(25 points) plz answer ASAP Use the Points in the figure to name the diagram.

find the measure of each angle acute angle in a right triangle where the measure of one acute angle is twice the difference of t

Marina86 [1]

Answer:

The measures of the acute angles are 38 and 52 degrees.

Step-by-step explanation:

In a right triangle, there are three angles, a right angle and two acute angles. In every traingle, the sum of the measures of the angles is 180 degrees. Let's call the acute angles $a$ and $b$ .

$a + b +90 = 180$

The problem also says that one angle is twice the difference of the other angle and 12. That would look like this:

$a = 2(b-12)$

Now we have two equations. If we simplify them, we get these:

$\left \{ {{a=90-b} \atop {a=2b-24}} \right.$

Now you can substitute $a$ in the first equation for $a$ in the second equation

$90-b=2b-24$

Add $b$ to both sides of the equation

$90 = 3b-24$

Add $24$ to both sides

$114 = 3b$

Divide both sides by 3

$38 = b$

Now, you can substitute $38$ for $b$ in the first equation and simplify.

$a = 90-38$

$a=52$

Therefore,

$a=52$ , and $b=38$

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3 0

2 years ago

Read 2 more answers

Each score in a set of data is multiplied by 3, and then 4 is subtracted from the result. If the original mean is 10 and the ori

olganol [36]

The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

Mean: 10*3 = 30

Standard deviation: 5*3 = 15

Secondly "change of origin" when every score in a data set by a constant, its mean get added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation

Mean: 30 - 4 = 26

Standard deviation: Remains same = 15

Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.

Learn more about Mean and standard deviation here

brainly.com/question/26841432

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5 0

1 year ago

X+7≥18<br> The solution is ??

frozen [14]

Answer:

$x \geq 11$

Step-by-step explanation:

$x+7 \geq 18$

$x \geq 18-7$

$x \geq 11$

5 0

3 years ago

Read 2 more answers

Graph: y – 3 = } (x + 2)

Natalija [7]

Answer:x2 355b. Hhgguyuy

Step-by-step explanation:

7 0

2 years ago

Sara hina and Arslan have a total of RS 390in their wallet . Sara has Rs. 7more than Hina .Arslan has 3 times what sara has . Ho

Brums [2.3K]

Answer:Sara hina and Arslan Have RS79.4,RS 72.4 and RS238.2 respectively.

Step-by-step explanation:

Step 1

Let the amount that hina has be x

the amount that sara has be represented as 7+x

and the amount that Arslan have be represented as 3(7+x)

such that the total amount in their wallet which is 390 can be expressed as

x+7+x + 3(7+x)=390

Step 2

Solving

x+7+x +21+3x=390

5x+28=390

5x==390-28

x=362/5=72.4

Hina has RS 72.4

Sara =7+x==72.4+77= RS 79.4

Arslan =3(7+x)=3 x 79.4=RS 238.2

5 0

2 years ago