I typically give 12% of money I receive to my church. My uncle died recently and left me some money. I donated $408 to my church in his memory. How much did he leave to me in his will?

Answer:

0.65 is a number greater than 0.6 but less than 0.7

Answer:

Jack is 31

Lacy is 10

Step-by-step explanation:

x - 9 = 22

since jack is 3 times as old as lacy,

the formula is

3x - 9 = 22

3x = 31

x = 10.3

So Jack is 31

And Lacy is 10

To prove this, subract 9 (years) from both ages

It will give you an approximate sum of 22 years for both their ages, as the question states

Since Lacy is a little over 10 years old, Jack is 31 instead of 30

The formula was taken from someone elses answer so sorry if it`s wrong

The other answer is just wrong.

There are 9•9•8 = 648 distinct 3-digit codes. The first digit can be any numeral from 1-9, the next digit can be any from 0-9 minus the one used in the first position, and the last digit can be any from 0-9 minus both the numerals used in the first two positions.

But that doesn't even account for the divisibility constraint.

Let the code be [tex]abc[/tex]. We can expand this as

[tex]100a + 10b + c[/tex]

In order for this to be divisible by 4, we observe that

[tex]100a + 8b + 2b + c = 4 (25a + 2b) + (2b+c)[/tex]

so we only need [tex]2b+c[/tex] to be divisible by 4.

The last digit must be even, so there are only 5 choices for the last digit. I list the possibilities and outcomes below. For some integer [tex]k[/tex], we need

[tex]c=0 \implies 2b=4k \implies b=2k[/tex]

[tex]c=2 \implies 2b+2=4k \implies b = 2k-1[/tex]

[tex]c=4 \implies 2b+4 = 4k \implies b = 2(k-1)[/tex]

[tex]c=6 \implies 2b+6 = 4k \implies b = 2k-3[/tex]

[tex]c=8 \implies 2b+8=4k \implies b = 2(k-2)[/tex]

Ignoring [tex]a[/tex] for the moment, in the cases of [tex]c\in\{0,4,8\}[/tex], [tex]b[/tex] is also even. This leaves 3 choices for [tex]c[/tex] and 2 choices for [tex]b[/tex].

Likewise, in the cases of [tex]c\in\{2,6\}[/tex], [tex]b[/tex] is odd. This leaves 2 choices for [tex]c[/tex] and 5 choices for [tex]b[/tex].

Now taking into account the choice for [tex]a[/tex], we have the following decision tree.

• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•3•3 = 18 codes.

• If [tex]a\in\{4,8\}[/tex] and [tex]c\in\{0,4,8\}\setminus\{a\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•2•3 = 12 codes.

• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{2,6\}\setminus\{a\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a,c\}[/tex] - a total of 2•1•5 = 10 codes.

• If [tex]a\in\{4,8\}[/tex] and [tex]c \in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}[/tex] - a total of 2•2•5 = 20 codes.

• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{c\}[/tex] - a total of 5•3•4 = 60 codes.

• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a\}[/tex] - a total of 5•2•4 = 40 codes.

Hence there are a total of 18 + 12 + 10 + 20 + 60 + 40 = 160 codes.

Answer:

D. Two hours exercising and eight hours cleaning

Step-by-step explanation:

Rob works part time at the Fallbrook Riding Stable. He makes $5 an hour exercising horses and $10 an hour cleaning stalls. Because Rob is a full-time student, he can work no more than 12 hours per week. However, he must make at least $60 per week.

x = hrs. exercising horses

y = hrs. cleaning stalls

Equations:

Hours he can work per week:

x + y ≤ 12

Amount of money he can make per week:

5x + 10y ≥ 60

Now, graph your equations into desmos.

As you can see in the graph, the correct answer is D (2, 8)

Check your answer by hand:

x + y ≤ 12

2 + 8 ≤ 12

10 ≤ 12

This statement is correct

5x + 10y ≥ 60

5(2) + 10(8) ≥ 60

10 + 80 ≥ 60

90 ≥ 60

This statement is correct

Therefore, the correct answer is D

Hope this helps!

Answer:

x = 3

Step-by-step explanation:

These angles are actually equal to each other

This is because when two lines intersect, the two opposite angles are the same.

