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3 years ago

ABCD is a parallelogram. If AB= 3x -7 and CD = 5x - 19, find x.

Mathematics

1 answer:

kakasveta [241]3 years ago

8 0

Answer:

x=6

Step-by-step explanation:

3x-7=5x-19

12=2x

x=6

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Dimensional analysis: How many atoms are in a kilogram of silver, if there are 6.02 x 10^23 atoms per mole and silver weighs 107

kondor19780726 [428]

Answer:

5.58×10²⁴ atoms.

Step-by-step explanation:

From the question given above, the following data were obtained:

1 mole of silver = 107.9 g

Number of atoms in 1 mole of silver = 6.02×10²³ atoms.

Number of atoms in a kilogram of silver =.?

Next, we shall convert 1 kg of silver to grams (g). This can be obtained as follow:

1 kg = 1000g

Therefore, 1 kg of silver is equivalent to 1000g.

Finally, we shall determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:

107.9 g of silver contains 6.02×10²³ atoms.

Therefore, 1000 g of silver will contain = (1000 × 6.02×10²³) / 107.9 = 5.58×10²⁴ atoms.

Thus, a kilogram of silver contains 5.58×10²⁴ atoms.

6 0

3 years ago

Solve each inequality. Then compare the solutions.<br><br> 3x +4> 16<br> - 2x + 19< 11

Makovka662 [10]

Answer:

$3x + 4 > 16 \\ 3x > 16 - 4 \\ \frac{3x}{3} > \frac{12}{3} \\ x > 4 \\ \\ - 2x + 19 < 11 \\ - 2x < 11 - 19 \\ - 2x < - 8 \\ \frac{ - 2x}{ - 2} > \frac{ - 8}{ - 2} \\ x > 4 \\ \\ comparing \\ 4 < x > 4$

7 0

3 years ago

Given the following function, find f(-2), f(0), and f(4).

borishaifa [10]

Answer:

f(-2) = 0

f(0) = -4

f(4) = 12

Step-by-step explanation:

Given the function f(x) = x^2 - 4, we must plug in the values substituting x for each of the answers.

f(-2) = (-2)^2 - 4

-2 times itself is a positive 4, therefore:

f(-2) = 4 - 4

f(-2) = 0

We do the same for each answer.

f(0) = (0)^2 - 4

f(0) = -4

f(4) = (4)^2 - 4

f(4) = 16 - 4

f(4) = 12

6 0

3 years ago

Test scores are normally distributed with a mean of 500. Convert the given score to a z-score, using the given standard deviatio

Bond [772]

Answer:

The percentage of students who scored below 620 is 93.32%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 500, \sigma = 80$