Over what interval is the quadratic function decreasing?


x ∈ (−∞,−2)
x ∈ (-2,−∞)*******
x ∈ (-2, ∞)
x ∈ (−∞,3)

9514 1404 393

Answer:

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = LWH . . . . . the product of length, width, height

This rectangular prism has a volume of ...

  V = (12 ft)(6 ft)(4 ft) = 288 ft³ . . . . rectangular prism volume

__

The volume of a triangular prism is found from the formula ...

  V = Bh

where B is the area of the triangular base, and h is the height of the prism (distance between the triangular bases). The triangular base area is found from ...

  A = 1/2bh . . . . .where b is the base of the triangle, and h is its height.

Here, we have ...

  B = 1/2(6 ft)(4 ft) = 12 ft²

  V = Bh = (12 ft²)(6 ft) = 72 ft³ . . . . triangular prism volume

__

The total volume of the given geometry is the sum of the volumes of the parts:

  aquarium volume = 288 ft³ +72 ft³ = 360 ft³

Answer:

65%

Step-by-step explanation:

2080/3200times100%

Answer:

H0 : μ = 1220

H1 : μ > 1220

Test statistic = 1.30

Step-by-step explanation:

Sample mean, x = 1235.91

Standard deviation, σ = 211.67

Sample size, n = 300

The hypothesis :

Null ; H0 : μ = 1220

Alternative ; H1 : μ > 1220

Tbe test statistic :

(x - μ) ÷ (σ/√(n))

(1235.91 - 1220) ÷ (211.67/√(300))

15.91 / 12.220773

= 1.3018

= 1.30

Answer:

The restrictions for x would be 14 > x > 5.

Step-by-step explanation:

Let the length of the rectangle be y and the width be x.

That being said, the equation would be as follows:

[tex]y = 7x + 8[/tex]

[tex]y - 8 = 7x[/tex]

[tex]x = \frac{y-8}{7}[/tex]

Therefore, substituting the two values of y into the equations, we would get:

[tex]x = \frac{43-8}{7}[/tex]

[tex]x = \frac{35}{7}[/tex]

[tex]x = 5[/tex]

And:

[tex]x = \frac{106-8}{7}[/tex]

[tex]x = \frac{98}{7}[/tex]

[tex]x = 14[/tex]

Therefore, x would be between 5 and 14, and the restrictions for x would be 14 > x > 5.

Hope this helped!

Answer:

It depends on what shape you have. Here are some formulas for different shapes.

Step-by-step explanation:

Rectangular prism: 2lw + 2lh + 2wh

Cylinder: 2 pi r² + 2 pi rh

Sphere: 4 pi r²

Cone: pi r² + pi rl

Square-based pyrimid: 1/2lp +B

I hope this helps!

Answer:

question is not clear

specify the table

Answer:

65 miles

Step-by-step explanation:

costs = flat fee + cost per mile * miles

46 = 7+ .60m

Subtract 7 from each side

46-7 = 7+.6m-7

39 = .6m

Divide each side by .6

39/.6 = m

65 miles

Answer:

3cm

use the formula for the volume of a cylinder

and substitute

9514 1404 393

Answer:

  tan(φ) = (x² -1)/(2x)

Step-by-step explanation:

In a right triangle, the tangent of one of the acute angles is the ratio of the opposite side to the adjacent side. Here, the length of the adjacent side is not given, but can be found from the Pythagorean theorem.

  adjacent side = √((x² +1)² -(x² -1)²) = √((x⁴ +2x² +1) -(x⁴ -2x²+1))

  adjacent side = √(4x²) = 2x

Then the tangent ratio is ...

  tan(φ) = (opposite side)/(adjacent side)

  tan(φ) = (x² -1)/(2x) . . . . . . for x > 0

Answer:

-6/7

Step-by-step explanation:

If we have two points, we can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 4 - -2)/( -5 -2)

   = ( 4+2) /(-5-2)

    = 6/-7

   = -6/7

Answer:

4-[tex]\frac{x}{2}[/tex]-[tex]x^{2}[/tex]

Step-by-step explanation:

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Red: 2

Blue: 4

Yellow: 4

[tex]\frac{2}{10}[/tex]

[tex]\frac{2/2}{10/2}=\frac{1}{5}[/tex]

Answer:

The experiment shows the frequency of results derived from tossing a coin

Answer:

a)89

b)89.45

Step-by-step explanation:

Answer:

There are 360º in a circle. 140º has been allocated to one angle.

There are 360-140 = 220º left in the circle.

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

x/3x-1 divided by x-2/2x

= x/3x-1 * 2x/x-2

= 2x^2/(3x-1)(x-2).

If we expand the denominator it is

2x^2/(3x^2-7x+2).

