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AveGali [126]
3 years ago
10

9 more than two-sevenths a number is 45. What is the number? Also, show an explanation.

Mathematics
1 answer:
photoshop1234 [79]3 years ago
3 0

Answer:

x=126

Step-by-step explanation:

let 'x' represent the unknown number

(2/7)x + 9 = 45

Subtract 9 from both sides

2/7x=36

Because the fraction is being multiplied by 'x' we can multiply both sides by its reciprocal (because a fraction multiplied by its reciprocal is 1 which would 'eliminate' it from the left side therefore isolating 'x').

x=126

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In the given figure △ABC ≅△DEC. Which of the following relations can be proven using CPCTC ?
Serhud [2]

Option B:

\overline{A B}=\overline{D E}

Solution:

In the given figure \triangle A B C \cong \triangle D E C.

If two triangles are similar, then their corresponding sides and angles are equal.

By CPCTC, in \triangle A B C \ \text{and}\ \triangle D E C,

\overline{AB }=\overline{DE} – – – – (1)

\overline{B C}=\overline{EC} – – – – (2)

\overline{ CA}=\overline{CD} – – – – (3)

\angle ACB=\angle DCE  – – – – (4)

\angle ABC=\angle DEC  – – – – (5)

\angle BAC=\angle EDC  – – – – (6)

Option A: \overline{B C}=\overline{D C}

By CPCTC proved in equation (2) \overline{B C}=\overline{EC}.

Therefore \overline{B C}\neq \overline{D C}. Option A is false.

Option B: \overline{A B}=\overline{D E}

By CPCTC proved in equation (1) \overline{AB }=\overline{DE}.

Therefore Option B is true.

Option C: \angle A C B=\angle D E C

By CPCTC proved in equation (4) \angle ACB=\angle DCE.

Therefore \angle A C B\neq \angle D E C. Option C is false.

Option D: \angle A B C=\angle E D C

By CPCTC proved in equation (5) \angle ABC=\angle DEC.

Therefore \angle A B C\neq \angle E D C. Option D is false.

Hence Option B is the correct answer.

\Rightarrow\overline{A B}=\overline{D E}

5 0
3 years ago
The average amount of time that students use computers at a university computer center is 36 minutes with a standard deviation o
frosja888 [35]

Answer:

2119 students use the computer for more than 40 minutes. This number is higher than the threshold estabilished of 2000, so yes, the computer center should purchase the new computers.

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 problem, we have that:

\mu = 36, \sigma = 5

The first step to solve this question is finding the proportion of students which use the computer more than 40 minutes, which is 1 subtracted by the pvalue of Z when X = 40. So

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

Z = \frac{40 - 36}{5}

Z = 0.8

Z = 0.8 has a pvalue of 0.7881.

1 - 0.7881 = 0.2119

So 21.19% of the students use the computer for longer than 40 minutes.

Out of 10000

0.2119*10000 = 2119

2119 students use the computer for more than 40 minutes. This number is higher than the threshold estabilished of 2000, so yes, the computer center should purchase the new computers.

8 0
3 years ago
Please help immediately
EleoNora [17]

Answer:

.90(85.00) would give the same result

Step-by-step explanation:

Rhonda is using the total cost of the item ($85.00) multiplied by the discount (10%) to find the total discount:  85 x 0.10 = 8.50.  Once Rhonda subtracts the discount ($8.50) from the total:  $85 - $8.50 = $76.50.  The other way to look at the problem, is that Rhonda is only paying for 90% of the total cost of the items, instead of 100% since she is receiving the 10% discount.  So, she would get the same final total by multiplying the cost of the items ($85.00) by 90%, or 0.90.  

4 0
3 years ago
I would appreciate if someone could answer this question I will give a brainlist for whoever explains and answers ;)
AleksandrR [38]

Answer:

Since this is a right triangle with one angle and hypotenuse given and opposite side unknown, we can use the definition of sine to find the unknown side.

sin 17 = x/hypotenuse = x/19

x = 19sin17 = 5.6

4 0
3 years ago
Please help me find the value of this angle?
yawa3891 [41]
I'm pretty sure it would have to be 155. Considering a flat line has an angle of 180 and if you subtract 180 from 25 you get 155.
7 0
3 years ago
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