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3 years ago

Identify the correct justification for each step, given that ∠2 and ∠3 are complementary, and m∠1=m∠3.

Mathematics

1 answer:

blondinia [14]3 years ago

6 0

Answer:

Option A is correct because sum of m<2 and m<3 are complementary. So m<2+m<3 =90° .

Step-by-step explanation:

Given: <2 and <3 are complementary angles.

Definition of complementary angles says if two angles sum is equal to 90 degrees then they are called complementary angles.

Statement Reason

1.<2 and <3 are complementary 1. Given

2. m<2+m<3 =90° 2. Definition of complementary <s

3. m<1= m<3 3. Given

4. m<1+m<2= 90° 4.Substitution property of =

5. <1 and <2 are complementary 5. Definition of complementary <s.

Option A matches with the given. We can not use addition properties of equality for statement 2 so, other options are incorrect.

So, according to the given options A is correct.

You can learn more about complementary angles at brainly.com/question/21400774

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Consider julie's scores on three final exams (x), along with the class means and standard deviations: subject x mean standard de

Viktor [21]

Consider julie's scores on three final exams (x), along with the class means and standard deviations: subject x mean standard deviation history 75 70 5 english 92 90 10 math 80 70 3 science 84 70 7 compared to the other students who took the test, in what class is was julie's highest score?

Answer: In order to find in what class Julie's has scored highest, we need to find the z score corresponding to Julie's score. The subject who has the highest z score will indicate that Julie has scored highest in that subject.

Z score for History:

$z=\frac{75-70}{5} =1$

z score for english:

$z=\frac{92-90}{10} =0.2$

z score for math:

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Since the z score for Math is highest, therefore, in Math class Julie's score is highest.

3 0

4 years ago

Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the mi

timama [110]

Answer:

(a)The missing measurements are 9 feet and $16\frac{1}{4}$ feet$ .

(b)Therefore, the length of the fence is $97\frac{1}{2}$ feet$

Step-by-step explanation:

The diagram of the yard is attached below.

(a)I have labeled the missing dimensions of the yard as x and y.

Therefore:

$y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9$ feet$

Similarly:

$x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4}$ feet$

The missing measurements are 9 feet and $16\frac{1}{4}$ feet$ .

(b)Length of the Fence

The fence is rectangular shaped with:

Length = $31\frac{1}{2}$ feet$

Width = $17 \frac{1}{4}$ feet$

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

$=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2}$ feet$

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4 years ago

The price of a computer component is decreasing at a rate of

vovangra [49]

Answer:

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Step-by-step explanation:

a) Each year, the price is multiplied by (1 - 14%) = 0.86. After t years, the price will be 0.86^t times what it was in the beginning. This function is an exponential function.

b) After 3 years, the price will be ...

$90×0.86^3 ≈ $57.25

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4 years ago