3. What is the value of the x in the solution to the system of linear equations below?

y = 8x − 8
3x + 2y = −16

A x = 0
B x = 2
C x = −5
D x = −8

Answer:

x < -6

Step-by-step explanation:

X/4 < -1.5

Multiply each side by 4

X/4*4 < -1.5*4

x < -6

Answer:1 yes. 2 yes. 3 no.

Step-by-step explanation:

i did it in the oms

Answer:

Janet has coins worth 252.5, 101, and 50.5.

Step-by-step explanation:

Let us call the three coins [tex]a,b[/tex], and [tex]c[/tex].

The first coin [tex]a[/tex] is 5 times another coin (let's say [tex]b[/tex]); therefore,

[tex]a = 5b[/tex],

and the third coin is 2 times the value of another coin (it's coin [tex]b[/tex]):

[tex]c =2b[/tex].

The total worth of all coins is 404; therefore,

[tex]a+b+c =404[/tex]

or

[tex]5b+b+2b =404[/tex]

[tex]8b =404[/tex]

[tex]\boxed{b = 50.5}[/tex]

with the value of [tex]b[/tex] in hand, we find [tex]a[/tex] and [tex]c[/tex]:

[tex]a = 5b = 5(50.5)[/tex]

[tex]\boxed{a = 252.5}[/tex]

and for [tex]c:[/tex]

[tex]c = 2 b = 2 (50.5)[/tex]

[tex]\boxed{c = 101}[/tex]

Thus, Janet has 3 coins worth 252.5, 101, and 50.5.

Answer:

x = 2.95

Step-by-step explanation:

Step 1:  Convert words into an expression

0.45 plus 9x equals 27

0.45 + 9x = 27

Step 2:  Solve for x

0.45 + 9x - 0.45 = 27 - 0.45

9x / 9 = 26.55 / 9

x = 2.95

Answer:  x = 2.95

Differential equation is a way to represents the relation between the functions and their variables. The solution to the differential equation given in the question is,

[tex]y=\dfrac{3}{15x-1}[/tex]

Given-

The equation in the question is,

[tex]{dy\times {dx}=5y^2[/tex]

Differential equation is a way to represents the relation between the functions and their variables.

Rewrite the equation,

[tex]\dfrac{dy}{5y^2} =dx[/tex]

Integration both sides,

[tex]-\dfrac{1}{5y} =x+c[/tex]

Here, c is the integrating constant.

Now the given initial condition is,

[tex]y(0)=3[/tex]

Use this for the integrated function to find the value of the constant,

[tex]-\dfrac{1}{5\times 3} =c[/tex]

[tex]c=-\dfrac{1}{15}[/tex]

Put this value in equation we get,

[tex]-\dfrac{1}{5y} =x-\dfrac{1}{15}[/tex]

[tex]y=\dfrac{3}{15x-1}[/tex]

Hence the solution to the differential equation given in the question is,[tex]y=\dfrac{3}{15x-1}[/tex]

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To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, use separation of variables and integration. Substitute the initial condition to find the specific solution.

To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, we can use separation of variables.

First, rewrite the equation as dy/y^2 = 5dx. Integrate both sides: ∫1/y^2 dy = ∫5 dx. This simplifies to -1/y = 5x + C.

Next, apply the initial condition y(0) = 3: -1/3 = 0 + C. Therefore, C = -1/3.

Substitute C back into the equation: -1/y = 5x -1/3. Solve for y: y = -1/(5x -1/3).

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Answer:

C (-2,1)

Step-by-step explanation:

−2x − y = 3 (1)

−9x − y = 17 (2)

(1) y = -2x - 3

(2) y = -9x - 17

-2x - 3 = -9x - 17

7x = -14

x = -2

y = -2(-2) - 3

y = 4 - 3

y = 1

Answer:

The dimensions of the sports field are 80 yards and 3 - 5x yards

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Width of the sports field = At least 60 yards

Area of the sports field = 240 - 400x square yards

We can conclude the shape of the sports field is rectangular.

