Simplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)

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:

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:

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: C. 96%  --------  APEX :D

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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The mean of a dataset if given by the sum of the elements divided by the number of elements:

[tex]M = \dfrac{2+6+7+9+9+9}{6} = \dfrac{42}{6}=7[/tex]

B. 7

The mean (also known as the average) is found by adding all of the numbers in the set together, then dividing the result by how many numbers are in the set.

First, add the numbers together.  [tex]2+6+7+9+9+9=42[/tex]

Finally, divide that by the amount of numbers in the set.  [tex]\frac{42}{6}=7[/tex]

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:

I think the answer is (c)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The only one that doesn't require the initial part, since the initial part should be 0, in order, for a relationship to be proportional is answer C.

A) Initial fee of $3  (we need the initial to be 0).

B) Initial height of 4 ft (we need the initial to be 0).

C) I see nothing about a starting or initial so far this is it!

D) Initial fee is 50 dollars (we need the initial to be 0).

Answer:

360 miles

Step-by-step explanation:

If you travel 90 miles in 1 ½ hours, it will take 360 miles if you drove 6 hours.

All you have to do is, multiply 1 ½  until you get to 6.

The easiest way is:

1 ½ = 90 miles

1 ½ (90 miles) x 2 = 3 or 180 miles

3 (180 miles) x 2 = 6 or 360

Therefore, 6 hours = 360 miles.

Final answer:

This detailed answer explains how to calculate distances based on speed and time using a specific formula.

Explanation:

The question is about calculating distances traveled based on time and speed.

To find the distance, use the formula: distance = speed × time.

Given 90 miles in 1 ½ hours, first find the speed: 90 miles ÷ 1.5 hours = 60 miles/hour.

Then for 6 hours of travel: distance = 60 miles/hour × 6 hours = 360 miles.

Answer:

[tex]y=-\frac{3}{2}x - 9/2[/tex]

Step-by-step explanation:

The slope - intercept equation is

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

where m = slope

and b = intercept

The line intercepts the y axis in -9/2, so b = -9/2

To calculate the slope we can take two points where the line passes:

p1= (-3, 0)

p2=(-1, -3)

the slope will be a fraction with the numerator being the difference in the y coordinates and the denominator the difference in the x coordinates

[tex]m=\frac{-3-0}{-1-(-3)}=\frac{-3}{2}[/tex]

replacing the values for m and b in the slope - intercept equation:

[tex]y=-\frac{3}{2}x - 9/2[/tex]

Answer:

Step-by-step explanation:

100 cm = 1 meter

200 cm = 2 meters

100 cm = 1 meter

150 cm = 150 / 100 = 1.5 meters.

1 meter = 100 cm

6.5 meters = 6.5 * 100 = 6500 cm

1 km = 1000 meters.

5 km = 5 * 1000 meters = 5000 meters.

1 meter = 100 cm

1.68 m = 100 * 1.68  

1.68 m = 168 cm

1 km = 1000 meters.

8.25 km = 8.25 * 1000 m = 8250 meters.

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:

5'4"

Step-by-step explanation:

In terms of height, the apostrophe ( ' ) stands for feet and the quotation mark ( " ) stands for inches.

Your first term includes 4 feet and 9 inches. There are 12 inches in a foot, so we can simplify this as being 57 (48+9) inches.

Your second term includes 7 inches.

Add your two terms (57 and 7) together, and you have 64 inches.

Again, there are 12 inches in a foot, so to convert 64 inches to feet, count how many times you can put 12 into 64 without surpassing 64.

12 / 24 / 36 / 48 / 60

This will result in 5 times, so you have 5 feet and 4 inches left over.

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]

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: 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

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: 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:

(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:

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:

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:

[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:

5(5 + 2).

Step-by-step explanation:

5 is a factor of 25 and 10 so :

15 + 10 = 5(5 + 2).

For this case we have that by definition, the distributive property establishes:

[tex]a (b + c) = ab + ac[/tex]

Then, using the above definition, we must write an expression equivalent to:

[tex]25 + 10[/tex]:

The largest integer that divides both numbers without leaving residue is 5, then:

[tex]5 (5 + 2) = 5 * 5 + 5 * 2 = 25 + 10[/tex]

Answer:

[tex]5 (5 + 2)[/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:

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:

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:

B. 40

Step-by-step explanation:

All triangle angles equal 180

100+40=140

180-140=40

B. 40 is the answer.

Answer:

64 : 27

Step-by-step explanation:

Given 2 similar figures with

ratio of lengths = a : b, then

ratio of volumes = a³ : b³

For 2 cylinders with ratio of lengths = 4 : 3, then

ratio of volumes = 4³ : 3³ = 64 : 27

Answer:

Its 64:27

Step-by-step explanation:

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}