Solve the equation using the multiplication property of equality and the reciprocal of 1 4 . 1 4 ( r − 5 2 ) = 1 8

Answer:

1. b.  2. a.  3. a.

Step-by-step explanation:

1. (f + g)x = f(x) + g(x)

= x^2 + 2x + 4

(f + g)(-1) =  (f + g)(x)  where x = 1 so it is

(-1)^2 + 2(-1) + 4

=  1 - 2 + 4

= 3.

2.  We find (f o g)(x) by replacing the x in f(x) by g(x):

= √(x + 1) and

(f o g)(3) =  √(3 + 1)

= √4

= 2.

3. (f/g) c  = f(x) / g(x)

= (x - 3)/(x + 1)

The domain is the values of x which give real values of (f/g).

x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.

The domain is (-∞, -1) U (-1, ∞)

Step-by-step explanation:

half life time-50%-8.4hr

so for 10%- 8.4/5=1.68 hr

now for 70%

1.68 × 7 = 11.76 hrs

to one decimal place - 11.8hrs

11.8 hours ago, there were 70% more of the substance if an isotope of lead has a half-life of 8.4 hours.

Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay.

Half-life period - 50% -8.4hours

so for 10%- 8.4/5 = 1.68 hour

now for 70%

1.68 × 7 = 11.76 hours

To one decimal place - 11.8hours

Hence, 11.8hours is the answer.

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Answer:

x=127°

Step-by-step explanation:First you have to solve for n and to do so you have to add the interior angles together and equal them to the remote exterior angle.

n+7+6n+22=197-5n

12n+29=197

12n=168

n-14

once you get n you have to plug it into 197-5n

197-5(14)

197-70

127

The required value of exterior angle  m∠x is 127.

From figure x is remote exterior angle m∠x=(197−5n)°. and y and z are interior angles m∠y=(6n+22)° and m∠z=(n+7)° respectively. value of x to be determine.

Angle made at outer side of the corner is called exterior angles.

Here, by properties,  sum of the interior angle = remoter exterior angle
So,
m∠x = m∠y + m∠z
197−5n = 6n+22+n+7
168 = 12n
n = 14
put n in m∠x
m∠x=(197−5n)°
m∠x=(197−5*14)°
m∠x=(197−70)°
m∠x=127°

Thus, the required value of exterior angle  m∠x is 127.  

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Answer:

❁ 25% ❁

Explanation:

❁ The answer would be 25% ❁

Answer:

just did this on a test and it was

The exponent 3 is an odd number.

Step-by-step explanation:

Hince the statements which justify it:

The base -2 is a negative number.

The exponent 3 is an odd number.

Julie gets a negative number for her final answer when solving the expression (-2)³ = -2 x -2 x -2

Because the base, -2, is a negative number.

When an odd number of negative numbers are multiplied together, the result is always negative.

In this case, there are three negative numbers (-2 x -2 x -2),

Which is an odd number, resulting in a negative answer.

However, since the base is negative, the result will always be negative for any odd exponent.

Therefore, the negativity of the base and the odd value of the exponent together lead to a negative final answer.

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Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.

(angle BAC) = (angle ACD)

3x+4 = x+28

3x-x = 28-4

2x = 24

x = 24/2

x = 12

So,

angle BAC = 3x+4 = 3*12+4 = 40 degrees

and

angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees

With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.

Answer:

v is 9

Step-by-step explanation:

it is 9 because if you simplify it is 8v=72 or 9

Answer:

v = 9

Step-by-step explanation:

3v + 5v = 72

combine like terms

8v = 72

Divide by 8

8v/8 = 72/8

v =9

Answer:

there's two

Step-by-step explanation:

q=(4-√24)/2=2-√6=-0.449

and

q=(4+√24)/2=2+√6=4.449

Answer:

x = 16

Step-by-step explanation:

3x - 10 = 2(x+3)

First step is solve this:

2(x+3) = 2*x + 2*3 = 2x + 6

then:

3x - 10 = 2x + 6

3x - 2x = 6 + 10

x = 16

Check:

3*16 - 10 = 2(16+3)

48 - 10 = 2*19 = 38

Answer:

x = 16

Step-by-step explanation:

you start off by isolating the variable

Answer:

25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Answer:

x = 0, x = 4

Step-by-step explanation:

12x - 21 = 5x + 7(x - 3)

First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.

Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.

Factor out a 5x --> 0 = 5x(x - 4)

If you want to solve for x, set 5x = 0 and x - 4 = 0.

For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.

For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.

Plug the values back into the original equation to check if it works

12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21

12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27

Hope this helps!

Answer:

infinite solutions

Step-by-step explanation:

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

Simplify

4x = 2x + 2x + 5*0

4x = 2x + 2x

4x = 4x

Divide by x

4 =4

This is always true so this has infinite solutions

Answer:

4) 3(x+2)

5) Cannot be factored

6)3(4x+10y)

Step-by-step explanation:

4)3x+6

3(x+2)

Proof:

3(x+2)

3x+6

5)2x-15

Cannot be factored.

