Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :
(i) the minimum value of f(x).
(ii) the value of x for which f (x) is a minimum

Lets solve

[tex]\\ \sf\longmapsto 7w<-56[/tex]

[tex]\\ \sf\longmapsto w<dfrac{-56}{7}[/tex]

[tex]\\ \sf\longmapsto w<-8[/tex]

Answer:

[tex]\boxed {\boxed {\sf w < -8}}[/tex]

Step-by-step explanation:

We are given an inequality and asked to solve for the variable w.

[tex]7w < -56[/tex]

In order to solve for w, we must isolate the variable. It is being multiplied by 7. The inverse of multiplication is division, so we divide both sides of the inequality by 7.

[tex]\frac {7w}{7} < \frac {-56}{7}[/tex]

[tex]w < \frac{-56}{7}[/tex]

[tex]w < -8[/tex]

w is less than -8 or w < -8.

Answer: 2(−5x^2 +9)(5x^2 +9)

Step-by-step explanation:

Given: 162-50x^4

Factor out 2:  2(81-25x^4)

Rewrite:  2(9^2-(5x^2)^2)

Use difference of squares:  2(9-5x^2)(9+5x^2)

Reorder (if you need to) 2(-5x^2+9)(5x^2+9)

Answer:

6(27 - 8x^4)

Step-by-step explanation:

162 - 50x^4 /2

2(81 - 24x^4) /3

6(27 - 8x^4)

Answer:

The correct options are:

1. Significantly different from

1. Inconsistent

Explanation:

Sales Data for Midwest:

Midwest region total stores Sales equal to 63.1%. The percentage for current store is less than total stores therefore data in the given table is not consistent. The data given is relatively for the first month sales and is significantly different from the other stores.

Answer:

In the picture

Step-by-step explanation:

From Plato / Edm

Answer:

The y intercept of f(x) is 8 and the equation of the horizontal asymptote is y = 0

Answered by GAUTHMATH

Answer:

∠CBA

Step-by-step explanation:

Answer:

<CBA

Step-by-step explanation:

The vertex has to be in the middle

<CBA

<ABC

or we can name it with just the vertex

<B

Answer:

I hope it is correct.. :)

Answer:

number to get a better price

Answer:

if I'm not wrong,then this is the equation

Step-by-step explanation:

CP=5000

SP=5085

VAT=13℅

now,

VAT amount=VAT℅ OF SP

=13℅ OF 5085

=13/100*5085

=rs.661.05

again,

profit℅= SP-CP/CP*100℅

=85/500*100

=17℅ answer

Answer:

x < 12

Step-by-step explanation:

x +4 <16

x < 16 - 4

x < 12

Please Mark me brainliest

Answer:

CP is 13 because 20-13=7 also you can subtract 20-7=13

So, here us your ans 13.

Answer:

Soil erosion is the natural process in which the topsoil of a field is carried away by physical sources such as wind and water. In this process, the soil particles are loosened or washed away in the valleys, oceans, rivers, streams or far away lands.

It occurs when the impact of water or wind separates and removes soil particles, causing the soil to deteriorate. Soil deterioration and low water quality due to erosion and surface runoff have become severe problems worldwide.

Answer:

Step-by-step explanation:

10f + 3 = 23 + 6f

4f + 3 = 23

4f = 20

f = 5

Answer:

f = 5

Step-by-step explanation:

10f + 3 = 23 + 6f

Move the variable to the left-hand side and change its sign

10f + 3 - 6f = 23

Move the constant to the right-hand side and change its sign

10f - 6f = 23 - 3

Collect like terms and Subtract the numbers

4f = 23 - 3

4f = 20

Then divide both sides of the equation by 4

f = 5

Answer:

C. Gregory's graph is incorrect because it shows 2 inches of growth for each week, when it should show 0.75 inches of growth each week

Step-by-step explanation:

Given that the plant grows 1.5 inches (y) every 2 weeks (x), it means that:

Rate of change = y/x = 1.5/2 = 0.75 inches per week

The graph he should create should have a rate of change of 0.75. that is, it should show 0.75 inches growth for every week.

The graph shown above has a rate of change of 2 inches per week.

Thus, the graph is incorrect. It should be showing 0.75 inches of growth per week instead of 2 inches.

|x| basically means the count of how far from zero. It will always be a positive number.