Since they are the same, you can set them equal to each other

Like so:

6x - 7 = 4x - 1

Then solve:

6x - 7 = 4x - 1

6x = 4x +6

2x = 6

x = 3

Answer:

A) -4

Step-by-step explanation:

Question

[tex]\sf evaluate \ \dfrac{-4+(m+2)}{n} \ \sf when \ m=\dfrac23 \ and \ \sf n=\dfrac13[/tex]

Solution

Substitute the given values of m and n into the original expression:

[tex]\sf \implies \dfrac{-4+(\frac23+2)}{\frac13}[/tex]

Carry out the operation in the brackets first [tex]\sf (\frac23+3)=\frac83[/tex]

[tex]\sf \implies \dfrac{-4+\frac83}{\frac13}[/tex]

Now carry out the operation in the numerator [tex]-4+\frac83=-\frac43[/tex]

[tex]\sf \implies \dfrac{-\frac43}{\frac13}[/tex]

Dividing by a fraction is the same as multiplying by the flipped version of the fraction (flipped = swap the numerator and denominator of the fraction we are dividing by):

[tex]\sf \implies -\dfrac43 \div \dfrac13=-\dfrac43 \times \dfrac31[/tex]

To multiply a fraction, simply multiply the numerators and multiply the denominators:

[tex]\sf \implies -\dfrac43 \times \dfrac31=\dfrac{-4 \times 3}{3 \times 1}=-\dfrac{12}{3}[/tex]

Finally simplify:

[tex]\sf \implies -\dfrac{12}{3}=-4[/tex]

Answer:

(15.23,41.016)

Step-by-step explanation:

WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.
[tex]= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125[/tex]
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:
[tex]= ((21 - 28.125)^{2} + (24 - 28.125)^{2} +(25 - 28.125)^{2} + (32 - 28.125)^{2} + (35 - 28.125)^{2} + (31 - 28.125)^{2} + (29 - 28.125)^{2} (28 - 28.125)^{2}[/tex]
[tex]= 148.877/8 = 18.6[/tex]
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:
[tex]= 28.125 + (1.96 *18.6)/(\sqrt{8} )[/tex]
[tex]= 41.016[/tex]
[tex]= 28.125 - (1.96 * 18.6)/(\sqrt{8}) = 15.23[/tex]
The confidence interval for this data set is (15.23,41.016)

Answer:

32.7 ± 2.262(1.19)

Step-by-step explanation:

See attached pictures

Using proportions, we have that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The scale is of 1 inch = 8 feet. What is the height for 2.5 inches? The rule of three is given by:

1 inch - 8 feet.

2.5 inches - x feet

Applying cross multiplication, the height in feet of the final building is given by:

x = 8 x 2.5 = 20 feet.

More can be learned about proportions at https://brainly.com/question/24372153

The height of the building is calculated by representing 1 inch as 8 feet. The final building has a height of 20 feet.

Scaling is the increase or decrease in the height of an object by a scale factor k.

Given that the scale used is:

1 inch = 8 feet. Hence:

Since the height of the building is 2.5 in, hence:

Height of the final building = 2.5 in * 8 ft per 1 in = 20 feet

The height of the final building is 20 feet.

Find out more on scaling at: https://brainly.com/question/25722260

Answer:

B

Step-by-step explanation:

-6x + 6 = 2x - 9

-6x + 15 = 2x

15 = 8x

x = 15/8

Answer:

2081days or 2086days

Step-by-step explanation:

1.9(365)=693.5

1.9(366)=695.4

693.5(3)=2080.5

695.4(3)=2086.2

Answer: (-6x - 5) • (2x + 3)

Step-by-step explanation:

((0 -  (22•3x2)) -  28x) -  15

Pull out like factors :

-12x2 - 28x - 15  =   -1 • (12x2 + 28x + 15)

Trying to factor by splitting the middle term

3.2     Factoring  12x2 + 28x + 15

The first term is,  12x2  its coefficient is  12 .

The middle term is,  +28x  its coefficient is  28 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   12 • 15 = 180

Step-2 : Find two factors of  180  whose sum equals the coefficient of the middle term, which is   28 .

