Select the equivalent expression.

(a^5 * 2^3)^3 = ?


1. a^8*2^9

2. a^15*2^6

3. a^8*2^6

3. a^15*2^9

Answer:

The shortest distance from A to C is [tex]AC=5\sqrt{13}\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shortest distance from A to C is the hypotenuse of the right triangle AYC

Applying the Pythagoras Theorem

[tex]AC^{2}=AY^{2} +YC^{2}[/tex]

step 1

Find the length YC (hypotenuse of the right triangle YBC)

Applying the Pythagoras Theorem

[tex]YC^{2}=YB^{2} +BC^{2}[/tex]

substitute the given values

[tex]YC^{2}=6^{2} +15^{2}[/tex]

[tex]YC^{2}=261[/tex]

[tex]YC=\sqrt{261}\ units[/tex]

step 2

Find the shortest distance from A to C

[tex]AC^{2}=AY^{2} +YC^{2}[/tex]

substitute the given values

[tex]AC^{2}=8^{2} +\sqrt{261}^{2}[/tex]

[tex]AC^{2}=325[/tex]

[tex]AC=\sqrt{325}\ units[/tex]

[tex]AC=5\sqrt{13}\ units[/tex]

Answer:

x = -16

Step-by-step explanation:

  3          

 (— • x) -  -24  = 0  

  2        

       -24     -24 • 2

   -24 =  ———  =  ———————

           1         2  

For this case we must solve the following equation:

[tex]\frac {3} {- 2x} = 24[/tex]

Multiplying by 2x on both sides of the equation:

[tex]-3 = 24 * 2x\\-3 = 48x[/tex]

Dividing between 48 on both sides of the equation:

[tex]x = - \frac {3} {48}[/tex]

We simplify:

[tex]x = - \frac {1} {16}[/tex]

Answer:[tex]x = - \frac {1} {16}[/tex]

Answer:

Step-by-step explanation:

A will.

Suppose the object is placed on (5,4)

If you rotate it 180o counterclockwise, the point will become (-5,-4) (both x and y will change signs.)

Moving one unit down will still leave you in quadrant III.

If you start in another quadrant, this answer will not be correct. If the point started out in quadrant 2, rotating it 180o counterclockwise will put you in quad 4. For example

Object Start: (-2,3)    Starts in quad 2

Image found: (- -2, - 3) = (2, - 3) which is in quad 4.

Answer:

The correct answer is option D. (3h + 7)(h – 6)

Step-by-step explanation:

It is given a quadratic function ,

3h² - 11h - 42

To find the factors of given function

3h² - 11h - 42  = 3h² - 18h  + 7h - 42

 = 3h(h -6) + 7(h - 6)

 =(h - 6)(3h + 7)

 = (3h + 7)(h – 6)

The correct answer is option D. (3h + 7)(h – 6)

Answer:

x < 3/2.

Step-by-step explanation:

1/3( 5x + 3) < 1/4(6x + 5)

5/3 x + 1 < 3/2x + 5/4

5/3 x - 3/2 x < 5/4 - 1

1/6 x < 1/4

x < 6/4

x < 3/2.

The value of the variable x is less than 3/2.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let x be the number.

One-third of the sum of 5 times a number and 3 is less than one-fourth the sum of six times that number and 5. Then the equation will be

(1/3)(5x + 3) < (1/4)(6x + 5)

Simplify the inequality, then the value of x will be

20x + 12 < 18x + 15

2x < 3

x < 3/2

The value of the variable x is less than 3/2.

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Answer:

[tex]\log_{144}(12)=\frac{1}{2}[/tex]

Step-by-step explanation:

First step identify the base.  The base is 144.

The exponent is the logarithm.

The number not mentioned is the one that goes inside.

In other words [tex]a^x=b[/tex] is equivalent to [tex]log_a(b)=x[/tex]

There are some restrictions on what a and b can be.

You read  [tex]log_a(b)=x[/tex] as log base a of b equals x

x is the exponent

a is the base

So we have log base 144 of 12 equals 1/2

[tex]\log_{144}(12)=\frac{1}{2}[/tex]

Answer:

The farmers will have the same amount of feed (300 lbs) in 3 days

Step-by-step explanation:

After dividing the total amounts of feed by the daily feed amounts, it’s found that the two farmers will have the same amount of feed left after approximately 3.5 days.

