The sum of two numbers is 46 and the difference is 10 . What are the numbers?

[tex]\text{The domain}\\\\x\neq0\ \wedge\ x\neq-2\ \wedge\ x\neq2[/tex]

[tex]\dfrac{5}{x^2-4}+\dfrac{2}{x}=\dfrac{2}{x-2}\qquad\text{subtract}\ \dfrac{2}{x-2}\ \text{from obth sides}\\\\\dfrac{5}{x^2-2^2}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5}{(x-2)(x+2)}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5x}{x(x-2)(x+2)}+\dfrac{2(x-2)(x+2)}{x(x-2)(x+2)}-\dfrac{2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2(x^2-4)-2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2x^2-8-2x^2-4x}{x(x-2)(x+2)}=0\\\\\dfrac{x-8}{x(x-2)(x+2)}=0\iff x-8=0\to\boxed{x=8}\in D[/tex]

The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.

To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:

Area = Length × Width

Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):

Area = 1/2 square mile

Length = 3/4 miles

1/2 = (3/4) × Width

To solve for the width (W), divide both sides by 3/4:

Width = (1/2) ÷ (3/4)

When dividing by a fraction, you can multiply by its reciprocal:

Width = (1/2) × (4/3)

Now, multiply the numerators and denominators:

Width = 4/6

The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

Width = 2/3

So, the width of the rectangular strip of land is 2/3 miles.

To know more about rectangular strip click here :

https://brainly.com/question/5031874

#SPJ2

Answer:

15?

Step-by-step explanation:

If Binu is 15, in 5 years they will be 20. And if Banu is 20 years older, in 5 years they will be 40 (becuase 15 + 20 = 35 and then + the 5 years) Thats twice Binu's age. So Binu is 15 I would assume?

Answer:

52

Step-by-step explanation:

One way is to simply count the number of yellow squares.

I count 52, so the area is 52 square units.

Another way is to find the area of the larger rectangle and subtract from it the area of the smaller rectangle.

The larger rectangle is 11 by 6. Area = 11 * 6 = 66.

The smaller rectangle is 7 by 2. Area 7 * 2 = 14.

Area shaded in yellow = 66 = 14 = 52

Answer: area = 52 square units

Answer:

"i cant do math cuz im pretty" such pick me vibes LOL

Step-by-step explanation:

Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.  

[tex]\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0[/tex]

and

[tex]\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x[/tex]

Logarithmic equations with infinite solutions have graphs that look like dying-out exponentials. They can have infinite solutions because there are infinitely many values of y that satisfy the equation.

Examples of Logarithmic Equations with Infinite Solutions:
1. Logarithms to the base 10 (common logarithms):

In the equations below, y is the exponent to which 10 must be raised to equal x, so y is the common logarithm (log) of x.
x = 10^y
x = 10^y+1

2. Logarithms to the base e (natural logarithms):

In the equations below, y is the power to which e must be raised to equal x, so y is the natural logarithm (ln) of x.
x = e^y
x = e^y+1

Both of these equations have graphs that look like dying-out exponentials. They have infinite solutions because there are infinitely many values of y that satisfy the equation. Whenever the base is positive and not equal to 1, logarithmic equations can have infinite solutions.

Final answer:

Jupiter has 67 moons.

Explanation:

To solve this problem, let's define j as the number of moons Jupiter has. According to the given information, Jupiter has 11 more than 4 times as many moons as Neptune, which has 14 moons. So, we can set up an equation: j = 4n + 11, where n is the number of moons Neptune has. Since Neptune has 14 moons, we can substitute that value into the equation: j = 4(14) + 11. Simplifying further, we get j = 56 + 11 = 67. Therefore, Jupiter has 67 moons.

Answer: 118.40, 300, $18,000

Step-by-step explanation:

a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]

   p(8) =  [tex]-\frac{8}{5} + 120[/tex]

          = -1.60 + 120

          = 118.40

b) R(x) = x * p(x)

         = [tex]x(-\frac{1}{5}x + 120)[/tex]

         = [tex]-\frac{1}{5}x^{2} + 120x[/tex]

           a=[tex]-\frac{1}{5}[/tex], b=120

x = [tex]\frac{-b}{2a}[/tex]

  = [tex]\frac{-120}{-\frac{2}{5}}[/tex]

  = [tex]\frac{-120(5)}{-2}[/tex]

  = 300

c)  R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]

R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]

           = -18,000 + 36,000

           = 18,000

***********************************************************************

sec θ = [tex]\sqrt{6}[/tex]

