I will give the brainiest if you get it right.

I Will Give The Brainiest If You Get It Right.

Answers

Answer 1

Answer:

  1 ≤ x < 7/4

Step-by-step explanation:

The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.

Inequality solutions

  f(4x -3) ≥ f(2 -x²)

  4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)

  x² +4x -5 ≥ 0 . . . . . subtract 2-x²

  (x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1

The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.

Domain restrictions

The domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values

Left side

  -8 < 4x -3 < 4

  -5 < 4x < 7

  -5/4 < x < 7/4

Right side

  -8 < 2 -x² < 4 . . . . . right side is always true

  x² < 10 . . . . . . . . . . . add x² +8

  |x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction

Solution

With the given domain restrictions on f(x), the inequality will be true on the interval ...

  1 ≤ x < 7/4

__

Additional comment

The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.

This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.

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I Will Give The Brainiest If You Get It Right.

Related Questions

Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.

Answers

Answer:

  k = 3

Step-by-step explanation:

The value of k is the amount by which the function f(x) is translated upward to give the function g(x). We can compare y-intercepts to see that the y-intercept of g(x) is 5 -2 = 3 units more than the y-intercept of f(x). This means ...

  g(x) = f(x) +3

Comparing to ...

  g(x) = f(x) +k

we see that k = 3.

What’s the difference between 4, 7/9 and 2 1/2

Answers

[tex]\huge \mathbb \orange{ANSWER} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]

[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]

[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]

[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]

Let x and b be positive real numbers so that log_b(x^2) = 10. Find log_3sqrtb (1/x)

Answers

The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex]  where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.

How to analyze and solve logarithmic expressions

Logarithms are trascendental functions, that is, functions that cannot be described algebraically.

In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:

[tex]\log_{b} x^{2} = 10[/tex]

[tex]2\cdot \log_{b} x = 10[/tex]

[tex]\log_{b} x = 5[/tex]

x = b⁵

Then, the value of the latter logarithm is:

log₃ (x⁻¹)[tex]^{1/b}[/tex]  

- b⁻¹ · log₃ x

- b⁻¹ · log₃ b⁵

- 5 · b⁻¹ · log₃ b

The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex]  where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]

Remark

The statement is poorly formated, correct form is described below:

Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].

To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/3181916

A very slow man walks

20 cm.in 0.5 left, what his

velocity in meter per second?

Answers

Displacement(d)=0.2m
Time taken(t)= 30 s(1min=60 s)
Velocity (v)=?
We know that,
Velocity (v) = d/t
=0.0067

What is the range of this data set?

36.6, 39.8, 33.3, 34.8, 35.8, 39.6, 36.7, 36.9, 37.5, 32.2, 33.1, 33.3

Answers

Answer:

Step-by-step explanation:

39.8 - 32.2 = 7.6

Range is subtracting the highest and lowest numbers by each other .

Based on the calculations, the range for this data set is equal to 7.6.

What is a range?

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, range is calculated by using this formula;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 39.8.Lowest number = 32.2.

Substituting the given parameters into the formula, we have;

Range = 39.8 - 32.2

Range = 7.6.

Read more on range here: https://brainly.com/question/9393969

How do you solve this?
2sinXcosX=sinX

Answers

Answer: X=60°
2sinXcosX = sinX
Divide through by 2sinX
cosX = 1/2
X = cos-1(1/2)
X= 60°

a bag contains coins of rupees 2 Rupees 1 and 50 paise, in ratio of 1 is to 2 is to 4. if the total amount is rupees 72 find how many 50 paise coins are there?

Answers

Answer:

Final answer -

[tex]number \: of \: 50 \: paise \: coins \: in \: the \: bag = 4x \\ \dashrightarrow{4 \times 12 = 48 \: coins}[/tex]

hope helpful :D

The number of 50 paise coins that we have in the bag with the respective other coins is; 48 coins

How to solve currency conversions?

Since the respective coins are in ratio of 1:2:4. Then, we can deduce the following;

Let number of 2 rupees coins in the bag = 1x

Let number of 1 rupees coins in the bag = 2x

Let number of 50 paise coins in the bag = 4x

Total amount of money = 72 rupees. Thus;

(2 * 1x) + (1 * 2x) + (0.5 * 4x) = 72

2x + 2x + 2x = 72

6x = 72

x = 72/6

x = 12

Thus, number of 50 paise coins = 4x = 4 * 12 = 48 coins

Read more about Currency Conversions at; https://brainly.com/question/11160294

#SPJ5

Does anyone know the answers? Need help!!

Answers

Answer:

nice handwriting

Step-by-step explanation:

Which of the binomials below is a factor of this trinomial?

x^2 + 8x + 16

A. x + 4

B. x - 4

C. x + 8

D. x - 8

Answers

The answer is A.

Pick A.

Good luck

NEED HELP ASAP The salaries of Nathan and Trisha are in the ratio of 5:9. Trisha's salary is £16800 more than Nathan's. Find Nathan's salary.​

Answers

Answer:

From the ratio

The difference is 9 - 5 = 4

Hence Trisha has 4 units more than Nathan and this resulted to 16800

Therefore 1 unit will be

16800 / 4 = 4200


Nathan’s salary is 5 units

5 * 4200 = 21000

Each of students reported the number of movies they saw in the past year. Here is what they reported.
11,6 ,9 ,16 ,12 ,18 ,14
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.

