F Which sentence has correct pronoun-antecedent agreement?A.The citizens of San Francisco is proud of its wharf area.B.The women outside the store waited impatiently for it to open so she could get inside.C.I don't know if the firefighters who survived the tragedy will ever get over the loss of their fellow workers.D.Dan noticed that man in the trench coat slouched down in his seat, as though they were hoping to avoid being recognized. Why does an individual maintain a better state of health under health maintenance organizations? Which statement is true about Earth's poles? A.Geographic poles are defined by Earth's rotation. B.Magnetic poles are defined by Earth's rotation. C.Earth's geographic South Pole moves about 10 km each year. D.Earth's south magnetic pole is aligned with its geographic South Pole. Can someone help mee, pls show the works.. Thx If F(x)=8x, which of the following is the inverse of F(x) mothers of infants with failure to thrive have been found to be ____ than mothers of infants without failure to thrive. Para que sirve conocer el contexto historico en el que se desarrolla una obra In order for the data in the table to represent a linear function with a rate of change of 8, what must be the value of m?A. m = 2B. m = 3C. m = 19D. m = 35Which is the correct answer??? _____ encourage employees to behave in a socially responsible manner. When you connect to your isp's pop, the isp and the equipment at the pop go through a process called _________, establishing the speed of the internet connection, and then proceed to _________? A solution is prepared by dissolving 16.2 g of benzene (c6h6) in 282 g of carbon tetrachloride (ccl4). the concentration of benzene in this solution is ________ molal. the molar masses of c6h6 and ccl4 are 78.1 g/mol and 154 g/mol, respectively. Steam Workshop Downloader