Mathematics College

what is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)

Answers

Answer 1
[tex] \frac{x+5}{x+2} - \frac{x+1}{x^{2}+2x } = \frac{x^{2}+4x-1 }{ x^{2} +2x} [/tex]
Answer 2

Answer:

[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]        

Step-by-step explanation:

Given two expression, we have to find the difference of these two.

[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]

[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]

[tex]\text{Taking (x+2) common from the denominator }[/tex]

[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]

[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]

which is required difference.

Related Questions

The solid shown are composed of prisms and half cylinders. Find the volume of the solid. Round to the nearest whole number.

Answers

dis too hard for me, plz vote brainliest and give me ur paypal for free answers

hey can you please help me posted picture of question

Answers

Answer:
Diagram D

Explanation:
1- let's get the base function:
We are given that:
f(6) = 9
f(7) = 10
f(8) = 11
f(9) = 12
From these givens, we can note that the function can be represented as follows:
f(x) = x + 3

2- let's get the inverse:
To get the inverse of a function, we will simply swap the x and y variable
This can be done as follows:
f(x) = x + 3
y = x + 3
Now, we swap:
x = y + 3
x - 3 = y + 3 - 3
y = x - 3

3- let's now get the values for the given x:
f(6) = 6 - 3 = 3
f(7) = 7 - 3 = 4
f(8) = 8 - 3 = 5
f(9) = 9 - 3 = 6
f(10) = 10 - 3 = 7
f(11) = 11 - 3 = 8
f(12) = 12 - 3 = 9

Comparing the calculated values with the given diagrams, we can note that the correct diagram is D

Hope this helps :)

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to represent the first three terms, respectively.] The three number are __, __, and __

Answers

ooh, fun

geometric sequences can be represented as
[tex]a_n=a(r)^{n-1}[/tex]
so the first 3 terms are
[tex]a_1=a[/tex]
[tex]a_2=a(r)[/tex]
[tex]a_2=a(r)^2[/tex]

the sum is -7/10
[tex]\frac{-7}{10}=a+ar+ar^2[/tex]
and their product is -1/125
[tex]\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3[/tex]

from the 2nd equation we can take the cube root of both sides to get
[tex]\frac{-1}{5}=ar[/tex]
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
[tex]\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r[/tex]
subsituting -1/5 for ar
[tex]\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r[/tex]
which simplifies to
[tex]\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}[/tex]
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
so
for 2r²-5r+2=0
a=2
b=-5
c=2

[tex]r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}[/tex]
[tex]r=\frac{5 \pm \sqrt{25-16}}{4}[/tex]
[tex]r=\frac{5 \pm \sqrt{9}}{4}[/tex]
[tex]r=\frac{5 \pm 3}{4}[/tex]
so
[tex]r=\frac{5+3}{4}=\frac{8}{4}=2[/tex] or [tex]r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}[/tex]

use them to solve for the value of a
[tex]\frac{-1}{5}=ar[/tex]
[tex]\frac{-1}{5r}=a[/tex]
try for r=2 and 1/2
[tex] a=\frac{-1}{10}[/tex] or [tex]a=\frac{-2}{5}[/tex]


test each
for a=-1/10 and r=2
a+ar+ar²=[tex]\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}[/tex]
it works

for a=-2/5 and r=1/2
a+ar+ar²=[tex]\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}[/tex]
it works


both have the same terms but one is simplified

the 3 numbers are [tex]\frac{-2}{5}[/tex], [tex]\frac{-1}{5}[/tex], and [tex]\frac{-1}{10}[/tex]

Answer:

2r²-5r+2=0

a=2

b=-5

c=2

Step-by-step explanation:

   

need help to do this

Answers

A graphing calculator can help you visualize the function and its various behaviors.

6. The horizontal and vertical asymptotes are y=1, x=4, and there is a "hole" at x=-2. The appropriate choice is ...
  F. Oblique asymptote y = 0

8. The denominator has degree 2 more than the numerator, so the end behavior will tend toward 0 as x gets large. The appropriate choice is ...
  J. As x → ±∞, f(x) → 0

To date, Ty has cumulative earnings of $107,600. This week he is paid $3,000. What's the total amount of social security tax for this week? Assume a rate of 6.2% on $110,100 for social security and 1.45% for Medicare.