2. Find the dimensions of the sports field.

A. We need to find the Greatest Common factor between 240 and 400, this way:

The factors of 240 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 .

The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 .

Then the greatest common factor is 80.

This GCF is also higher than 60, therefore it's one of the dimensions of the sports field.

Now, we calculate the other side of the sports, this way:

Second dimension of the sports field = (240 - 400x)/80

Second dimension of the sports field = 3 -5x

The dimensions of the sports field are 80 yards and 3 - 5x yards

Answer:

80(3-5x)

Step-by-step explanation:

240-400x

GCF: 80

Factored expression: 80(3-5x)

Answer:

Supplementary

Step-by-step explanation:

Since the two angles add up to 180 degrees, they are supplementary

Answer:

Reflexive

Step-by-step explanation:

The reflexive property of equality says that a given real number is always equal to itself.

For example :

[tex]y = y[/tex]

[tex]a = a[/tex]

[tex]b = b[/tex]

[tex]5 = 5[/tex]

are all examples of reflexive properties of equality.

[tex]4 + 9 = 4 + 9[/tex]

can be simplified to

[tex]13 = 13[/tex]

Which is explains why it is the reflexive property.

The wise man's age can be calculated by solving the equation 400 - 3x= 244, leading to the solution that he is 52 years old.

To determine the wise man's age, we need to set up an equation based on the given statement:

Let's call the wise man's age x

The statement says, "400 reduced by 3 times my age is 244." This can be written as:

400 - 3x = 244

To find x, follow these steps

400 - 3x = 244

3x = 400 - 244

3x = 156

x = 156 / 3

x = 52

So, the wise man is 52 years old.

Answer:

64°

180°-29°-87°=64°

Answer:

330 degrees

Step-by-step explanation:

a full rotation is 360 degrees and if you subtract 30 from 360 its 330

Final answer:

To complete a full rotation, Greg's ceiling fan, which has already rotated 30 degrees, needs to rotate one more time, as there are 330 degrees left to reach 360 degrees, which is a full rotation.

Explanation:

Greg's ceiling fan rotates 30 degrees and stops. To determine how many more times the fan needs to rotate to complete a full rotation, first, we need to know that one full rotation is equal to 360 degrees. As the fan has already rotated 30 degrees, we subtract this from 360 degrees:

360 degrees - 30 degrees = 330 degrees.

Now, because one full rotation is 360 degrees, we divide the remaining degrees by 360 to find the number of additional rotations needed:

330 degrees / 360 degrees per rotation = 0.9167 rotations.

Since a fan cannot complete a fraction of a rotation in terms of action, Greg's ceiling fan would need to rotate one more time to make it a complete rotation.

Mercury's distance = 5.8 x 10¹⁰

Venus' distance = 1.86 farther or more than Mercury's, namely 1.86(5.8 x 10¹⁰)

Earth's distance = 2.58 farther or more than Mercury's, namely 2.58(5.8 x 10¹⁰)

[tex]\bf \stackrel{\textit{venus' distance}}{1.86(5.8\times 10^{10})}\implies \begin{cases} 1.86(58000000000)\\ 107880000000\\ 1.0788\times 10^{11} \end{cases} \\\\\\ \stackrel{\textit{earth's distance}}{2.58(5.8\times 10^{10})}\implies \begin{cases} 2.58(58000000000)\\ 149640000000\\ 1.4964\times 10^{11} \end{cases}[/tex]

about how many meters farther is Earth's than Venus?  well, we can simply get their difference, we know the Earth is farther than Venus, so we can just subtract Venus' distance from Earth's to get the difference, namely 149640000000 - 107880000000.

[tex]\bf \stackrel{earth}{149640000000} - \stackrel{venus}{107880000000}~~ = ~~41760000000\implies \stackrel{\textit{rounded up}}{4.2\times 10^{10}}[/tex]

Answer:

Answer:

A-H are all true facts except for C which is false. that you have to show and prove are true and false.

