What is the solution to the system?

X+y+z=2
2x+y-z=-1
X=5-2z

Answer:

-8.95 ,, -8.36 ,, 7/28 ,, 8 22/40

Step-by-step explanation:

Answer:

-8.95, -8.36, 7/28, 8 22/40

Step-by-step explanation:

Answer:

  A)  125 inches squared

Step-by-step explanation:

The lateral area is the product of the perimeter of the base, and the height:

  (25 in)(5 in) = 125 in²

__

If you draw the net for the object, you will see that the rectangle representing the lateral area has these dimensions.

[tex]w=\dfrac{1+i+i}{i(1+i)+2}\\\\w=\dfrac{1+2i}{i-1+2}\\\\w=\dfrac{1+2i}{1+i}\\\\w=\dfrac{(1+2i)(1-i)}{1+1}\\\\w=\dfrac{1-i+2i+2}{2}\\\\w=\dfrac{3+i}{2}\\\\w=\dfrac{3}{2}+\dfrac{1}{2}i[/tex]

To find the value of w, substitute the given value of z into the equation for w. Simplify the expression to obtain the value of w in the form x + iy, where x and y are real numbers.

To find the value of w, we first substitute the given value of z into the equation for w.

Given z = 1 + i, we have:

w = (1 + i + i) / (i(1 + i) + 2)

Simplifying the numerator:

w = (1 + 2i) / (i + i^2 + 2)

Since i^2 = -1, we can rewrite the equation as:

w = (1 + 2i) / (-1 + i + 2)

Simplifying further:

w = (1 + 2i) / (1 + i)

To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.

w = ((1 + 2i)(1 - i)) / ((1 + i)(1 - i))

w = (1 - i + 2i - 2i^2) / (1 - i^2)

Using i^2 = -1 again:

w = (1 + i + 2i + 2) / (1 - (-1))

Simplifying the numerator:

w = (3 + 3i) / 2

Dividing both terms by 2:

w = 3/2 + 3/2i

Therefore, w = 3/2 + 3/2i in the form x + iy, where x = 3/2 and y = 3/2 are real numbers.

Answer:

C. A=1/2bh

The formula for the area of a triangle is 1/2bh

Answer:

3/2

Step-by-step explanation:

3^-4 x 2^3 x 3^2/2^4 x 3^-3

base 3 will be numerator and base 2 will be denominator:

3^-4 * 3^2 * 3^3 / 2^4*2^-3

Now add the exponents of the base:

3^-4+2+3/ 2^4-3

3^-4+5/ 2^1

3/2

The correct option is 3/2 ....

2a. 14,9; 2b. 15,4; 2c. 30,8; 3. 32

For 2a., you have to set it up like this: csc 48° = 20⁄x [OR sin 48° = ˣ⁄20]. Then you would have to isolate the variable by getting rid of the denominator. The cosecant function has an extra step because you will get xcsc 48° = 20. As stated, isolate the variable; this time, divide by csc 48°. This is what 20 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2b., you have to set it up like this: sec 39° = ˣ⁄12 [OR cos 39° = 12⁄x. Then you would have to isolate the variable by getting rid of the denominator. The cosine function has an extra step because you will get xcos 39° = 12. As stated, isolate the variable; this time, divide by cos 39°. This is what 12 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2c., you have to set it up like this: cot 64° = 15⁄x [OR tan 64° = ˣ⁄15]. Then you would have to isolate the variable by getting rid of the denominator. The cotangent function has an extra step because you will get xcot 64° = 15. As stated, isolate the variable; this time, divide by cot 64°. This is what 15 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

Now, for 3., it is unique, but similar concept. In this exercise, we are solving for an angle measure, so we have to use inverse trigonometric ratios. So, we set it up like this: cot⁻¹ 1⅗ = m<x [OR tan⁻¹ ⅝ = m<x]. We simply input this into our calculator and we get 32,00538321°. When rounded to the nearest degree, we get 32°.

WARNING: If you use a graphing calculator, you have to input it uniquely because most graphing calculators do not have the inverse trigonometric ratios programmed in their systems. This is how you would write this: tan⁻¹ 1⅗⁻¹. You set 1⅗ to the negative first power, ALONG WITH the inverse tangent function, because without it, your answer will be thrown off. Since Cotangent and Tangent are multiplicative inverses of each other, that is the reason why the negative first power is applied ALONG WITH the inverse tangent function.

