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3 years ago

The vector PQ =(-3,2).Given that the point P is (1,4), find the coordinates of thepoint Q.

Mathematics

1 answer:

Yakvenalex [24]3 years ago

7 0

Answer:

Q = (- 2, 6 )

Step-by-step explanation:

PQ = q - p ← q and p are the position vectors

Add p to both sides

q = PQ + P = (- 3, 2) + (1, 4) = (- 3 + 1, 2 + 4) = (- 2, 6 ), that is

Q = (- 2, 6 )

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Straight angles Are extremely important in geometry. When two lines intersect , they form multiple angles. In the diagram below,

rusak2 [61]

When two straight lines intersect, the vertical opposite angles intersect. the other two angles are also equal. Let the known angle be x, then the other two adjacent angles are obtained subtracting twice of x from 360 and dividing the result by 2.

Therefore, the table can by filled as follows:

Row 1:

Given <GEF = 120°

<FEM is adjacent to <GEF, thus
$\angle FEM= \frac{360-2(120)}{2} \\ \\ = \frac{360-240}{2} = \frac{120}{2} =60^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <MEH = 120°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 60°.

Row 2:

Given <MEH = 150°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 150°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 30°.

Row 3:

Given that <FEM = 25°

<FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 155°

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 25°.

Row 4:

Given that <HEG = 45°

<HEG is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(45)}{2} \\ \\ = \frac{360-90}{2} = \frac{270}{2} =135^o$

<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <FEM = 45°

<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 135°.

4 0

4 years ago

Read 2 more answers

PLEASE HELP ASAP!!!!! <br><br>Which function could be shown in the graph below?<br>

Leokris [45]

Answer:

The answer is A

Step-by-step explanation:

I draw a graph

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4 years ago

Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewe

viktelen [127]

"Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1)Her gross weekly pay is currently $225.00.

(2)An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D EACH statement ALONE is sufficient.

E Statements (1) and (2) TOGETHER are NOT sufficient."

<h3><u>Answer:</u></h3>

Option D

EACH statement ALONE is sufficient.

<h3><u>Solution:</u></h3>

Given that, Carmen currently works 30 hours per week at her part-time job.

Her gross hourly wage were to increase by $1.50,

We have to find how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

Now, we are also given that,

(1)Her gross weekly pay is currently $225.00.

Let her hourly wage be $n.

Now, from 1 ⇒ her weekly payment = $225

$\begin{array}{l}{\rightarrow \text {Number hours worked } \times \text {hourly wage }=225} \\\\ {\rightarrow 30 \times n=225} \\\\ {\rightarrow 10 \times n=75} \\\\ {\rightarrow 2 n=15} \\\\ {\rightarrow n=7.5} \\\\ {\text {So her hourly wage is } \$ 7.5}\end{array}$

Now, after increasing the hourly age by 1.5 her hourly wage will be 7.5 + 1.5 = $9

And let the new number of hours required needed to work to get the same weekly wage be m hours.

$\begin{array}{l}{\text {Then, } m \text { hours } \times \$ 9 \text { per hour }=\$ 225} \\\\ {\rightarrow m \times 9=225} \\\\ {\rightarrow m=25}\end{array}$

So, she has to work work 25 hours to get the same amount.

<em>(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. </em>

Let the hourly wage be $ “a”

$\text { Then, } 20 \% \text { of } a=\$ 1.5 \rightarrow \frac{20}{100} \times a=1.5 \rightarrow 20 a=150 \rightarrow a=\$ 7.5$

Here, we got hourly wage from 2, which means we can obtain the new working time again by using the same process used in 1.

Hence, both statements are alone sufficient to solve the question. So option D is correct.

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4 years ago

PLEASE HELP IM BEGGING What steps do you use to solve a system of two equations using substitution?

dmitriy555 [2]

Answer:

B is equal to 2.5 and C is equal to -2.5

Step-by-step explanation:

You would first subtract b-3c from 3b-45c

Your equation would be:

3b-45c-(b-3c)=120-10

Then simplify the equation but distributing the negative sign:

3b-45c-b+3c=110

Then reorder the equation:

3b-b-45c+3c=110

Which equals 2b-42c=110

Then divide both sides by 2:

b-21c=55

b=55+21c

Subsitute 55+21c for b:

3(55+21c)-45c=120

Distribute the 3:

165+63c-45c=120

165+18c=120

Subtract 165 from both sides:

18c=120-165

18c=-45

Divide by 18 for both sides

c= -2.5

To find b, substitute -2.5 for c in the b=55+21c

b=55-52.5

b=2.5

Please correct me if I am wrong.

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3 years ago

What is the gcf of 7x^2, 7x and -28

Anika [276]

Answer:

Step-by-step explanation:

7 is a number that goes into all of the other numbers

7 X x^2 =7x^2

7 X x = 7x

7 X -4 = -28

6 0

4 years ago

The vector PQ =(-3,2).Given that the point P is (1,4), find the coordinates of thepoint Q.​

The vector PQ =(-3,2).Given that the point P is (1,4), find the coordinates of thepoint Q.