Rate of change Purr Island (5 questions name the letter to the workings answer and matched it)  Show constant = 4 cats per year also seen as 40% rate of change. The common factor of 3 is only seen up on year 1 and year 4.   as year 0 shows 2 and 4 does not fit into 2. Explain year 2 that 4 does not fit into 10 on year 2 does not as 2p-6p-10p-14p-18p may change 10p over the last 3 years and CF 3 does not fit into that or any individual (adjacent) proceeding years.

Step-by-step explanation:

The rate of change Meow Island : 3 of the 8 questions is asked to say true to all of them (name the letter to the answer the workings after you wrote this and matched it) Shows it triples = and yes they have common factors of 3 show 2, 6, 18, 54, 162 each share a common factor of 3, draw tree diagrams  or show common factors of 3 and state you compare them to factors of 2    162>2x81   162> 3x27  54>2x27   54>3x18   18>2x9

18>3x6  6>2x3  6>3x2   2>2 population start number this doesnt have a common factor until it is factored into 6 ro show a common factor for 6. This also proves linear change occurs over the 4 years as population 2-156 is a series of  4 changes and underline the >3x numbers.  

Answer:

y = ¾x  

Step-by-step explanation:

y = mx + b, where

m = slope and

b = y-intercept

If slope = ¾ and y-intercept =0,  the equation is

y = ¾x

N = N₀* [tex](\frac{1}{2} )^{\frac{t}{h} }[/tex]

where N is how much you currently have

N₀ is the starting amount

t is the time

and h is the half life of the substance.

The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.

The half-life formula for a radioactive isotope is given by:

amount remaining = (amount initial) × e^(-t/t1/2)

Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.

Answer:

Answer : A   x=0

Step-by-step explanation:

hello :

f(x)= 2e^x + 1      graph red

g(x)= 1/2e^x + 5/2   graph bleue

2e^x + 1

= 1/2e^x + 5/2

by graphic solution   one solution x=0

Answer:

d) x=3

Step-by-step explanation:

Answer:

A) -1

Step-by-step explanation:

The missing graph is attached.

The possible answers were:

-1

-2

-3

-4

The average rate of change of a function f(x) on a≤x≤b is given by:

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

We want to find the best estimate of the average rate of change for the quadratic function on the interval 0 ≤ x ≤ 4.

From the graph, f(0)=0 and f(4)=-4

[tex] \frac{f(4) - f(0)}{4 - 0} = \frac{ - 4 - 0}{4 - 0} = \frac{ - 4}{4} = - 1[/tex]

Answer:

NO SOLUTION

Step-by-step explanation:

Step 1:  Subtract 5 from both sides

|x| + 5 - 5 ≤ 1 - 5

|x| ≤ -4

x ≤ NO SOLUTION

Answer:  NO SOLUTION

Answer:

B.  No

Step-by-step explanation:

We can test this theory using Pythagorean's theorem:

a² + b² = c²

12² + 20² = 24²

144 + 400 = 576

544 ≠ 576

So you can conclude that this is not a right triangle.

Answer:

83

Step-by-step explanation:

Add the numbers together

Answer:

80

Step-by-step explanation:

14 + 16 = 30

30 + 11 = 41

41 + 2 = 43

43 + 6 = 49

49 + 6 = 55

55 + 15 = 70

70 + 2 = 72

72 + 11 = 83, which, rounded to the nearest tenth, is 80

Step-by-step explanation:

-1 / 2 + x = -21 /4

x = -21/4 + 1/2

x = (-21 + 2)/4

x = -19/4

Step-by-step explanation:

1) Given quadratic expression is [tex]x^2-2x+2[/tex]

First equate the given expression to zero then we will find the roots.

Since the given equation is quadratic hence it has two roots.

For the quadratic equation we have that [tex]ax^2+bx+c=0[/tex]

Therefore roots [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] here a and b are coefficients of [tex]x^2andx[/tex] respectively and c is a constant

[tex]x^2-2x+2=0[/tex] here a=1 ,b=-2 and c=2

Now Substitute the values in [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] we get

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

[tex]=\frac{2\pm \sqrt{4-8}}{2}[/tex]

[tex]=\frac{2\pm \sqrt{-4}}{2}[/tex]

[tex]=\frac{2\pm \sqrt{4i^2}}{2}[/tex]

[tex]=\frac{2\pm2i}{2}[/tex]

[tex]=2(\frac{1\pm i}{2})[/tex]

[tex]x=1\pm i[/tex]

Therefore [tex]x=1+i[/tex] and [tex]x=1-i[/tex] are the roots of the given quadratic equation.  

