Given the function w(x) = 9x + 8, evaluate w(5). Explain all steps.

The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.

Let the expression be 4+(6+8u)

4 + (6 + 8u) = (4 + 6) + 8u

The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.

Adding (distributing) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms. Solve the equation and simplify, if needed.

The expression be 4+(6+8u)

4+(6+8u) = (4 + 6)+8u

Therefore, the correct answer is distributive property.

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The logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

The logarithmic equation is given as:

f(x) = log₈(x + 1) + 4

The parent function of the logarithmic equation is

y = log₈(x)

When the logarithmic equation is translated 1 unit left, we have:

y = log₈(x + 1)

When the logarithmic equation is translated 4 units up, we have:

y = log₈(x + 1) + 4

This means that the logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

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The relationship between d and t.

d = 49t

The correct equation is C.

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

speed = 49 miles/hour

Distance

Time

as we know :

Speed = Distance  /  Time .

Then:

49 = Distance/Time

Distance = 49*Time .

the relationship between d and t ( d = 49t).

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I understand that the question you are looking for is :

A cheetah runs at a speed of 49 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?

A. d = 49 + t

B. t = 49 + d

C. d = 49t

D. t = 49d

Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

According to the statement

we have to tell and explain about the types of shapes which are required for the creations of 3-D figure.

For this purpose, Firstly we have to know about the 3-D figures.

So,

A shape is a graphical representation of an object or its external boundary and outline, as opposed to other properties such as color, texture, or material type.

A plane shape is constrained to lie on a plane, in contrast to solid 3-D shapes.

After that we know that the

When the all dimensions of a given shape can be observed at the same time, then its is said to be in a 3-D. However, polygons are shapes which has 3 or mores sides. Examples are: trigon, hexagon, octagon etc.

Thus, since the in the 3-D figure have 8 sides connected which is greater than their width.

This confirms that the sides of the figure made up of eight congruent rectangles, because the 3-D figure has eight regular sides. Then, the height of the figure would be the length of the rectangles.

After that all this condition, Two regular octagons and eight congruent rectangles are perfect for the creation of 3-D figures.

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The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.

The formula for calculating the percentage increase of a number is

%increase = 100 × (Final - initial)/initial

Consider the number as 'x'

The result when the number is multiplied by 1.36 is 1.36x

So, the percentage increase is calculated as follows:

%increase = 100 × (Final - initial)/initial

Where Initial = x and Final - 1.36x

⇒ %increase = 100 × (1.36x - x)/x

⇒ %increase = 100 × x(1.36 - 1)/x

⇒ %increase = 100 × 0.36

⇒ %increase = 100 × 36/100

∴ %increase = 36

Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.

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The function can be solved as follows:

(h - g)(2.1) = 3.51

g(x) = 2x² + 3x - 9

h(x) = x² + 2x - 6

(h - g)(x) = h(x) - g(x)

(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)

(h - g)(x) =  2x² + 3x - 9 - x² - 2x + 6

(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6

(h - g)(x) = x² + x - 3

Therefore,

(h - g)(2.1) = (2.1)² + (2.1) - 3

(h - g)(2.1) = 4.41 + 2.1 - 3

(h - g)(2.1) = 6.51 - 3

(h - g)(2.1) = 3.51

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Step-by-step explanation:

so ,

Question 6 :-

5 × (3+4) - 4

first solve the Bracket ......

5 × (7) - 4

after multiplication ......

35 - 4

= 31

so , Answer is 1st one ....

Question 7 :-

8 + 1/2 × (6-2) -1

so , here also solve the Bracket first .....

8 + 1/2 × (4) - 1

after multiplication .....

8 + 2 - 1

after + and - .......

10 - 1

= 9 .......

so , Answer is 2nd one .....

Answer:

Q6: 5 times the sum of 3 and 4, then subtract 4.

Q7: Add 8 to half the difference of 6 and 2, then subtract 1.

Step-by-step explanation:

[tex]5 \times (3 + 4) -4[/tex]

• First of all, we can see that 5 is being multiplied by something, so we can say "5 times...".

• Next we see that the 5 was being multiplied by the sum of 3 and 4, so we can combinedly say "5 times the sum of 3 and 4...".

• And finally, we see that 4 is taken away from the result. Therefore we can say " 5 times the sum of 3 and 4, then subtract 4".

[tex]8 + \frac{1}{2} \times (6-2) -1[/tex]

• Firstly, we can see that 8 is being added to something, so we can say "Add 8...".

• Next, we see that 8 was being added to [tex]\bf \frac{1}{2}[/tex] of something, so we can combinedly say "Add 8 to half of...".

• Then we see that the difference (i.e., result of subtraction) of 6 and 2 was being halved. Therefore we say "Add 8 to half of the difference of 6 and 2...".

• Finally, we can see that 1 is subtracted from the result. Therefore, we can say "Add 8 to half of the difference of 6 and 2, then subtract 1".

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Area of shaded region is equal to :

Area of rectangle - Area of two triangles ~

1. Area of rectangle :

[tex]\qquad \sf  \dashrightarrow \: length \times width[/tex]

[tex]\qquad \sf  \dashrightarrow \: 20 \times 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]

2. Area of first triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]

3. Area of second triangle :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 \times 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]

Area of shaded region is :

[tex]\qquad \sf  \dashrightarrow \: 300 - (15 + 60)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 300 - 75[/tex]

[tex]\qquad \sf  \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]

All the x-values in the interval for which the function is equal to its average value [tex]5-\sqrt{5}[/tex] .

An interval program language period accommodates the numbers mendacity between specific given numbers. for instance, the set of numbers x gratifying 0 ≤ x ≤ five is a c programming language that contains zero, five, and all numbers among 0 and five.

The interval program language period is the distinction between the higher class restriction and the lower magnificence restriction. As an example, the dimensions of the class c program language period for the first class is 30 – 21 = 9. further, the size of the class c programming language for the second magnificence is forty – 31 = nine.

In arithmetic, an interval language is fixed of actual numbers that carry all actual numbers mendacity among any numbers of the set. For example, the set of numbers x pleasurable zero ≤ x ≤ 1 is a  language that includes zero, 1, and all numbers in between.

f(x)=(91-55 [0,1]

value of the function on the interval [0,1] is (9-0)

Let x-5=3

now, find the value of x, for which

f(x) =(2x-5) 2 =

5/X-5 =√5

24 X = 54√5 and 5. √5

Strs [ay] and 5- 5-√5 €0.4]

value of x is 5- sqrt15

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Correct option is A. The value of f(3) is -11

The value of x = 3 corresponds to the following function on the piece wise

[tex]f(x) = -3x -2[/tex]

Substitute 3 for x

[tex]f(3) = -3(3) -2[/tex]

Expand

[tex]f(3) = -9 -2[/tex]

Evaluate -9 -2

[tex]f(3) = -11[/tex]

Hence, the value of f(3) is (a) -11

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Answer: A.) -11

Step-by-step explanation: i hope this helps :)

The roots of the given polynomials exist  [tex]$x=8+\sqrt{10}$[/tex], and [tex]$x=8-\sqrt{10}$[/tex].

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0$$[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$[/tex]

simplifying the equation, we get

[tex]$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\[/tex]

[tex]$&x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are [tex]$x=8+\sqrt{10}$[/tex], and

[tex]$x=8-\sqrt{10}$[/tex].

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Answer:

x=8-[tex]\sqrt{10}[/tex] and x=8+[tex]\sqrt{10}[/tex]

Step-by-step explanation:

It was right for me

Answer:

Step-by-step explanation:

a) start at the origin (0,0) then go 4 boxes to the right, 3 up

b) start at the origin (0,0) then go 4 boxes to the right, 5 down

c) start at the origin (0,0) then go 2 boxes to the left, 3 up
d) start at the origin (0,0) then go 2 boxes to the left, 5 down

See below for the description of the figure

The equation is given as:

36 + 27 = 9 * (4 + 3)

Open the bracket

36 + 27 = 9 * 4 + 9 * 3

The above when represented on a figure is represented by the given figure.

From the figure, we have the following highlights:

This means that the figure has 7 columns and 9 rows where the partitions on the figure are the product of the rows and column in each partition

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Answer:

its A

Step-by-step explanation:

Answer: The first one (A)

Step-by-step explanation:

The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.

The domain for the given function is x ≥ -3.

Thus, its range is x ≤ - 1/2.

To find the inverse, we equate f(x) = y, to get:

(-1/2)√(x + 3) = y,

or, √(x + 3) = -2y.

Squaring both sides, we get:

x + 3 = (-2y)²,

or, x + 3 = 4y²,

or, x = 4y² - 3.

Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.

The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.

Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.

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The provided question is incomplete. The complete question is:

"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the inverse of the given function.

f(x) = (-1/2)√(x + 3), x ≥ -3

f⁻¹(x) =   x² -   , for x ≤    ."

The correct option of this expression is (B) 2(x-3)(x-4)

What is expression?

Given, expression is ;  2x²-14x+24 = 0

Now take common 2 from  this expression  both side.

        2(  x² - 7x + 12) = 0

          2(x² - (4 +3)x + 12) = 0

        2 (  x² - 4x - 3x + 12) = 0

        2 ( x( x - 4 ) -3 ( x - 4 )) = 0

        2  ( x - 3 ) ( x - 4 ) = 0

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The complete question is -

Select the correct answer. Which expression is equivalent to the given expression? 2x²-14x+24

A.(2x-12)(x-2)

B.2(x-3)(x-4)

C.2(x-8)(x+3)

D.2(x-5)(x-2)

The total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

External radius of the hollow cylinder = 10.5 cm

Internal radius of the hollow cylinder = 10.1 cm

Height of the hollow cylinder = 56 cm

Cost to Polish Outer Surface: 20 paisa/sq. cm.

Surface Area of Hollow Cylinder = Circumference [tex]*[/tex] height

Surface area of hollow cylinder = 2 π r h

= 2 π (10.5 cm) 56 cm

= π (21)(56)

= 3692.64 [tex]cm^2[/tex] (Using π ≈ 3.14 rounding to 2 digits)

Total Cost of metallic cylinder [tex]$= 3692.64 cm^2 * 20 paisa/cm^2[/tex]

= 73,852.8 paisa

= Rs. 738.58

Therefore, the total cost of polishing it's outer surface 20 paisa per square cm exists Rs. 738.58.

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If Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The price of the bonds is: $1,039.11.

We would be making use of financial calculator to find or determine the price of the bonds (Present value) by inputting the below data:

N represent Number of years = 12 x 2 = 24

I represent Interest rate= 7.5 % / 2 =3.75 %  

PMT represent Periodic payment= (8% x 1000) / 2 = $40

FV represent Future  value= $1,000

PV represent Present value=?

Hence;

PV (Present value) = $1,039.11

Therefore if Renfro Rentals has issued bonds that have an 8% coupon rate ,payable semiannually. The price of the bonds is:  $1,039.11.

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Answer:

(a) 22cm^2

Step-by-step explanation:

(a) 6*3=18

2*2=4

4+18=22

Answer:

13. x^2 + y^2 = 3

14. B

Step-by-step explanation:

13. Since it's centered at the origin, (0, 0), the values of h and k in (x - h)^2 + (y - k)^2 =  r^2 are equal to zero. So we simply have x^2 + y^2, and since the radius is the square root of 3, squaring the radius gives us 3.

14. B is the only circle with both a radius of 3 that's also shifted to the right 1 and down 2, since it's centered at (h, k), which is (1, -2).

Hope this helps! Brainliest, please :)

The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

According to the statement

we have given that the some data of the marks of 18 students and we have to make the plot of that data.

So, For this purpose, we have given that the

A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.

And it is used to find the median and the lower value and the maximum value.

So, The median become:

median = n /2

median = 18/2

median = 9th term and

median value is 71.

And then the lower value of the data is a 53.

And the upper value of the data is a 89.

So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.

So, The box and whisker plot is a 71 and 53 and 89 which represent the

median, upper value and lower value.

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Answer:

4

Step-by-step explanation:

The part of the function that is (2x - 1)² has a minimum value of 0. The reason is that any real number you for x will give you a positive, negative, or zero value for 2x - 1. When you square it, you must get a non-negative answer.

Then you add 4, and you get a value that is greater than or equal 4.

Answer:

a. 1056 ft

b. 52.8 ft

Step-by-step explanation:

1 mile = 5280 feet

a.

[tex]\frac{1}{5} *5280 = 1056[/tex]

Therefore 1/5 of a mile is 1056 feet.

b.

[tex]\frac{1}{100} *5280=52.8[/tex]

Therefore 1/100 of a mile is 52.8 feet

This real-world problem has the limitations 75< x <110 and 0< y[tex]\leq[/tex] 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y [tex]\leq[/tex]50.

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The lowest grade he could earn is 120% of the grade at the end of the semester.

The following statement is given:

I have 90% after about 75% of the semester.

We are asked to find the lowest grade by the end of this semester.

A percentage is a number expressed as a fraction of 100.

- 50% = 50/100 = 1/2

- 25% = 25/100 = 1/4

- 20% = 20/100 = 1/5.

We can write this statement "I have a 90% grade after about 75% of the semester" as:

90% grade  =  75% semester.............(1)

By the end of the semester means at 100% semester.

Multiplying equation (1) by 100/ 75 on both sides of the equation.

We get,

(100/75) x 90% grade = (100/75) x 75% semester

(100 x 90)/75 % grade = 100% semester

120% grade = 100%

Thus the lowest grade he could earn is 120% of the grade at the end of the semester.

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Answer:

12 square in

Step-by-step explanation:

In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.

A = pi*r*r = 3*2*2 = 12 square in

Answer:

12 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.

--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 in^2.