A. $186.00
B. $155.00
C. $180.00
D. $57.66

Answers

Final answer:

The total Social Security tax for Ty's earnings this week, given his total earnings are now $110,600, is $155.00. This calculation considers the Social Security tax rate of 6.2% up to the income threshold of $110,100. Thus, option B is correct.

Explanation:

The question involves calculating the Social Security tax for Ty's earnings this week. With cumulative earnings to date at $107,600 and an additional $3,000 this week, Ty's total earnings for the year are now $110,600.

Since the Social Security tax rate is 6.2% and applies only up to an income of $110,100, we will only apply the tax rate to the $110,100 threshold, not the full $110,600. The week's Social Security tax is then:

0.062 × $110,100 = $6,826.20 (for the entire year so far)

Since we only need to find out the tax for this week's earnings, we need to calculate the tax that was already paid on the first $107,600:

0.062 × $107,600 = $6,671.20

The additional Social Security tax for this week is the difference between the two:

$6,826.20 - $6,671.20 = $155.00

Therefore, the total Social Security tax for this week is $155.00, which corresponds to option B.

The total amount of Social Security tax for Ty this week is $155.00. Hence, the correct option is B.

To calculate the total amount of Social Security tax for Ty this week, we must apply the 6.2% rate to his weekly pay of $3,000. However, since his cumulative earnings to date are $107,600 and the Social Security tax applies only up to $110,100, we need to determine how much of his $3,000 weekly salary is subject to this tax.

To find this, we subtract his current earnings from the maximum amount that is subject to Social Security tax: $110,100 - $107,600 = $2,500. Only $2,500 of Ty's $3,000 salary is taxable for Social Security purposes since he has reached the threshold beyond which Social Security tax is not levied on additional income.

Therefore, this week's Social Security tax is 6.2% of $2,500, which equals $155.00. As the rate for Medicare does not cap, the full $3,000 is subject to the Medicare tax at a rate of 1.45%, leading to a Medicare tax amount of $43.50. However, as the question only asks for the Social Security tax, the answer is B. $155.00.

A particular model of walkie talkie can broadcast in a circular .the radius of the broadcast area is 10,000 feet. find the area of the circle to the nearest square foot use 3.14 for pi

Answers

A = pi * r * r 

A = 3.14 * 10000 * 10000 = 314000000 ft^2

If w = <3.5, -6> and z = <-1.5, -4>, what is the resulting vector for 2w − z?

Answers

We have the following vectors:
 w = <3.5, -6>
 z = <-1.5, -4>
 We want to find:
 2w - z
 Substituting we have:
 2w - z = 2 (<3.5, -6>) - (<-1.5, -4>)
 Rewriting we have:
 <7, -12> + <1.5, 4>
 Adding component to component:
 <(7 + 1.5), (-12 + 4)>
 <8.5, -8>
 Answer:
 The resulting vector is:
 <8.5, -8>

Answer:

C. <8.5, -8>

Step-by-step explanation:

for PLATO users

What is 8640minutes in days?(remember ,there are 60minutes in an hour and 24 in a day

Answers

[tex]8640min (\frac{1 hr}{60 min}) (\frac{1 day}{24 hr}) = 6 days[/tex]
There are 60 minutes in an hour. And 24 hours in a day. So logically if you have common math sense. Then you would multiply them together and get the total number of minutes in each day. Then you would divide 8640 (because it was minutes) by the number of minutes in the day and you would get you number which would be 6. Again I literally think that if you had common math sense you would just lowkey understand that. With all sarcasm involved 

Find the sum of these polynomials.

(x2 – x + 7) + (9x2 + 6) =

Answers

Hi there! The answer is B.

[tex]( x^{2} -x+7)+(9 x^{2} +6)[/tex]
First work out the parenthesis.

[tex] x^{2} -x+7+9 x^{2} +6[/tex]
Rearrange the expression.

[tex] x^{2} +9 x^{2} -x+7+6[/tex]
Now collect the terms.

[tex]10 x^{2} - x+13[/tex]
The answer is B.

~ Hope this helps you!

Answer:B

Step-by-step explanation:

What proportion is more than 2.0 standard deviations from the mean?

Answers

the emeperical rule or 68-95-99.7% rule gives the approximate percentage of the data that fall within or standard deviation (68%) two standard deviations (95%) and three standard deviations (99.7%) of the mean. this rule should be applied only when the data is approximately normal. 

Final answer:

The proportion of data more than 2.0 standard deviations away from the mean in a normal distribution is less than 5%, consisting of 2.5% in the upper tail and 2.5% in the lower tail.

