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The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions

The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x^2

Rewrite as:

x^2 + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x^2 + 4x - 5 ≥ 0

Expand

x^2 + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)

The function decreases at (-∞,4).

So, we have:

5 - x^2 ≥ 3x - 5

Rewrite as:

x^2 + 3x - 5 - 5 ≤ 0

Evaluate the like terms

x^2 + 3x - 10 ≤ 0

Expand

x^2 + 5x - 2x - 10 ≤ 0

Factorize the expression

x(x + 5) - 2(x + 5) ≤ 0

Factor out x + 5

(x - 2)(x + 5) ≤ 0

Solve for x

x ≤ 2 or x ≤ -5

Rewrite as:

-5 ≤ x ≤ 2

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Read more about inequalities at:

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The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.

The volume of the sphere is calculated as follows:

volume = 4 / 3 πr³

where

The lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:

volume of lower sphere = 4 / 3 × 3.14 × 25³

volume of lower sphere = 196250 / 3

volume of lower sphere = 65416.6666667

volume of lower sphere = 65416.7 m³

volume of higher sphere = 4 / 3 × 3.14 × 22.5³

volume of higher sphere = 143066.25 / 3

volume of higher sphere = 47688.75

volume of higher sphere = 47688.8 m³

The approximate total volume = 65416.7 + 47688.8  = 113105.45 m³

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Answer:

vertex is a point where two sides meet

Step-by-step explanation:

The y-intercept of the function is: b=10

Step-by-step explanation:

Given the table

x                 y

1                 8

2                6

3                4

4                2

Taking any two points to find the slope

(1, 8)

(2, 6)

The slope between (1, 8) and (2, 6) is:

We know that the slope-intercept form of the line equation is

where m is the slope and b is the y-intercept.

Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).

8 = -2(1) + b

8 = -2 + b

b = 8+2

b = 10

Thus, the y-intercept of the function is: b=10

Answer:

x³/3 - x² + C

Step-by-step explanation:

∫ x² - 2x + 8 dx

= x³/3 - x² + C

when finding the derivative, you need to take the power plus 1 then divide by the power x^(2+1)/(2+1) = x³/3

the same goes for 2x and the 2/2 is 1 so you would get x²

since you are finding the derivative for x and 8 is a constant it equals zero.

when integrating you always need to add C at the end and C stands for a constant. The only time you do not add C is when the integral goes from one constant to the next.

Example: [tex]\int\limits^1_0 {x^2 - 3x +9} \, dx[/tex] like this...

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

x + 2y = –1

(-3) + 2y = -1

-3 + 2y + 3 = -1 + 3

2y = 2

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

[tex]P= \dfrac FA \implies F = PA[/tex]

Answer:

Step-by-step explanation:

Prove by multiplication

Similarly

So the expression is 5873/8

Now

We can prove the given statement to multiplication

Multiply with 8

And

Yes

We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800

Answer:

(-3, 0) and (1, 0)

(0, 4)

Step-by-step explanation:

x-intercept is the point where y = 0.

y-intercept is the point where x = 0.

or points ...

f(x) = y = -4×|x + 1| + 8

let's start with the y-intercept (x = 0)

y = -4×1 + 8 = -4 + 8 = 4

the y-intercept point (only 1 point) is (0, 4).

for x = 0 the absolute value function contains 0+1. and that is always +1.

the x-intercept(s) :

0 = -4×|x + 1| + 8 (dividing by -4)

0 = |x + 1| - 2

|x + 1| = 2

because of the absolute value we have 2 possibilities :

+(x + 1) = 2

x + 1 = 2

x = 1

and

-(x + 1) = 2

-x - 1 = 2

-x = 3

x = -3

so the points of x-intercept are (-3, 0) and (1, 0)

Step-by-step explanation:

Answer: 78 /5 = 15.6 = 16 taxis. Step-by-step explanation: I HOPE THIS WILL HELP YOU AND MARK IT AS BRAINLIEST ANSWER PLEASE.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]

Answer:

Step-by-step explanation:

The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.

Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...

