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zhenek [66]
2 years ago
13

vector u is represented by the directed line segment RS and vector v is represented by the directed line segment OP. if R=(8,-2)

, S=(11,-6), O=(-3,-9), and P=(0,-13), are u and v equal?
Mathematics
1 answer:
melamori03 [73]2 years ago
8 0

The given points are

R=(8,-2) , S=(11,-6), O=(-3,-9), and P=(0,-13)

To find the value of u and v, we have to perform subtraction of the points . That is

u= RS = =

v = OP =  =

Since we get the same values of u and v , therefore the two vectors are equal .

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Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each
sergiy2304 [10]

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is x^{2} -30x+224\geq 0

Part 2) Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Part 1) Find the inequality that describes the relationship between the number of cookies each one of them has

Let

x----> the number of cookies when Jessica started

30-x ----> the number of cookies when Martha started

we know that

Each of them ate 6 cookies from their bag

so

The cookies left in each bag are

(x-6)  ----> Jessica

and (30-x-6)=(24-x) ---> Martha

The product is equal to (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

so

(x-6)(24-x)\leq 80\\ \\24x-x^{2}-144+6x\leq 80\\ \\-x^{2} +30x-144-80\leq 0\\ \\-x^{2} +30x-224\leq 0

Multiply by -1 both sides

x^{2} -30x+224\geq 0

Part 2) Solve the quadratic equation

x^{2} -30x+224\geq 0

Solve by graphing

The solution is x=16 cookies

so

(30-x)=30-16=14 cookies

therefore

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

The number of cookies left in each bag  is equal to

Jessica

16-6=10 cookies

Martha

14-6=8 cookies

Jessica has at least 2 cookies more than Martha

5 0
2 years ago
Read 2 more answers
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y
andriy [413]

Answer:

Step-by-step explanation:

We want a line parallel to 3x − 4y = 7.  Any such line will have an equation of the same form but a different constant.

If the new line is to pass through the point (-4, -2), replace x with -4 and y with -2.  We obtain:

3(-4) − 4(-2) = -12 + 8 = -4.  Thus, the desired new equation is 3x − 4y = -4.

This could also be written as 3x − 4y + 4 = 0.  We could also solve this for y, obtaining:

3x + 4 = 4y, or  y = (3/4)x + 1.

8 0
2 years ago
Read 2 more answers
The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of
grandymaker [24]

Answer:

At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Step-by-step explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

<u><em>Let </em></u>\mu<u><em> = mean gross annual incomes of certified welders</em></u>

So, Null Hypothesis, H_0 : \mu = $20,000    

Alternate hypothesis, H_A : \mu \neq $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is <u>One-sample z test</u> <u>statistics</u> as we know about the population standard deviation;

                              T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean income

            \sigma = population standard deviation = $2,000

            n = sample size

Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

3 0
2 years ago
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as signi
klio [65]

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

  1. When the first dice is 5 and the second is 6.
  2. When the first dice is 6 and the second is 5.

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

P=\dfrac{X}{N}=\dfrac{2}{36}=0.055

This probability is not equal or less than 0.05, so it is not significant at 0.055.

3 0
2 years ago
10. If PQRS is a parallelogram, then P - R is:<br>(a) 20<br>(b) 30<br>(c) 90<br>(d) 0​
statuscvo [17]

Answer:

d) 0

Step-by-step explanation:

P -R = 0

Because in parallelogram, opposite angles are equal.

4 0
2 years ago
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