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ella [17]
3 years ago
11

What is the value of x in the equation LaTeX: \frac{3}{2}\left(4x-2\right)-3x=5-\left(x+2\right) 3 2 ( 4 x − 2 ) − 3 x = 5 − ( x

+ 2 ) ?
Mathematics
1 answer:
Helen [10]3 years ago
6 0

Answer:

3/2

Step-by-step explanation:

Given the equation 3/2(4x-2)-3x = 5-(x+2)

Open the parenthesis

3/2(4x) - 3/2(2) -3x = 5-x-2

6x-3-3x = 3-x

3x-3 = 3-x

Collect like terms

3x+x = 3+3

4x = 6

Divide both sides by

4x/4 = 6/4

x = 3/2

Hence the value of x is 3/2

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Please help me!!! i will gladly give brainliest :)
True [87]

Given:

ΔONP and ΔMNL.

To find:

The method and additional information that will prove ΔONP and ΔMNL similar by the AA similarity postulate?

Solution:

According to AA similarity postulate, two triangles are similar if their two corresponding angles are congruent.

In ΔONP and ΔMNL,

\angle ONP\cong \angle MNL       (Vertically opposite angles)

To prove ΔONP and ΔMNL similar by the AA similarity postulate, we need one more pair of corresponding congruent angles.

Using a rigid transformation, we can prove

\angle NOP\cong \angle NML

Since two corresponding angles are congruent in ΔONP and ΔMNL, therefore,

\Delta ONP\sim \Delta MNL        (AA postulate)

Therefore, the correct option is A.

8 0
3 years ago
Read 2 more answers
Suppose that 70% of college women have been on a diet within the past 12 months. A sample survey interviews an SRS of 267 colleg
Fofino [41]

Answer:

The probability that 75% or more of the women in the sample have been on a diet is 0.037.

Step-by-step explanation:

Let <em>X</em> = number of college women on a diet.

The probability of a woman being on diet is, P (X) = <em>p</em> = 0.70.

The sample of women selected is, <em>n</em> = 267.

The random variable thus follows a Binomial distribution with parameters <em>n</em> = 267 and <em>p</em> = 0.70.

As the sample size is large (n > 30), according to the Central limit theorem the sampling distribution of sample proportions (\hat p) follows a Normal distribution.  

The mean of this distribution is:

\mu_{\hat p} = p = 0.70

The standard deviation of this distribution is: \sigma_{\hat p}=\sqrt{\frac{p(1-p}{n}} =\sqrt{\frac{0.70(1-0.70}{267}}=0.028

Compute the probability that 75% or more of the women in the sample have been on a diet as follows:

P(\hat p \geq 0.75)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}} \geq \frac{0.75-0.70}{0.028}) =P(Z\geq0.179)=1-P(Z

**Use the <em>z</em>-table for the probability.

P(\hat p \geq 0.75)=1-P(Z

Thus, the probability that 75% or more of the women in the sample have been on a diet is 0.037.

7 0
3 years ago
Please help me I need to submit this asap
frez [133]

Answer:

D

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\frac{f(b)-f(a)}{b-a}

Here { a, b ] = [ - 1, 2 ], thus

f(b) = 4 ← from (2, 4 )

f(a) = \frac{1}{2} ← from (- 1, \frac{1}{2} ) , thus

average rate of change = \frac{4-\frac{1}{2} }{2-(-1)} = \frac{\frac{7}{2} }{3} = \frac{7}{6} → D

8 0
3 years ago
Explain why there are infinitely many solutions to the equation<br> sin X = 1/2
Soloha48 [4]

Answer:

Well, everything can be turned into a half.

Step-by-step explanation:

7 0
3 years ago
Divide $150 into the ratio 2:5:3
pentagon [3]

Answer:

$30, $75, $45

Step-by-step explanation:

We can set up an equation, where x is an unknown value:

2x+5x+3x=150

10x = 150

x=15

Now that we know what x is, we can plug x in to solve for 2x, 5x, and 3x:

2x=2*15=30

5x=5*15=75

3x=3*15=45

Therefore, the answer is $30, $75, $45

5 0
2 years ago
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