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3 years ago

Find the value of x

Mathematics

1 answer:

GuDViN [60]3 years ago

7 0

Answer:

x = 12

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

3x+19 + 5x = 115

Combine like terms

8x + 19 = 115

Subtract 19 from each side

8x+19 -19 = 115 -19

8x = 96

Divide each side by 8

8x/8 = 96/8

x =12

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Komok [63]

The rules of exponents tell you to add exponents in the numerator and subtract those in the denominator. A power of a power causes the exponent to be multiplied.

$\dfrac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^2x^{-4}z^{3}}=2^{3}x^{(3\cdot3-3-(-4))}y^{-4}z^{(2\cdot3-2-3)}\\\\=\dfrac{8x^{10}z}{y^{4}}$

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3 years ago

Ben made a model (shown below) of the square pyramid he plans to build when he grows up.

elena-s [515]

Answer:

$336 m^2$

Step-by-step explanation:

The surface area of a square pyramid is the sum of the area of the squared base + 4 times the area of each triangular face, therefore:

$A=A_b + 4A_t$

where:

$A_b=L^2$ is the area of the base, where

L is the length of the base

$A_t=\frac{1}{2}Lh$ is the area of each triangular face, where

h is the height of the face

Substituting,

$A=L^2+2Lh$

For the model in this problem,

L = 12

h = 8

Therefore, the surface area here is:

$A=12^2 +2(12)(8)=336$

4 0

3 years ago

Read 2 more answers

Drag the simplified value into the box to match each expression.

AveGali [126]

Answer:

2^{3} +1⋅4−3 = 9

2^{0}+10−4⋅2 = 3

3+5^{2} -6⋅4 = 4

Step-by-step explanation:

4 0

3 years ago

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Mashcka [7]

Answer:

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Step-by-step explanation:

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3 years ago

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

Aleks [24]

Answer:

A.) 24.08 seconds

B.) 825.42 metres

Step-by-step explanation:

function of time is given as

h ( t ) = − 4.9 t 2 + 118 t + 115 .

Where a = -4.9, b = 118, c = 115

Let's assume that the trajectory of the rocket is a perfect parabola.

The time t the rocket will reach its maximum height will be at the symmetry of the parabola.

t = -b/2a

Substitute b and a into the formula

t = -118/-2(4.9)

t = 118/9.8

t = 12.041 seconds

Since NASA launches the rocket at t = 0 seconds, the time it will splash down into the ocean will be 2t.

2t = 2 × 12.041 = 24.08 seconds

Therefore, the rocket splashes down after 24.08 seconds.

B.) At maximum height, time t = 12.041s

Substitute t for 12.041 in the function

h ( t ) = − 4.9 t 2 + 118 t + 115

h(t) = -4.9(12.041)^2 + 118(12.041) + 115

h(t) = -4.9(144.98) + 118(12.041) + 115

h(t) = -710.402 + 1420.82 + 115

h(t) = 825.42 metres

Therefore, the rocket get to the peak at 825.42 metres

6 0

3 years ago