6)12x+30y

3(4x+10y)

Proof:

3(4x+10y)

12x+30y

Hope this helps ;) ❤❤❤

Answer:

A. 30 degrees

Step-by-step explanation:

Set the two angles equal to each other:

3x-15 = 45-x

Solve for x:

4x -15 = 45

4x = 60

x = 15

Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.

45 - 15 = 30

Answer:

A 30 degrees

Step-by-step explanation:

Answer:

8!

Step-by-step explanation:

SIMPLIFY

6X-12=4X+4

PUT LIKE TERMS TOGETHER

6X-4X=4+12

SIMPLIFY

2X=16

X=16/2

X=8

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

        ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                       PEACE!

Hey there! I'm happy to help!

First, let's use the distributive property to remove the parentheses. We multiply the number on the outside by each number on the inside.

3(2x-4)

We multiply the 3 by the 2x, giving us 6x, and we multiply the 3 by the -4, giving is -12.

4(x+1)

We do 4 times x which is 4x, and 4 by 1, which is 4.

This gives us this equation.

6x-12=4x+4

Now, we want to solve for x. We want to move all the numbers to the right side and all the x's to the left side so we can figure out what x is equal to.

6x-12=4x+4

We add 12 to both sides, canceling it out on one side and adds it to the other to keep the equation at the same value.

6x=4x+16

We subtract 4x from both sides.

2x=16

We divide both sides by 2.

x=8

Have a wonderful day! :D

Answer:

Slope: [tex]\frac{5}{3}[/tex]

Y-intercept: -2

Step-by-step explanation:

Conveniently, this equation is already in slope-intercept form.

The slope is always the constant of proportionality, which we multiply x by.

Therefore the slope is  [tex]\frac{5}{3}[/tex].

The y-intercept is always the constant that comes after the x term, which is -2.

So the y-intercept is -2.

Hope this helped!

Answer:

Slope: 5/3

Y-intercept: -2

Step-by-step explanation:

Since your equation is already in slope intercept form, it makes it easier for you to identify the slope and y-intercept.

In your equation ([tex]y = \frac{5}{3} x -2[/tex]) the coefficient of 5/3 is your slope and your constant of -2 is your y-intercept.

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer: please find the answer in the explanation.

Step-by-step explanation:

1.) The distance is not proportional to time. Because the distance was constant from time = 3 seconds to 10 seconds.

2.) A person running down a field to score a touchdown. Not enough information.

3. A dog jogging at a constant speed for 20 minute. The distance is proportional to time because of the constant speed.

4.) The distance is proportional to time because their is increase in distance covered and increase in time taken.

5.) A truck passing through the 4 cities at a constant speed. The distance is proportional to time because the speed is constant.

6.) A horse running around a race track. Distance is not proportional to time because this is not a linear motion.

Answer:

[tex]\boxed{y = -2}[/tex]

Step-by-step explanation:

Hey there!

To find y when x is -5 we go to -5 on the x-axis.

When at -5 find where the blue line is vertical to -5,

which is -2.

Hope this helps :)

Answer:The minimum of function A occurs 1 unit higher than the minimum of function B.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Trust

Answer:

2

Step-by-step explanation:

The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The expression is given below.

⇒ |5x + 1 / 2y²|

The value of the expression at x = 3 and y = 2, then we have

⇒ |5(3) + 1 / 2(2)²|

⇒ |15 + 1 / 2(4)|

⇒ |16 / 8|

⇒ 2

The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.

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Answer:

Each column will be the same height.

Step-by-step explanation:

Mode refers to the most occurring number, and there are five within a data set that is 4 wide, so there will be 5 columns of equal length.

Answer:

7 units

Step-by-step explanation:

(number line:)

<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->

         there are 7 units from 1 to -6 (you don't count the 0)

(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)

Answer:

[tex]\huge\boxed{\sf 7\ units}[/tex]

Step-by-step explanation:

To find that how much far they are from each other, we can subtract both of them.

=> 1 - (-6)

=> 1 + 6

=> 7 units

So, they are 7 units apart from each other.