  1100x +1300(x+0.03) = 255

  2400x +39 = 255 . . . simplify

  2400x = 216 . . . . . . subtract 39

  x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x

Rosa invested $1100 at 9%, and $1300 at 12%.

Answer:

C) 11.1

Step-by-step explanation:

7.4 -(-3.7)

- and - make +

7.4 + 3.7 = 11.1

19.6 gallons

Explanation:

Answer:

The probability of Joe spinning a 1 is a 1 out of 4 chance and the probability of him flipping heads is a 50/50 chance

Step-by-step explanation:

The spinner only has 4 numbers therefore getting any number out of those four would be a 1/4th probability. As for the coin, the coin only has 2 sides so there is a 50% chance it lands on heads or a 50% chance it lands on tails.

Step-by-step explanation:

a volume is created (calculated) by multiplying 3 dimensions (e.g. length, width and height).

am area is created by multiplying 2 dimensions (e.g. length and width).

but a scale factor applies only to any length in the model (but then separately for every dimension of the model).

so, when we multiply 2 dimensions, we have to multiply the scale factor with every dimension (2 times) in there too.

and for 3 dimensions 3 times.

so,

1.

the scale factor 1/100 or 0.01 says that every side of the model cube is 1/100 the side length of the real cube.

and so, while the volume of the real cube is

side × side × side = 3,401,244 ft³,

the volume of the model cube is

side × 1/100 × side × 1/100 × side × 1/100 =

= side × side × side × (1/100)³ =

= real volume × 1/1,000,000 =

= 3,401,244 / 1,000,000 = 3.401244 ft³

2.

the scale factor is 3/4.

that means that it applies to length as well as to width of the floor.

so, the area of the first floor is

length × width = 1,260 ft²

and the area of the second floor is then

length × 3/4 × width × 3/4 =

= length × width × (3/4)² =

= area first floor × 9/16 = 1,260 × 9/16 = 708.75 ft²

Answer:

Yes

Step-by-step explanation:

Because it has 4 sides and 4 x 2 = 8

Answer:

Just give me the questions and ill do it

Step-by-step explanation:

Step-by-step explanation:

this is the answer for you

Answer:

6.46 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]

[tex]t = 6.46[/tex]

Answer:

The answer is g(x) = 10x + 15

Step-by-step explanation:

Here, If we assume the value of x is 1 we get,

g(x) = 10x + 15

g(1) = 10(1) + 15

g(1) = 10 + 15

g(1) = 35

Here, We get the answer 35.

Now,

f(x) = 2•3ˣ

f(1) = 2•3¹

f(1) = 2•3

f(1) = 6

Here, We get the answer 6.

Now,

h(1) = 5x² + x + 10

h(1) = 5(1)² + 1 + 10

h(1) = + 5 + 1 + 10

h(1) = + 16

Thus, The answer is g(x) = 10x + 15.

-TheUnknownScientist 72

Answer:

Step-by-step explanation:

The angle containing y and 63 are vertically opposite. They are equal.

y + 23 = 63                   Subtract 23 from both sides

y +23-23 = 63 - 23

Answer y = 40

Answer:

2

Step-by-step explanation:

1 ⅚ + ⅙ = 1 6/6, also known as, 2

Answer:

Step-by-step explanation:

top = 120sq m

middle = 17sq cm

bottom = 102 sq feet

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

Replace x with π/2 - x to get the equivalent integral

[tex]\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

but the integrand is even, so this is really just

[tex]\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

Substitute x = 1/2 arccot(u/2), which transforms the integral to

[tex]\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du[/tex]

There are lots of ways to compute this. What I did was to consider the complex contour integral

[tex]\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz[/tex]

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

[tex]\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}[/tex]

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

[tex]\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}[/tex]

and it follows that

[tex]\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}[/tex]

The expression for the simplified total gas used is 1.43x.

let the gas used on the way to camp "x"

Then the gas used on the way back can be calculated as follows:

360 / 420 × 0.5 × x

To calculate the total fuel used, We need to add this to the 'x' used on the way.

Therefore,

total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x

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