**NOTE: 1⅗ = 8⁄5

Take into consideration:

sin θ = O\H

cos θ = A\H

tan θ = O\A

sec θ = H\A

csc θ = H\O

cot θ = A\O

I hope this helps you out alot, but if you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

Step-by-step explanation:

The given equation is √2x+1+3=0

And we have been given that x= 4

I do not agree with the solution because it does not give any real solution. It only gives possible solution. If you plug the value 4 in the original equation you will get 8 and the square root of 8 is a complex number.  Thus 4 is an extraneous solution....

Answer:

I do not agree with the student because there is no real solution.

Solving the equation only gives possible solutions, but you must check them in the original equation.

Checking the solution in the original equation shows that 4 is an extraneous solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution of the system of equations are the coordinates of the point of intersection.

We have two parallel lines. The intersection point does not exist.

Therefore, this system of equations has no solution.

Answer:

The x-intercept is (6,0).

The y-intercept is (0,-21/2).

Step-by-step explanation:

So we are told this is a line.

Linear equations in the form y=mx+b tell us the slope,m, and the y-intercept,b.

So we are going to write our equation in this form to determine x- and y- intercept.

Let's begin.

First thing I'm going to is compute the slope.  The slope can be found by lining up the points vertically and subtracting them vertically then put 2nd difference over 1st difference.

Let's do that:

 (   -10  ,  -28)

- (    -6  ,   -21)

-----------------------

   -4             -7

So the slope is -7/-4 which is 7/4.

Now we know our equation to be in this form

y=(7/4)x+b

Use one of the points along with y=(7/4)x+b to find b.

Doesn't matter which one, you get to choose.

How about (-2,-14)?

-14=(7/4)(-2)+b

-14=-7/2+b

Add 7/2 on both sides:

-14+7/2=b

-21/2=b

So our equation is

[tex]y=\frac{7}{4}x-\frac{21}{2}[/tex]

So we already know the y-intercept is (0,-21/2).

We knew this because we were putting into slope-intercept form.

Now to find the x-intercept, set y=0 and solve for x:

[tex]0=\frac{7}{4}x-\frac{21}{2}[/tex]

Clear the fractions; multiply both sides by 4:

[tex]0=7x-42[/tex]

Add 42 on both sides:

[tex]42=7x[/tex]

Divide both sides by 7:

[tex]\frac{42}{7}=x[/tex]

So x=6

The x-intercept is (6,0).

Answer:

-1

Step-by-step explanation:

2x-10

-------------- = 3x

4

Multiply each side by 4

     2x-10

4*-------------- = 3x*4

      4

2x-10 = 12x

Subtract 2x from each side

2x-10 -2x = 12x-2x

-10 = 10x

Divide each side by 10

-10/10 =10x/10

-1 =x

Answer:-1

Step-by-step explanation:GOT it right on my quiz (FLVS)

Answer:

D. x=-6 y= -11

Step-by-step explanation:

y= x -5

y= 2x +1

2y=2x- 10

y=2x+1

y= -11

-11= x-5

+5 +5

-6=x

Answer:

6n = 18p

Step-by-step explanation:

Answer: n=3p

Step-by-step explanation:

Step-by-step explanation:

the correct answer is c

Using sampling concepts, it is found that the sentence is:

C. If a population is all actors, a sample of the population could be movie actors.

A sample is a group taken from the population. It has to come from a more restrict group of the population, that is, an subset of the population.

In option A, baseball players is a subset of all athletes, so all athletes would be the population and baseball players would be the sample. The same can be applied in options B and D.

In option C, movie starts is a subset of all actors, thus the roles of sample and population are correct.

A similar problem is given at https://brainly.com/question/25119689

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 48

b = x

c = 50

^^^Plug these numbers into the theorem

[tex]48^{2} +x^{2} =50^{2}[/tex]

simplify

2304 + [tex]x^{2}[/tex] = 2500

Isolate x^2 by subtracting 2304 to both sides

[tex]x^{2}[/tex] = 196

To remove the square from x take the square root of both sides to get you...

14 = x  

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]g(x)=x+6[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x+8[/tex]

If f(x) is shifted 2 units to the right

then

The rule of the translation is

[tex]g(x)=f(x-2)[/tex]

so

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

[tex]g(x)=x+6[/tex]

Answer:  The correct option is

(D) [tex]g(x)=x+6.[/tex]

Step-by-step explanation:  Given that the following function is shifted 2 units to the right :

[tex]f(x)=x+8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to write the equation when the function (i) is shifted 2 units to the right.

We know that

if a function is shifted 2 units to the right, then its x co-ordinate is reduced by 2 units.

Therefore, the equation of the new function is given by

[tex]g(x)=f(x-2)=(x-2)+8=x+6.[/tex]

Thus, the required function is [tex]g(x)=x+6.[/tex]

Option (D) is CORRECT.

