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3 years ago

2. Determine if the two quadrilaterals are similar, if they are, state the scale factor.

Mathematics

1 answer:

rusak2 [61]3 years ago

7 0

Answer:

Yes, they are similar. The scale factor is 5/3

Step-by-step explanation:

The longest to the shortest side of quadrilateral KLMJ are: JM, ML, KJ, LK

The longest to the shortest side of quadrilateral QPSR are: QP, PS, RQ, SR

If the two quadrilaterals are similar, the following proportion must be satisfied:

JM = k*QP

ML = k*PS

KJ = k*RQ

LK = k*SR

where k is the scale factor. Solving for k and replacing with lengths:

k = 25/15 = 24/14.4 = 20/12 = 15/9 = 5/3

From the figure, we can also see that:

∠M ≅ ∠P

∠L ≅ ∠S

∠R ≅ ∠K

∠Q ≅ ∠J

Therefore, the two quadrilaterals are similar.

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MariettaO [177]

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's find out the gradient (Slope " m ") of line q ;

$\qquad \sf \dashrightarrow \:m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$\qquad \sf \dashrightarrow \:m = \dfrac{4 - 0}{0 - 1}$

$\qquad \sf \dashrightarrow \:m = - 4$

Now, since we already know the gradient let's find of the equation of line by using its Slope and one of the points using point slope form of line :

$\qquad \sf \dashrightarrow \:y - 4 = m(x - 0)$

$\qquad \sf \dashrightarrow \:y = mx + 4$

Now, plug in the value of gradient ~

$\qquad \sf \dashrightarrow \:y = - 4x + 4$

here we can clearly observe that, the Area under the curve can easily be represented as :

$\qquad \sf \dashrightarrow \:y < - 4x + 4$

Since, all the values of y that lies in the shaded region is smaller than the actual value of y for the corresponding values of x in the equation of line q

5 0

2 years ago

Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $7.50. Barry orders o

Evgesh-ka [11]

Answer:

Coffee = $2.00

Juice = $1.50

Doughnut = $1.00

Step-by-step explanation:

Given

Let:

$c = coffee\\ j= juice\\ d = doughnut$

So, we have:

Anna

$2c + j + 2d = 7.50$

Barry

$c + 3d = 5.00$

Cathy

$3c + j + 4d = 11.50$

Required

The price of each

We have:

$2c + j + 2d = 7.50$

$c + 3d = 5.00$

$3c + j + 4d = 11.50$

Make c the subject in: $c + 3d = 5.00$

$c = 5.00 - 3d$

Substitute $c = 5.00 - 3d$ in $2c + j + 2d = 7.50$ and $3c + j + 4d = 11.50$

$2c + j + 2d = 7.50$

$2[5.00 - 3d] + j + 2d = 7.50$

$10.00 - 6d+ j + 2d = 7.50$

Make j the subject

$j = 7.50 - 10.0 +6d - 2d$

$j = -2.50 +4d$

$3c + j + 4d = 11.50$

$3[5.00 - 3d] + j + 4d = 11.50$

$15.00 - 9d + j + 4d = 11.50$

Make j the subject

$j = 11.50 - 15.00 + 9d -4d$

$j = -3.50 + 5d$

So, we have:

$j = -3.50 + 5d$ and $j = -2.50 +4d$

Equate both values of j

$-3.50 + 5d = -2.50 + 4d$

Collect like terms

$5d - 4d = 3.50 -2.50$

$d = 1.00$

Substitute $d = 1.00$ in $j = -3.50 + 5d$

$j = -3.50 + 5d$

$j = -3.50 + 5 * 1.00$

$j = -3.50 + 5.00$

$j = 1.50$

To solve for c, we substitute $d = 1.00$ in $c + 3d = 5.00$

$c + 3 * 1.00 =5.00$

$c + 3.00 =5.00$

Solve for c

$c =- 3.00 +5.00$

$c =2.00$

7 0

3 years ago

1/20

Vladimir [108]

Answer:

120th caller

Step-by-step explanation:

120 is the common number by 40 and 30. trust me on this I'm really good at this subject in math.

8 0

3 years ago

Divide 1-k^3 by k-1

UNO [17]

Answer:

k 2 + k + 1

Step By Step:

Cancel the common factor.

Then.

k 2 + k +1 by 1

Gets you k2+k+1

7 0

3 years ago

Sal bought 2 shirts and a hat. Sal remembers each shirt was $10, and the total was $50. Which equation helps answer the question

Oksana_A [137]

Answer: the hat= $30. The equation you would use to solve is 2s+h=50

Step-by-step explanation:

2s+h=50

2(10)+h=50

20+h=50

-20. -20

h=30

3 0

3 years ago