Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 7(x + 2) = 35[/tex]

[tex]\qquad \tt \rightarrow \: 7x + 14 = 35[/tex]

[tex]\qquad \tt \rightarrow \: 7x = 35 - 14[/tex]

[tex]\qquad \tt \rightarrow \: 7x = 21[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{21}{7} [/tex]

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Using linear function concepts, it is found that a set of ordered pairs with a slope of [tex]-\frac{1}{2}[/tex] is perpendicular to the given set.

A linear function is modeled by:

y = mx + b

In which:

When two sets are perpendicular, the multiplication of their slopes is -1. The set (1,8) and (2,10) has slope given by:

m = (10 - 8)/(2-1) = 2.

Then, for the perpendicular set:

2m = -1

m = -1/2.

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Answer:

Step-by-step explanation:

A pack of sugar costs £1.25 for 500g. How much for 1kg?

500g = 1/2Kg or 0.5 Kg

so 1.25£ is 0.5Kg (1/2)

1.25 * 2 = 2.50£ is your answer

Answer:

2.5

Step-by-step explanation:

Change 500g into kg

500g=500/1000kg

        =0.5kg

If                  0.5kg cost 1.25

what about 1kg

   = (1*1.25)/0.5

   = 1.25/0.5

   =2.5

Answer:

k = g + a

Step-by-step explanation:

g = k - a ( add a to both sides )

g + a = k , that is

k = g + a

I assume [[x]] stands for "the largest integer smaller than or equal to x".

If x is already an integer, then x itself satisfies the definition. 23 is an integer that is equal to 23. So [[23]] = 23.

Answer:

3

Step-by-step explanation:

bc im vary smert

Answer:

15

Step-by-step explanation:

Start by factoring each number into primes.

30  =  2 · 3 · 5

60  =  2 · 2 · 3 · 5

75  =  3 · 5 · 5

Look for prime numbers used in all three factorizations and include these common primes in the greatest common factor (GCF).

Since 3 is used at least one time in all three factorizations, the GCF will contain one 3.

Since 5 is used at least one time in all three factorizations, the GCF will contain one 5.

Therefore, the GCF Fireside Flowers can use to divide the flowers into equal groups is 3 · 5 = 15.

Answer:

Whether you're buying a new car or a used car, or even leasing a car, you'll have to pay state sales tax. Nearly every state has a sales tax, ranging from under 3 percent to over 8 percent. The national average in the United States is 5.75 percent.

Please mark brainlest!

By understanding and applying the concepts of dilation and quadratic functions, the function g(x) is a vertically dilated version of f(x) by a factor of 5.

In this questions we know two quadratic equations of the form y = a · x². f(x) is known as the canonical function as a = 1 and g(x) is the consequence of dilating f(x) vertically by a factor of 5. Now we proceed to present graphically between the two functions.

In a nutshell, the function g(x) is a vertically dilated version of f(x) by a factor of 5.

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Answer:

False

Step-by-step explanation:

Beacuse the equation is 4+2>5 with equals 7

Answer:

x = 4 ...In the equation, substitute 4

4 + 2 > 5

6 > 5

(This sign > means greater than)

(This sign < means less than)

In this case of the equation, 6 > 5, it's True

Answer:

30 miles is the actual distance.

Step-by-step explanation:

3 3/4 = 15/4

15*2=30

f(p) = 3p - 2

f(2) = 3(2) - 2

f(2) = 6 - 2

f(2) = 4

Therefore, the answer is 4, so option C :)

Step-by-step explanation:

9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....

[tex]...[/tex] :)..

Answer:

son's present age = 30

father's present age=60

Step-by-step explanation:

his son's present age = x years

his father's present age = 2x years

before 20 years his son's age=(x-20) years

before 20 years father's age=(2x-20) years4(x-20)=(2x-20)

4x-80=2x-20

4x-2x=80-20

2x=60

x=30

All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

The rational root theorem suggests that for a polynomial function

f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

In the question, we are asked to find the potential rational roots of

f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.

Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.

By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},

or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.

Now, we can write all potential roots by calculating p/q.

p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}

Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

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Answer:

3  1/2

Step-by-step explanation:

Put '3' where 'y' is and compute :

[12 -3(3) ] / 2   + 3 [ (2(3)-4 )/3) =

   3/2              +   2  

    =   3  1/2

Answer:

y = -x +2

Step-by-step explanation:

Equation of a line in slope-intercept form :

   y = mx + b    where m = slope and 'b' is the y-axis intercept

y = -x-2    is in this form.....  slope m = -1      b = -2

   the parallel line will have the same slope = -1 and will look like

        y = -x + b

       to calculate the value of 'b' for this line, substitute in the point given:

             -2 = - (4) + b      shows b = 2

  so your line becomes   y = -x + 2

Answer:

  y =-x + 2

Step-by-step explanation:

    Parallel lines have same slope.

     y = -x - 2

Compare with the equation of the line in slope y-intercept form: y =mx + b

Slope = m = -1

So, equation of line: y = -x + b

Point(4 ,-2) is going through this line. so, substitute x = 4 & y = -2 in the above equation.