To solve this problem, you need to find out how many days it takes for both farmers to run out of feed. For the first farmer, divide the total amount of feed (700 pounds) by the amount he uses each day (200 pounds). This comes to 3.5 days. For the second farmer, divide his total feed (1000 pounds) by the amount he uses each day (350 pounds), which comes to approximately 2.857 days.

Since we want to know when they will have the same amount of feed left, we look for the higher number, because the first farmer will still have feed left when the second farmer runs out. Therefore, the two farmers will have the same amount of feed left after around 3.5 days.

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Answer:

Part 1) The length of the diagonal of the outside square is 9.9 units

Part 2) The length of the diagonal of the inside square is 7.1 units

Step-by-step explanation:

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

[tex]x=a+b=4+3=7\ units[/tex]

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

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

substitute

[tex]c^{2}= 4^{2}+3^{2}[/tex]

[tex]c^{2}=25[/tex]

[tex]c=5\ units[/tex]

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

[tex]D^{2}= x^{2}+x^{2}[/tex]

[tex]D^{2}= 7^{2}+7^{2}[/tex]

[tex]D^{2}=98[/tex]

[tex]D=9.9\ units[/tex]

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

[tex]d^{2}= c^{2}+c^{2}[/tex]

[tex]d^{2}= 5^{2}+5^{2}[/tex]

[tex]d^{2}=50[/tex]

[tex]d=7.1\ units[/tex]

If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is  9.9 units

units and the length of the diagonal of the inside square rounded to the nearest tenth is 7.1 units

Let's solve its step by step

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

x=a+b=4+3=7 units

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

[tex]c^(2)= a^(2)+b^(2)[/tex]

substitute

[tex]c^(2)= 4^(2)+3^(2)[/tex]

[tex]c^(2)=25[/tex]

c=5 units

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

[tex]D^(2)= x^(2)+x^(2)[/tex]

[tex]D^(2)= 7^(2)+7^(2)[/tex]

[tex]D^(2)=98[/tex]

D=9.9 units

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

[tex]d^(2)= c^(2)+c^(2)[/tex]

[tex]d^(2)= 5^(2)+5^(2)[/tex]

[tex]d^(2)=50[/tex]

d=7.1 units

Answer:

3

Step-by-step explanation:

g(-1) means what is g(x) when x=-1.

So find -1 under the column labeled x and then scroll directly to the right of that and you should see what g(-1).  It is 3

Here are my examples:

g(-8)=6

g(-5)=-2

g(-1)=3

g(0)=-5

Final answer:

The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula x = -b/(2a). The vertex represents the highest or lowest point on the graph depending on whether a is positive or negative.

Explanation:

The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula. The vertex formula is x = -b/(2a), which gives the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute the x-coordinate into the equation y = ax + bx². The vertex of the parabola represents the highest or lowest point on the graph, depending on whether the coefficient a is positive or negative.

Answer:

(f+g)(1)

equals

3

Step-by-step explanation:

(f+g)(1) is f(1)+g(1).

f(1) means what y corresponds to x=1 so f(1)=-1.

g(1) means what y corresponds to x=1 so g(1)=4.

So (f+g)(1)=f(1)+g(1)=-1+4=3.

Answer: C. 96%  --------  APEX :D

The situation "The time it takes to read a book depends on the number of pages in the book" in function notation is: A. Time(pages).

In Mathematics, a function is typically used in mathematics for uniquely mapping an input variable (domain or independent value) to an output variable (range or dependent value).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

In this context, we can logically deduce that time is a function of the number of pages, so it should be written in function notation as follows:

Time(pages).

Complete Question:

Which of the following shows the situation below in function notation?

The time it takes to read a book depends on the number of

pages in the book.

A. Time(pages)

B. Book(pages)

C.Pages(time)

D. Book(time)

Answer:

See attachment

The relation is not a function.

The domain is [-4.1,3.9]

The range is [-2.1,5.9]

Step-by-step explanation:

The given relation has ordered pairs (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)

It is implied in the ordered pairs that the relation is a continuous function.

We plot the points and connect them with straight lines as shown in the attachment.

The relation is not a function because its graph fails the vertical line test.

In other words, we have an x-coordinate that corresponds to more than one y-coordinate.

-4.1 corresponding to 3.9 and -2.1 at the same time.

The domain is the set of values for which the function is defined.

The domain is [-4.1,3.9]

The range refers to the corresponding y-values for which the function exists.

The range is [-2.1,5.9]

Answer:

A, B, E, F

Step-by-step explanation:

In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg.

That makes choice E possible.

In a 30-60-90 triangle, the long leg is sqrt(3) times the length of the short leg.

That makes choices A, B, and F possible.

Answer:

First option.

Option 5.

Option 6.

Step-by-step explanation:

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value [tex]a[/tex].

2) Side opposite to 60 will be value [tex]a\sqrt{3}[/tex].

3) Hypotenuse will be [tex]2a[/tex].

So let's look and see:

First option: [tex]AB=4[/tex] and [tex]BC=4\sqrt{3}[/tex]

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

So [tex]a=4[/tex] here.

So the side opposite of 60 using the formula should be [tex]4 \sqrt{3}[/tex] which it is here.

So first option looks good.

Second option: [tex]BC=2\sqrt{3}[/tex] and [tex]AC=2[/tex].

We aren't given the side opposite to 30.

AC is the hypotenuse so 2a=2 which means the side opposite to 30 is a=2/2=1.

This means using the formula that the side opposite to 60 will be [tex]1\sqrt{3}=\sqrt{3}[/tex] but we don't have that.

So not option 2.

Third option: [tex]AB=3[/tex] and [tex]AC=3\sqrt{3}[/tex]

AB is the side opposite of 30, so we have [tex]a=3[/tex]

AC is the hypotenuse so that side should be [tex]2a=6[/tex] and it isn't.

Option 3 is not working.

Fourth option: [tex]BC=10[/tex] and [tex]AC=4\sqrt{3}[/tex]

So we have that [tex]2a=4\sqrt{3}[/tex] which means [tex]a=2\sqrt{3}[/tex] and so [tex]a\sqrt{3}=2\sqrt{3}\sqrt{3}=2(3)=6[/tex] but that is a contradiction because we have this value should be 10.

Not option 4.

Option 5: [tex]AB=7[/tex] and [tex]AC=14[/tex]

So we have [tex]a=7[/tex] and [tex]2a=14[/tex] so this looks good.

Option 6: [tex]AB=11[/tex] and [tex]BC=11\sqrt{3}[/tex]

[tex]a=11[/tex] so [tex]a\sqrt{3}=11\sqrt{3}[/tex] which is what we have.

Option 6 works.

Answer:

1/2 • 1 = 1/2

Step-by-step explanation:

It shows that anything multiplied by 1 is itself.

Answer:

1/2· 1= 1/2

Step-by-step explanation:

When multiplying by 1, you will get the same number.

Answer:

[tex]\large\boxed{y-4=\dfrac{1}{2}(x+2)\text{- point-slope form}}\\\boxed{y=\dfrac{1}{2}x+5\text{- slope-intercept form}}[/tex]

Step-by-step explanation:

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

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope [tex]m=\dfrac{1}{2}[/tex] and the point [tex](-2, 4)[/tex].

Substitute:

[tex]y-4=\dfrac{1}{2}(x-(-2))[/tex]

[tex]y-4=\dfrac{1}{2}(x+2)[/tex] - point-slope form

Convert to the slope-intercept form (y = mx + b):

[tex]y-4=\dfrac{1}{2}(x+2)[/tex]         use the distributive property

[tex]y-4=\dfrac{1}{2}x+1[/tex]         add 4 to both sides

[tex]y=\dfrac{1}{2}x+5[/tex] - slope-intercept form

Answer:

The domain is {1,2,3,4,5}

The range is {150,135,120,105,90}

Step-by-step explanation:

Domain is the set of x-values (x axis) and Range is the set of y-values (y axis).

Now if you look at the relation (points given), you can see the 5 points corresponds to 1,2,3,4, adn 5 in the x axis (minutes). So this is the domain - 1,2,3,4,5.

If we look at the y-axis (Heart Rate) , the values corresponding to 1,2,3,4,and 5 are 150, 135, 120, 105, and 90. These are the range.

Hence the last choice is the correct answer.

Answer: Domain = {1,2,3,4,5}

Range = {150,135, 120,105, 90}

Step-by-step explanation:

We know that,

Domain : Set of all input values .

Range : Set of output values.

In a graph, x values are the input values and y values are output values.

Given : The graph shows Melissa's heart rate in beats per minute be) during the first few minutes other cool down after  jogging .

In the graph, number of minutes are shown by x-values and heart rate are shown by y-values.

Thus from graph, Domain = {1,2,3,4,5}

Range = {150,135, 120,105, 90}

Answer:

1380 meters

Step-by-step explanation:

perimeter of a rectangle :2(l+b)

2(150 +80)

2(230)

460 meters of wire for one round

for three rounds :3×460=

1380 meters

Answer:

x = 1.47  or x = -7.47

Step-by-step explanation:

x²+6x+9=20

This is a quadratic equation

x²+6x+9-20=0

x²+6x-11=0

Step 1 : Write the quadratic formula

x = -b±√b²-4(a)(c)

              2a

Step 2 : Substitute values in the formula

a = 1

b = 6

c = -11

x = -6±√6²-4(1)(-11)

              2(1)

x = -6±√80

          2

x = -3 + 2√5 or x = -3 - 2√5

x = 1.47         or x = -7.47

!!

Answer:

x=1.472 or x=-7.472

Step-by-step explanation:

Lets begin by rearranging the equation into the format ax²+bx+c=0

The equation will be:

x²+6x+9-20=0

x²+6x-11=0

We shall use the quadratic formula to solve the equation.

x=[-b±√(b²-4ac)]/2a

=[-6±√(6²-4×1×-11)]/2

=[-6±√80]/2

=[-6±8.944]2

x= Either (-6+8.944)/2 or x= (-6-8.944)/2

Solving for x in each case gives:

x=1.472 or x=-7.472

Answer: H. 35 games

Step-by-step explanation: Set up a proportion.

5/8 = X/56

Cross multiply.

5 x 56 = 280

8 x X = 8x

The cross multiplied equation will be 280=8x.

Divide by 8 in order to isolate x.

x=35

They will win 35 games.

Answer:

The answer is H. 35 games

Answer:

[tex]96x^4y+104x^2y^2[/tex]

is the simplified form of

your given problem:

[tex](12x^2+13y)(4x \times 2xy)[/tex].

Step-by-step explanation:

So the given problem is this:

[tex](12x^2+13y)(4x \times 2xy)[/tex]

I'm going to do the multiplication in the second ( ).

Nothing can be done in the first ( ) because the operation is addition and those two terms aren't like terms.

[tex](12x^2+13y)(8x^2y)[/tex]

I got x^2 because of x(x) part.

Now we get to distribute 8x^2y to both terms in the ( ).

[tex]12x^2 \cdot 8x^2y+13y \cdot 8x^2y[/tex]

Adding exponents on bases that have the same variable:

[tex]96x^4y+104x^2y^2[/tex]

Answer:

y-4 =-1(x+1)  point slope form

y-2 = -1(x-1)

y = -x +3  slope intercept form

Step-by-step explanation:

We have 2 points, we can find the slope

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

   = (2-4)/(1--1)

   (2-4)/(1+1)

     -2/2

   =-1

The slope is -1

Then we can use point slope form to find an equation

y-y1 =m(x-x1)

y-4 = -1(x--1)

y-4 =-1(x+1)  point slope form

Using the other point

y-2 = -1(x-1)

Distribute the -1

y-2 = -1x +1

Add 2 to each side

y-2+2 = -x+1+2

y = -x +3  slope intercept form

Answer:

(5, 9)

Step-by-step explanation:

Given the 2 equations

x = 5 → (1)

y = 2x - 1 → (2)

x = 5 is the value of the x- coordinate.

Substitute x = 5 into (2) for the corresponding value of y

y = (2 × 5) - 1 = 10 - 1 = 9

Solution is (5, 9 )

Answer: The expression (equation/formula) for the volume of a:  

     " right rectangular prism " ;   is represented by:

____________________________________________________

                    →   " V  =  L * w * h  "   ;

____________________________________________________

in which:   all the dimensions are in the same "units of measurement" (or converted to the same "units of measurement" ;  

and in which:

      " V " is the "volume" of the right rectangular prism; in the "cubic units" ; or written as:  "units³ "  ;  or, [insert the particular units used}^ ³  "   ;

  →  that is, [units] raised to the "3rd [third] power" ; assuming these units are the same  same "fundamental units of measurement"  as the "other 2 (two) values in the expression".  

    If we are given no specific units of measurement whatsoever, then we use the generic term, "units" as the "units of measurement" ; and we express the "volume; "V" ;  of a "right rectangular prism" as:  " units ³ " ; or "cubic units" ;

        in our answer— if we are asked to solve for the:

                     "volume; "V";  of a "right rectangular prism" ;

_________________________________________________

and in which:  

            "L" represents the "length" of a "right rectangular prism" ;

            "w" represents the "width" of a "right rectangular prism" ;

            "h" represents the "height" of a "right rectangular prism" .

_________________________________________________

To given an example:

  Say we have a "right rectangular prism" ; with the given measurements:

    width , "w" :   w = 2 units;  

    length, "L"  :    L  = 3 units ;

    height, "h" :    h =  8 units.

_________________________________________________

We are asked to "find the volume " ;  of this "right recentangular prism" .

The formula for the volume;  "V" ;  of this "right rectangular prism" ;

is:

_________________________________________________

          →    Volume  =  Length * width * height ;

that is:

          →    V =  L  * w * h  ;  

Solve for the volume;  "V" .

_________________________________________________

          →   V  =  L  * w * h   ;    Now plug in the values given:

          →   V =  (3 units)  * (2 units)  * (8 units) ;

                    =  3 * 2 * 8 * (units) * (units) * (units) ;

                    =  3 * 2 * 8 * units ³  ;

                    =  48 units ³ .    

_________________________________________________                    

Hope this answer— and explanation—is helpful to you!

     Wishing you the best in your academic pursuits

               — and within the "Brainly" community!

_________________________________________________

Answer: A

Step-by-step explanation:

Answer:

it would be the 4th option

Step-by-step explanation:

all the above are wrong except the fourth option because a 3-D square or cube is made up of 6 equal squares. I hope this helps a-lot. : )

The 3-D figure Scarlett can make and the combinations of shapes she can use is a square prism with six squares.

A square prism is a three-dimensional object that is made up of six squares.

The volume of a square prism = length x width x height.

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Answer:

D. 3

Step-by-step explanation:

In the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], which in this case is 3.

I am joyous to assist you anytime.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The slope of the line y + 1 = 3 (x - 4) is 3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y + 1 = 3 (x - 4)

y + 1 = 3 (x - 4)

Subtract 1 on both sides.

y = 3(x - 4) - 1

y = 3x - 12 -1

y = 3x - 13

This is in the form of y = mx + c

Now,

Slope = m

m = 3

Thus,

The slope of the line y + 1 = 3 (x - 4) is 3.

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Answer:

B. 40

Step-by-step explanation:

All triangle angles equal 180

100+40=140

180-140=40

B. 40 is the answer.

[tex]\left(1-\dfrac{2}{3}\right)\cdot\dfrac{6}{9}=\dfrac{1}{3}\cdot \dfrac{2}{3}=\dfrac{2}{9}[/tex]

The pharmacist has 2 more prescriptions left to review that you filled.

To find out how many prescriptions the pharmacist has left to review, we can follow these steps:

1. Calculate the total number of prescriptions filled by you:

[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times \text{Total prescriptions} \][/tex]

2. Calculate the number of prescriptions reviewed by the pharmacist:

[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times \text{Total filled prescriptions} \][/tex]

3. Calculate the number of prescriptions left for the pharmacist to review:

[tex]\[ \text{Prescriptions left to review} = \text{Total filled prescriptions} - \text{Prescriptions reviewed by pharmacist} \][/tex]

Let's put the numbers into these equations. Assuming there were initially 9 prescriptions:

1. Total filled prescriptions:

[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times 9 = 6 \][/tex]

2. Prescriptions reviewed by pharmacist:

[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times 6 = 4 \][/tex]

3. Prescriptions left to review:

[tex]\[ \text{Prescriptions left to review} = 6 - 4 = 2 \][/tex]