[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]

adjacent² + opposite² = hypotenuse²

      1²       + opposite² =      (√6)²

      1         + opposite² =        6

                   opposite² =        5

                   opposite =        √5

csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]

cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]

sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]

cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]

tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]

**********************************************************************

Answer: 144°

Step-by-step explanation:

[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]

π(5x) = 180(4π)

    x   = [tex]\frac{180(4\pi)}{5\pi}[/tex]

         = 36(4)

         = 144

Answer:  [tex]y -3 = \frac{4}{11} (x - 11)[/tex]

Step-by-step explanation:

We can use the point-slope formula to write the equation of a line given a point on the line and the slope of the line:  

Slope = m

Given point (x₁,y₁)

Formula = (y-y₁) = m(x-x₁)

Given point: (11,3); slope: 4/11

Answer : [tex]y - 3 = \frac{4}{11} (x - 11)[/tex]

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]

Answer:

See attachment.

Step-by-step explanation:

The main part of the function is an absolute value function and so it forms a V with the center of the V at (0,0). The sides of the V go up and over 1 unit at a time. However, since 2 is added to the it outside of the absolute value, the center of the V moves from (0,0) to (0,2). The sides stay the same. The division by 2 changes the sides. The sides move from up and over 1 unit to up 1 unit and over two units. It spreads or widens the graph. Lastly, the interval selects a specific part of the graph only from 0 to 6 on the x-axis. This takes just one side of the V and looks like a line segment. See attachment.

Answer:

We are given a function,

[tex]y=\frac{|x|+2}{2}[/tex]    if 0 ≤ x < 6

We need to draw the graph of the function.

We know that Parent function of the given function is Modulus function | x |.

Consider given function,

[tex]y=\frac{|x|+2}{2}[/tex]

[tex]y=\frac{|x|}{2}+\frac{2}{2}[/tex]

[tex]y=\frac{|x|}{2}+1[/tex]

So, the given function is translated 1 unit upward and compressed by factor of 1/2.

So the obtained graph is attached.

Answer:

[tex]y=3x[/tex]

y=57, when x is 19.

Step-by-step explanation:

We are asked to write an equation of variation where y varies directly as x.

Since we know that a directly proportional equation is in form: [tex]y=kx[/tex], where k is the constant of proportionality.

Upon substituting x=5 and y= 15 in our equation of variation we will get,

[tex]15=k*5[/tex]

[tex]k=\frac{15}{5}[/tex]

[tex]k=3[/tex]

Upon substituting k=3 in the standard equation of variation we will get our desired equation of variation as: [tex]y=3x[/tex].

Now let us find y, when x is 19.

[tex]y=3*19[/tex]

[tex]y=57[/tex]

Therefore, y equals 57, when x is 19.

Answer:

200 adults

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know children and adults attended. We will let c be the number of children and a be the number of adults. Since 200 people attended, then c+a=200.

We also know they made $800 and adult tickets cost $4 and child tickets cost $2. We can write 2c+4a=800.

We will solve by substituting one equation into the other. We start by solving the first equation for c. c+a=200 becomes c=200-a.

Now we substitute c=200-a into 2c+4a=800. Simplify and isolate the variable a.

This means that 200 adults attended and 0 children attended.

Answer:

Function formula P(t) = -52t +480

Step-by-step explanation:

here, P(t) denotes the number of pages to read and t represents the time in hour.

Given the statement: Shryia read a 480-page-long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 pages left to read.

⇒Total number of page in a long book = 480

After reading for 1.5 hours, she had 402 pages left to read.

Then,

Total number of page Shryia read in 1.5 hours is:

[tex]480-402 = 78[/tex]

Constant rate at which she is reading her book = [tex]\frac{78}{1.5} = 52[/tex] page per hour

Then, the function formula is given by:

P(t) = -52t + 480 ;  where t is in hours.

Check:

P(t) = -52t + 480

P(1.5) = -52(1.5) + 480 = -78 + 480 = 402     True.

Answer:

x = 1.3472 to the nearest ten thousandth.

Step-by-step explanation:

14^x + 1 = 36

14^x = 35

Taking logarithms:-

x ln 14 = ln 35

x = ln 35 / ln 14

= 1.3472.

The solution, rounded to the nearest ten-thousandth, is x = 1.5404.

To solve the equation [tex]14^x + 1 = 36[/tex], we first isolate the exponential term by subtracting 1 from both sides of the equation, which gives us [tex]14^x = 35.[/tex]

The next step is to take the logarithm of both sides of the equation.

