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Grace [21]
3 years ago
15

Enter a range of values for x. 85° 25 5x - 10 [ ? ] Enter

Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0
<h3>Answer: 2 < x < 7</h3>

==================================================

Explanation:

We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.

Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)

In symbols we say

5x - 10 < 25

We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.

Put the two inequalities together and we get 0 < 5x - 10 < 25

------------

Solve for x

0 < 5x - 10 < 25

0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides

10 < 5x < 35

10/5 < 5x/5 < 35/5 ... dividing all sides by 5

2 < x < 7

We have x between 2 and 7, and not equal to either endpoint.

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Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between
ivolga24 [154]

Answer:

  • 197.93 km

Step-by-step explanation:

Let the base camp is point A and boats' locations after two hours are points B and C.

By connecting the three points together we get a triangle ABC with sides:

  • AB = 50*2 = 100 km
  • AC = 70*2 = 140 km

The angle between AB and AC is:

  • 60 + 50 = 110 degrees (opposite directions from south)

We are looking for the distance BC, which can be found by using the law of cosines:

  • BC² = AB² + AC² - 2AB*AC*cos ∠BAC
  • BC² = 100² + 140² - 2*100*140*cos 110°
  • BC²  = 39176.56 (rounded)
  • BC = √39176.56 = 197.93 km (rounded)

The distance between the boats is 197.93 km.

7 0
2 years ago
The Washingtons but a studio apartment for $240,000. They pay a down payment of $60,000. What percent of the purchase price woul
Ludmilka [50]
It would be 5%. I know the answer is right I just don’t know how to explain it. Sry. But I hope this helps.
5 0
3 years ago
Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work.
docker41 [41]
<span>3x^2y^2 − 2xy^2 − 8y^2 =
y^2 (3x^2 - 2x - 8) =

factoring with leading coefficient:

for ax2+bx+c find two numbers n,m, that m*n = a*c and m+n = b
</span><span><span>
3x^2 - 2x - 8
a=3, b=-2, c=-8
</span>a*c = 3*(-8) = -24
-24=(-6)*4 and -6+4=-2, so m=-6 and n=4

replace bx with mx + nx and factor by grouping
</span><span>
3x^2 - 2x - 8 = </span>3x^2 -6x + 4x -8 = 3x(x-2) + 4(x-2) = (3x+4)(x-2)

answer:
<span>3x^2y^2 − 2xy^2 − 8y^2 = y^2(3x+4)(x-2)</span>

7 0
3 years ago
Point Q is plotted on the coordinate grid. Point P is at (10, −20). Point R is vertically above point Q. It is at the same dista
bixtya [17]

Answer:

Point R is at (−20, 10), a distance of 30 units from point Q

Step-by-step explanation:

Q has coordinates (-20,-20).

P has coordinates (10,-20)

Since point R is vertically above point Q, it will have the same x-coordinate as Q.

Let R have coordinates (-20,y).

It was given that;

|RQ|=|PQ|

\Rightarrow |y--20|=|10--20|

\Rightarrow y+20=10+20

\Rightarrow y=10+20-20

\Rightarrow y=10.

The coordinates of R are (-20,10).

The dstance from Q is 30 units.

3 0
3 years ago
Read 2 more answers
236462700.806 to the nearest cent
Rzqust [24]

Answer:

236462700.81

Step-by-step explanation:

The nearest cent refers to the hundreds place, because 100 pennies (or cents) make 1 dollar. We look at the number to the right of the hundredths place and if it is less than 5 we round down, but if it is 5 or more we round up. Since 6 is more than five we round up, and are left with 236462700.81.

8 0
2 years ago
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