Represent the system of linear equations 3x+y-5=0 and 2x-y-5=0 graphically. From the graph write solution of the system and also the area of the triangle formed by the lines and y axis

Answer:

Step-by-step explanation:

to decrease a number by 40% i would do

100% = number you got

50% divide by 2

10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%

then take the 40% away from the 100%

hope this helps :)

Answer:

7 x 9 x 11 x 13  +  13  is a composite number because the answer is a positive number which is 9022.

7 x 9 x 11 x 13  +  13  is a positive integer that can be formed by multiplying small positive numbers which are 7, 9, 11 and 13. Equivalently, 9022 is a positive integer that has at least one divisor other than 1 and itself. For example, 9022 can be divided by 2. 9022 is exactly a number but it is not a prime number.

I hope you will understand my explanation!

Answer:

All real values of x such that x ≥-3

Step-by-step explanation:

g(x) = sqrt(x+3)

A sqrt must be greater than or equal to zero

sqrt (x+3) ≥ 0

Square each side

x+3≥ 0

Subtract 3 from each side

x ≥-3

The restrictions on x are x ≥-3

That means the domain is x ≥-3

All real values of x such that x ≥-3

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

[tex]g(x)=\sqrt{x+3}[/tex]

A square root must have a value of greater than or equal to 0.

[tex]\sqrt{x+3}\geq 0[/tex]

Square both sides.

[tex]x+3\geq 0[/tex]

Subtract 3 from both sides.

[tex]x\geq -3[/tex]

Answer:

Hope this helps. If not let me know and I'll explain it better

Answer:

2 < h <= 3

Step-by-step explanation:

4 + h <= 7

h <= 3          (subtract 4 on both side)

h + 1 > 3

h > 2           (subtract 1 on both side)

So, 2 < h <= 3

Answer: 52.9

Step-by-step explanation:

The value 5 is rounded up.

Hope it helps <3

Answer:

52.9

Step-by-step explanation:

round up using the last number. since its 5, you round up

Answer:

H. 1/9.

Step-by-step explanation:

The area of a circle is calculated by solving for π[tex]r^2[/tex].

The smallest circle has an area of π[tex]1^2[/tex] = π * 1 = π.

The middle ring will then have an area of π[tex]2^2[/tex] - π = π * 4 - π = 4π - π = 3π.

The largest ring will then have an area of π[tex]3^{2}[/tex] - π[tex]2^{2}[/tex] = 9π - 4π = 5π.

5π + 3π + π = 9π

So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.

Your answer is H. 1/9.

Hope this helps!

Answer:

80 pages

Step-by-step explanation:

Let's use a ratio to solve:

pages : seconds

   12    :       9

    4     :       3

    [tex]p[/tex]     :      60

It would seem that [tex]p[/tex] would equal 80. The printer can print 80 pages in 60 seconds or one minute.

Answer:

Radius = 6.46 meters

Height = 1.46 meters

Step-by-step explanation:

The volume of a cylinder = πr²h

In the above question, we were given

r = (x + 5) meters

h = x meters

Volume = 192 cubic meters

Hence,

192 = π × (x + 5)² × x

192 = π × (x² + 10x + 25) × x

192 = π × (x³ + 10x² + 25x)

Divide both sides by π

192/π = x³ + 10x² + 25x

61.115498147 = x³ + 10x² + 25x

x³ + 10x² + 25x - 61.12

This Quadratic equation is a polynomial

x = 1.46119

From the above:

Radius = (x + 5)meters

Radius = 1.46119 + 5 = 6.46119 meters

Approximately to 2 decimal places = 6.46 meters

Height = x meters

Height = 1.46119 meters

Approximately to 2 decimal places = 1.46 meters

Answer:

<2, <5

Step-by-step explanation:

<2 is a vertical angle so it is equal to 110

<5 is a corresponding angle and since the lines are parallel it is also equal to 110

Answer:

84cm²

Step-by-step explanation:

