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Masteriza [31]
3 years ago
12

What is the image point of (1, -3) after a translation right 5 units and up 2 units?

Mathematics
1 answer:
Natali [406]3 years ago
8 0

Answer:(6, -1)

Step-by-step explanation:

You might be interested in
the side length ofthe square porch behind macis house is (3x + 2) feet. The porch has a perimeter of (14x - 2) feet. What are th
andriy [413]

Answer:

The porch is 17 ft by 17 ft

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

P = 4( 3x+2)

P = 12x+8

We know P = 14x-2

14x-2 = 12x+8

Subtract 12x from each side

14x-2 -12x = 12x+8-12x

2x -2 = 8

Add 2 to each side

2x-2 +2 = 8+2

2x= 10

Divide by 2

2x/2 = 10/2

x = 5

The side  is 3x+2

                 3*5+2

                  15+2

                   17

The porch is 17 ft by 17 ft

5 0
3 years ago
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box cos
RideAnS [48]

Answer:

Jillian sold 15 ten-oz bags and 9 sixteen-oz bags.

Step-by-step explanation:

Let x represent number of 10-oz bags and y represent number of 16-oz bags.

We have been given that Jillian sold 24 boxes of cookies in total. We can represent this information in an equation as:

x+y=24...(1)

We are also told that 10 oz. box costs $3.50, while the 16 oz. box costs $5.00, so the cost of x 10-oz bags would be 3.50x and cost of y 16-oz bags would be 5y.

At the end of one week, she collected $97.50. We can represent this information in an equation as:

3.5x+5y=97.50...(2)

Now, we will use substitution method to solve our system of equations. From equation (1), we will get:

y=24-x

Substitute this value in equation (2):

3.5x+5(24-x)=97.50

3.5x+120-5x=97.50

-1.5x+120=97.50

-1.5x+120-120=97.50-120

-1.5x=-22.5

\frac{-1.5x}{-1.5}=\frac{-22.5}{-1.5}

x=15

Therefore, the number of 10-oz boxes sold be Jillian is 15.

Now, we will substitute x=15 in equation (1) to solve for y.

15+y=24

15-15+y=24-15

y=9

Therefore, the number of 16-oz boxes sold be Jillian is 9.

8 0
2 years ago
Please help, which one is the correct choice?
bazaltina [42]
222222222222 my good friend
5 0
2 years ago
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
2 years ago
Anybody know!!!! SOS
ikadub [295]

Answer:

x = 50

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon of n sides is

(n - 2)180

This polygon is a quadrilateral with 4 sides. n = 4

(n - 2)180 = (4 - 2)180 = 2(180) = 360

The sum of the measures of the interior angles of the quadrilateral is 360 degrees.

We have angles of 110 deg, 2x deg, x + 10 deg, and 90 deg. We add their measures and set teh sum equal to 360. Then we solve for x.

x + 10 + 2x + 110 + 90 = 360

3x + 210 = 360

3x = 150

x = 50

4 0
2 years ago
Read 2 more answers
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