What is the inverse of this function?
f(x)=√x
+ 3, x ≥ − 3
f-¹(x) =
x²-
-
for x ≤

The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

What is Quadratic formula?

To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,

x = - b ± √b² - 4ac / 2a

The given expression is;

- 2x² + 4x = 5

Now, The given equation is solve by using Quadratic formula as;

- 2x² + 4x = 5

Move terms to the left side

- 2x² + 4x - 5 = 0

- ( 2x² - 4x + 5 ) = 0

2x² - 4x + 5 = 0

Compare with quadratic equation ax²+ bx + c = 0 we get;

a = 2, b = -4, c = 5

Since, Quadratic formula is,

x = - b ± √b² - 4ac / 2a

Hence, Substituting all the values of a, b and c in quadratic formula we get;

x = - (-4) ± √(-4)² - 4*2*5 / 2*2

x = 4 ± √16 - 40 / 4

x = 4 ± √-24 / 4

x = 4 ± 2√-6 / 4             ( Since, i = √-1  )

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

So, The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

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Speed is 0.01 miles per minute.

we know speed is = distance/ time

since we need speed in miles per minute we need to convert km into miles.

and hours in minute.

distance= 5km

1km= 0.621371 miles

5km= 50.621371 miles = 3.10686 miles= 3.12 miles

1hour= 60 minutes

4.5 hour = 4.5×60 minutes=270 minutes

speed= distance in km/time in minutes=3.12 miles/270 minutes

speed = 0.012 miles per minute

speed is 0.01 miles per second.

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The probability of rolling a 3 first, then an even number, is 1/12.

So, in the given situation the first roll has no effect on the second roll because they are separate events.

Because they are independent, the probabilities of the two events can be multiplied.

Now, we will multiply the two probabilities as follows:

Therefore, the probability of rolling a 3 first, followed by rolling an even number is 1/12.

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Answer:

199 miles

Step-by-step explanation:

if you multiply 33 in 6 places it gives 198 then you plus 1 to get $25.00

GOOD RIGHT please rate

The equation expressed in terms of x is x = √47/ 2

A line segment can be defined as the part of a line that connects two points which are considered to be its endpoints.

From the information given, we have that LN is a line with segments LM, MN and LN and M is the midpoint between L and N

Now, the equation is expressed as;

LM + MN = LN

Where;

Substitute the values

x² + x² + 9x = 56

collect like terms

2x² = 56 - 9

2x² =  47

To make 'x' the subject of formula

x² = 47/ 2

Find the square root of both sides

x = √47/ 2

Thus, the equation expressed in terms of x is x = √47/ 2

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The complete table is

x         y

-5      49

-1        9

0       -1

1        -11

From the question, we are to fill in the table for the given values of x

Using the given equation,

y = -10x - 1

Determine the value of y when x = -5

y = -10x - 1

y = -10(-5) - 1

y = 50 - 1

y = 49

Determine the value of y when x = -1

y = -10x - 1

y = -10(-1) - 1

y = 10 - 1

y = 9

Determine the value of y when x = 0

y = -10x - 1

y = -10(0) - 1

y = 0 - 1

y = -1

Determine the value of y when x = 1

y = -10x - 1

y = -10(1) - 1

y = -10 - 1

y = -11

Hence, the complete table is

x         y

-5      49

-1        9

0       -1

1        -11

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3:15=3/15

The numerator and the denominator can both be divided by 3.

so, it is 1/5 which is equal to 1:5.

The simplest ratio of triangles to total shapes is 1 : 6.

Given that, there are 3 triangles and 15 circles.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, total number of shapes

= 3+15

= 18

Now, ratio of triangles to total shapes is 3 : 18

So, the simplest form = 1 : 6

Hence, the simplest ratio of triangles to total shapes is 1 : 6.

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The formula for E is given as   E = L/250M

According to the question we have been given that the level of monsters is measured by as follows

                  L = 250M E      (1)

 where , M = number of monsters

              E = experience of monsters.

Now we need to find the formula for E. For that we will solve equation (1) for E .

                  L = 250M E

Dividing both the sides by 250M we get

                  L/250M = E

          or,    E = L/250M

Thus above is the equation or the formula for E.

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Using proportions, it is found that Elena's group hiked 6.3 km each day.

A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, we have that Priya's group hiked 19 kilometers in 5 days, hence the daily amount is found applying the proportion as follows:

19/5 = 3.8 km a day.

Elena's group hiked 2.5 km a day more, hence:

3.8 + 2.5 = 6.3 km a day.