Answer:

r = ∛(3V/4π)

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³.

We want to solve this first for r³ and then for r.

Multiplying both sides of V = (4/3)πr³ by 3 yields an equation without fractions:  3V = 4πr³.

Dividing both sides of this equation by 4π isolates r³:

       3V

r³ = -------

       4π

To find r, take the cube root of both sides of

       3V

r³ = -------

       4π

obtaining r = ∛(3V/4π)

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=113 \end{cases}\implies 113=\cfrac{4\pi r^3}{3}\implies 339=4\pi r^3 \\\\\\ \cfrac{339}{4\pi }=r^3\implies 26.98\approx r^3\implies \sqrt[3]{26.98}=r\implies 2.999 \approx r\implies \stackrel{\textit{rounded up}}{3=r}[/tex]

Answer:

y - 9 = 1/2(x + 3)

Step-by-step explanation:

For the equation y = -2x + 8, your slope, m, is -2. To find the slope for a line perpendicular to the original line, we do the opposite reciprocal of this number. The slope of the perpendicular line is 1/2.

Point-slope form is: y - y1 = m(x - x1) where x1 and y1 are the x- and y-coordinates of an ordered pair.

With this new slope for the perpendicular line, and the point we are given, we just plug in the info.

Your equation is: y - 9 = 1/2(x + 3)

Answer:

y=800 km

Step-by-step explanation:

Let the distance traveled by train be y and by bus be x.

Bus -x

Train -y

y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)

The sum of the two is equal to 1450

x+y=1450

The two equations form simultaneous  equations which when solved simultaneously give the values of x and y.

y+x=1450

y-x=150

Adding the two we get:

2y=1600

Divide both sides by two:

y=800 km

Y is the distance traveled by train= 800 km

Answer:

the correct answer is D. Funtion 1 and 3 have the same rate of change but funtion 1 has greater y intercept

Step-by-step explanation:

If we organize the funtion 1, we have y= 2x+8

Funtion 2 the need to calculate the slope m = (y2-y1)/(x2-x1) the point on the y represent (y2,x2) and is (4,0) the point onn the x axis is (x1,y1) and is (-2,0)

So, m=(4-0)/(0-(-2) => m=(4/2) => m=2

Then, y=m(X-Xo) + Yo  . From the plot, I choose (x2,y2) as (Xo,Yo) So, (0,4)

y=2(X-0) +4 then y= 2x+4

From 3 equation the choose the value x=o and g(x)= 5 and x=1 and g(x)=7 and following the same m=(7-5)/(1-0) the slope is m=2. Following the same procedure before I choose x=0 and y=5

Then the equation is: y=2(x-0) + 5

So, opcion D is true

Answer:

108 feet cubed

Step-by-step explanation:

i think its 24 because you do l*w*h so 4 times 6 equals 24, times 4.5 and its 108.

Answer : The volume of the swimming pool is, [tex]142ft^3[/tex]

Step-by-step explanation :

In the given figure, there are two figures are included which are cuboid and 2 hemisphere.

As we know that 2 hemisphere combine to form a sphere.

Volume of swimming pool = Volume of cuboid + Volume 2 hemisphere

Volume of swimming pool = Volume of cuboid + Volume sphere

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

where,

l = length of cuboid = 6 ft

b = breadth of cuboid = 4 ft

h = height of cuboid = 4.5 ft

r = radius of sphere = [tex]\frac{Diameter}{2}=\frac{4ft}{2}=2ft[/tex]

Now put all the given values in the above formula, we get:

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

Volume of swimming pool = [tex](6ft\times 4ft\times 4.5ft)+(\frac{4}{3}\times 3.14\times (2ft)^3)[/tex]

Volume of swimming pool = [tex]108ft^3+33.49ft^3[/tex]

Volume of swimming pool = [tex]141.49ft^3[/tex]

Volume of swimming pool ≈ [tex]142ft^3[/tex]

Therefore, the volume of the swimming pool is, [tex]142ft^3[/tex]

Answer:

Step-by-step explanation:

None of them do to me. The last one does not. And certainly the second last one cannot.

In B, you are subtracting 4 from zero which doesn't work.

A adds 0 to 4 which gives 4

Unless I misreading D and O is a variable (sneaky), there is no answer.

1) Find the unit rate

$18/6 attendees = 3

2) Apply the unit rate to find the answer

$48/$3= 16 attendees

Therefore, there can be 16 attendees if the budget is $48.

Hope this helps!

Answer:

6!

or

6*5*4*3*2*1

or

720

Step-by-step explanation:

The word 'PLANTS' contains no letter more than once.