So the answer is A. |-20| <  20

because 20 is not greater than 20

Answer:

(0+a)/2 , (0+a)/2

= (a/2, a/2)

Answered by GAUTHMATH

Answer:    [tex]\fbox{C} \: \: \: \dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]

Step-by-step explanation:

36,070 = 3.607 · 10⁴ ≈ 4 · 10⁴

29,029 = 2.9029 · 10⁴ ≈ 3 · 10⁴

Let's how manytimes greater the distance to the bottom of Challenger Deep is than the distance to the top of Mount Everest:

[tex]\dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]

Answer:

C

Step-by-step explanation:

First, the question is asking how many times greater the distance to the Challenger Deep is compared to Mount Everest. This means that the Challenger Deep will be on top, with the distance to Mount Everest on the bottom.

Next, we can see that in our answers, we are only given one significant digit. This means that we have to round our original numbers to the nearest significant digit and work from there. For Challenger Deep, 36,070 must be rounded to the nearest ten thousandth as it is in the ten thousands. Therefore, it must be rounded to 40,000 or 30,000. As 36,070 is closer to 40,000 than 30,000 (we can tell this because the second number, 6, is greater than 5, so we round up), we can represent this as 40,000. For Mount Everest, we can round 29,029 to either 20,000 or 30,000. 30,000 is the appropriate choice here because 9, the second number, is greater than 5.

Therefore, our ratio is now 40,000 / 30,000 . Our answers are written in scientific notation, so we must convert our numbers to those values.

Let's start with 40,000 . Our one significant digit is 4, so we can write this as 4 * something. For each number in 10 to the power of x (x is a placeholder value), we add x amount of zeros. For example, for 4 * 10², we add 2 zeros, making it 400. There are 4 zeros here, so to write this in scientific notation, we have 4 * 10^4

Similarly, for 30,000 , we can write this as 3 * 10^4 as there are 4 zeros.

Our ratio is thus 40,000 = 4*10^4 , which is the Challenger Deep value rounded, over 30,000 = 3 * 10^4, which is the Mount Everest value rounded. We can write this as [tex]\frac{4*10^{4}}{3*10^{4}}[/tex], or C

Answer:

94.5

Step-by-step explanation:

Every 8 dollars means he saves 4.2 dollars

180 ÷ 8 = 22.5

22.5 × 4.2 = 94.5

Answer: 94,5

180:8 *4,2=22,5 *4,2 =94,5

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

x-1+ 1 /5*( x-1)=0

(x-1)*6/5=0

x=1

Answer:

1/4

Step-by-step explanation:

b+-sqrt b^2-4ac all over 2a

Answer:

12/17

Step-by-step explanation:

Let

Numerator of the fraction = x

Denominator of the fraction = x + 5

The fraction is

x / (x + 5)

if both the numerator and denominator are increased by 3, the the resulting fraction becomes 3/4.

x + 3 / (x + 5) + 3 = 3/4

x + 3 / x + 8 = 3/4

Cross multiply

(x + 3)4 = (x + 8)3

4x + 12 = 3x + 24

4x - 3x = 24 - 12

x = 12

Recall,

x / (x + 5)

= 12 / (12 + 5)

= 12/17

The original equation = 12/17

Answer:

the larger one is 183

Step-by-step explanation:

[tex]x + y = 262 \\ x - y = 104 \\ y = 262 - x \\ x - (262 - x) = 104 \\ x - 262 + x = 104 \\ 2x = 104 + 262 \\ 2x = 366 \\ x = 183 \\ y = 262 - 183 \\ y = 79[/tex]

Answer:

192 squared centimeters

Step-by-step explanation:

area equal to 1/2 * base * perpendicular height

1/2*24*16

=192 squared centimeters

Answer: 192 cm squared

Step-by-step explanation:

Area of a triangle: 1/2bh

1/2x basex height

Base= 24 cm

Height: 16 cm

24x16=384

1/2x384= 192

192 cm squared

Hope this helps:) and brainliest would be appreciated thanks!

Answer:

AB=44.98298

Step-by-step explanation:

Since this is  a right triangle, we can use trig functions

cos theta = adj / hyp

cos 12 = 44/AB

AB cos 12 = 44

AB = 44/ cos 12

AB=44.98298

Answer:

8p^3 ( 2p -3)

Step-by-step explanation:

16p^4 - 24p^3

8*2* p^3 *p - 3*8*p^3

Factor out the common terms

8p^3 ( 2p -3)

Answer:

C

Step-by-step explanation:

this is an arithmetic sequence (we add something from element to element).

"an" describes the salary during the nth year.

a1 = $3000

a2 = a1 + 600

a3 = a2 + 600 = a1 + 600 + 600 = a1 + (3-1)×600

an = a1 + (n-1)×600 = 3000 + (n-1)×600

so,

a15 = 3000 + (15-1)×600 = 3000 + 14×600 = $11400

Answer:

i think the answer is y = 3x + 4

Step-by-step explanation:

:)