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quiz 4-1 : classifying and solving for sides/angles in triangles gina wilson (all things algebra) URGENT

Answers

Answer 1

Answer:

Answer:

14.

$x = 11$ $m<B = 108$ $m<C= 36$ $m<D = 36$

15.

$x = 4$ $WX = 25$ $XY = 17$ $WY = 25$

Step-by-step explanation:

Solving (14):

$BC = BD$

$m<B = 13x - 35$

$m<C = 5x - 19$

$m<D = 2x + 14$

First, we solve for x.

Since sides $BC = BD$ , then

$m<C = m<D$

This is so because the theorem of ASA (Angle-Side-Angle)

So, we have:

$5x - 19 = 2x + 14$

Collect Like Terms

$5x - 2x = 19 + 14$

$3x = 33$

Divide both sides by 3

$x = 11$

Solving for m<B, m<C and m<D.

We simply substitute 11 for x in their respective expressions.

$m<B = 13x - 35$

$m<B = 13*11 - 35$

$m<B = 143 - 35$

$m<B = 108$

$m<C = 5x - 19$

$m<C= 5*11 - 19$

$m<C= 55 - 19$

$m<C= 36$

$m<D = 2x + 14$

$m<D = 2*11 + 14$

$m<D = 22 + 14$

$m<D = 36$

Solving (15):

$<X = <Y$

$WX = 9x - 11$

$XY = 4x + 1$

$WY = 7x - 3$

First, we solve for x.

Since $<X = <Y$ , then

$WX = WY$

This is so because the theorem of SAS (Side-Angle-Side)

So, we have:

$9x - 11 = 7x - 3$

Collect Like Terms

$9x - 7x = 11-3$

$2x = 8$

Divide both sides by 2

$x = 4$

Solving for WX, WY and XY

We simply substitute 4 for x in their respective expressions.

$WX = 9x - 11$

$WX = 9 * 4 - 11$

$WX = 36 - 11$

$WX = 25$

$XY = 4x + 1$

$XY = 4 * 4 + 1$

$XY = 16 + 1$

$XY = 17$

$WY = 7x - 3$

$WY = 7 * 4 - 3$

$WY = 28 - 3$

$WY = 25$

96

Step-by-step explanation:

Put x = 5 to the expression 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)

4(5 - 2)(5 + 3) + 7(5 - 2)(5 - 5) - 6(5 - 3)(5 - 5)

= 4(3)(8) + 7(3)(0) - 6(2)(0) = 96 + 0 - 0 = 96

Final answer:

The value of the given expression 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5) when x = 5 is 50.

Explanation:

The problem is asking to solve an expression for a given value of x. The given expression is 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5). We will start by substituting x = 5 into this expression.
In the first term, we substitute 5 in place of x in (x - 2) to get (5 - 2) = 3. Similarly, we substitute 5 in place of x in (x + 3) to get (5 + 3) = 8. Then, the first term becomes 4 * 3 * 8 = 96. We follow similar steps for the other two terms and calculate the values for those terms as -70 and 24 respectively. Finally, we add these three term values to arrive at the final result: "96 - 70 + 24 = 50".

Learn more about Substitution in Expressions here:

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Four times the quotient of 3 and 4

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The quotient of 3 and 4 is 0.75.

3/4 = 0.75

0.75 x 4 = 3...

So the answer is 3.

Disk requests come in to the disk driver for cylinders 10, 22, 20, 2, 40, 6, and 38, in that order. A seek takes 6 msec per cylinder. How much seek time is needed for (a) First-come, first served. (b) Closest cylinder next. (c) Elevator algorithm (initially moving upward). In all cases, the arm is initially at cylinder 20.

Answers

Answer:

Step-by-step explanation:

The order for FCFS is: 20->10->22->20->2->40->6->38.

Distance is

10+12+2+18+38+34+32 = 146

cylinders, so time is

146* 6 = 876 sec.

The order for elevator is:

20->20->22->38->40->10->6->2.

Distance is

0+2+16+2+30+4+4 = 58

cylinders, so time is

58 * 6 =348 msec.

The order for CCN is:

20->20->22->10->6->2->38->40.

Distance is

0+2+12+4+4+36+2 = 60

cylinders, so time is 60 * 6 =360 msec.

Patricia, audrey, and laticia are in a nursery buying plants for their gardens. Patricia orders six magnolias and two camellias. Audrey orders four camellias and three azaleas. leticia orders three magnolias, two camellias, and four azaleas. If patricia, audrey, and leticia paid $168.00, $150.30, and $222.50 respectively, what are the individual costs of a magnolia, a camellia, and an azalea?