what is the importance of mathematics?

Answer:

D 40 and 50

Step-by-step explanation:

Complimentary angles are equal to 90

Answer: D, 40 and 50

Steps:

1. Since complementary angles equal 90 degrees, 4r + 5r = 90

2. 4r + 5r is 9r

3. This makes the equation, 9r=90

4. Divide both sides by 9, and then you get r=10

5. Substitute r=10 into 4r and 5r

6. This should make 4(10) and 5(10)

7. Multiply and then get 40 and 50

Answer:

60

Step-by-step explanation:

x² = 144×25

= 3600

x =√3600 =60

9514 1404 393

Answer:

Step-by-step explanation:

The perimeter of a rectangle is given by ...

  P = 2(L +W) . . . . . where L and W represent the length and width

Filling in the given values, we have ...

  24 = 2(y +x)

Solving for y, we get ...

  12 = y + x . . . . . divide by 2

  y = 12 -x . . . . . . subtract x

The length y is the difference between 12 and the width x.

__

We want both x and y to be non-negative, so possible values of y range from 0 to 12.

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent amounts invested at 6% and 9%, respectively.

  y = 3x +58 . . . . . . . the amount invested at 9%

  0.06x +0.09y = 1097.19 . . . . . . total interest earned

__

Substituting for y, we have ...

  0.06x +0.09(3x +58) = 1097.19

  0.33x + 5.22 = 1097.19 . . . . . . . . . simplify

  0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22

  x = 3309 . . . . . . . . . . . . . . . . divide by 0.33

  y = 3(3309) +58 = 9985

$3309 is invested at 6%; $9985 is invested at 9%.

Answer:

122.5

Step-by-step explanation:

Use the area formula for a trapezoid (attached below as an image):

A = area in sq cm

a = top base

b = bottom base

h = height

Correspond the correct values with the variables:

a = 14

b = 21

h = 7

A = 1/2 * (14 + 21) * 7

A = 1/2*(35)*7

A = 17.5 * 7

A = 122.5 sq cm

Hope this helps (●'◡'●)

Answer:

6/5 n = a

Step-by-step explanation:

n = 5/6a

Multiply each side by 6/5

6/5 n = 6/5 * 5/6a

6/5 n = a

Answer:

[tex]532 cm^{2}[/tex]

Step-by-step explanation:

Answer:

the green area stands for the safe operation space

Step-by-step explanation:

u say b×h meaning say 80degrees ×9cm which is 720..

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

Answer:

Step-by-step explanation:

We know:

All triangles have internal angles that add up to 180°.

And

All right triangles have acute angles that up to 90°.

Therefore

x + 30° + 90° = 180°

x + 120° = 180°     |subtract 120° from both sides

x + 120° - 120° = 180° - 120°

x + 30° = 90°     |subtract 30° from both sides

x + 30° - 30° = 90° - 30°

The size of angle x will be 60°

It is a plane figure with three straight sides and three angles.

The steps are as follow:

z = 90°

y = 30°

x = ?

∴ x + y + z = 180°

∴ x + 30 + 90 = 180

∴ x + 120 = 180

∴ x = 60°

So the size of angle x will be 60°

Learn more about triangle here:

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Answer:

x < -5

Step-by-step explanation:

- 2x - 7 > x+ 8

Add 2x to each side

- 2x+2x - 7 > x+2x+ 8

-7 > 3x+8

Subtract 8 from each side

-7-8 > 3x+8-8

-15 > 3x

Divide by 3

-15/3 > 3x/3

-5 >x

x < -5

Answer:

The complete question is defined in the attached file please find it.

Step-by-step explanation:

For question 1:

[tex]\to 4-(3+1)^2 - 6\div 2 +4 \\\\\to 4-(4)^2 - 6\div 2 +4\\\\\to 4-16 - 3 +4\\\\\to 4-19 +4\\\\\to 4-15\\\\\to -11[/tex]

For question 2:

[tex]\to 7x^3 +2x -5x^2+6+ x+ 9+ 3x^3 +12x^2 \\\\\to 7x^3 +3x^3+12x^2 -5x^2+2x+x+9+6 \\\\\to 10x^3 +7x^2+3x+15 \\\\[/tex]

For question 3:

[tex]\to (2x^5- 3x^2+4)-(x^5+2x^2+7)\\\\\to 2x^5- 3x^2+4-x^5-2x^2-7\\\\\to x^5- 5x^2-3\\\\[/tex]

For question 4:

[tex]\to 3x^2(4x^3- 2x^2+7x -4) \\\\\to 12x^5- 6x^4+21x^3 -12x^2 \\\\[/tex]

For question 5:

[tex]\to 6x^2+9x-7 \ \ \text{when} \ \ x=2\\\\\to 6(2)^2+9(2)-7 \\\\\to 6(4)+9(2)-7 \\\\\to 24+18-7 \\\\\to 24+11 \\\\\to 35[/tex]

Answer:

B. ⁴/3π(6)³

Step-by-step explanation:

Formula for volume of a sphere = ⁴/3πr³

Where,

radius (r) = 6 units

Plug in the given value into the volume formula

Volume of the sphere = ⁴/3 × π × (6)³

Volume of the sphere = ⁴/3π(6)³

The expression that represents the volume of the given sphere is therefore ⁴/3π(6)³ cubic units.

The expression for the volume of the sphere is:

V = (4/3)*3.14*(6)^3

For a sphere of radius R. the volume is given by:

V = (4/3)*pi*R^3

Where pi = 3.14

Here we know that the radius is 6 units, so we can write the volume as:

V = (4/3)*3.14*(6)^3

As you can see, the second option (counting from the top) is the correct one.

If you want to learn more about spheres:

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Answer:

640 feet

Step-by-step explanation:

Count the length of each side. Add the lengths. Multiply by 20.

Start at the top left corner.

6 across

2 down

3 across

3 down

3 across

2 down

6 across

7 up

total = 32

32 X 20 = 640

Answer:

áedw

Step-by-step explanation:

đá

Answer:

75

Step-by-step explanation:

Answer:

1 + 1 = 3 - 1 = 2

Step-by-step explanation:

Im Smart

(4)^2-3(4)=4Answer:

Step-by-step explanation:

Answer:

If i am not wrong the answer is 12

Answer:

Yes

Step-by-step explanation:

Given:

Number of people (n) = 30

Mean wage in california = 24.66

Incomplete information;

Sample mean =23.41

Standard deviation = 2.35

Yes, the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

Answer:

the one above is correct

Step-by-step explanation:

h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).

Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.

The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).

x-intercept = (2, 0)

y-intercept = (0, 7.5)

Step-by-step explanation:

The x-intercept can be found by setting y = 0. Thus,

[tex]15x + 4(0) = 30 \Rightarrow x = 2[/tex]

Therefore, the x-intercept is (2, 0).

The y-intercept can be found by setting x = 0:

[tex]15(0) + 4y = 30 \Rightarrow y = 7.5[/tex]

Therefore, the y-intercept is at (0, 7.5)

Answer:

i think its 7b^2+4c^2 ?

Step-by-step explana

Answer:

222

Step-by-step explanation:

add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222

The probability would be 1/52, since there are only 1 two of diamonds in all 52 cards.

Final answer. 1/52  or 1.92%

Answer:

13/52

Step-by-step explanation:

a standard 52-card deck has 13 diamond cards (1,2,3,4,5,6,7,8,9,10,J,Q,K)

P(diamond) = number of diamonds/number of cards in a deck = 13/52

Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.