Explanation:

The proportion of values more than 2.0 standard deviations from the mean in a normal distribution is less than 5% because according to the empirical rule, 95% of the data falls within 2 standard deviations of the mean. Therefore, if you are looking at a normal distribution and you want to know the proportion of data that lies beyond 2 standard deviations from the mean, you would subtract 95% from 100%, which is 5%. This is then split between both tails of the distribution, so you have 2.5% in the upper tail and 2.5% in the lower tail, for a total of 5% more than 2 standard deviations away from the mean.

Consider the following grsph of a quadratic function.

Answers

y=a(x+4)(x+2)
[tex]y=\frac{7}{8}\left(x+4\right)\left(x+2\right)[/tex]

look at clock blair arrived a the bus stop at 45 minutes ago what time did blaire arive at the bus stop?

Answers

she arrived at 1:30 p.m

you and your friend are both knitting scarves for charity . you knit 8 rows each minute and have already knitted 10 rows . your friend knits 5 rows each minute and has already knitted 19 rows . when will you both have knitted the same amount of rows ?

Answers

To find when you both would have knitted the same amount of rows, you will list the multiples of the numbers 5 and 8.  The reason is that you knit this many each minute.

5, 10, 15, 20, 25, 30, 35, 40 (after 8 minutes)
8, 16, 24, 32, 40 (after 5 minutes)

You and your friend will knit the same number of rows after 8 minutes for you and 5 minutes for your friend.

After 3 minutes you both have knitted the same amount of rows.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, You knit 8 rows each minute and have already knitted 10 rows.

Your friend knits 5 rows each minute and has already knitted 19 rows.

Assuming t is the time when will you both have knitted the same amount of rows,

8t + 10 = 5t + 19.

8t - 5t = 19 - 10.

3t = 9.

t = 3 minutes.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

# 12 Q please find the volume

Answers

The answer is 1256.0 cm^3
The can of soup is a cylinder.
To find the area of a cylinder, the formula is [tex] \pi [/tex] x r^2 x h
Plug in the given into the formula.

The answer  to your question would be 1256.0 cm^3


The can of soup is a cylinder.
Area of cylinder = the formula is  x r^2 x h

Substitute all the given and it will give you the answer of 1256.0 cm^3.

The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. she performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650. the calculated value of the z test statistic is a positive number that leads to a p-value of 0.080 for the test. 22 referring to scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. what would be the p-value of this one-tail test? 0.040 0.960 0.840 0.160

Answers

Hello. 

Since the calculated p-value for a two-tailed test is 0.080, the p-value of a one-tailed test is half of it, which is 0.040.

Remember that the p-value is the area of the rejection region under the normal curve. The p-value of a two-tailed test will double the p-value of a single-tailed test considering all parameters to be the same. 

Final answer:

The p-value for the one-tailed test, with the alternative hypothesis that the mean is greater than 650, is half the two-tailed p-value. Hence, the one-tailed p-value is 0.040.

Explanation:

The quality control engineer initially performed a two-tailed test with the null hypothesis that the mean force necessary to produce cracks in stressed oak furniture is 650. The calculated z-test statistic led to a two-tailed test p-value of 0.080. If the engineer had chosen an alternative hypothesis that the mean was greater than 650, the test would have been a one-tailed test. In a one-tailed test, you would only consider the probability on the side of the distribution that corresponds to the alternative hypothesis. Therefore, since the original two-tailed p-value was 0.080, for the one-tailed test, we would take half of that value which results in a p-value of 0.040.

SOMEONE PLEASE PLEASE HELP ASAP

Answers

The correct answer is A. NGNGA

To find a sequence is arithmetic, we are going to find its common difference: [tex]d=a_{n}-a_{n-1}[/tex]
where
[tex]d[/tex] is the common difference
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence
To find if a sequence is geometric, we are going to find its common ratio: 
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
where
[tex]r[/tex] is the common ratio 
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence

1) 3,4,6,10,18
For [tex]a_{n}=4[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]d=a_{n}-a_{n-1}[/tex]
[tex]d=4-3[/tex]
[tex]d=1[/tex]
For [tex]a_{n}=6[/tex] and [tex]a_{n-1}=4[/tex]:
[tex]d=6-4[/tex]
[tex]d=2[/tex]

For [tex]a_{n}=4[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
[tex]r= \frac{4}{3} [/tex]
For [tex]a_{n}=6[/tex] and [tex]a_{n-1}=4[/tex]:
[tex]r= \frac{6}{4} [/tex]
[tex]r= \frac{3}{2} [/tex]
We can conclude that the sequence is neither arithmetic nor geometric.

2) [tex] \frac{25}{4} , \frac{5}{2} ,1...[/tex]
For [tex]a_{n}= \frac{5}{2} [/tex] and [tex]a_{n-1}= \frac{25}{4} [/tex]:
[tex]d=a_{n}-a_{n-1}[/tex]
[tex]d=\frac{5}{2}-\frac{25}{4}[/tex]
[tex]d=- \frac{15}{4} [/tex]
For [tex]a_{n}=1[/tex] and [tex]a_{n-1}= \frac{5}{2} [/tex]:
[tex]d= 1-\frac{5}{2}[/tex]
[tex]d= -\frac{3}{2} [/tex]

For [tex]a_{n}= \frac{5}{2} [/tex] and [tex]a_{n-1}= \frac{25}{4} [/tex]:
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
[tex]r= \frac{\frac{5}{2} }{\frac{25}{4} } [/tex]
[tex]r= \frac{2}{5} [/tex]
For [tex]a_{n}=1[/tex] and [tex]a_{n-1}= \frac{5}{2} [/tex]:
[tex]r= \frac{1}{\frac{5}{2}} [/tex]
[tex]r= \frac{2}{5} [/tex]
We have a common ratio, we can conclude that the sequence is geometric.

3) [tex] \frac{2}{3} , \frac{4}{6} , \frac{8}{9} ...[/tex]
For [tex]a_{n}=\frac{4}{6}[/tex] and [tex]a_{n-1}= \frac{2}{3}[/tex]:
[tex]d=\frac{4}{6}-\frac{2}{3}[/tex]
[tex]d=0[/tex] 

For [tex]a_{n}=\frac{4}{6}[/tex] and [tex]a_{n-1}= \frac{2}{3}[/tex]:
[tex]r= \frac{\frac{4}{6}}{\frac{2}{3}} [/tex]
[tex]r=1[/tex]
For [tex]a_{n}=\frac{8}{9}[/tex] and [tex]a_{n-1}= \frac{4}{6}[/tex]:
[tex]r= \frac{\frac{8}{9}}{\frac{4}{6}} [/tex]
[tex]r= \frac{4}{3} [/tex]
We can conclude that the sequence is neither arithmetic nor geometric.

4) 3,15,75...
For [tex]a_{n}=15[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]d=15-3[/tex]
[tex]d=12[/tex]
For [tex]a_{n}=75[/tex] and [tex]a_{n-1}=15[/tex]:
[tex]d=75-15[/tex]
[tex]d=60[/tex]

For [tex]a_{n}=15[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]r= \frac{15}{3} [/tex]
[tex]r=5[/tex]
For [tex]a_{n}=75[/tex] and [tex]a_{n-1}=15[/tex]:
[tex]r= \frac{75}{15} [/tex]
[tex]r=5[/tex]
We have a common ratio, we can conclude that the sequence is geometric.

5) 5,-11,-27
For [tex]a_{n}=-11[/tex] and [tex]a_{n-1}=5[/tex]:
[tex]d=-11-5[/tex]
[tex]d=-16[/tex]
For [tex]a_{n}=-27[/tex] and [tex]a_{n-1}=-11[/tex]:
[tex]d=-27--11[/tex]
[tex]d=-27+11[/tex]
[tex]d=-16[/tex]
We have a common difference, we can conclude that the sequence is arithmetic.

What is the domain of the step function f(x) = ⌈2x⌉ – 1?

Answers

f(x) is defined for "all real numbers."
Answer:

The domain of the given step function is:

                       The set of all the real numbers.

Step-by-step explanation:

Ceiling function--

The ceiling function also known as the least integer function is the function which takes the largest value of the integer for a non-integer number which lie between the two integers , and gives the integer itself if the number is integer.

and it is given by:

[tex]f(x)=\left \lceil x \right \rceil[/tex]

(

For example--

if x= 0.5

then f(x)=1  since x lie between 0 and 1

if x= -2.5

Then f(x)= -2

since x lie between -3 and -2.

if x=3

then f(x)=3  )

Also, the function is defined for all real values of x.

i.e. The domain of such a function is: All real numbers.

The function f(x) is given by:

[tex]f(x)=\left \lceil 2x \right \rceil-1[/tex]

Hence, the domain is all the real numbers.

