Solve for x: 1 < x + 3 < 4

The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)

The equation of the function is given as

f(x) = 4x³ - x² + 16x - 4

Factor out x from the equation of the function

So, we have

f(x) = 4x³ - x² + 16x - 4

Group the terms in 2's

f(x) = (4x³ - x²) + (16x - 4)

Factorize the expression in the bracket

So, we have

f(x) = x²(4x - 1) + 4(4x - 1)

Factor out 4x - 1

So, we have

f(x) = (x² + 4)(4x - 1)

Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)

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Answer:

12.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step: 1

-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1

Step: 2

-Graph the 90: From what I understand it should be a horizontal line with its point on 90y

Sorry if this doesn't help very late where I am.

A linear function which has the same y-intercept of 5 as the one that is represented by the graph is: table 1.

Mathematically, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2), the slope of the line is given by:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is 5.

At points (-3, -4), the y-intercept of this line can be calculated by using the slope-intercept form:

y = mx + c

Where:

Making y-intercept (c) the subject of formula, we have:

y-intercept, c = y - mx

y-intercept, c = -4 - 3(-3)

y-intercept, c = -4 + 9

y-intercept, c = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

 3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

As given in the question,

Sonia takes a walk everyday which is equal to

= 4/5 mile

Moreover, she has completed a part of her daily targeted distance =  3/5 mile

We need to find, what part of the total distance which Sonia covers daily, has she covered just now by covering 3/5 mile of distance.

Part of the total distance which Sonia covers daily, from the distance she has covered just now by covering 3/5 mile of distance

= (Distance covered by Sonia)/ (Total distance covered by Sonia)

= (3/5) / (4/5)

= (3/5) × (5/4)

= 3/4 mile

Therefore,,   3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

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For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]

In this question, we have been given a function f(x) = 3x² - 4

We need to write the rule obtained when finding f^(-1)

Le f(x) = y          ........(1)

y =   3x² - 4

We find the value of x.

3x² = y + 4

x² = (y + 4)/3

x = ±√[(y + 4)/3]

From (1),

f^{-1}(y) = ±√[(y + 4)/3]

Since the choice of the variable is arbitrary, we can write this as ,

f^{-1}(x) = ±√[(x + 4)/3]

Therefore, for given function the rule obtained when finding f^(-1) is  ±√[(x + 4)/3]

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Answer:

∠ R = 75°

Step-by-step explanation:

you are correct with answers to a, b, c

d

the sum of the 3 angles in Δ QRS = 180° , that is

∠ Q +∠ R + ∠ S = 180° , so

55° + ∠ R + 50° = 180°

∠ R + 105° = 180° ( subtract 105° from both sides )

∠ R = 75°

Answer: 91 ft

Step-by-step explanation:

Since WZ=1287ft .XY=54ft

WX is congruent to YZ

so WX= 1/2 (128-54)

= 1/2 x(<—times) 74

=37ft

WY= WX + XY

=37+54

= 91ft

1. 135, 205, 330, 275, and 365 are divisible by 5.

2.  1, 4, and 7 can be filled in the blank space to make it divisible by 3.

3. 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.

4. 81 is the only composite number all the other nos. are prime.

Divisibility rules are methods for determining whether a number is divisible by a certain number or not without actually dividing.

We know numbers that are divisible by 5 are those numbers

having 5 or 0 in their unit place.

∴ 135, 205, 330, 275, and 365 are divisible by 5.

A number is divisible by 3 if the sum of all the digits is divisible by 3.

∴ 3,71_ has a digit sum of 11, so 1, 4, 7 can be filled in the blank space to make it divisible by 3.

A list of all the factors of 30 is those numbers that divide 30 completely.

∴ 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.

We know composite numbers are those numbers that are not prime.

∴ 81 is the only composite number all the other nos. are prime and they have only two factors 1 and the number itself.

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Answer:

x ≤ 6 I think!

Answer: [tex]x\leq 6[/tex]

Step-by-step explanation: [tex]4x\leq 38-14[/tex]. Move the 14 to the right side first.

Then you would get [tex]4x\leq 24[/tex]

Divide 4 on both side

[tex]x\leq 6[/tex]

The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4)  is one solution

The equation is given as

7x + 3 - 8 = 2(5x - 4)

The above equation is a linear function with one variable

So, we have

7x + 3 - 8 = 2(5x - 4)

Open the brackets

So, we have

7x + 3 - 8 = 10x - 8

Subtract 10x from both sides of the equation

So, we have

-3x + 3 - 8 = - 8

Subtract (3 - 8) from both sides of the equation

So, we have

-3x = - 3

Divide by -3

x = 1

The above equation is true because it has a definite solution

Hence, the number of solutions in the equation is one

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Answer:wish i could help

Step-by-step explanation:......

The monthly salary of an executive is $6483.

What is monthly salary?

A salary is the amount of money that an employee receives from their employer each month, particularly when they work in a profession like education, law, or medical.

Given: An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 5700 dollars. She earns a total of 83500 dollars per year.

To find the salary for each month.

First to subtract the Christmas bonus from the total amount.

83500 - 5700 = 77800.

So, the salary from each month is,  77800/12 = 6483

Therefore, the salary for each month is, $6483.

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The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

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Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.  12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

Given that,

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.

We have to find how long will the projectile be above the ground at a height more than 9000 feet.