Perímetro de un rectángulo = 2L + 2W

Representemos la longitud del rectángulo = L

En la pregunta anterior se nos dijo que el ancho del rectángulo = es menor que 5 en la longitud

Por lo tanto, ancho del rectángulo = L - 5

Perímetro del rectángulo = 38 cm

Por lo tanto

38 = 2 (L) + 2 (L - 5)

38 = 2L + 2L - 10

38 + 10 = 4L

48 = 4L

L = 48/4

L = 12 cm

La longitud del rectángulo = 12 cm

Como L = 12, encontramos el ancho

Ancho = L - 5

= 12 cm - 5 cm

= 7 cm

El ancho del rectángulo = 7 cm

En la pregunta nos pidieron encontrar el área del rectángulo.

Área del rectángulo = Largo × Ancho

Área del rectángulo = 12 cm × 7 cm

Área del rectángulo = 84cm²

Answer:

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Step-by-step explanation:

Well slope-intercept form is [tex]y = ax + b[/tex].

Let's start with the slope.

In this case, finding the slope is easy.

It should have a negative slope.

So we can cross out answer choices A. and C.

Also, we can cross out D. because it just makes no sense, -10/3, if you start from the y-intercept and go down 10 and across 3, yeah that's

not the slope.

So we can cross out D.

The only answer choice left is B.

We can tell the y-intercept is 1/2 because like come on so B is the correct answer.

B. [tex]y = -\frac{3}{10}x + \frac{1}{2}[/tex]

Looking at the graph, we can figure out our y-intercept or b simply by looking at the line to see where it intersects the y-axis.

So, we can see that the line intersects the y-axis at 1/2 or 0.5

That means, our y-intercept or b is 1/2 (0.5).

Now, to find out the slope of the line, we can pick two pairs of coordinates on the line and plug it into the slope equation to figure out the slope.

Let's use the two coordinate pairs: (-5, 2) and (0, 1/2).

Plug it in.

1/2 - 2 = - 1.5

0 - - 5 = 5

-1.5/5 = -0.3

Convert it into a fraction: -0.3 = -3/10

Thus, our slope intercept form for this line is: y = -3/10 + 1/2

Answer:

2πr + 4a = 8

Step-by-step explanation:

Answer:

44.8

Step-by-step explanation:

cos α = adjacent leg/hypotenuse

cos 48° = 30/x

x = 30/(cos 48°) = 44.8

Answer:

Step-by-step explanation:

7x² - 4x - 3 = 0

Rewrite - 4x as a difference

That's

7x² - 7x + 3x - 3 = 0

Factorize the expression

7x( x - 1) + 3 ( x - 1) = 0

(7x + 3)( x - 1 ) = 0

7x + 3 = 0 x - 1 = 0

7x = - 3 x = 1

x = -3/7

The solutions are

x = - 3/7 or x = 1

Hope this helps you

Answer:

The speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.

Since the wind is moving south east, it is at 45 south of east or a bearing of 135.

Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles

Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles

The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles

The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles

The total vertical displacement of the plane is 176.64 miles - 42.43 miles =   134.21 miles

The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles

The direction of this displacement is thus

Ф = tan⁻¹(total vertical displacement/total horizontal displacement)

= tan⁻¹(134.21/62.43)

= tan⁻¹(2.1498)

= 65.05°

= 65.1° to the nearest tenth degree.

The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.

So the speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

v= 4/3πr³

4/3×314/100×8×8×8

•

= 2,143.573

Answer:

84

Step-by-step explanation:

Surface area is the combined area of the 2 dimensional planes.

6 × 5 + 3 × 4 × 1/2 × 2 + 6 × 3 + 4 × 6

30 + 12 + 18 + 24

= 84

The surface area is 84 square centimeters.

Answer:

5

Step-by-step explanation:

Since y equals 200 + 10x and y also equals 5x, then

200 + 10x = 50x

Subtract 10x from both sides.

