What is the slope of the line that passes through the points (-9, 8) and (–21, 10)?
Write your answer in simplest form.

The base of the triangular garden is calculated as 40 ft

The given parameters include:

The area of a triangle is given as;

[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]

Now solve for 'b' = 30 ft + 10 ft  =  40 ft

Therefore, the base of the garden is 40 ft

To learn more about area of a triangle visit: https://brainly.com/question/2391510

Answer:

Not very sure what you mean,

But in the provided set, 8 is the greatest number, and 1 is the smallest.

Hope this helps!!

Answer:

Step-by-step explanation:

If A is 170 less than B, than the equation for that is:

A = B - 170 (1) where the word "is" means equals and less than is subtraction.

If the total of A + B is 1520, then

A + B = 1520 (2). Sub equation (1) into equation (2):

(B - 170) + B = 1520 and

2B - 170 = 1520 and

2B = 1690 so

B = 845. Building B is 845 feet tall and Building A is

A = 845 - 170 (this is equation (1) with the height of B subbed in) so

A = 675 feet

675 + 845 should equal 1520 according to our equation. And of course it does.

Answer: 675 + 845 should equal 1520 according to our equation. And of course it does.

Answer:

see it

Step-by-step explanation:

Answer:

Use inequalities.

At certain x values.

Step-by-step explanation:

[tex]3 \leqslant x \leqslant 6[/tex]

[tex] - \infty < x < \infty [/tex]

[tex]x = 6[/tex]

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.

[tex]x^2=441+196-311.5925[/tex] and

[tex]x^2=325.4075[/tex] so

x = 18.0 or just 18

Answer:

90 days

Step-by-step explanation:

b= number of days til  her birthday

s = number of days til summer

b+s =135

b = 2s

2s+s = 135

3s = 135

Divide by 3

3s/3 =135/3

s =45

b = 2s = 2(45) = 90

Answer: This quadratic equation has two real solutions.

Step-by-step explanation:

[tex]y=x^{2} -11x+7\\\\D=(-11)^{2} -4 \cdot 7=121-28=93 \: > 0\\\\x=\dfrac{11 \pm \sqrt{93} }{2}[/tex]

Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].

Answer:

12

Step-by-step explanation:

2²×3

I hope its correct

Answer:

4

[tex] {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14[/tex]

Answer:

(6, -9)

Step-by-step explanation:

let: 8x + 2y = 30 be equation (a).

7x + 2y = 24 be equation (b).

[tex]{ \bf{equation \: (a) - equation \: (b) : }}[/tex]

[tex] (8 - 7)x + (2 - 2)y = (30 - 24) \\ x + 0y = 6 \\ x = 6[/tex]

substitute for x in equation (a):

[tex] (8 \times 6) + 2y = 30 \\ 48 + 2y = 30 \\ y = - 9[/tex]

Answer:

x=2

y=1.732

Step-by-step explanation:

we use the formulae.....

SOHCAHTOA

where..Cos 60°=1/x

cos60=0.5

0.5=1/1

X=2

0.8660=y/2

y= 1.732

Answer:

Agree with Sharon

Step-by-step explanation:

A terminating decimal includes numbers beyond the decimal point.

An integer is a whole number.

4 is a whole number so it's an integer which is what Sharon said.

Answer:

24feet

Step-by-step explanation:

the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying

Answer:

A) -3/2

Step-by-step explanation:

You pick the difference between the two points and divide them.

y-axis: 2-(-1)= 3

x-axis: -3-(-1) = -2

So slope is -3/2

Answer: y=2/3X- 4/3

Step-by-step explanation:

Slope = (4-2)/(4-1)=2/3

Y-2=2/3(x-1)

Y-2=2/3x-2/3

Y=2/3X-2/3+2

Y=2/3X-4/3

Answer:

you have 38 friends

Step-by-step explanation:

because you have to add I think so

Answer:

38 friends

Step-by-step explanation:

Answer:

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(\frac{2e}{x})[/tex]

Step 2: Simplify

9514 1404 393

Answer:

  a) 2.038 seconds

  b) 5.918 meters

  c) 1.076 seconds

Step-by-step explanation:

For the purpose of answering these questions, it is convenient to put the given equation into vertex form.

  h = -4.9t² +9.2t +1.6

  = -4.9(t² -(9.2/4.9)t) +1.6

  = -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²

  = -4.9(t -46/49)² +290/49

__

a) To find h = 0, we solve ...

  0 = -4.9(t -46/49)² +290/49

  290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9

  √(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds

The ball takes about 2.038 seconds to fall to the ground.

__

b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:

  290/49 m ≈ 5.918 m

The maximum height of the ball is about 5.918 m.

__

c) We want to find t for h ≥ 4.5.

  h ≥ 4.5

  -4.9(t -46/49)² +290/49 ≥ 4.5

Subtracting 290/49 and dividing by -4.9, we have ...

  (t -46/49)² ≥ 695/2401

Taking the square root, and adding 46/49, we find the time interval to be ...

  -√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49

The difference between the interval end points is the time above 4.5 meters. That difference is ...

  2√(695/2401) ≈ 1.076 . . . . seconds

The ball is at or above 4.5 meters for about 1.076 seconds.

__

I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.

_____

Additional comment

I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.

"Vertex form" for a quadratic is ...

  y = a(x -h)² +k . . . .  where the vertex is (h, k) and 'a' is a vertical scale factor.

In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)

9514 1404 393

Answer:

  C. More than 1 solution

Step-by-step explanation:

Divide the second equation by 3.

  y -x = -3

Add x.

  y = x -3

This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."

JWL = JWI + IWL

87 = (2x + 24) + (3x - 12)

87 = 5x + 12

5x = 75

x = 15

Hope this helps!

The value of the variable x will be 15. Then the correct option is A.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The measure of the angle ∠JWL will be 87°.

The angle ∠JWI and angle ∠IWL will be the linear angle.

Then the sum of the angle ∠JWI and angle ∠IWL is equal to the angle ∠JWI.

          ∠JWI + ∠IWL = 87°

(2x + 24) + (3x – 12) = 87

                    5x + 12 = 87

                           5x = 87 – 12

                           5x = 75

                             x = 75 / 5

                             x = 15

Thus, the value of the variable x will be 15.

Then the correct option is A.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

Step-by-step explanation:

the inequality is

[tex]c + 8 > 30[/tex]

Answer:

1. $11747.083

2. $29,253

3. $24222.04

4. $1542.23

Step-by-step explanation:

Message for explanation if you want.

Answer:

0.9894 = 98.94% probability that he does not have a TBI.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Negative screen

Event B: Does not have a TBI.

Probability of a negative screen:

93 are negative and do not have a TBI.

1 is negative and has a TBI.

Out of 112.

So

[tex]P(A) = \frac{93+1}{112} = \frac{94}{112}[/tex]

Probability of a negative screen and not having a TBI:

93 are negative and do not have a TBI, out of 112, so:

[tex]P(A \cap B) = \frac{93}{112}[/tex]

One of the veterans has a negative screen and wants to know the probability that he does not have a TBI.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{93}{112}}{\frac{94}{112}} = \frac{93}{94} = 0.9894[/tex]

0.9894 = 98.94% probability that he does not have a TBI.

Answer:

[tex]{ \tt{y = 3x + 7}}[/tex]

Step-by-step explanation:

General equation of a line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

m is the slope, and c is the y-intercept:

m = 3, and c = 7

Answer:

Step-by-step explanation:

Given,

[tex] {25x}^{2} - \frac{1}{49} [/tex]

[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]

Since,

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

Then,

[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]