Answer:

cant see it

Step-by-step explanation:

just type it out

Answer:

2/7

Step-by-step explanation:

Answer:

I'll setup the problem, then you can do the calculations

Step-by-step explanation:

Perimeter = 2width(W) + 2length (L)

Area = LW

L = 2.5 + 2W

LW = 62.5

substitute L in equation for area

[tex]2.5W + {2W}^{2} = 62.5 \\ \\ {2W}^{2} + 2.5 - 62.5 \\ \\ use \: quadratic \: solution \\\frac{ - b ± \sqrt{ {b}^{2} - 4ac}}{2a} [/tex]

a = 2; b = 2.5; c = 62.5

send a comment if you have a question

The perimeter of a rectangle.

P = 2 ( length + width )

The area of a rectangle.

Area = length x width

The perimeter of the rectangle shape garden bed is 32 feet.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

A rectangular shape Landscaper:

Width = W

Length = 2.5 + W

Area = 62.5 square feet

The perimeter of a rectangle.

P = 2 ( length + width )

The area of a rectangle.

Area = length x width

Now,

Area = 62.5

length x width = 62.5

(2.5 + W)  x W = 62.5

2.5W + W² = 62.5

W² + 2.5W = 62.5

W² + 2.5W - 62.5 = 0 ______(A)

The roots of this equation (A) are:

W = 6.75 and W = -9.25 (eliminated)

Now,

Length = 2.5 + 6.75 = 9.25 feet

Width = 6.75 feet

The perimeter of the rectangle.

P = 2 ( length + width )

P = 2 x (9.25 + 6.75)

P = 2 x 16

P = 32

Thus,

The perimeter of the rectangle shape garden bed is 32 feet.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ2

Answer:

216 yd³

Step-by-step explanation:

Volume of a rectangular prism

= product of the three orthogonal sides

= 6yd * 6yd * 6yd

= 216 yd³

Answer:

216

Step-by-step explanation:

:)

Answer: first one is x≥-8 second one is x<6

Step-by-step explanation: for the first one you divide both sides by 7 and the second won do the same except divide by 9 on each side

Hello,

7x ≥ -56

⇔ 7x / 7 ≥ -56 / 7

⇔ x ≥ -8

S = [-8 ; +∞[

9x < 54

⇔ 9x / 9 < 54 / 9

⇔ x < 6

S = ]-∞ ; 6]

:-)

Answer:

Mean speed = 41.3 mph

Step-by-step explanation:

Given that,

The speeds of an automobiles are given below:

20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58

We need to find the mean speed of the cars.

Mean = sum of observations/ no. of observation

[tex]M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3[/tex]

So, the mean speed of the cars is equal to 41.3 mph.

Answer:

imagine the upper triangle as the same as the lower one, but rotated by 180° around the corner point they share, and resized.

the base of the smaller triangle is resized by a factor of 3/4.5, or reduced: 1/1.5

we just take the length from the hypotenuse of the bigger triangle and resize it to, either by multiplying with 1/1.5 or by dividing by 1.5

personally, I find the latter easier.

x = 7.5/1.5 = 5

Answer:

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Answer:

Time for a round trip = 12.5 hours

Step-by-step explanation:

Mother's house = 250 miles

Total distance for the round trip = 250 + 250 = 500 miles

Given speed = 40 mph

Find time .

[tex]Speed = \frac{distance }{Time }\\\\Time = \frac{distance }{speed } = \frac{500}{40} \\\\Time = 12.5 \ hours[/tex]

Answer:

41

Step-by-step explanation:

substitute x=-2 and y=6, we know

8×6 +4×(-2) -(2×(-2) +3) = 48-8-(-1) =41

Answer:

41

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

8y + 4x - (2x + 3)

x = -2

y = 6

Step 2: Evaluate

Step-by-step explanation:

my answer is in the image above

Answer:

The p-value of the test statistic from the standard normal table is 0.0017 which is less than the level of significance therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to support the claim that less than 20% of the pumps are inaccurate.

Step-by-step explanation:

Here, 1304 gas pumps were not pumping accurately and 5689 pumps were accurate.

x = 1304, n = 1304 + 5689 = 6993

The level of significance = 0.01

The sample proportion of pump which is not pumping accurately can be calculated as,

The claim is that the industry representative less than 20% of the pumps are inaccurate.

The hypothesis can be constructed as:

H0: p = 0.20

H1: p < 0.20

The one-sample proportion Z test will be used.

The test statistic value can be obtained as:

[tex]Z=\frac{\hat{p}-P}{\sqrt{\frac{P(1-P))}{n}}}\\\\Z=\frac{0.186-0.20}{6993}\\\\Z=-2.927[/tex]

Answer:

D. 56

Step-by-step explanation:

The general solution for the number of combinations with repetition is represented by the following expression:

[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)

Where:

[tex]n[/tex] - Total number of elements.

[tex]r[/tex] - Number of the sample.

If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:

[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]

[tex]x = 56[/tex]

Hence, correct answer is D.