The elevations of a town is 450 feet above sea level. The elevation of a lake is 25 feet below sea level. What is the difference between the elevations of the town and lake?

9514 1404 393

Answer:

  21 ≤ x < 48.3343

  19.4030 < t ≤ 62 1/3

Step-by-step explanation:

This sort of geometry has shown up in a number of different problems. Perhaps the most difficult was one in which the angles were given a specific linear relationship. Here, one of the angles is fixed, making the problem somewhat simpler.

The most straightforward approach is to simply say the unknown angle must lie between 0° and 180°. It turns out that is not the possible range of values. Rather there is a limit on the unknown angle. It will have an extreme value when both triangles are isosceles. The lengths of the equal sides in that case can be determined using the triangle with both angle and base length specified.

__

a) For the triangle to be isosceles (MA = MH = MY), the side lengths must satisfy ...

  AM·sin(62°/2) = 7.1/2

  AM = 3.55/sin(31°) ≈ 6.89269

At that point, angle HMY will satisfy ...

  AM = (6.33/2)/sin((2x -42)°/2)

  3.55/sin(31°) = 3.165/sin(x-21°)

  (x -21)° = arcsin(3.165/3.55·sin(31°)) ≈ 27.3343°

  x = 48.3343

Because angle HMY can be smaller than this value, its minimum is 0:

  2x -42 = 0

  x -21 = 0

  x = 21

That is, x can range between 21 and 48.3343.

__

b) Using similar logic on the other triangles, we find the unknown angle has an extreme value when the triangles are isosceles: CA = CB = CD = CD. As above, this will occur when ...

  (3t -7)° = 2·arcsin(17/16·sin(24°)) ≈ 51.2091°

  t = 19.4030

In this geometry, because AB > DE, the angle can only get larger than 51.2091°. Its upper limit is 180°, meaning that ...

  3t -7 ≤ 180

  3t ≤ 187

  t ≤ 62 1/3

In this geometry, the value of t can range between 19.4030 and 62 1/3.

_____

Additional comment

As we said at the beginning, your computer may be expecting you to come up with an answer that makes the unknown angle lie between 0 and 180°. For that range of angles, you have ...

  0 ≤ 2x-42 ≤ 180  ⇒  0 ≤ x -21 ≤ 90  ⇒  21 ≤ x ≤ 111

  0 ≤ 3t -7 ≤ 180  ⇒  0 ≤ t -7/3 ≤ 60  ⇒  7/3 ≤ t ≤ 187/3

Answer: 4.8

Step-by-step explanation:

Answer: y-intercept: (0, 12)

Step-by-step explanation:

[tex]a_n[/tex] = 9 − 3 (n − 1)

Use the slope-intercept form to find the slope and y-intercept.

  The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

     y = mx + b

  Find the values of m and b using the form y = mx + b.

     m = −3

     b = 12

  The slope of the line is the value of m, and the y-intercept is the value of b.

     Slope: −3

     intercept: (0, 12)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

  Find the x-intercept.

     To find the x-intercept(s), substitute in 0 for y and solve for x.

        0 = −3x + 12

      Solve the equation.

        Rewrite the equation as −3x + 12 = 0.

              −3x + 12 = 0

         Subtract 12 from both sides of the equation.

              −3x = −12

         Divide each term by −3 and simplify.

              x = 4

     x-intercept(s) in point form.

     x-intercept(s): (4, 0)

  Find the y-intercept.

     To find the y-intercept(s), substitute in 0 for x and solve for y.

        y = −3 ⋅ 0 + 12

   Solve the equation.

     Remove parentheses.

           y = −3 ⋅ 0 + 12

       Simplify −3 ⋅ 0 + 12.

           y = 12

     intercept(s) in point form.

     intercept(s): (0, 12)

  Create a table of the x and y values.

      x | y

     0 | 12

     4 | 0

Graph the line using the slope and the y-intercept, or the points.

Slope: −3

intercept: (0, 12)

Answer:

$3,700

Step-by-step explanation:

16% of 2500=400

400×3(years)=1,200

2500+1200=3700

Answer:

discrete

explanation:

Continuous keeps going but for blood pressure it has to stay in a certain zone.

When you multiply a whole number by a fraction, multiply the whole number by the numerator, then divide that by the denominator.

70 x 3/4 = (70 x 3) /4  = 210/4 = 52.5

Answer:

105/2 simplified - 52 1/2

Step-by-step explanation:

I got this answer by turning 70 into a fraction - 70/1 and using cross multiplication.

The correct matching will be given as A-1, B-3, and C-2.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The general equation is given below.

y = ax²

If the value of a is negative then downward parabola and if the value of a is positive then upward parabola.

If the value of a is less than one then parabola shrinks and if the value of a is more than one then parabola spreads.

Graph A is upward and shrinks parabolas so the equation will be y = x⁸.

Graph B is downward parabolas so the equation will be y = -3x⁸.

Graph C is upward and wider parabolas so the equation will be y = 0.25x⁸.  

Then the correct matching will be given as A-1, B-3, and C-2.

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ1

Answer:

x = 10

Step-by-step explanation:

Given the 2 equations

12x - 6y = 60

24x + 6y = 300

Adding the 2 equations term by term will eliminate the y- term, that is

36x + 0 = 360

36x = 360 ( divide both sides by 36 )

x = 10

Answer:

Perimeter: 30.4 cm

Area:57.76

Step-by-step explanation:

6cm+1.6cm=7.6cm

Perimeter:7.6x4

Area:7.6x7.6

Answer:  The unit rate is $5 per  mug.

Step-by-step explanation:

To find the the unit rate, you will find the amount  one mug will cost.

If there are 9 mugs  then to get it to one, you will have to divide 9 by 9, and the same way you will have to divide 45 by 9.

45 / 9 = 5  

Answer:

a) h = 15

b) x = 4

Step-by-step explanation:

a) set up a proportion:

  5 = h

   8     24

cross-multiply:

8h = 120

h = 15

b) x + 5 = x + 5 + 15

   5x + 1    5x + 1 + 35

cross-multiply:

(x + 5)(5x + 36) = (5x + 1)(x + 20)

5[tex]x^{2}[/tex] + 61x + 180 = 5[tex]x^{2}[/tex] + 101x + 20

180 = 40x + 20

160 = 40x

x = 4

Answer:

We can conclude that the distance from Sandy's Hotel to Trader Joes' Store is:

Step-by-step explanation:

From the coordinate plane, we can clearly identify that:

The distance from Sandy's Hotel to Trader Joes' Store can be calculated such as:

[tex]d=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

The distance between (-8, 9) and (-4, 2)

[tex]d=\sqrt{\left(-4-\left(-8\right)\right)^2+\left(2-9\right)^2}[/tex]

  [tex]=\sqrt{\left(-4+8\right)^2+\left(2-9\right)^2}[/tex]

  [tex]=\sqrt{4^2+7^2}[/tex]  

   [tex]=\sqrt{16+49}[/tex]

    [tex]=\sqrt{65}[/tex]

    [tex]=8.06[/tex] miles

Therefore, we can conclude that the distance from Sandy's Hotel to Trader Joes' Store is:

Answer:

For one hour Luke biked uphill 3 miles. After biking 3 miles uphill for one hour Luke stopped  at the store for 2 hours.

Step-by-step explanation:

Answer:

the answer is 144 feet and I don't really have an explanation

Answer:

Radius = 12 feet

Step-by-step explanation:

The area of a circle formula is Area = pi r^2 ("r" represents the radius)

The area of Circle Q is 144pi

You can substitute "Area" with 144pi, which would look like this:

144pi = pi x r^2

Now divide both sides with "pi", which gives:

144 = r^2

Finally, square root both sides:

sqrt(144) = sqrt(r^2)                     (sqrt = square root)

And that gives

12 = r

So the radius is 12 feet.

Answer:

The answer is B

Step-by-step explanation:

Answer:

ans is B sorry if it's direct

Answer:

a) x = 2   b) y = 5

Step-by-step explanation:

For a)

NOTE: Since line EC bisects angle FEG, it will be divided into 2 equal parts

angle FEG = 58

angle FEC = 11x + 7

angle CEG = 11x + 7

So:

58 = (11x + 7) + (11x + 7)

58 - 7 - 7 = 11x + 11x

44 = 22x

x = 2

For b)

angle AED = 16y + 10

angle AED = 90°

90 = 16y + 10

90-10 = 16y

y = 80/16

y = 5

Answer:

0.667

Step-by-step explanation:

Answer:

-14

if you are happy with my answer, please give brainliest :)

Step-by-step explanation:

-12+(-2)=-14

Answer: -14

Step-by-step explanation:

I know the answer but i dont know if it is supposd to be an equation

6 times 2+  (-8 divided by 4

       12                 -2

            12+-2

            -14

so what you put in the box will be the expression i just did

Pemdas

Parentheses

Exponents

Multiply

Divide

Add

Subract

Answer:

B

Step-by-step explanation:

The rate at Randy's store is 1 gallon of gas for $3

The rate at Sarah's store is 1 gallon of gas for $2.80

So, Randy's store is more expensive.

Answer:

Angel U=65

Step-by-step explanation:

115+x=180

x=180-115

x=65

65+50+x=180

x=180-115

x=65

angles: 50, 65,65

this triangle is isosceles

Check:

50+65+65=180

Answer:

the answer would be A because when u subtract it the answer is $5.21

Answer:

the answer is $3

Step-by-step explanation:

I just looked it up lol

Answer:

c

Step-by-step explanation:

Answer:

A. AAS(Angle-Angle-Side)

Step-by-step explanation:

From the image, you can already see 1 angle and 1 side measured.

But, angle KLJ and angle MLN are congruent to each other as well because they are vertical angles (angles on opposite sides). And vertical angles are always congruent to each other.

So in total, we have 2 angles and 1 side congruent to each other,

<KLJ and <MLN

<LKJ and <LMN

KJ and MN

From the other (based on the image), they are ordered in a angle angle, side format. So the answer is AAS.

Hope I was able to help! Good Luck!

Answer: The length is 15 feet.

Step-by-step explanation:

But, the problem is asking for the length...

Answer:

x=1/45

Step-by-step explanation:

do the inverse

please mark it as brainliest!!<3