2) Given that the number 16 has four roots.In other words, there are four complex numbers that can be entered in the square .

Let x be the given number 16

i.e., x=16

[tex]=2^4i^4[/tex] ( by using the formula [tex](ab)^m=a^mb^m[/tex] )

[tex]=16(1)[/tex] ( by [tex]i^2=-1[/tex] and [tex]i^4=(i^2)^2=(-1)^2=1[/tex] )

[tex]x^4=16=(2i)^4[/tex]

Therefore [tex]x^4=(2i)^4[/tex]

Since powers are same we can equate the bases ( bases are equal )

Therefore x=2i,2i,2i,2i are the roots of the given number 16 and they are complex numbers too

f(–2) = 1

Solution:

The table represents a function.

            x               f(x)

           –6               3

           –2                1

             0                4

             3               –2

To find the value of f(–2):

f(–2) means the value of f(x) for the corresponding x value –2.

In the table, if the x value is –2, then f(x) is 1.

See the value of f(x) which correspond to x = –2.

Hence f(–2) = 1.

Answer:

B

Step-by-step explanation:

From annual salary of 42,600, we have to subtract the following percentages:

Social Security:

0.062 * 42,600 = 2641.2

Medicare:

0.014 * 42,600 = 596.4

State Income Tax:

0.03 * 42,600 = 1278

Federal Income Tax:

0.13 * 42,600 = 5538

Total Deductions (from percentages) = 2641.2 + 596.4 + 1278 + 5538 = 10053.6

Now, remaining salary:

42,600 - 10053.6 = 32546.4 (annual)

Divided by 12 to get monthly:

32546.4 / 12 = 2712.2 (monthly)

Now, monthly deductions are:

260 + 280 = 540

Net Salary: 2712.2 -  540 =2172.2

Based on the information given his monthly net paycheck is: b. $2172.20.

Deduction

Social security=42,600×62%

Social security = 2641.2

Medicare=42,600×1.4%

Medicare = 596.4

State Income Tax= 42,600×3%

State Income tax = 1278

Federal Income Tax=42,600×13%

Federal Income Tax = 5538

Total Deductions = 2641.2 + 596.4 + 1278 + 5538

Total deduction= 10053.6

Net paycheck:

Net paycheck=(42,600 - 10,053.6)/12- (260 + 280)

Net paycheck=32,546.4/12-540

Net paycheck= 2712.2 -  540

Net paycheck=$2172.2

Therefore, his monthly net paycheck is: b. $2172.20.

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Answer:3xy

Step-by-step explanation:18x^2y^3= 3,6,x,x,y,y,y

6xy^2=. 3,2,x,y,y

3x^3y=. 3,x,x,x,y

All three have this in common a 3xy

The greatest common factor of the given polynomial's terms 18x^2y^3-6xy^2+3x^3y is 3xy. This is determined by factoring each term, and finding the greatest factor that occurs in all of the lists.

In mathematics, the greatest common factor (GCF) of a set of terms in a polynomial, is the largest term that divides each term exactly. To find the greatest common factor for the given polynomial 18x^2y^3-6xy^2+3x^3y, first, we list the factors for each term.

The term 18x^2y^3 factors as 2*3*3*x*x*y*y*y, the term -6xy^2 factors as -2*3*x*y*y, and the term 3x^3y factors as 3*x*x*x*y.

The greatest factor that occurs in all three lists is 3*x*y, so 3xy is the greatest common factor of the polynomial’s terms.

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Answer:

158

Step-by-step explanation:

20 + 60 + 40 = 120 + 38 = 158

I think this is right. (I tired)

Answer:

its C or 16

Step-by-step explanation: