Which expression is equivalent to (3/4)^-2 A: -9/16 B: 16/9 C: -6/8 D: 9/16

Arrange the following set of decimal numbers in order from smallest to largest.

Setler [38]

Answer:

Step-by-step explanation:

0.31=0.3100

0.409=0.4090

0.414=0.4140

0.4186

arranging smallest to largest

0.3100,0.4090,0.4140,0.4186

or 0.31,0.409,0.414,0.4186

6 0

3 years ago

What is the y-intercept of y = 5 (6.8)^x a. 5 b. 6.8 c. 1 d. x

ivolga24 [154]

The answer to this question is A, the graphs y intercept is 5

7 0

2 years ago

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

8 0

2 years ago

2. The number of atoms of a particular chemical element is modelled by

____ [38]

9514 1404 393

Answer:

a) 600

b) see below

c) 1.26 hours

Step-by-step explanation:

a) The value of y when x=0 is the coefficient of the exponential term:

y = 600·3^(-0) = 600·1 = 600

There were 600 atoms to start.

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b) see attached for a graph

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c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.

If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.

150 = 600·3^(-x)

150/600 = 3^(-x)

log(1/4) = -x·log(3)

x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595

After about 1.26 hours, there were 150 atoms.

6 0

3 years ago

Find (3.3 × 10^4) + (1.9 × 10^5)

scoundrel [369]

Answer:

$2.23 \times 10^{5}$

Step-by-step explanation:

We have to find the sum of two numbers following the steps as described in the question.

The question is in the form of fill in the blanks.

Now, the given sum is $(3.3 \times 10^{4} )+(1.9 \times 10^{5} )$

= $(3.3 \times 10^{4} )+(19 \times 10^{4} )$

= $(3.3+19) \times 10^{4}$

= $22.3 \times 10^{4}$

= $2.23 \times 10^{5}$ (Answer)

5 0

3 years ago