It is say 6 letter word.

_  _  _ _ _ _

There are 6 ways to choose the first blank (after than there are 5 letters left to choose from)

After the first blank, there are 5 letter left to choose from so there are 5 ways to choose the second blank.

Then 4 ways for the third blank.

3 ways for the fourth blank.

2 ways for the fifth blank.

1 way for the sixth blank.

Now to figure out the number of permutations you must multiply the number of different ways we have above for each blank.

That is we are doing 6*5*4*3*2*1 or 6!

There are 720 different permutations of the letters in the word 'PLANTS' when used without repetition. This is calculated as the factorial of the number of letters, which is 6. Therefore, 6 factorial (6!) equals 720.

The subject of the question falls under the topic of permutations in Mathematics. The question is asking for the number of different ways that the letters in the word 'PLANTS' can be arranged if all letters are used without repetitions. This is a concept in combinatorics, a subject of discrete mathematics that deals with counting and arranging objects.

To solve this, we need to calculate the factorial of the number of letters in the word 'PLANTS'. There are 6 letters in the word. The factorial of a number (denoted as n!) is the product of all positive integers less than or equal to that number. Therefore, the number of permutations is 6!, which equates to 6 x 5 x 4 x 3 x 2 x 1 = 720.

So, there are 720 different permutations of the letters in the word 'PLANTS' if all the letters are used without repetition.

https://brainly.com/question/23283166

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The answer is:

They spent $176 together.

We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.

Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:

[tex]p(t)=5x^{4}-3x^{3}+2x^{2}+24[/tex]

Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:

[tex]p(t)=2(5x^{4}-3x^{3}+2x^{2}+24)[/tex]

Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.

Calculating we have:

[tex]p(2)=2(5*(2)^{4}-3*(2)^{3}+2*(2)^{2}+24)=2(5*16-3*8+2*4+24)[/tex]

[tex]p(2)=2(5*16-3*8+2*4+24)=2(80-24+8+24)=2*88=176[/tex]

Hence, we have that they spent $176 together.

Have a nice day!

Answer:

c

Step-by-step explanation:

Answer:

[tex]g(x)=\frac{x-12}{4}[/tex]

Step-by-step explanation:

To find the inverse of y=4x+12, all you need to is swap x an y and then remake y the subject.

y=4x+12

Swap x and y:

x=4y+12

Solve for y:

Subtracting 12 on both sides:

x-12=4y

Dividing 4 on both sides:

[tex]\frac{x-12}{4}=y[/tex]

So [tex]g(x)=\frac{x-12}{4}[/tex]

Answer:

[-12 + x]\4 = g(x)

Step-by-step explanation:

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

I guess one more does not hurt.

Notice that choice D is equivalent to the given equation y = -4x - 12.

The only equation that does not cross the given equation is y = -4x.

They have THE SAME SLOPE. This means they are parallel and thus lead to NO SOLUTION.

ANSWER: y = -4x

Answer:

[tex]y=-4x[/tex]

Step-by-step explanation:

A Linear System with no solution, therefore inconsistent, is graphically represented by a pair of parallel lines.

According to Analytic Geometry, a parallel line shares the same slope.

Given the options, the only parallel line to [tex]y=-4x-12[/tex] is [tex]y=-4x[/tex] Since [tex]y=-4(x+3)[/tex] despite having the same slope, is actually the same line [tex]y=-4x+12[/tex]

So [tex]y=-4x[/tex] will form a system that has no solution.

Answer:

d no is correct

I hope it will help you

The equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

According to the theorem;

[tex]x^2 + y^2 = r^2[/tex]

Given the following

x = [tex]r cos \theta[/tex]

y = [tex]r sin \theta[/tex]

Substitute into the formula

[tex](rcos \theta)^2 + (r sin \theta)^2 = r^2\\cos^2 \theta + sin^2 \theta =1[/tex]

Multiplying through by minus, the equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

Learn more on Pythagoras theroem here: https://brainly.com/question/343682

Answer:

[tex]\large\boxed{\left(-\dfrac{6}{5},\ -\dfrac{8}{5}\right)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+y=-4&(1)\\y=3x+2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\2x+(3x+2)=-4\\2x+3x+2=-4\qquad\text{subtract 2 from both sides}\\5x=-6\qquad\text{divide both sides by 5}\\\boxed{x=-\dfrac{6}{5}}\qquad\text{put it to (2)}\\\\y=3\left(-\dfrac{6}{5}\right)+2\\\\y=-\dfrac{18}{5}+\dfrac{10}{5}\\\\\boxed{y=-\dfrac{8}{5}}[/tex]