     -180    +    -1    =    -181

     -90    +    -2    =    -92

     -60    +    -3    =    -63

     -45    +    -4    =    -49

     -36    +    -5    =    -41

     -30    +    -6    =    -36

     -20    +    -9    =    -29

     -18    +    -10    =    -28

     -15    +    -12    =    -27

     -12    +    -15    =    -27

     -10    +    -18    =    -28

     -9    +    -20    =    -29

     -6    +    -30    =    -36

     -5    +    -36    =    -41

     -4    +    -45    =    -49

     -3    +    -60    =    -63

     -2    +    -90    =    -92

     -1    +    -180    =    -181

     1    +    180    =    181

     2    +    90    =    92

     3    +    60    =    63

     4    +    45    =    49

     5    +    36    =    41

     6    +    30    =    36

     9    +    20    =    29

     10    +    18    =    28    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  10  and  18

                    12x2 + 10x + 18x + 15

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2x • (6x+5)

             Add up the last 2 terms, pulling out common factors :

                   3 • (6x+5)

Step-5 : Add up the four terms of step 4 :

                   (2x+3)  •  (6x+5)

            Which is the desired factorization

Answer: (-6x - 5) • (2x + 3)

Answer:

Find the base, and then the height of this rhombus;

Base: 7 square units

Height: 7 square units

Multiply your base by the height to get the area;

Because the formula for the area of a rhombus is, A = BH

So,

A = 7(7)

A(area) = 49 square units.

Answer:

C

Step-by-step explanation:Only one that makes sence just look at the graph

given ,

a circle of radius 12 inches

and [tex]\theta[/tex] = 45°

now we know that ,

[tex]\\{Area \: of \: sector = \frac{\theta}{360\degree} \times \pi \: r {}^{2} } \\ \\ [/tex]

let's now plug in the values of radius and theta as 12 inches and 45° respectively ,

[tex]\\\dashrightarrow \: \frac{45}{360} \times \frac{22}{7} \times 12 \times 12 \\ \\ \dashrightarrow \: \frac{1}{8} \times \frac{22 \times 12 \times 12}{7} \\ \\ \dashrightarrow \: \frac{22 \times 12 \times 12}{56} \\ \\ \dashrightarrow \: \frac{3168}{56} \\ \\ \dashrightarrow \: 56.57 \: inches {}^{2} (approx.)[/tex]

hope helpful :D

Using the Central Limit Theorem, it is found that the values of the population standard deviation [tex]\sigma[/tex] needed are given by:

a) [tex]\sigma = 32[/tex]

b) [tex]\sigma = 16[/tex]

c) [tex]\sigma = 4[/tex]

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that n = 16.

Item a:

s = 8, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]8 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 32[/tex]

Item b:

s = 4, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 16[/tex]

Item c:

s = 1, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]1 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 4[/tex]

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

the answer is

x^{2}-31x+5b

Step-by-step explanation:

width is 6 units

P=2(l+w)

p=2(l+6)

l+6=p/2

l= (p/2)-6

The length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

A perimeter is a closed route that surrounds, outlines, or embraces a rectangle. The perimeter of a rectangle is given by the formula,

[tex]\rm Perimeter= 2(Length +width)[/tex]

As it is given that the width of the rectangle is 6 units, while the perimeter of the rectangle is P. Now if we write about the perimeter of the rectangle, it can be written as,

[tex]\rm Perimeter= 2(Length +width)[/tex]

[tex]P = 2(l+6)\\\\\dfrac{P}{2} = (l+6)\\\\l = \dfrac{P}{2}-6[/tex]

Hence, the length of the reactangle with a width of 6 units and perimeter p units is (P/2)-6 units.

Learn more about Perimeter:

https://brainly.com/question/2142493

Answer:

the width is 9in

Step-by-step explanation:

perimeter of triangle =3×16 = 48

let w= width of rectangle

perimeter of triangle = perimeter of rectangle

48= 2(15 +w)

24= 15 + w

w= 9

7x-10=6x-5

We simplify the equation to the form, which is simple to understand

7x-10=6x-5

We move all terms containing x to the left and all other terms to the right.

+7x-6x=-5+10

We simplify left and right side of the equation.

