Please help!!!!!! I'll mark you brainiest!!!! Rewrite the statement in if-then form: Adjacent angles share a common side.

Answer:

(a) 30 feet

(b) 30 feet.

Step-by-step explanation:

Given that the opening of a tunnel that travels through a mountainside can be modeled by

[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.

[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]

[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]

(a) At the ground level, [tex]y=0[/tex]

So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.

For, [tex]y=0[/tex], the extreme points of the tunnel.

[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]

[tex]\Rightarrow (x-15)(x+15) =0[/tex]

[tex]\Rightarrow x= 15, -15[/tex]

So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].

Hence, the width of the tunnel at the ground level

[tex]= | x_1 - x_2 |[/tex]

[tex]=|15-(-15)|[/tex]

[tex]=30[/tex] feet.

(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.

First determining the value of x for which the slope of the graph is zero.

[tex]\frac{dy}{dx}=0[/tex]

From equation (i),

-2x=0

[tex]\Rightarrow x=0[/tex]

And  [tex]\frac{d^2y}{dx^2}= -2[/tex]

which is always negative, so at x=0 the value of y is maximum.

Again, put x=0 in equation (i), we have

[tex]y=\frac{-2}{15}{0^2-225}[/tex]

[tex]\Rightarrow y=30[/tex] feet.

Hence, the tunnel is 30 feet tall.

Answer:

a) [tex]p \geq 60\,ft^{2}[/tex], b) [tex]w \geq 36\,ft[/tex], c) [tex]1\,qt \leq q \leq 2\,qt[/tex], d) [tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex]

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let [tex]p[/tex] the surface area of plywood, measured in square feet, and the inequation is:

[tex]p \geq 60\,ft^{2}[/tex] (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let [tex]w[/tex] the total length of wood planks, measured in feet, and the inequation is:

[tex]w \geq 36\,ft[/tex] (Eq. 2)

c) Between 1 and 2 quarts of paint

Let [tex]q[/tex] the total capacity of paint, measured in quarts, and the inequation is:

[tex]1\,qt \leq q \leq 2\,qt[/tex] (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let [tex]p[/tex], [tex]w[/tex] and [tex]q[/tex] the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

[tex]0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65[/tex] (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

Read more:

https://brainly.com/question/11067755

Answer:

14

Step-by-step explanation:

5+(3*3)

5+9

14

Answer:

m  = −3

Step-by-step explanation:

Use the slope formula to find the slope  m .

Answer:

x=11

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

-9=-x-5

-9+5=-x

-4=-x

x=4

Answer:

1/8 tablespoons

Step-by-step explanation:

Since the child needs to take 1/2 tablespoons off medicine per day in 4 equal doses, you will divide the 1/2 tablespoons into 4 equal doses, so you need to divide by 4.

You can do this by multiplying 1/2 by 1/4.

[tex]\frac{1}{2} * \frac{1}{4} = \frac{1}{8}[/tex]

Answer:

it would be 1/8

Step-by-step explantion:

simply divide

1/2÷4

=1/8

(that should be right)

Answer:

Step-by-step explanation:

a: 2

b: 4

c: 3

d: 4

e: 6

Answer:

Distributive property

Answer:

23,999

Step-by-step explanation:

Un refrigerador de $8,500.50

Un televisor de $3,500.50

Una computadora de $6,900.00

Una lavadora de $4,999.00

8,500.50 + 3,500.50 + 6,999.00 + 4,999.00 = 23,999.00

Answer:

false

Step-by-step explanation:

all rectangles are squares not all squares are rectangles

Answer:

(2x - 9)(2x + 9)

Step-by-step explanation:

4x^2 - 81 = (2x - 9)(2x + 9)

Answer:

(2x+9)(2x-9)

Step-by-step explanation:

kind of simple actually

4x^2-81=(2x+9)(2x-9)

Answer:

$24,970

Step-by-step explanation:

22,000+(99,000•0.03)=22,000+2,970=24,970

Answer: 7:35 a. M

Step-by-step explanation:

Given that:

Snooze on alarm = 5 minutes

Snooze on cellphone = 7 minutes

If both activates at 7:00 a. M

Time at which both will activate again ;

Obtain the Lowest Common Multiple of 5 and 7

_5 __|5 ___|7

_7__ |1 ___|7

____ |1 ___| 1

Lowest common multiple = (5 * 7) = 35

Hence, both alarms will sound together again after 35 minutes = 7:00a.m + 35 minutes = 7:35 A. M

Answer:

120.8 feet

Step-by-step explanation:

Answer:

2447.40

Step-by-step explanation:

48,948 * .05 = 2447.40

Answer:

2447.40 that the answer

Answer:

$5.58

Step-by-step explanation:

Because divide 12 by 67:

67 ÷ 12 = 5.58

5.58 is the answer

Hope this helped! Pls Brainliest!

Answer:

$5.58

Step-by-step explanation:

$67.00÷12=$5.58

Hope this helps!

Answer:

2^2 x 5 x 9.

Step-by-step explanation:

This will give you the answer because when multiplying all of this you will get 180. Answer B.

hey mate☺️☺️ here's your answer......

4x'4 + 1

Answer:

1) 4x^(2)+11x+6 Factored--> (4x+3) (x+2)

2) 4x^(2)+10x+6 Factored--> (2x+3)(2x+2)

3) 4x^(2)+14x+6 Factored--> (x+3)(4x+2)

Step-by-step explanation:

Factor: 4x^(2)+11x+6 (step by step)

1) Split the second term (11x) into two terms

      4x^2 + 8x + 3x + 6

2)Factor out common terms in the first two terms, then in the last two terms.

      4x(x + 2) + 3(x + 2)

3) Factor out the common term x + 2

      (x + 2) (4x + 3)

Repeat the above steps for similar questions!

Answer:

$800 per 40 hours

Step-by-step explanation:

In photo

Answer:

134

Step-by-step explanation:

Your answer is simply 134

Answer:

1. Is -3, or answer choice C

Answer:

75

Step-by-step explanation:

Use order of operations to solve this.

P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction.

First, do 20 x 4.

[tex]80 - 100 / 20[/tex]

Then, divide 100/20.

[tex]80 - 5[/tex]

= 75

Answer:c

Step-by-step explanation:

Answer:

a) [tex]\sqrt{90}[/tex]

Step-by-step explanation:

The square root of 90 is approximately 9.487.