Answer:

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Step-by-step explanation:

Given that:

y = 6x - x² , y = 8  about  x = 2

To find the volume of the region bounded by the curves about x = 2; we have the radius of the cylindrical shell to be x - 1, the circumference to be 2 π (x -2 ) and the height to be 6x - x² - 8

6x - x² - 8

6x - x² - 8 = 0

-x² + 6x - 8 = 0

x² - 6x + 8 = 0

(x -4) (x - 2  ) = 0

So;

x = 2 , x = 4

Thus, the region bound of the integral  are from a = 2 and b = 4

Therefore , the volume of the solid can be computed as :

[tex]V = \int \limits ^b _a \ 2x \times f(x) \ dx[/tex]

[tex]V = \int \limits ^4_2 2 \pi (x -2) (6x -x^2 -8) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (6x^2 - x^3 -8x -12 x - 2x^2 +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 (8x^2 -x^3-20x +16) \ dx[/tex]

[tex]V = 2 \pi \int \limits ^4_2 ( -x^3+8x^2-20x +16) \ dx[/tex]

[tex]V = 2 \pi [\dfrac{ -x^7}{4}+\dfrac{8x^3}{3} -\dfrac{20x^2}{2} +16x]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(4^4-2^4)}{4}+\dfrac{8(4^3-2^3)}{3} -\dfrac{20(4^2-2^2)}{2} +16(4-2) ]^4_2[/tex]

[tex]V = 2 \pi [\dfrac{ -(256-16)}{4}+\dfrac{8(64-8)}{3} -10(16-4)} +16(2) ][/tex]

[tex]V = 2 \pi [\dfrac{ 4}{3}][/tex]

[tex]\mathbf{V = [\dfrac{ 8 \pi }{3}] }[/tex]

Answer:

28 units²

Step-by-step explanation:

→ Work out the size of the triangle if it was a full rectangle

Height = 4 and Base = 2

→ Work out area of triangle

0.5 × Height × Base ⇒ 0.5 × 4 × 2 ⇒ 2 × 2 ⇒ 4

→ Minus the area of the triangle from the "imaginary full' rectangle

Area of rectangle = Length × Width ⇒ 8 × 4 ⇒ 32

32 - 4 = 28

Answer:

[tex]\huge\boxed{28\ units^2}[/tex]

Step-by-step explanation:

The figure consists of a triangle, a square and a rectangle.

Area of Triangle:

[tex]\sf \frac{1}{2} (Base)(Height)\\Where \ Base = 2 , Height = 4 \\=> \frac{1}{2} (2)(4)\\=> 4\ units^2[/tex]

Area of Square:

[tex]\sf (Length)(Length)\\(4)(4)\\=> 16\ units^2[/tex]

Area of rectangle:

[tex]\sf (Length)(Width)\\Where \ Length = 4 , Width = 2\\=> (4)(2)\\=> 8 \ units^2[/tex]

Area of the whole figure:

=> 4 + 16 + 8

=> 28 units²

Problem 1.

My thinking is that the furthest you can get is have two points at each opposite corner, so the distance between them is sqrt(2). If we have two other points with this property, then all four corners are filled up. It is possible to pick two points where the distance is 1 unit.

Then a fifth point can be placed at the center such that the distance from it to any of the corners is sqrt(2)/2. We placed the fifth point at the center to try to get as far away as possible from the other four points.

Basically we're trying to find the worst case scenario (leading to the largest distance possible) and seeing how we can fill up the square. This establishes the upper bound. Any other kind of scenario will have a distance less than the upper bound.

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

Problem 2.

For this one, I'm not sure what to make of it. The terminology is a bit strange so I'm not going to be fairly helpful here. Sorry about that.

If I had to guess, I'd assume it has something to do with the fact that a plane is uniquely defined by 3 points. That fourth point is not coplanar with the other three, which helps define the semi-spherical portion. The fifth point is just extra. The points can't be all collinear or else a plane won't form. Though to be honest, I'm still not sure about problem 2. I'd get a second opinion.

Answer:

x=9

Step-by-step explanation:

PQ + QR + RS = PS

2x-6 + 1 + x-4 = 18

Combine like terms

3x -9 = 18

Add 9 to each side

3x-9+9= 18-9

3x = 27

Divide by 3

3x/3 = 27/3

x = 9

Answer:

RS=5

Step-by-step explanation:

solve for x:

2x-6+1+x-4 = 18

combine like terms

3x-9=18

subtract both sides to make x isolated

3x=27

divide by 3 to get x

x=9

RS=x-4

RS=9-4

RS=5

Answer:

the answer is D

Step-by-step explanation:

y=x-1

2=3-1

2=2

y=-3x+11

2=-3(3)+11

2=-9+11

2=2

Answer:

Step-by-step explanation:

If both lines pass through the point (3, 2), we automatically know that (3, 2) is the soution of the system of linear equations given here, AND that (3, 2) is a solution of equation A and equation B both.

Answer:

-18

Step-by-step explanation:

x2 - y2 - z2 if x=-2, y=3, and z=4

x2 - y2 - z2

(-2) 2 - (3)2 - (4)2

(-4) - (6) - (8)

-10 -8

-18

Answer:

18

Step-by-step explanation:

Answer:

Hey there!

What we know:

What we would like to know:

First, let's find AB.

Sine 58= AB/65

Solving for AB, we see that it is about 55.12 m.

Next, let's find BD.

Sine 42= BD/55.12

Solving for BD, we see that it is about 36.88 m.

Let me know if this helps :)