Answers should be rounded to the closest hundredth.

The function is

h(t)=-16t²+900t+175

-16t²+900t+175>9000

-16t²+900t+175-9000>0

-16t²+900t-8825>0

The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.

Gives the roots of a quadratic equation ax² + bx + c = 0.

x = [-b ± √(b² - 4ac)]/2a.

Now, We get

t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)

t=[-900 ± √(810000-564800)]/-32

t=[-900 ± √(245200)]/-32

t=[-900 ± 495.17]/-32

First,

t=[-900 + 495.17]/-32

t=[-404.83]/-32

t=12.65

Second,

t=[-900 - 495.17]/-32

t=[-1395.17]/-32

t=43.59

Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

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Answer:

No solution

Step-by-step explanation:

6 + 2x = 2(x - 3)

6 + 2x = 2x-6

No solution

Answer: the value of a = 14.72 and if you evaluate it.

Have a good day

g = a - [tex]\frac{h}{2}[/tex]

Answer:

f(x) ≥ 0

In interval notation Range:  [0, ∞]

Step-by-step explanation:

Regardless of the value of x, |x+5| ≥ 0 and there is no upper bound on f(x)

Answer: C

Step-by-step explanation: Got it right for my test

how do i delete an answer?

P, which is the principal invested is $7,000 whereas the T is 0.75

What is simple interest?

The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest  rate and the time whose formula is as given below:

I=PRT

I=simple interest amount in dollars=unknown

P=principal investment=actual amount invested on simple interest basis=$7000

R=annual simple interest rate=8.3%

T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)

I=$7000*0.083*0.75

I=$435.75

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The correct statement are;

1. The radius of the circle is 3 units.

2. The center of the circle lies on the x-axis.

3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The equation of circle will be;

⇒ x² + y² - 2x - 8 = 0

The standard form of the equation of circle is;

⇒ x² + y² + 2gx + 2fy + c = 0

Where,

The center of circle = (-g , -f)

The radius of circle = √g² + f² - c

Since, The equation of circle will be;

⇒ x² + y² - 2x - 8 = 0

Compare with the standard form of circle, we get;

⇒ 2gx = - 2x

⇒ g = - 1

And, 2fy = 0

⇒ f = 0

Hence, The center = ( -g , -f) = (- (-1) , 0)

                                           = (1, 0)

Clearly, This shows the center of circle is lies on x - axis.

Radius of circle = √g² + f² - c

Substitute all the values we get;

Radius of circle = √g² + f² - c = √(-1)² + 0 - (-8)

                                            = √9

                                            = 3

Thus, The radius of the circle is 3 units.

Now, For the equation of circle x² + y² = 9,

Radius = √9 = 3 units.

So, The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Therefore, The correct statement are;

1. The radius of the circle is 3 units.

2. The center of the circle lies on the x-axis.

3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]

[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]

Answer:

2.8 pounds

Step-by-step explanation:

she spends on both types of bell peppers =

$2.56+$1.92=$4.48

$1.60 = 1 pound

$4.48 = ?

= 4.48/1.60

= 2.8 pounds

According to the solving the factorized value of the given equation is:

(4x-5). (3x+1).

Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.

Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.

Detailed explanation:

12x² - 11x-5

12x²+4x-15x-5

4x(3x+1) - 5(3x+1)

(4x-5). (3x+1)

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Answer:

Step-by-step explanation:

The requried, simple interest rate for Vince's loan was 7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Amount = Principal [1 + rate×time]

We can use the simple interest formula to solve this problem, where:

Simple interest = Principal x Rate x Time

In this case, the principal is $500, and the time is 2 years. We can rearrange the formula to solve for the rate:

Rate = Simple interest / (Principal x Time)

The total amount paid back, including the principal and the interest, is $570. So, the simple interest can be calculated as:

Simple interest = Total amount paid - Principal

Simple interest = $570 - $500

Simple interest = $70

Substituting these values into the formula, we get:

Rate = $70 / ($500 x 2)

Rate = $70 / $1000

Rate = 0.07 or 7%

Therefore, the simple interest rate for Vince's loan was 7%.

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AAnswer:

Step-by-step explanation:

Answer:

14.90 $ 527.86- 349.11 = 178.75 divided by 12 pta members is 14.89 rounded would be 14.90 the answer depends if u want to round it

Step-by-step explanation:

sub to imaginefn in utube

The most appropriate choice for ratio will be given by-

Ratio of red and orange to the other Skittles  = 8 : 9

What is ratio?

Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent

Here,

Number of red Skittles Rory has = 5

Number of yellow Skittles Rory has = 8

Number of purple Skittles Rory has = 6

Number of green Skittles Rory has = 4

Number of orange Skittles Rory has = 11

Total number of red and orange skittles = 5 + 11

                                                                   = 16

Total number of other skittles = 8 + 6 + 4

                                                  = 18

Ratio of red and orange to the other Skittles = 16 : 18

                                                                         = 8 : 9

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The slope of the line in the given diagram = rise/run = 1/2.

The slope of a line is determined as the ratio of the rise of the line to the run of the line.

The rise of a line = change in y

The run of a line = change in x.

The red line in the image attached below shows the rise of the line which is, 1 units.

The blue line represents the run, which is, 2 units.

The slope of the line = 1 units/2 units = 1/2.

Therefore, we can state that the slope of the line = 1/2.

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