Hey can you please help me posted picture of question

Answers

Sample space for:
First shooting a basketball. Two options: X or O
Then rolling a die. Six options: 1, 2, 3, 4, 5, or 6

Sample space:
X1
X2
X3
X4
X5
X6
O1
O2
O3
O4
O5
O6

Answer: Options:
A. X1
C. O6
F. X6

the volume of a rectangle is 672 inches. the hieght of the prism is 8 incheswhich measurement in inches could be the dimensions of the base?explain and justify your answer

Answers

the correct question is
The volume of a rectangular prism is 672 in³, the height of the prism is 8 inches which measurement in inches could be the dimensions of the base?explain and justify your answer

we know that
volume of a rectangular prism=area of the base*height of the prism
area of the base=Volume/height 
Volume=672 in³
height=8 in
area of the base=672/8----> 84 in²
This means that the length and width can be any pair of numbers that has a product of 84 in²

examples
8*8, 9*64/9, 2*32, 16*4, etc

Keep in mind that the dimensions not necessarily are whole numbers, there are actually infinitely answers to this problem

The answer is 6 inches

Find the slope and y-intercept fotv

Answers

The line rises 2 units for each 3 it goes horizontally.
  Slope: 2/3

The line crosses the y-axis at y=0.
  y-intercept: 0

find the surface area of the solid formed by the net

Answers

The net appears to describe a cylinder with diameter 8.46 ft and height 17.25 ft. The total surface area is the sum of the areas of the circles and the rectangle.

The area of a circle with diameter d is given by
  A = (π/4)d²
The area of the rectangle is the product of its length (πd) and width (h).
  A = πdh
So, the total area is the sum of the areas of 2 circles and the rectangle:
  A = 2(π/4)d² +πdh
  A = πd(d/2 +h)
  A = π(8.46 ft)(4.23 ft +17.25 ft) = 181.7208π ft²
  A ≈ 570.89 ft²

The surface area of the cylinder formed by the net is about 570.89 ft².

The function f(t) = 25 sin (pi over 2t) + 10 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? (5 points)

A. Maximum: 25°; minimum: 10°; period: pi over 2 hours
B. Maximum: 35°; minimum: 35°; period: 8 hours
C. Maximum: 100°; minimum: −15°; period: pi over 2 hours
D. Maximum: 35°; minimum: −15°; period: 4 hours

Answers

f(t) = 25 sin [(π/2) t] + 10

By graphing the given function
The correct option is D
D. Maximum: 35°; minimum: −15°; period: 4 hours

Answer:

The correct answer is: Option: D

D. Maximum: 35°   ;  minimum: −15°  ; Period: 4 hours

Step-by-step explanation:

We are given a function f(t) as:

          [tex]f(t)=25\sin (\dfrac{\pi}{2}t)+10[/tex]

We know that the maximum value of the function is obtained when the sine function is maximum.

i.e. when sine takes the value=1

and the minimum value of the function is obtained when the sine function is minimum.

i.e. when sine takes the value= -1

Hence, the minimum value of the function is:

-25+10= -15

and the maximum value of the function is:

25+10=35

Also the period of the function of the type:

[tex]f(x)=a\sin(bx)+c[/tex]

is:

[tex]Period=\dfrac{2\pi}{b}[/tex]

Hence, here we have: b=π/2

Hence, period is:

[tex]Period=\dfrac{2\pi}{\dfrac{\pi}{2}}\\\\\\Period=4[/tex]

         Hence, option: D is the correct answer.

For the data set below, compute the standard deviation. Round to the nearest hundredth. 2, 3, 5, 8 2.03 2.20 2.6 4.5

Answers

Final answer:

To calculate the standard deviation, compute the mean, subtract it from each data point, square the results, average those and take the square root. Round to the nearest hundredth, and for one standard deviation below the mean, subtract the standard deviation from the mean.

Explanation:

To calculate the standard deviation of a data set, you can use a calculator or a computer. The formula for standard deviation is the square root of the variance, which is the average of the squared differences between each data point and the mean of the data set. Let's compute the mean and standard deviation of the provided data set: 2, 3, 5, 8, 2.03, 2.20, 2.6, 4.5.

Calculate the mean (average) of the data.Subtract the mean from each data point and square the result.Find the average of these squared differences.Take the square root of this average to get the standard deviation.

You may round the standard deviation to the nearest hundredth as requested.

