The segments shown below could form a triangle.

The answer is:

Range: All the real numbers or (-∞,+∞)

To solve the problem, we need to rewrite the variable "x" as "y" and the variable "y" as "x", and then, isolate "y". Then, we need to look if there is any restriction to the resulting value of "y".

We are given the function:

[tex]y=log_8(x)[/tex]

Now, rewriting we have:

[tex]x=log_8(y)[/tex]

Then, isolating we have:

[tex]8^{x} =8^{(log_8(y))}\\\\8^{x}=y[/tex]

Therefore, we can see that the resultant function is a quadratic or polynomial function, we need to remember that there is no restriction for this type of functions, it means that the range of the function is equal to the Real numbers where the values of  "x" exist.

Hence, the answer is:

Range: All the real numbers or (-∞,+∞)

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

Volume= 82.4in³

Step-by-step explanation:

Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. It's units are always "cubic"

To find the volume of sphere, we will use the following formula of Volume:

Volume = 4/3 πr³

Put the values in the formula:

As we know that the value of π is 22/7 or 3.14

Radius = 2.7

According to the formula:

Volume = 4/3 * 3.14 *(2.7)³

Volume= 4/3* 3.14(19.683)

Volume=4/3(61.80462)

Volume=247.21848/3

Volume= 82.4in³....

Answer:

B

Step-by-step explanation:

A triangle has both x and y values making it 2D. A 1D object is a point, a 3D object is a cube or something, and a 0D object is nothing.

Answer:

A. 14 meters

B. 24 meters

Step-by-step explanation:

A. Mellisa starts at 29 meters deep, then rises 15 meters.  So her final depth is 29 − 15 = 14 meters.

B. Melissa starts at 40 meters deep, then rises 2 m/min for 8 minutes.  That means she rises a total distance of 2 × 8 = 16 meters.  So her final depth is 40 − 16 = 24 meters.

Answer:

At one point, Mellisa is 29 meters below the surface of the water.

A.

As she swims around for the fish, she swims for 12 mins and rises upward by 15 meters.

So, her final depth at the end of the 12 minutes = [tex]29-15=14[/tex] meters

B.

Mellisa is at a depth of 40 meters. Every minute, she rises 2 meters.

So, in 8 minutes she will rise [tex]2\times8=16[/tex] meters

Her depth will be = [tex]40-16=24[/tex] meters

Answer:

Given that the function is a model of miles per hour with x being representative of time in seconds, you simply have to plug 2 into the equation for each x.

Therefore,

g(x) = x^4 - 4x^2 + 7x - 8

becomes

g(x) = 16 - 16 + 14 - 8 = 6 miles per hour.

So, 6 mph is your answer!!

At rate of 6 miles per hour the rollercoaster travelling at 2 seconds.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

g(x) = [tex]x^4[/tex] - 4x² + 7x - 8

where x is time measured in seconds.

Now, the speed of roller-coaster for t= 2 seconds

g(2) =  [tex]x^4[/tex] - 4x² + 7x - 8

g(2) =  [tex]2^4[/tex] - 4(2)² + 7(2) - 8

g(2)= 16 - 16 + 14 - 8

g(2) = 6 miles per hour.

Hence, the speed 6 miles per hour.

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Answer:

So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]

Step-by-step explanation:

Since we are dividing by a linear factor, I'm going to use synthetic division.

Since the linear factor that we are dividing by is (x-5), I'm going to put 5 on the outside:

5    |     1       -12       8

      |              5      -35

      |--------------------------

           1         -7      -27

So the quotient x-7 while the remainder is -27.

So [tex]\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}[/tex]

You could do long division if you prefer:

           x-7

         ------------------------

(x-5) |   x^2-12x+8

        - (x^2-5x)

        --------------------------

                -7x+8

              -(-7x+35)

         ---------------------

                     -27

You still get the same thing that the quotient is x-7 and the remainder is -27.

Answer:

x=1

Step-by-step explanation:

5x + 2 = 3x + 4(2x - 1)

Distribute the 4

5x + 2 = 3x + 8x - 4

Combine like terms

5x + 2 = 11x - 4

Subtract 5x from each side

5x -5x + 2 = 11x - 5x - 4

2 = 6x-4

Add 4 to each side

2+4 = 6x-4+4

6 = 6x

Divide each side by 6

6/6 =6x/6

1= x

The value of x is 1 for equation 5x + 2 = 3x + 4(2x - 1).

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Given,

[tex]5x+2=3x+4(2x-1)\\[/tex]

[tex]5x+2=3x+8x-4[/tex]

On transposing like terms on one side of the equation.

[tex]5x-3x-8x=-4-2\\-6x=-6[/tex]

On multiplying -1 on both sides,

[tex]-6x\times(-1)=-6(-1)\\6x=6[/tex]

On dividing by 6 on both sides,

[tex]\frac{6x}{6}=\frac{6}{6}\\x=1[/tex]

Hence, the value of x is 1.

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Answer:

i thought its -9

Step-by-step explanation:

cut x/x of first side

now cut x/x

Answer:

They are 2 and 3.

Step-by-step explanation:

2 * 3 = 6

Answer:  the correct option is

(B) F T → T.

Step-by-step explanation:  We are given to find the truth value of he following conditional statement :

"If the grass is red, then the snow is white."

Let us consider that

p : the grass is red. This is a false statement

and  

q : the snow is white. This is a true statement.

So, we get

p  →  q

F  → T, which is true (T).

Thus, the required answer is  F T → T

Option (B) is CORRECT.

Answer:

$2520

Step-by-step explanation:

Taking the dimensions of the office floor from the plan to be;

[tex]15ft*28ft[/tex]

Area of the floor to be covered will be the product of the sides dimensions

[tex]=15*28=420ft^{2}[/tex]

Cost of putting tile on the floor

1ft²=$1

420ft²=?

=[tex]\frac{420*1}{1} =420[/tex]

=$420

Cost of putting a carpet on the floor

1ft²=$5

420ft²=?

[tex]=\frac{420*5}{1} =2100[/tex]

=$2100

Estimated cost

Total estimated cost =cost for putting tiles+cost for putting carpet

=$420+$2100=$2520

Answer:

(x,y)= (5,1)

Step-by-step explanation:

4x+2y=22

3x-2y=13

2y=22-4x

3x-2y=13

3x-(22-4x)=13

x=5

3·5-2y=13

y=1

(x,y)= (5,1)

Answer:

(5, 1); x = 5 and y = 1.

Step-by-step explanation:

Step 1: Add the system of equations

4x + 2y = 22

3x - 2y = 13

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

7x = 35

Step 2: Solve for x

x = 5

Step 3: Substitute the value of x in one of the original equations

4(5) + 2y = 22

Step 4: Solve for y

20 + 2y = 22

2y = 2

y = 1

Step 5: Write your answer as an ordered pair

(5, 1)

Answer:

$97.16 per day

Step-by-step explanation:

Total amount you have = $668.00

You have to spent $85.00  on the last day.

$668.00-85.00

=$583

It means you have $583 for the remaining 6 days in the week.

If you spend equal amount of money each day , you can calculate it by dividing remaining amount and number of days

=583/6

=$97.16

It means you can spend $97.16 per day....

Answer:

5m^6 + 2m^4 + 5m^3

hope this works!!!!

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², simplify each term by subtracting 2 from the exponents. The result is 5m⁶ + 2m⁴ + 5m³. The correct answer is D).

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², follow these steps

Write the given expression: (10m⁸ + 4m⁶ + 10m⁵) / 2m².

Divide each term in the numerator by 2m² separately:

(10m⁸ / 2m²) + (4m⁶ / 2m²) + (10m⁵ / 2m²).

Simplify each term:

5m⁶ + 2m⁴ + 5m³.

The final result is 5m⁶ + 2m⁴ + 5m³.

The correct option is D).

In this division, we use the rule of exponents: when dividing terms with the same base, subtract the exponents.

The division by 2m² reduces the power of 'm' in each term by 2. So, 10m⁸ becomes 10m⁶, 4m⁶ becomes 2m⁴, and 10m⁵ becomes 5m³. The constants 10 and 4 remain unchanged. The simplified expression is the final result.

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Answer:

-9-3/1-(-7)

Step-by-step explanation:

Answer:

The slope of given line = -3/2

Step-by-step explanation:

Points to remember

slope of the line with end points (x1, y1) and (x2, y2) is given by,

Slope = (y2 - y1)/(x2 - x1)

To find the slope of the line

Here (x1, y1) = (-7, 3) and (x2, y2) = (1, -9)

Slope = (y2 - y1)/(x2 - x1)

 = (-9 - 3)/(1 - -7)

 = (-12)/8

 = -3/2

Therefore the slope of given line = -3/2

Answer:

Step-by-step explanation:

The two represents 2000

The one represents 10

The fraction you want is 10/2000 = 1/200 or 0.005

The value represented by the digit 1 in the number 2010 is 1/200 of the value represented by the digit 2. This is determined by comparing their place values, with 1 in the tens place and 2 in the thousands place.

To determine the value represented by the digit 1 in the number 2010, we need to understand place value.

→ The digit 1 is in the tens place, so its value is 10 (1 × 10).

→ The digit 2 is in the thousands place, so its value is 2000 (2 × 1000).

The fraction of the value represented by the digit 1 to the value represented by the digit 2 is calculated as follows:

→ Fraction = Value of digit 1 / Value of digit 2

                = 10 / 2000

                = 1/200

Therefore, the value represented by the digit 1 is 1/200 of the value represented by the digit 2 in the number 2010.

Answer:

The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

Step-by-step explanation:

Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.

Monthly compound interest rate = P(1+r/n)^nxt

n=12 (number of months in a year)

t=1 (number of years)

Annually compound interest rate = P(1+r/n)^nxt

n=1 (because it is for 1 year only)

t=1 (number of years=1)

Step 2 : Lets assume that P is $100 in both banks and time is 1 year.

Step 3 : Lets substitute the values to find out which one is better.

Monthly compound interest rate = P(1+r/n)^nxt

Monthly compound interest rate = 100(1+0.14/12)^12x1

Monthly compound interest rate = 114.93

114.93 - 100 = $14.93 per month

14.93 x 12 = $179.16 for 12 months or 1 year

Annually compound interest rate = P(1+r/n)^nxt

Annually compound interest rate = 100(1+1.6/1)^1x1

Annually compound interest rate = 260

260-100 = $160 for 1 year

Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

!!

Answer:

The Unity Bank is offering a good plan.

Step-by-step explanation:

Unity Bank offers a monthly compounded interest rate of 0.14%

So, yearly rate will be = [tex]0.14\times12=1.68[/tex]% or 0.0168

Sunrise Banking offers 1.6% or 0.016 interest compounded annually.

Lets check an example with these two rates.

The compound interest formula is = [tex]A=P(1+r/n)^{nt}[/tex]

Lets take P = $1000 and t = 1 year

Case 1: when r = 1.68% and n = 12

Putting the values in formula we get

A = [tex]1000(1+0.0168/12)^{12}[/tex]

= [tex]1000(1.0014)^{12}[/tex]

A = $1016.92

Case 2: when r = 1.6% and n = 1

Putting the values in formula we get

A = [tex]1000(1+0.016/1)^{1}[/tex]

= [tex]1000(1.016)^{1}[/tex]

A = $1016.00

So, we can see that the first case gives more return than second one.

Therefore, the Unity Bank is offering a good plan.

Answer:

C. y = x2 + 8x + 12

Step-by-step explanation:

To find x intercept/zero, substitute y = 0

0 = x^2 + 8x + 12

x^2 += 8x + 12 = 0

x^2 + 8x + 12 = 0

Solve the quadratic equation

x = -8±[tex]\sqrt{8^2 -4(12)[/tex] / 2(1)

any expression multiplied by 1 remains the same

x= -8±[tex]\sqrt{8^2 - 4(12)[/tex] / 2(1)

Evaluate the power

8^2

write the exponentiation as a multiplication

8(8)

multiply the numbers

64

x = -8±[tex]\sqrt{64 - 4(12)[/tex] / 2(1)

multiply the numbers

x = -8±[tex]\sqrt{64 - 48[/tex] / 2(1)

any expression multiplied by q remains the same

x = -8±[tex]\sqrt{64-48[/tex] /2

subtract the numbers

x = -8±[tex]\sqrt{16[/tex] / 2

calculate the square root

x= -8± 4 / 2

x= -8 + 4 / 2

x= -8 - 4 / 2

simplify the expression

x = -2

x = -8 - 4 / 2

x = -2

x = -6

final solutions are

x1 = -6, x 2 = -2

Answer:

C

Step-by-step explanation:

In division when bases are same you do top exponent minus bottom exponent.

So here you do t^(12-6) which is t^6.

Hello There!

X = 6

First, we would add 5 to both sides so adding 5 to -5 is 0 and adding 5 to 7 is 12 so we would get the equation 2x = 12

Next, we would divide 2x by 2 and divide 12 by 2 and we would get a quotient of 6.

Our final answer is x = 6

Answer:

x=6

Step-by-step explanation:

2x - 5 = 7

Add 5 to each side

2x-5+5= 7+5

2x = 12

Divide by 2

2x/2 = 12/2

x = 6

Answer:

To make something as small as possible or easier for something in particular.

Hope I helped!

Answer:

(

x

+

4

)

(

x

+

9

)

=

0

Your answer would be x=-4 and x=-9.

Explanation::

(

x

+

4

)

(

x

+

9

)

x

times  

x

=

x

2

x

(

9

)

+

x

(

4

)

=

13

x

4

times  

9

=

36

=  

x

2

+

13

x

+

36

Answer:

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).

Step-by-step explanation:

To factore the given quadratic with leading coefficient one, you must find two numbers that add to be and multiply to be c.

a=1

b=-13

c=36

So we need two numbers that multiply to be 36 and add to be -13.

These numbers are -4 and -9 since

(-4)(-9)=36 and -4+-9=-13.

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).

[tex]\huge{\boxed{5.5x+10}}[/tex]

We multiply the class fee by the number of classes. [tex]\bf{5.5x}[/tex]

A registration is a one-time fee, so it is simply added. [tex]5.5x \bf{+10}[/tex]

Answer:

Step-by-step explanation:

Let the base of the board is x feet away from the wall .

And the hypotenuse, which is represented by the length of the board be 15 foot .

So here we have adjacent represented by the base and the hypotenuse .

And cosine function relates adjacent and hypotenuse , which is cos 60=15/x

And the value of cos 60 is half .

Performing cross multiplication

1/2=15/x

Dividing both sides by 2

x=7.5ft

Answer:

7.5 feet.

Step-by-step explanation:

The boardgame resting against the wall is creating a triangle rectangle and as it is forming a 60º angle with the ground that would be solve with the cosine of 60, which is the value of the division of the hypotenuse by the adjacent side, which would be the distance from the base of the board game to the wall:

Cos60= .5

cos60=adjacent side/hypotenuse

.5= adjacent side/15

adjacent side= 15x.5

Adjacent side=7.5 feet

Answer:

Part 1) [tex]c=21.9\ units[/tex]

Part 2) [tex]B=61.1\°[/tex]

Part 3) [tex]A=28.9\°[/tex]

Part 4) [tex]C=90\°[/tex]

Step-by-step explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

substitute the given values

[tex]c^{2}=10.6^{2}+19.2^{2}[/tex]

[tex]c^{2}=481[/tex]

[tex]c=21.9\ units[/tex]

step 2

Fin the measure of angle B

we know that

In the right triangle

[tex]tan(B)=b/a[/tex]

substitute the given values

[tex]tan(B)=19.2/10.6[/tex]

[tex]B=arctan(19.2/10.6)=61.1\°[/tex]

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

[tex]B=61.1\°[/tex]

[tex]C=90\°[/tex]

substitute

[tex]A+61.1\°+90\°=180\°[/tex]

[tex]A=28.9\°[/tex]

Answer:

A = 28.9 degrees, B = 61.1 degrees, c = 21.9

Step-by-step explanation:

I got it correct on founders edtell

Answer:

ab( b+c)

Step-by-step explanation:

abb +abc

There is an a and  b in each term

What remains goes inside the parentheses

ab( b+c)

Answer:

ab(b+c)

Step-by-step explanation:

Take out each variable like you would any other number

abb+abc

ab(b+c), This is the answer, with the distributive property, you can convert it back to its original form.

ab*b+ab*c=ab^2+abc

Answer:

16 packs

Step-by-step explanation:

u just have to divide 224 by 14 to get 16

the school wants to get 224 clocks, they clocks come in packs of 14, so each pack has 14 clocks, how many packs are needed?

well, how many times does 14 go into 224? 224 ÷ 14, and you know what that is.

Answer:

[tex]\large\boxed{A.\ y\leq-2x+3,\ y\leq x+3}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

=============================================

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points:

(0, 3) - y-intercept → b = 3 (for both lines)

f(x)

(0, 3), (1, 1)

[tex]m=\dfrac{1-3}{1-0}=\dfrac{-2}{1}=-2[/tex]

Substitute:

[tex]f(x):\ y=-2x+3[/tex]

The shaded region is below the solid line. Therefore: [tex]y\leq-2x+3[/tex]

g(x):

(0, 3), (2, 5)

[tex]m=\dfrac{5-3}{2-0}=\dfrac{2}{2}=1[/tex]

Substitute:

[tex]g(x):\ y=1x+3=x+3[/tex]

The shaded region is below the solid line. Therefore: [tex]y\leq x+3[/tex]

Answer:

b

Step-by-step explanation:

Answer:

V =91.845 ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is the radius and h is the height

V = pi (1.5)^2 *13

Letting pi = 3.14

V = 3.14 (1.5)^2 * 13

V =91.845 ft^3

Answer:

V=91.89

Step-by-step explanation:

Given:

radius, r= 1.5 ft

height, h=13 ft

volume of cylinder= pi *r^2 *h

V=3.14 *(1.5)^2 *13

V=91.89 ft^3 !

Answer:

The length of the floor is [tex](15x^{2}+4x)\ ft[/tex]

Step-by-step explanation:

we know that

The area of a rectangle ( classroom floor) is equal to

[tex]A=LW[/tex]

in this problem we have

[tex]A=(30x^{3}+8x^{2})\ ft^{2}[/tex]

[tex]W=2x\ ft[/tex]

substitute in the formula and solve for L

[tex](30x^{3}+8x^{2})=2x(L)[/tex]

Divide by 2x both sides

[tex]L=(15x^{2}+4x)\ ft[/tex]