We could use any base for the logarithm, but it's common to use base 10 or the natural logarithm base (e). In this case, let's use the natural logarithm:

[tex]ln(14^x) = ln(35)[/tex]

We can then use the property of logarithms which allows us to bring the exponent down as a multiplier:

[tex]x * times ln(14) = ln(35)[/tex]

Now, you can solve for x by dividing both sides by ln(14):

[tex]x = ln(35) / ln(14)[/tex]

Using a calculator, we find the quotient and then round to the nearest ten-thousandth:

x = 1.5404

This value is the solution to the original equation.

Answer:8

Step-by-step explanation:6%3=2

4x2=8

I swear its 8 check if i'm wrong I dare you

Answer:

84°

Step-by-step explanation:

2 complementary angles sum to 90°

let x be the angle then complement = x - 78, hence

x + x - 78 = 90 ( add 78 to both sides )

2x = 168 ( divide both sides by 2 )

x = 84

hence the angle is 84°

Answer:

The simplified form of the given expression is 6-a.

Step-by-step explanation:

The given expression is

[tex](3-a)\cdot 2+a[/tex]

According to distributive property.

[tex]a\cdot (b+c)=ab+ac[/tex]

Use distributive property.

[tex]3(2)-a(2)+a[/tex]

[tex]6-2a+a[/tex]

Combine like terms.

[tex]6+(-2a+a)[/tex]

[tex]6-a[/tex]

Therefore the simplified form of the given expression is 6-a.

Answer:

r=0.6

Step-by-step explanation:

Consider geometric sequence

[tex]b_1=6,\\ \\b_2=3.6,\\ \\b_3=2.16,\\ \\b_4=1.296,...[/tex]

In geometric sequence

[tex]b_i=b_{i-1}\cdot r,[/tex]

then

[tex]b_2=b_1\cdot r[/tex]

and

[tex]3.6=6r,\ r=\dfrac{3.6}{6}=0.6.[/tex]

Note that

[tex]2.16=3.6\cdot 0.6,\\ \\1.296=2.16\cdot 0.6.[/tex]

This means that ratio r=0.6.

Answer:

Domain: [tex]( -\infty,\infty )[/tex] and Range: [tex][ -1,\infty )[/tex]

Step-by-step explanation:

We have the parametric equations [tex]x= 2t[/tex] and [tex]y=t^{2}+t+3[/tex].

Now, we will find the values of 'x' and 'y' for different values of 't'.

t                       :   -3       -2.5     -2     -1.5     -1     0       1      1.5      2

[tex]x= 2t[/tex]             :   -6       -5       -4       -3      -2    0      2      3        4

[tex]y=t^{2}+t+3[/tex]  :    9       6.75     5     3.75     3    3      5     6.75     9

Now, we can see that these parametric equations represents a parabola.

The general form of the parabola is [tex]y=ax^{2}+bx+c[/tex].

Now, we have the point ( x,y ) = ( 0,3 ). This gives that c = 3.

Also, we have the points ( x,y ) = ( -2,3 ) and ( 2,5 ). Substituting these in the general form gives us,

4a - 2b + 3 = 3 → 4a - 2b = 0 → b = 2a.

4a + 2b + 3 = 5 → 4a + 2b = 2 → 2a + b = 1 →  2a + 2a = 1 ( As, b = 2a ) → 4a = 1 → [tex]a=\frac{1}{4}[/tex].

So, [tex]b=\frac{1}{2}[/tex].

Therefore, the equation of the parabola obtained is [tex]y=\frac{x^{2}}{4}+\frac{x}{2}+3[/tex].

The graph of this function is given below and we can see from the graph that domain contains all real numbers and the range is [tex]y\geq -1[/tex].

Hence, in the interval form we get,

Domain is [tex]( -\infty,\infty )[/tex] and Range is [tex][ -1,\infty )[/tex]

Answer:

Domain:

[tex](-\infty,\infty)[/tex]

Range:

[tex][2.75,\infty)[/tex]

Step-by-step explanation:

we are given parametric equation as

[tex]x=2t[/tex]

[tex]y=t^2+t+3[/tex]

We can change into rectangular equation

we can eliminate t from first equation and plug into second equation

[tex]x=2t[/tex]

[tex]t=\frac{x}{2}[/tex]

now, we can plug that into second equation

[tex]y=(\frac{x}{2})^2+\frac{x}{2}+3[/tex]

now, we can draw graph

Domain:

we know that

domain is all possible values of x for which any function is defined

we can see that our equation is parabolic

and it is defined for all values of x

so, domain will be

[tex](-\infty,\infty)[/tex]

Range:

we know that

range is all possible values of y

we can see that

smallest y-value is 2.75

so, range will be

[tex][2.75,\infty)[/tex]

Answer:

So when you flip the coin 8 times and you get tails 3 of the times then you should do 3 plus 5 and you will get 8 as your total again so then the answer is 5 out of 8 total.