Answers

Answer:

18+16+14+12+11+9+6=8686÷7=12.2812.28=13

Answer:

12.3

Step-by-step explanation:

11+6 +9 +16 +12 +18 +14 =86

86/7 = 12.28571

Tenths is the place value of the digit that appears after the decimal. It represents the 1/10 position of the digit

          (12.3) rounded  to the nearest tenth.

 

i need help with this problem

Answers

Answer:

Disagree

Step-by-step explanation:

because it looks like less than 45

Larger is 32 ounces and sells for 2.99 and smaller is 18 ounce and sells for 1.59
What is the better buy

Answers

Divide price by size of each and compare the u it price:


2.99/32 = 0.0934 per ounce


1.59/18 = 0.0883 per ounce


The 18 ounce do $1.59 has a lower cost per ounce so is the better buy

A data set is normally distributed with a mean of 8.1 and a standard deviation of 3.8.
What percentage of the data is above 8.6?
Enter your answer as a number to the nearest whole percentage, like this: 42%

Answers

Answer:

  45%

Step-by-step explanation:

Your graphing calculator, statistics app, or spreadsheet can tell you that 45% of the normally-distributed data is above 8.6 when the mean is 8.1 and the standard deviation is 3.8.

Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1

Answers

Answer:

Step-by-step explanation:

Arithmetic sequaence:

[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]

[tex]a_2 = -3*4^2-1\\[/tex]

    = -3*16 -1

     = -48 - 1

    = -49

difference = second term - first term

                 = -49 -(-13)

                = -49 + 13

             d = -36

[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]

[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]

= 5*(-135)

= -675

A 22° B 54° С What is the measure of AD? O 108° 0 27° 126 54°​

Answers

Answer:

A. 108

sorry if im wrong but if u am I'm so sorry

Which number is a common multiple of 3 and 4?
A) 8
B) 14
C) 32
D) 48

Answers

Answer:

LCM of 3 and 4 is 12

Step-by-step explanation:

This is your answer

Answer:

The answer is D.

Step-by-step explanation:

To find the common multiple you would divide each answer choice by both numbers & if the are whole numbers then there is your answer. If it is a number with a decimal somewhere then that is not the answer.

Which of the following is true of the numbers 4 and 10?

A. The greatest common factor is
B. The least common multiple is
C. The greatest common factor is 20.
D. The least common multiple is 40.​

Answers

Answer:

None

Step-by-step explanation:

Answer is isn't there

the gcf = 2

the LCM = 20

-0.5(14a - 22) = ? this for my work, please help me.

Answers

Answer:

-7a+11

Step-by-step explanation:

112 is 80% of what number?

A. 140

B. 896

C. 1,400

D. 8,960

Answers

Answer:

A

Step-by-step explanation:

112/0.8 = 140

Answer:

A

Step-by-step explanation:

I am not sure about the answer

Please help i wan't a good grade but I can't figure this out.

Answers

Answer:

angle DCE

Angle DEC

Angle ABF

Step-by-step explanation:

you had the wrong order

help me please mark U as BRAINLIEST​

Answers

Hope this helps. Good luck

What angles are acute GFE mlk dbc dba

Answers

Answer:

d and a

Step-by-step explanation:

an acute is an angle less than 90 degrees. a 90 degree angle is a right angle (klm) the only 2 angles smaller than (klm) are (gfe) and (dba)

What is a2+b2+c2? Thank you for your help.

Answers

Answer:

Pythagoras theorem

Step-by-step explanation:

dhebbd

A car travels 80 miles on 3 gallons of gas. At the same rate (in miles per gallon) l, how many miles will the car be expected to travel on 5 gallons of gas?

A. 48

B. 130

C. 133 1/5

D. 160

Answers

Answer:

C

Step-by-step explanation:

Which expression is equivalent to the following complex fraction?

Answers

Consider the fraction first ;

[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]

[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]

[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]

Hence, Option B) is required answer

Write the rate in lowest terms.
During a bad storm there was 2 in of rain in 4 hr.
The rate in lowest terms is_____?

Answers

Answer:

1/2 in/hr

Step-by-step explanation:

2 in / 4h   =   1/2 inch per hour

Need some help 54 pts

Answers

Step-by-step explanation:

as shown in the picture.

you can comment if there is a problem

Use the distributive property to write the following expressions in expanded form. 4(x +y)

Answers

Answer:

4x+4y

Step-by-step explanation:

Answer:

4x + 4y

Step-by-step explanation:

To do this you need to know that the number (or variable) on the outside of the parenthesis must be multiplied to all of the numbers/variables on the inside of the parenthesis.

So here, you want to multiply x by 4:

4x

Then multiply y by 4:

4y

And because the expression is adding the x and y, it comes out as:

4x + 4y

A store sells a workout outfit that consists of a jacket, a t-shirt, and a pair of shorts. The store purchases the jacket for $34, the t-shirt for $9, and the shorts for $12. The percent of markup is 28%. Find the selling price of the outfit.

PS: include show work please I have to submit this in like 3 hours thankyou

Answers

Answer:

The Outfit costs $70.4.

Step-by-step explanation:

Add the selling price together

34 + 9 + 12 = 55

Multiply by the markup (Profit)

100% = 1

28% = 0.28

55 x 1.28 = 70.4

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