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3 years ago

WILL GIVE BRAINLIEST

Mathematics

2 answers:

Tanya [424]3 years ago

8 0

Answer:

Step-by-step explanation:

These are similar triangle

We can use ratios to solve

12 12+4

------ = ----------

9 9+DC

Using cross products

12( 9+DC) = 9*(12+4)

12 (9+DC) = 9*16

Divide each side by 12

12/12 (9+DC) = 9*16/12

9+DC = 12

Subtract 9 from each side

9+DC-9 =12-9

DC =3

notka56 [123]3 years ago

8 0

Answer:

3 units

Step-by-step explanation:

We can see that triangle ADE is similar to triangle ACB.

Therefore the ratios of the lengths of their sides must be equal.

We can write AD/AC = AE/AB

we are given AD = 9, AE = 12 and AB = 12 + 4 = 16

Substituting the above values into the equation:

AD/AC = AE/AB

9 / AC = 12/16 (rearranging)

(AC)(12) = (9)(16)

AC = (9)(16)/12

AC = 12

We can also see that

DC = AC - AD

DC = 12 - 9

DC = 3 units

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Please help i am stuck and trying not to fail lol. also if you can show work pls

wel

Given:

The figure of rectangle.

To find:

a. The diagonal of the rectangle.

b. The area of the rectangle.

c. perimeter of the rectangle.

Solution:

(a)

In a right angle triangle,

$\sin \theta=\dfrac{Perpendicular}{Hypotenuse}$

$\sin 30=\dfrac{12}{Hypotenuse}$

$\dfrac{1}{2}=\dfrac{12}{Hypotenuse}$

$Hypotenuse=12\times 2$

$Hypotenuse=24$

So, the diagonal of the of the rectangle is 24 units.

(b)

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

$\tan 30=\dfrac{12}{Base}$

$\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}$

$Base=12\sqrt{3}$

Length of the rectangle is 12 and width of the rectangle is $12\sqrt{3}$ . So, the area of the rectangle is:

$Area=length \times width$

$Area=12 \times 12\sqrt{3}$

$Area=144\sqrt{3}$

So, the area of the rectangle is $144\sqrt{3}$ sq. units.

(c)

Perimeter of the rectangle is:

$P=2(length+width)$

$P=2(12+12\sqrt{3})$

$P=24+24\sqrt{3}$

$P\approx 65.57$

Therefore, the perimeter of the rectangle is about 65.57 units.

4 0

3 years ago

A spinner can land on either red, blue, green, or yellow (the wedges are the same size). you spin twice. what is the probability

melisa1 [442]

There are four (4) colors to choose from. The number of sample space is equal to 4. With the condition given in this item, the probability of landing on blue on the first spin is equal to 1/4. Similarly, the probability of landing on yellow on the second spin is 1/4.

P = (1/4)(1/4)

P = 1/16

Answer: 1/16

5 0

4 years ago

A person must score in the upper 7% of the population on an admissions test to qualify for membership in society catering to hig

olya-2409 [2.1K]

Answer:

The minimum score a person must have to qualify for the society is 162.05

Step-by-step explanation:

Problems of normally distributed samples can be 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 problem, we have that:

Test scores are normally distributed with a mean of 140 and a standard deviation of 15. This means that $\mu = 140, \sigma = 15$ .