200 = 40x

Divide both sides by 40.

5 = x

Answer: He must sell 5 sculptures.

Answer:

The airplane is 222 miles far from the airport.

Step-by-step explanation:

After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:

Airplane flies 290 miles (east) (290 km with an angle of 0º)

[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]

Airplane flies 290 miles (northwest) (290 km with and angle of 135º)

[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]

The resultant vector is equal to the sum of the two vectors:

[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]

[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]

[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]

The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:

[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]

[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]

The airplane is 222 miles far from the airport.

Answer:

C. all whole numbers

Step-by-step explanation:

Well Roberts can’t have a negative income and due to the number of violins being whole numbers, it is impossible to have 2.273 violins.

Hence, the annual income can only be whole numbers

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the hypotenuse we use Pythagoras theorem which is given by

a² = b² + c²

where a is the hypotenuse

So we have

a² = 10² + 3²

a² = 100 + 9

a² = 109

Hope this helps you

Answer:

10.4

Step-by-step explanation:

[tex]A = 1500(1.00167)^{12t}[/tex]

=================================

Explanation:

You could use the formula

[tex]A = P(1+\frac{r}{n})^{nt}[/tex]

to plug in P = 1500, r = 0.02 and n = 12 to get the answer above. This is the compound interest formula. The interest rate r is divided into n = 12 to account for monthly compounding. The original exponent t turns into 12t. So for instance, if t = 2 years go by, then 12*t = 12*2 = 24 months have gone by.

Answer:

I think that it should be

[tex] {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

[tex] {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)[/tex]

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

[tex]{(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} = 3(a - b)(b - c)(c - a)[/tex]

I am done .

I think that it should be

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

Step-by-step explanation:

Here,

we take , a - b = A,b-c = B , c - a= C

A+B+C = 0

we know that,

{a}^{3}  +  {b}^{3}  +  {c}^{3}   - 3abc = (a + b + c)(  {a}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca)

Here , A+B+C = 0

so,

A^3 +B^3 + C^3 = 3 ABC

now we put the values

{(a - b)}^{3}  +  {(b - c)}^{3}  +  {(c - a)}^{3}  = 3(a - b)(b - c)(c - a)

I am done .

Answer:

2.5 or 2 1/2

Step-by-step explanation:

i caculated do order of operations

Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.

Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.

"a to b"

"a:b"

There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).

a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.

The number in a terms ratio quantities of both numbers are to be positive

Answer:

[tex]Slope (m) = -\frac{2}{3}[/tex]

Step-by-step explanation:

To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.

Thus, on the line, let's pick 2 points as our coordinate pairs at:

When x = -6, y = 5 => (-6, 5), and

When x = 3, y = -1 => (3, -1)

Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)

[tex] Slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] Slope (m) = \frac{-1 - 5}{3 - (-6)} [/tex]

[tex] Slope (m) = \frac{-1 - 5}{3 + 6} [/tex]

[tex] Slope (m) = \frac{-6}{9} [/tex]

[tex]Slope (m) = -\frac{2}{3}[/tex]

Answer:

The steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Answer:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation:

f(x) = –3/4x + 9

The inverse, f¯¹(x) of the above expression can be obtained as follow:

f(x) = –3/4x + 9

Let y = f(x)

y = –3/4x + 9

Interchange x and y

x = –3/4y + 9

Making y the subject of the expression, we have:

x = –3/4y + 9

Rearrange

x – 9 = –3/4y

Cross multiply

4(x – 9) = –3y

Divide both side by –3

–4/3(x – 9) = y

Clear bracket

y = –4/3x + 12

Replace y with f¯¹(x)

f¯¹(x) = –4/3x + 12

Therefore, the steps include:

1. y = –3/4x + 9

2. x = –3/4y + 9

3. x – 9 = –3/4y

4. –4/3(x – 9) = y

5. y = –4/3x + 12

6. f¯¹(x) = –4/3x + 12

Step-by-step explanation: