A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
* Infinitely many solutions exist because the two situations describe the same line.
* Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
* No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
* Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.

[tex]\frac{11z}{z+3}=13-i,z\in\mathbb{C}[/tex]

First, multiply both sides by [tex]z+3[/tex],

[tex]11z=(13-i)(z+3)[/tex]

[tex]13z+39-iz-3i=11z[/tex]

Collect terms and put z on the left,

[tex]2z-iz=3i-39[/tex]

[tex]z(2-i)=3i-39[/tex]

[tex]z=\frac{3i-39}{2-i}[/tex]

Division of complex numbers is defined by multiplying both denominator and numerator with complex conjugate of the denominator,

[tex]z=3\frac{(i-13)(2+i)}{(2-i)(2+i)}[/tex]

Multiply out,

[tex]z=3\frac{2i-1-26-13i}{5}[/tex]

[tex]z=3\frac{-11i-27}{5}[/tex]

The result is,

[tex]z=-\frac{81}{5}-\frac{33}{5}i[/tex]

Hope this helps :)

Answer:

1000

Step-by-step explanation:

35^2: 1225

15^2: 225

1225 - 225

Answer: 6 m

A ball thrown upwards from the altitude 4 m,

hits a roof and returns back to the ground.

upward movement:  s= −t²+3t+4

downward movement: s=-2t²+t+7

Step-by-step explanation:

Let's calculate the intersection:

[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]

Sorry, i have forgotten the picture.

Answer:

4.13=4.130

If there is a 0 at the end of a decimal then you can drop it.

The statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

From the given options the correct expression which represents equality will be 4.13 = 4.130. The value of both the numbers is the same. There is not any significance of 0 at the end of the expression.

Therefore, the statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.

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Answer:

-27

Step-by-step explanation:

Let x = 6 and y = -3

[tex]-(6)+7(-3)\\-6-21\\-27[/tex]

Answer:

Step-by-step explanation:

Please Mark my answer brilliant

Answer:

450 people

Step-by-step explanation:

The number of people running a race this year will be 450.

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that last year, Rob set up the Road Runner Race for his school. The race was 1,200 meters long and 188 people signed up to run the race. 38 people did not show up to run. This year, there will be 3 times as many runners as last year.

The number of people running a race this year:-

Number = ( 188 - 38 ) x 3

Number = 150 x 3

Number = 450

Therefore, the number of people running a race this year will be 450.

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Answer:

y=3/2x^2+4x-2

Hope it helps

Answer:

f'(1) = 7/2

Step-by-step explanation:

We are given the function: [tex]f'(x)=\frac{7}{2\sqrt{x} }[/tex]

To find f'(1), substitute the value for x and evaluate it.

[tex]f'(1)=\frac{7}{2\sqrt{1} }\\\\f'(1)=\frac{7}{2(1)}\\\\f'(1)=\frac{7}{2}[/tex]

Therefore, f'(1) = 7/2.

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

Answer:

16 ft

Step-by-step explanation:

Each edge of wall = √256 ft = 16 ft

Answer:

Step-by-step explanation:

-8 *  9 * 1

If you are going to get - 72, you need to have an odd number of minus signs.

4 * 3 * - 6

You must be careful of the limits. You can't use something like 36 * 2  * 1 because the numbers don't fall within +/- 10

You could use 6*6*-2

9514 1404 393

Answer:

Step-by-step explanation:

If Charles is 22 years older, he will be double Danielle's age when she is 22. If that is 10 years from now, Danielle is 12 and Charles is 34.

Answer:

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Answer:

C. 10,080

Step-by-step explanation:

We can multiply to find how many minutes there are in 1 day.

24 * 60 = 1,440

Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.

1,440 * 7 = 10,080

Best of Luck!

Answer:

15

Step-by-step explanation:

Complementary angles add to 90 degrees

8x+27 + 6x-21 = 90

Combine like terms

14x+6 = 90

Subtract 6 from each side

14x+6-6 = 90-6

14x = 84

Divide by 14

14x/14 = 84/14

x=6

We want angle B

B = 6x-21 = 6*6-21 =36-21 = 15

Answer:

D.

Step-by-step explanation:

5/4=1.25, -2[tex]\sqrt{2}[/tex] = -2.828

Therefore,

1.25 (5/4), 1.04, -0.34, -2.828 (-2[tex]\sqrt{2}[/tex]), -17

Answer:

53,800,013

need brainliest!!!

Answer:

s snsnnssjsjjsnsnsjs

es 17 es

Answer:

Step-by-step explanation:

I think the answer should be that there is an if -- then way the statement is worded. Quite often if then statements are used in this kind of experiment. Beyond that I can't make any comment. I don't know that it truly is testable, but it sounds like it should be.

Answer:

The hypothesis includes an explanation and makes a prediction.

Step-by-step explanation: I took the quiz on primavera and got that answer

9514 1404 393

Answer:

  a.

Step-by-step explanation:

For an even-index radical, ...

  [tex]\sqrt[n]{x^n}=|x|\qquad\text{n even}[/tex]

This lets us simplify the given expression as follows:

  [tex]\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}[/tex]

Answer:

x = 2515

Step-by-step explanation:

5000 = 2x - 30

2800 = x

140 kilograms of corn is needed to feed 2800 chickens.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the number of kilograms of corn needed to feed 5000 chickens is 30 less than twice the number of kilograms needed to feed 2800 chickens.

Assume that [x] kilograms of corn is needed to feed 2800 chickens.

for 2800 chickens → [x] Kg of corn is needed

for 1 chicken → [x/2800] Kg of corn is needed.

So, we can write -

5000 × [x/2800] = 2x - 30

50x/28 = 2x - 30

50x = 28(2x - 30)

50x = 56x - 28 x 30

50x - 56x = - 840

- 6x = - 840

6x = 840

x = 140

Therefore, 140 kilograms of corn is needed to feed 2800 chickens.

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Answer:

boys : girl

5 : 6

Step-by-step explanation:

boys : girl

480: 576

Divide each side by 96

480/96 : 576/96

5 : 6

Boys = 576

Girl = 480

Now , dividing both numbers by GCF.

[tex] \large\bf{\red{ \longrightarrow}} \tt \: \frac{ \cancel{480} \: ^{5} }{ \cancel{576} \: ^{6} } \\ [/tex]

[tex] \large\bf{\red{ \longrightarrow}} \tt \: \frac{5}{6} \\ [/tex]

Answer:

It's yes

Step-by-step explanation:

Answer:

yep

Step-by-step explanation:

number is even, so it can be evenly divided by 2. :)

Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula

The values of, t, for which the height of the rocket is 82 feet are;

t = 12.21 seconds or t = 0.42 seconds

Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth

The known parameters of the rocket are;

The initial upward velocity of the rocket, v = 202 ft./s

The given function representing the height, h, (in feet) after t seconds is presented as follows;

H = 202·t - 16·t²

The unknown;

The time for which the height of the rocket is 82 feet

Method;

Substitute H = 82 feet in the height function equation and solve for t as follows;

When H = 82, we get;

82 = 202·t - 16·t²

Therefore;

16·t² - 202·t + 82 = 0

Dividing the above equation by 2 gives;

(16·t² - 202·t + 82)/2 = 0/2

8·t² - 101·t + 41 = 0

By using the quadratic formula, we get;

[tex]\mathbf{t = \dfrac{101 \pm \sqrt{(-101)^2 - 4 \times 8 \times 41} }{2 \times 8} = \dfrac{101 \pm \sqrt{8889} }{16}}[/tex]

Therefore, the values of t given by rounding off to the nearest hundredth are;

t = 12.21 or t = 0.42

The values of the time, t, at which the height of the rocket is 82 feet are t = 12.21 seconds or t = 0.42 seconds

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Answer:

Step-by-step explanation:

Point-slope equation for line of slope m that passes through (x₀, y₀):

y-y₀ = m(x-x₀)

Slope =3 and (x₀, y₀)=(-3,0)

y = 3(x+3)

y = 3x+ 9

:::::

Slope-intercept equation for line of slope m and y-intercept b:

y = mx+b

m=1 and b= -4:

y = x-4