            -2 = -4 + b

          -2 + 4 = b

              [tex]\sf \boxed{b = 2}[/tex]

Equation of the required line:

            [tex]\sf \boxed{\bf y = -x + 2}[/tex]

Answer:

the answer is (3,4) is the solution to line A but to not line B

Answer:

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180

Alternate interior angles: When two parallel lines are intersected by a transversal, the pair of angles on the inner side of  each of these lines but on the opposite side of the transversal are called  alternate interior angles

In ΔABC,

  ∠1 + 90 + 38 = 180    {angle sum property of triangle}

         ∠1 + 128 =  180

               ∠1     = 180 - 128

            [tex]\sf \boxed{\bf \angle 1 = 52^ \°}[/tex]

AB // CD and AC is transversal.

 [tex]\sf \boxed{\bf \angle 3 = 38^\circ}[/tex]   {Alternate interior angles are equal}

In ΔACD,

      ∠2 + ∠3 + 63 = 180 {angle sum property of triangle}

       ∠2 + 38 +63  = 180

               ∠2  + 101 =180

                         ∠2 = 180 - 101

                      [tex]\sf \boxed{\bf \angle 2 = 79^ \°}[/tex]

The following are the appropriate notations is P(EIF)=P(E n F) / P(F).

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

As, from the property of conditional probability

P(EIF)=P(E n F) / P(F)

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Fold tracing paper so that the line segment's endpoints line up with each other ,  Option D is the correct answer.

A perpendicular is a line drawn at 90 degree to a given line or line segment .

Fold tracing paper so that the line segment's endpoints line up with each other.

After drawing a line segment ,

when the end point will be on each other and a crease will be made by pressing the paper , The crease formed will be perpendicular to the line segment.

Therefore,  Option D is the correct answer.

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Answer:

The correct answer is C.

Step-by-step explanation:

Fold tracing paper so that the line segment's endpoints line up with each other.

Answer:

7x² + 5x - 9

Step-by-step explanation:

(9x + 1) - (- 7x² + 4x + 10) ← distribute parenthesis by - 1

= 9x + 1 + 7x² - 4x - 10 ← collect like terms

= 7x² + 5x - 9

By direct observation on the graph and concept of relative minimum, we conclude that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).

Let be f a function that exists in a interval [a, b], there is a value c such that f(c) < f(x), for x ≠ c and x ∈ [a, b]. In this case, f(c) is the relative minimum of f. By direct observation, we find that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).

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Answer:

see below

Step-by-step explanation:

Acid in = acid out             acid out = 10 liters of 20% = .2 * 10 = 2

x = 5% amount

10-x = 40% amount

.05x  + .40 ( 10-x) =   .20 (10)

.05x + 4 - .4x = 2

-.35x = -2

x = 5.7 liters   of 5 %        10 - 5.7 = 4.3 liters of 40%

The value of g(-3)=-9

The function is a relation between two sets X and Y which are one-one or many-one. Here set X is called the domain and set Y is called codomain.

For example: f(x)=3x+9

To get the value of the function at any point of x, we have to put the number in the function to get its function value.

For example the value of f(x) in above function at x=a will be f(a)=3a+9

Similarly given function in the question

g(x)=2x+3

to get the value of g(x) at x=-3 put the value of x in the function,

g(-3)= 2(-3)+3 = -3

Therefore the value of g(-3) is -3.

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Answer:

0,5                    b

Step-by-step explanation:

Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.

A linear function is modeled by:

y = mx + b

In which:

Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:

C(n) = 1200 + 45n.

Now, we have to solve for n when C(n) = 4800, hence:

1200 + 45n = 4800

45n = 3600

n = 3600/45

n = 80.

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Answer:

$882.75

Step-by-step explanation:

825 x 7% = 57.75 <- thats the price of the tax

57.75 + 825 = 882.75

Step-by-step explanation:

[tex] = 3 \sqrt{6} [/tex]

[tex] = \sqrt{ {3}^{2}.6 } [/tex]

[tex] = \sqrt{9.6} [/tex]

[tex] = \sqrt{54} [/tex]

The answer is A.