Step-by-step explanation:

The probability that all the remaining flips will be tails is 1/32, or approximately 0.03125.

The probability of getting tails on each coin flip is 50 percent since a fair coin has two equally likely outcomes: heads or tails.

If the first three coin flips resulted in tails, the remaining five coin flips are independent events. The probability of getting tails on each of the remaining flips is still 50 percent.

The probability of getting all the remaining flips to be tails is calculated by multiplying the probabilities of each individual flip. Since there are five remaining flips, the probability is 0.5 raised to the power of 5, or 1/32 (approximately 0.03125).

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ12

Answer:

the answer is a

Step-by-step explanation:

Answer:

C=25d

Step-by-step explanation:

We write an equation where C or cost is my output and d or days is my input. I should be able to put in any number of days and find the cost. Let's gather some data:

River Ramble

Day 1 $25(1)=25 cost

Day 2 $25(2)=50 cost

Day 3 $25(3)=75 cost

Day d $25(d)=C.

Our equation is C=25d.

Answer: Census.

Step-by-step explanation:

Given statement:- A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is.

This research is an example of a census because research in which information is obtained through the responses that all available members of an entire population give to questions.

In other words "Census is an official survey of population in a certain area and records various details about the individuals".

The study querying every factory worker in Ohio for their birth year to determine the average age of all U.S. factory workers is a census, as it attempts to gather data from every member of the entire population of interest. (First option)

The research study done to find the average age of all U.S. factory workers where the researchers asked every factory worker in Ohio their birth year is an example of a census. A census involves gathering information about every individual in the entire population of interest.

In this case, the population of interest would be all factory workers, and by querying every one of them (assuming it was indeed every single factory worker in Ohio), it constitutes a census, not a survey, which typically involves a representative sample.

It is not a convenience sample since that would imply a non-random selection based on ease of access, and it's not a simple random sample because not all members of the larger population (nationwide factory workers) have an equal chance of being included.

Answer:

y=0.5x-2

Step-by-step explanation:

if it is perpendicular to the line y=-2x-6, then you know that its slope is the negative reciprocal of that line, and it has a different y intercept which you need to solve for using the point given. You solve by plugging in the x and y values from the point and plugging in the slope into the standard equation, and solving for b, the y intercept

y=0.5x+b

1=0.5(6)+b

1=3+b

-2=b

The equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6  is y = 0.5x - 2.

From the classic definition of straight lines, we know that if we have to find an equation of a straight line being perpendicular to another straight line then the slope of the new equation of straight lines becomes negative reciprocal of the slope of given perpendicular line.

Mathematically, let m1 be the slope of the new straight line and m be the slope of the given perpendicular line, then we have

m1 = -(1/m)

Now, we have given equation y = -2x - 6

Thus slope of the required equation is say (m1) = -(-1/2) = 0.5

Thus the equation formed is y = (m1)x + c [where c is the y-intercept]

∴ y = 0.5x + c

The point given is (6,1) , thus y = 1 and x = 6

Thus the given equation can be formed as

⇒ 1 =  0.5*6 + c

∴  c = 1 - 0.5*6 = -2

The value of y-intercept of the required straight line is -2

The equation of straight line formed is y = 0.5x - 2.

Thus the equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y = − 2x − 6  is y = 0.5x - 2.

To learn more about equation of straight line, refer -

https://brainly.com/question/7669240

#SPJ2

Answer:

28 degrees

Step-by-step explanation:

180 = 10x + 5 + 65 because they are supplementary. x = 11.

Angle 2 = 180 - (Angle 1 + (4x - 7))

Angle 2 = 180 - ((180 - 65) + 4x - 7)

Angle 2 = 180 - (115 + 4x - 7)

Angle 2 = 180 - 152

Angle 2 = 28 degrees

Answer:

852 miles

Step-by-step explanation:

We presume the speed is constant, so the satellite will travel 3/8 the distance in 3/8 the time.

... d = (3/8)·(2272 miles) = 852 miles

_____

1 minute is 1/8 of 8 minutes, so 3 minutes is 3/8 of 8 minutes.