+1x=+5

We divide both sides of the equation by 1 to get x.

x=5

Answer:

The farmer can predict that 55 cows in the entire population have no spots.

Step-by-step explanation:

The farmer can predict that 40 cows in the entire population have no spots, the correct option is C.

Suppose we're given that:

Favourable Cases X (in count, in sample)

Sample Size N

Level of significance =[tex]\alpha[/tex]

Then, the sample proportion of favorable cases is:

[tex]\hat{p} = \dfrac{X}{N}[/tex]

The critical value at the level of significance[tex]\alpha is Z_{1- \alpha/2}[/tex]

The corresponding confidence interval is:

[tex]CI = & \displaystyle \left( \hat p - z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}, \hat p + z_c \sqrt{\frac{\hat p (1-\hat p)}{n}} \right)[/tex]

The given information;

The farmer took a random sample of 40 cows out of 200 total cows and found that 11 of those cows have no spots. We can use this sample data to make a prediction about the entire population using statistical inference.

Now,

Plugging in the values, we get:

CI = 0.275 ± 1.96sqrt((0.275(1-0.275))/40)

CI = 0.275 ± 0.139

CI = (0.136, 0.414)

This means that we can be 95% confident that the true proportion of cows with no spots in the entire population lies between 0.136 and 0.414.

the farmer can predict that between 13.6% and 41.4%

Therefore, by confidence interval the answer will be  farmer can predict that 40 cows in the entire population have no spots

Learn more about confidence interval for population proportion here:

https://brainly.com/question/16427118

#SPJ3

Answer:

$600,000

Step-by-step explanation:

GIven;

Alex had $750,000 he lost 80%

To Find;

How many dollars did he lose ​

Solve;

$750,000 * 80% = 600,000

Hence, Alex lost $600,000.

~Learn with Lenvy~

Answer:75,000

Step-by-step explanation:he has 750,000 but he loses 80% so he has 75,000 about.

Answer:

Given:

[tex] \\ {\tt{A = \left [ \: \begin{array}{ c c c} \: \: \: \: 2 & -3 & - 5 \\ - 1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1& - 3 & - 4\end{array} \: \: \: \right] \: and \: B = \left[\begin{array}{c c c} \: \: \: \: 2 & - 2 & - 4 \\ - 1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & - 2 & - 3\end{array} \right]}}[/tex]

Matrix A is of order 3 × 3 and Matrix B is of order 3 × 3

To Show:

Formula Used:

[tex]\\ { \rm{ \left[ \begin{array}{c c c} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array} \right] \times \left[ \begin{array}{c c c} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \\ b_{31} & b_{32} & b_{33} \end{array} \right] = \: \left[ \begin{array}{c c c} \: \: a_{11}b_{11} + a_{12}b_{21} + a_{13}b_{31} & a_{11}b_{12} + a_{12}b_{22} + a_{13}b_{32} & a_{11}b_{13} + a_{12}b_{23} + a_{13}b_{33} \\ \: \: a_{21}b_{11} + a_{22}b_{21} + a_{23}b_{31} & a_{21}b_{12} + a_{22}b_{22} + a_{23}b_{32}&a_{21}b_{13} + a_{22}b_{23} + a_{23}b_{33} \\ \: \: a_{31}b_{11} + a_{32}b_{21} + a_{33}b_{31}&a_{31}b_{12} + a_{32}b_{22} + a_{33}b_{32} & a_{31}b_{13} + a_{32}b_{23} + a_{33}b_{33}\end{array} \right]}}[/tex]

If A is a matrix of order a×b and B is a matrix of order c×d , then matrix AB exits and is of order a×d , if and only if b = c.

[tex] \: \: [/tex]

If A is a matrix of order a×b and B is a matrix of order c×d , then matrix BA exits and is of order c×b , if and only if d = a.

