If the area is 30cm and the length is 13,23 cm., what will be the width in
cm?​

Given:

The system of equations is:

Line A: [tex]y=x-4[/tex]

Line B: [tex]y=3x+4[/tex]

To find:

The solution of given system of equations.

Solution:

We have,

[tex]y=x-4[/tex]              ...(i)

[tex]y=3x+4[/tex]           ...(ii)

Equating (i) and (ii), we get

[tex]x-4=3x+4[/tex]

[tex]-4-4=3x-x[/tex]

[tex]-8=2x[/tex]

Divide both sides by 2.

[tex]-4=x[/tex]

Substituting [tex]x=-4[/tex] in (i), we get

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

[tex]y=-8[/tex]

The solution of system of equations is (-4,-8).

Now verify the solution by substituting [tex]x=-4, y=-8[/tex] in the given equations.

[tex]-8=-4-4[/tex]

[tex]-8=-8[/tex]

This statement is true.

Similarly,

[tex]-8=3(-4)+4[/tex]

[tex]-8=-12+4[/tex]

[tex]-8=-8[/tex]

This statement is also true.

Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.

Answer:

Option (1)

Step-by-step explanation:

From the graph of the piecewise function,

There are two pieces of the function,

1). Segment (1) having x < 0

2). Segment (2) having x ≥ 0

Segment (1),

Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)

Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                     = [tex]\frac{2-1}{-2-0}[/tex]

                                     = [tex]-\frac{1}{2}[/tex]

Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],

[tex]y-y'=m(x-x')[/tex]

[tex]y-2=-\frac{1}{2}(x+2)[/tex]

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

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

[tex]y=-0.5x+1[/tex] For x < 0

Segment (2),

Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)

Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]

                                    = 2

Equation of the segment passing through (0, -2) and slope = 2,

y - y' = m(x - x')

y + 2 = 2(x - 0)

y = 2x - 2 For x ≥ 0

Therefore, Option (1) will be the correct option.

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 30°

Opposite Leg = 7

Hypotenuse = x

Step 2: Solve for x

Answer:

x = 14

Step-by-step explanation:

Given :-

Solution :-

Since, it's right triangle we can use trignometery equations;

In this case we need to use sine equation.

sin θ = opposite side / hypotenuse

plug the values

sin 30° = 7 / x.

cross multiplication

x = 7 / sin 30°

Evaluate

x = 7 / 0.5

x = 14

Answer:

the answer is 113.398 grams

Answer:

2/3-4

3 1/3

-1*3.3=-3.3

-3 1/3 divided by 5/6

-4

so a

Hope This Helps!!!

Answer:

-2/3+4÷5/6

-2+12÷3÷5/6

10/3÷5/6

10/3x6/5

2/1x2/1

4/1

4

Step-by-step explanation:

hope this is helpful

Answer:

98.97

Step-by-step explanation:

I used my notes on page 34

Answer:

The probability is 0.5

Step-by-step explanation:

If there is a 50% chance of rain, then there is also a 50% chance of not rain.

Now let's write all the probabilities:

(just take the percentage and divide it by 100%)

Probability of rain: p = (50%/100%) =  0.5

probabiity for the squirrel to find food when it rains: q = (25%/100%) = 0.25

Then the joint probability, this is, the probability that rains and that the squirrel finds food, is equal to the product of these two probabilities, this is:

P1 = 0.5*0.25 = 0.125

And we also have the case where there is no rain.

Probability that does not rain: p' = (50%/100%) = 0.5

Probability that the squirrel finds food if doesn't rain: q = (75%/100%) = 0.75

The joint probability is:

P2 = 0.5*0.75 = 0.375

The total probability that the squirrel will find food is equal to the sum of the probabilities of the squirrel finding food if there is rain, and the probability of the squirrel finding food if there isn't rain, so the total probability is:

P = P1 + P2 = 0.125 + 0.375 = 0.5

Answer:

(-4,8)

Step-by-step explanation:

    x + 4y = 28

+  -x + y = 12

5y = 40

y = 8

-x + (8) = 12

-x + 8 = 12

-x = 4

x = -4

Answer:

7 / 6

Step-by-step explanation:

Given the points:

points (0, 0) and (6, 7)

Point 1 : x1 = 0 ; y1 = 0

Point 2 : x2 = 6 ; y2 = 7

The rise = y2 - y1 = 7 - 0 = 7

The run = x2 - x1 = 6 - 0 = 6

Ratio of Rise to Run = Rise / Run = 7 / 6

Answer:

354 $ is correct

Step-by-step explanation:

your v id dead

Answer:

x = -10

Step-by-step explanation:

verticle angles are congruent

80 + x = 70

Subtract 80 from both sides

x = -10

Answer:To test for divisibility, you look for answers that are whole numbers when you divide 59859 by either 2, 3, 5, 9, or 10.