To find the value that is one standard deviation below the mean, subtract the standard deviation from the mean.

if you throw a rubber ball toward the ground at an angle, it will bounce up feom the ground at the same angle. find the unknown angle measure in the drawing at the right.

Answers

30°

A strait line is 180°
75°+75°=150°
180°-150°=30°

The equation of a hyperbola is 5x2 − y2 = 25. What is the area of the asymptote rectangle?

Answers

[tex]\bf \textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases}\\\\ -------------------------------\\\\ 5x^2-y^2=25\implies \cfrac{5x^2}{25}-\cfrac{y^2}{25}=1\implies \cfrac{x^2}{5}-\cfrac{y^2}{5^2}=1 \\\\\\ \cfrac{(x-0)^2}{(\sqrt{5})^2}-\cfrac{(y-0)^2}{5^2}=1\qquad \begin{cases} a=\sqrt{5}\\ b=5 \end{cases}[/tex]

now, the asymptotes rectangle is a rectangle that is (a+a) in width and (b+b) in length, thus its area is 2a*2b,

[tex]\bf \stackrel{2a}{2\sqrt{5}}~~\times ~~\stackrel{2b}{2\cdot 5}\implies 20\sqrt{5}[/tex]

please help.............

Answers

Any of several graphing calculators are suitable for this. Desmos is a free on-line one that is easy to learn and use.

What is the sum of the numbers in the series below? 15 + 11 + 7 + . . . + (–129)

Answers

your answer if you are in algebra 2 and you have this on online school would be -2,109
Final answer:

The sum of the numbers in the series is -8208.

Explanation:

The sum of a series can be found using the formula for the sum of an arithmetic series, which is given by:

Sum = (n/2)(first term + last term),

where n is the number of terms and the first and last terms are provided in the series. In this case, the first term is 15 and the last term is -129. The common difference between each term is -4.

Using the formula, we have:

Sum = ([-129 - 15]/2)(15 + -129) = (-144/2)(-114) = 72 * -114 = -8208.

Therefore, the sum of the numbers in the series is -8208.

A car rental agency charges $50 per week plus $0.50 per mile to rent a car. What is the weekly cost to rent the car, f, as a function of the number of miles driven during the week, x. How many miles did you drive during the week if the weekly cost to rent the car was $100?

Answers

A) The cost in dollars is given as 50 + 0.50x, so ...
  f(x) = 0.50x +50

B) You want to find x for f(x) = 100. Substitute the given numbers and solve for x.
  100 = 0.50x +50
  50 = 0.50x
  50/0.50 = x
  100 = x
You drove 100 miles during the week if the cost was $100.
Final answer:

The weekly cost to rent the car, f, as a function of the number of miles driven during the week, x, is f = 50 + 0.50x. If the weekly cost to rent the car was $100, the number of miles driven during the week is 200 miles.

Explanation:

The weekly cost to rent the car, f, as a function of the number of miles driven during the week, x, can be calculated using the formula f = 50 + 0.50x. This is because the car rental agency charges $50 per week plus $0.50 per mile. To find the number of miles driven during the week if the weekly cost to rent the car was $100, we can substitute f = 100 into the formula and solve for x:

100 = 50 + 0.50x

50 = 0.50x

x = 100/0.50

x = 200

Therefore, the number of miles driven during the week is 200 miles.

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icole wants to buy a pair of jeans. The original cost of the jeans is $42.50, and the markup is 10 percent. How much will she have to pay for the jeans? $44.50 $46.75 $52.50

Answers

42.50 * 10% or 0.10 = 4.25

42.50 + 4.25 = 46.75.

She will have to pay $46.75 for the jeans. 

you deposit $3000 into a bank account that pays 1.25% annual interest, compounded semi-annually. how much interest does the account earn after 4 years?

Answers

Final answer:

To find the amount of interest earned on a bank account after 4 years, use the compound interest formula. After plugging in the values, the account earns approximately $162.89 in interest.

Explanation:

To calculate the amount of interest earned on a bank account after 4 years, we need to use the formula for compound interest: A = P(1 + r/n)^(nt) - P. In this case, the initial deposit (P) is $3000, the annual interest rate (r) is 1.25%, compounded semi-annually (n = 2), and the time period (t) is 4 years. Plugging in these values, we get:



A = 3000(1 + 0.0125/2)^(2*4) - 3000



Solving this equation, we find that the account earns approximately $162.89 in interest after 4 years.

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