[tex] \: \: [/tex]

For Matrix AB, a = 3, b = c = 3, d = 3 , thus Matrix AB is of order 3×3

[tex]\\ { \rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = \left[\begin{array}{c c c} \: \: \: \: 2(2)-3(-1)-5(1) & \: \: \: \: 2(-2)-3(3)-5(-2) & \: \: \: \: 2(-4)-3(4)-5(-3) \\ -1(2)+4(-1)+5(1) & -1(-2)+4(3)+5(-2) & -1(-4)+4(4)+5(-3)\\ \: \: \: \: 1(2)-3(-1)-4(1) & \: \: \: \: 1(-2)-3(3)-4(-2) & \: \: \: \: 1(-4)-3(4)-4(-3) \end{array} \right]}}[/tex]

[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 4 + 3 - 5 & \: \: \: -4 -9 + 10 & \: \: -8 - 12 + 15 \\ -2 - 4 + 5 & \: \: \: \: \: \: + 2 + 12 - 10 & \: \: \: \: \: 4 + 16 - 15 \\ \: \: \: \: \: 2 + 3 - 4 & \: \: -2 - 9 + 8 & -4 - 12 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right]}}[/tex]

[tex]\\ {\rm{Matrix \: AB = \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: 5 \\ \: \: \: \: 1 & -3 & -4 \end{array} \right] = Matrix \: A}}[/tex]

For Matrix BA, a = 3, b = c = 3, d = 3 , thus Matrix BA is of order 3 × 3

[tex]\\ {\rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] \times \left[ \begin{array}{c c c} \: \: \: \: 2 & -3 & -5 \\ -1 & \: \: \: \: 4 & \: \: \: \: 5 \\ \: \: \: \: \: 1 & -3 & -4 \end{array} \right]}}= \left[ \begin{array}{c c c} \: \: \: \: \: 2(2) -2(-1) -4(1) & \: \: \: \: 2(-3) -2(4) -4(-3) & \: \: \: \: 2(-5) -2(5) -4(-4) \\ \: -1(2) + 3(-1) + 4(1) & -1(-3) + 3(4) +4(-3) & -1(-5) + 3(5) + 4(-4) \\ \: \: \: \: \: 1(2) -2(-1) -3(1) & \: \: \: \: 1(-3) -2(4) -3(-3) & \: \: \: \: 1(-5) -2(5) -3(-4) \end{array} \right][/tex]

[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 4 + 2 - 4 & \: \: \: -6 -8 + 12 & \: \: -10 - 10 + 16 \\ -2 - 3 + 4 & \: \: \: \: \: \: +3 + 12 - 12 & \: \: \: \: \: + 5 + 15 - 16 \\ \: \: \: \: \: 2 + 2 - 3 & \: -3 -8 +9 & \: \: \: \: \: -5 -10 + 12 \end{array} \right] = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right]}}[/tex]

[tex]\\{ \rm{Matrix \: BA = \left[ \begin{array}{c c c} \: \: \: \: 2 & -2 & -4 \\ -1 & \: \: \: \: 3 & \: \: \: \: 4 \\ \: \: \: \: 1 & -2 & -3 \end{array} \right] = Matrix \: B}}[/tex]

Answer:

x=10

Step-by-step explanation:

Answer:

x is 10 degrees

Step-by-step explanation:

180-90=90

(2x+3)+(5x+17) = 90

7x+20=90

7x=70

x=10

Answer:

Step-by-step explanation:

Hope this helps

Answer:

387-141=246

Step-by-step explanation:

    387

   - 141

-------------

     246

Answer:

120

Step-by-step explanation:

 Given:

3 Lines

A line with points M, H, K intersects a line with points J, H, L at point H.

A line extends from point H to point P between angle K H J.

Angle M H L is 140 degrees and angle K H P is 20 degrees.

Solve:

Since, Angle M H L is 140 degrees and angle K H P is 20 degrees.

Then 140 - 20 = 120

Answer is 120

~Lenvy~

Answer:

180-52=128

Do mark BRAINLIEST

Answer:

2.013  to 3 DP's.

Step-by-step explanation:

f(4.04)  will be very close to the tangent line.

Equation of tangent line

is y - 4 = m(x - 10)

m = (4-2) / (10-4) = 1/3

y - 4 = 1/3(x - 10)

y = 1/3x - 10/3 + 4

y = 1/3x + 2/3

So the require estimate of f(4.04)

= 1/3(4.04) + 2/3

= 2.013333

the answer is b if i remeber

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.

  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.

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

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

  1 ≤ x < 7/4

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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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