To start divide it by each of them:

59859/2=29929.5

59859/3= 19953

59859/5= 11971.8

59859/9= 6651

59859/10= 5985.9

Now look at which of the choices are whole numbers

3 and 9 are the only non decimal numbers, therefore, C would be your answer.

Step-by-step explanation:

Answer:

option E, C

Step-by-step explanation:

From the graph we will find the equation of g(x).

g(x) is a parabola with vertex ( h, k) = ( 0, 9)

Standard equation of parabola is ,  y = a (x - h)² + k

                                                     y = a (x - 0)² + 9

                                                     y = ax² + 9 ----------  ( 1 )

Now we have to find a .

To find a we will take another point through which the parabola passes .

Let it be ( 3, 0).

Substitute ( 3 , 0 ) in  ( 1 ) =>  0 = a (3 )² + 9

                                     => - 9 = 9a

                                     => a = - 1

Substitute a = - 1 in ( 1 ) => y = -1 x² + 9

                                  => y = - x² + 9

Therefore , g(x) = -x² + 9

Now using the table we will find h(x)

 [tex]h(x) = 4^{x}[/tex]

So g(x) = -x² + 9 and [tex]h(x) = 4^{x}[/tex]

Option A : both function increases on ( 0, ∞ ) - False

               [tex]\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9[/tex]

                                  [tex]= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty[/tex]

g(x) decreases on ( 0 , ∞)

             [tex]\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}[/tex]

                                [tex]= \infty[/tex]

h(x) increases on ( 0, ∞)

option B : g(x) increasing on (- ∞, 0) - False

      g(x) = -x² + 9

       g( -2 ) = - (-2)² + 9

                 = - 4 + 9 = 5

       g ( -5) = - ( -5)² + 9

                =  - 25 + 9 = - 14

   As the value of x moves towards - ∞ , g(x) moves towards - ∞

   Therefore g(x) decreases on  (- ∞, 0)

Option C: y intercept of g(x) is greater than h(x) - True

         y intercept of g(x) = ( 0 , 9 )

         y intercept of h(x)  = ( 0 , 1 )

Option D : h(x) is a linear function - False

Option E : g(2) < h(2) - True

        g(x) =  -x² + 9

        g(2) = -(2)² + 9 = - 4 + 9 = 5

        h(x) = 4ˣ          

        h(2) = 4² = 16      

Answer:

First Option

Step-by-step explanation:

Answer:

nx12=p

Step-by-step explanation:

So every pack has 12 pencils. You multiply the packs of pencils that José bought with how much pencils per pack. Since José bought "n" packs of pencils, the equation is nx12. But the answer is also unknown since we don't know how much packs José bought, so the answer is "p", or the total number of pencils José bought.

Answer:

C

Step-by-step explanation:

Using the rule of exponents/ radicals

[tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] , then

[tex]121^{\frac{1}{2} }[/tex] = [tex]\sqrt{121}[/tex] = 11 → C

Answer:

it helps you balance your checkbook

Step-by-step explanation:

Balancing your checkbook means that you do a check in your account that shows how much money is available.

I hope it helps❤️

Answer:

Here is your answer

Step-by-step explanation:

xy = 1

Hope you like it : )

Answer:

Step-by-step explanation:

Surface area:

Volume:

Answer:

> V = 217.68 cm³

> S = 227.14 cm²

Step-by-step explanation:

We are required to find the surface area and the volume of the given figure . This question is from Combination of solids . As we can see that this figure is made up of a cuboid and cylinder.

Firstly let's find out the volume .

> V = V_( cuboid) + V_(cylinder)

> V = 9cm × 4cm × 5cm + π × ( 2cm)²× 3cm

> V = 180 cm³ + 3.14 × 4cm² × 3cm

> V = 180 cm³ + 37.68 cm³

> V = 217.68 cm³

Lets find the surface area :-

> S = S_( cuboid) + S_( cylinder) - πr²

> S = 2( 9×4 + 4× 5 + 5×9) cm² + 2×π×2cm × 3cm - 3.14 × (2cm)²

> S = 239.7 cm² - 12.56 cm²

> S = 227.14 cm²

Note :-

Answer:

4 m

Step-by-step explanation:

Since the flower garden is square :

Both length and width are equal :

Let :

Original side length = x

Increased length = x + 3

Area of square = s² (s = side length)

New area = 49 m²

That is ;

(x + 3)² = 49

Original length, x can be calculated thus ;

Take square root of both sides

x + 3 = √49

x + 3 = 7

x = 7 - 3

x = 4

Hence, original length of each side = 4 m

Answer:

8. B

9. B

Step-by-step explanation:

add all sides to get perimeter

multiply sections of the area to get area (length times width)

Answer:

it would be 4

12-4×2=12-8=4

Step-by-step explanation:

hope it helps you

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