Elena's group hiked 6.3 km each day.

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The value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.

Rewrite the above expression properly as follows:

Divide 4 5/6 ÷ -2 1/7

Using LaTeX, the above expression can be further represented as

[tex]4 \frac{5}{6} \div - 2\frac 17[/tex]

Rewrite the above fractions and express it as improper fractions

[tex]\frac{29}6 \div -\frac{15}7[/tex]

Rewrite the above fractions and express it as products

[tex]\frac{29}6 \times -\frac7{15}[/tex]

Evaluate the product in the above expression

[tex]-\frac{203}{90}[/tex]

Rewrite the above expression as a mixed fraction

[tex]-2\frac{23}{90}[/tex]

Hence, the value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]

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Answer:

  -7 ≤ x ≤ -4

Step-by-step explanation:

You want a compound inequality that expresses the same relation as a number line graph with solid dots at -7 and -4, and shading between.

The graph shown is indicating values of x lie between -7 and -4, including those values. As an inequality, this is written ...

  -7 ≤ x ≤ -4

Answer:

15g i think sorry if i am rong but i tryed

Step-by-step explanation:

Answer:

B.

Give me brainliest answer

I hope I could help

Using a linear function and the work integral, it is found that the work that was done lifting the sand this far is of 944 ft-lb.

A linear function is modeled by the following rule:

y = mx + b

In which:

For the weight of the bag of sand in this problem, we have that:

Hence the weight of the bag after being lifted x feet is given by:

W(x) = 144 - 4x.

The work realized for a function f(x) in an interval [a,b] is given by the following integral:

[tex]W = \int_{a}^{b} f(x) dx[/tex]

For this problem, the function and the bounds of the interval are given as follows:

Hence the work is given by:

[tex]W = \int_{a}^{b} (144 - 4x) dx[/tex]

W = 144x - 2x², from x = 0 to x = 18.

Applying the Fundamental Theorem of Calculus:

W = 144(18) - 2(18)² - 144(0) + 2(0)² = 1944 ft-lb.

The work that was done lifting the sand this far is of 944 ft-lb.

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The number of kilometers represented by 8cm is 80km.

According tot he question we have been the proportion of scaling on the map which is as follows:

                             1 cm : 10 km   or it is also written as   1cm/10km

We need to find the number of kilometers represented by 8 cm

Let the number of kilometers that we need to find be x km. Mathematically the proportion can be written as

                              8 cm : x km     or it is written as    8cm / x km

Also both the proportion will be equivalent. Therefore, the proportion is equal to

                              1/10 = 8/x

we will solve this for x, we get

                                x = 8*10

                                x = 80 km

Hence the number of kilometers represented by 8cm is 80 km

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \underset{gradient}{\stackrel{slope}{m}} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y - 2 = \cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x[/tex]

When Sue wrote a double fact. It has a sum less than 10 and greater than 4. The addends are each less than 5, the numbers that she wrote include 4+4 and 3+3.

It is given that the sum is greater than 4 and smaller than 10.

If the sum is less than 10 and greater than 4 that limits you to 5,6,7,8,9

It should be noted that 5+5 is 10, and the sum has to be lower then 10.

The addends are less than 5 so it could be 4+4, 4+3, 4+2, 4+1

This shows that Sue might have written 5,6,7, or 8.

Therefore, the numbers are 3+3 and 4+4.

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The values of t for which the ball's height is 16 feet are 1.84s and 0.41s

From the question, we are to determine all values of t for which the ball's height is 16 feet

From the given information,

The equation that represents the ball's height (in feet) after t second is

h = 4 + 36t - 16t²

To determine all values of t for which the balls height is 16 feet, we will put h = 16 in the equation

That is,

h = 4 + 36t - 16t² becomes

16 = 4 + 36t - 16t²

Rearranging

16t² - 36t + 16 - 4 = 0

16t² - 36t + 12 = 0

Divide through by 4

4t² - 9t + 3 = 0

Solve the quadratic equation using the general formula

t = [-b±√(b²-4ac)]/2a

a = 4, b = -9, c = 3

t = [-(-9)±√((-9)²- 4(4)(3))]/2(4)

t = [9±√(81- 48)]/8

t = [9±√(33)]/8

t = [9±5.74]/8

t = [9+5.74]/8 or  [9-5.74]/8

t = 14.74/8 or  3.26/8

t = 1.84 or 0.41

Hence, the values of t for which the ball's height is 16 feet are 1.84s and 0.41s

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The journal entries to record (a) the payroll and (b) the employer's payroll tax expense for the month are as follows:

a) The payroll:

Debit Sales salaries $125,000

Debit Office salaries 35,000

Credit:

 Federal income tax withholding payable 32,300

 Medical insurance withholding payable 7,370

 Social security tax withholding payable 10,200

 Medicare tax withholding payable 2,550

 Cash $107,580

b) The employer's payroll tax expense:

Debit Payroll Tax Expense $975

Credit:

 Federal Unemployment Tax Payable $200

 State Unemployment Tax Payable $775

SUTA = 3.1% of $25,000 = $775

FUTA = 0.8% of $25,000 = $200

Sales salaries $125,000

Federal income tax withheld 32,300

Office salaries 35,000

Medical insurance withheld 7,370

Social security tax withheld 10,200

Medicare tax withheld 2,550

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Answer:

[tex]\left \{ {{-x+2=0} \atop {x+2y=7}} \right.[/tex]

-x + 2 = 0 --> -x = -2

x + 2y = 7 --> x + 2y = 7              

                    ________  

                    2y = 7-2 = 5 --> y = 5/2

x = -2y + 7 --> x = -5 + 7 --> x = 2

---

Have a nice day!

Answer:

B

Step-by-step explanation:

a c and d are unessecary answers

|3.7−(−1.5)|

The initially reported temperature was 3.7 however the temperature changed to -1.5.

Answer:

[tex]5^{14/5}[/tex]

Step-by-step explanation:

[tex]\frac{5^3}{5^{1/5}} \\ \\ 5^{3-\frac{1}{5}} \\ \\ =5^{14/5}[/tex]

Given function y =45(0.974)ˣ is a function of exponential decay and percentage rate of decrease is 2.6%.

The exponential function is an function f(x) = a(b)ˣ

a = initial amount when x= 0

b= base that is multiplied and it is greater than 0

And x is the variable in the exponent

When b> 1 , the values of this function goes up and up and then this function shows exponential growth.

When 0< b< 1, the values of this function becomes smaller as x increases then this function shows exponential decay.

And r is the percentage rate of change where b =r +1

Given function is y = f(x) = 45(0.974)ˣ

When we compare it with standard function f(x) = a(b)ˣ

we get a = 45 and b =0.974

As b is between 0 and 1 in this case, therefore this function is exponential decay.

b =r+ 1

therefore r = b-1 = 0.974-1 = -0.026

converting 0.026 to percentage we get -0.026*100= -2.6% ( negative sign shows decrease)

Therefore, we can say that the given function represents exponential decay function and rate of decrease is 2.6%

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We need to know about

linear equation

to solve this problem. (a) The equation that will allow Robel to calculate what his total cost will be is 52+94n (b) Robal's total cost if he decides to stay 3 nights is $334

A

linear equation

is one that has

one or two variables

in it, the variables in a linear equation are linearly related to each other which means that the graph of such an equation is a straight line.

In part (a) it is said that Robel is charged $52 as a one time fee and the

cost per night

is $94, let us consider the

total cost to be t

and the

number of nights he stays be n,

then the equation for the total cost will be

t=52+94n

In part (b) we have to find out the total cost if he stays 3 nights, which means n=3,

substituting the value of n

in the equation for total cost

t=52+94x3=334

Therefore we found out that the

equation for Robel's total cost

is 52+94n and the total cost if he stays for 3 nights is $334.

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Answer:120

Step-by-step explanation:

so if its a 10x12 plane that would be 10 12 times so 10+10+10+10+10+10+10+10+10+10+10+10

or 12+12+12+12+12+12+12+12+12+12

Answer:

y = -⅔+2x

Step-by-step explanation:

Hope this helps!!

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation in slope-intercept form is given as,

y = mx + c

Where m is the slope and c is the y-intercept.

The equation for y is y = 2x - 2/3

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 4 is an equation.

2x = 4x is an equation

We have,

3y - 6x = -2

Add 6x on both sides.

3y = -2 + 6x

3y = 6x - 2

Divide both sides by 3.

y = (6x - 2)/3

y = 2x - 2/3

This is in the form of an equation in slope-intercept form.

The equation in slope-intercept form is given as,

y = mx + c

Where m is the slope and c is the y-intercept.

Thus,

The equation for y is y = 2x - 2/3

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Answer: 560

Step-by-step explanation: i had this exact question on OW

Answer:

a₅₃ = 560

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 12 and d = a₂ - a₁ = - 1 - (- 12) = - 1 + 12 = 11 , then

a₅₃ = - 12 + (52 × 11) = - 12 + 572 = 560