Which inequality is equivalent to 4 x − 2 y ≤ 8 ?

First you must distribute the numbers outside the parentheses to the numbers inside the parentheses

Let's start with the first one:

9(x-2) + 3(5-2x) = 2

9(x - 2)  

9*x + 9*-2

9x + (-18)

9x - 18

so...

9x - 18 +  3(5-2x) = 2

Now on to the second set of parentheses:

9x - 18 + 3(5-2x) = 2

3(5 - 2x)

3*5 + 3*-2x

15 + (-6x)

15 - 6x

so...

9x - 18 + 15 - 6x = 2

Now you must combine like terms. This means the numbers with the same variables must be combined...

First set of like terms:

9x - 18 + 15 - 6x = 2

9x + (-6x)

3x

so...

3x - 18 + 15 = 2

Second set of like terms:

3x - 18 + 15 = 2

-18 + 15

-3

so...

3x - 3 = 2

Now bring -3 to the right side by adding 3 to both sides (what you do on one side you must do to the other). Since -3 is being negative on the left side, addition (the opposite of negative/subtraction) will cancel it out (make it zero) from the left side and bring it over to the right side.

3x + (- 3 + 3) = 2 + 3

3x + 0 =5

3x = 5

Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.

3x/3 = 5/3

x = [tex]\frac{5}{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

6: d, 7: b and c, 8: a

Step-by-step explanation:

6) The answer is (d).

We have,

0.00001131 =1.131×0.00001

= 1.131/100000

= 1.131×10^-5.

So, this is correct answer.

7) This question have two answers (b) and (c), both are correct.

(b) 480000-97000

= 4.8x100000-9.7x10000

=4.8x10^5-9.7x10^4

(c) 4.8x10^5-9.7x10^4

= 4.8x10^5-0.97x10^5

= (4.8-0.97) x10^5

=3.83x10^5

8)(a)

(4 x 10^3)(5x10^7).

= 4x5x10³x10^7

= 4x5x10^(3+7).

Answer:

18 inches in width and 7 inches in height

Using kite, the dimensions of the layer of film the Caleb will apply is 18 inches in width and and 7 inches in height.

A Kite is "quadrilateral with two distinct pairs of congruent consecutive sides".

If a kite is quadrilateral, then "its diagonal are perpendicular and exactly one diagonal each other".

According to the question,

A window is in the shape kite has an height of 14 inches and a width of 18 inches. Caleb wants to apply a layer of plastic film on the top half of the kite shape window. The window has dimensions of width 18 inches and 14 inches of height.

In order to the find new dimensions to apply a layer of plastic film on the top half of the kite shape window only if we divide the height by two then we get new dimensions on the top half of the kite shape window.

= [tex]\frac{14}{2}[/tex]

=7 inches

Hence, new dimensions to apply a layer of plastic film on the top half of the kite shape window is 18 inches in width and and 7 inches in height.

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Answer:

Remember, 1 is the multiplicative identity.  That means that we can multiply a value by 1 and not change the value, only change the units.

For example:  If we have 3 dozen eggs, how many eggs do we have?

             3 dozen

          (3 dozen)*(12 eggs / 1 dozen) = 36 eggs    (dozen cancels out, leaving only eggs)

In this problem:

   (16 miles / 1 week)

   (16 miles / 1 week)*(52 weeks / 1 year)       (weeks cancel out, leaving miles/year)

   832 miles/year

Note: with either 365 (or 366) days in a year, there are 365/7 = 52.14 weeks in a year, but we'll use 52 because the problem gave miles/week.

Step-by-step explanation:

Answer: I think it is the last one

Step-by-step explanation: if you work it out, it equally 6x-2

Answer:

6x-2

Step-by-step explanation:

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

When x=5 the value of the expression is 28

Now we check with each expression given in the options

Plug in 5 for x in each option

[tex]-6x-1=-6(5)-1=-30-1= -31[/tex]

[tex]-6x+2=-6(5)+2=-30+2= -28[/tex]

[tex]6x+1=6(5)+1=30+1= 31[/tex]

[tex]6x-2=6(5)-2=30-2=28[/tex]

So 6x-2 gives us 28 when x=5

Answer:

The answers to your three problem question are shown

1) the value of p is

p = -1

2) The coordinates of the focus are

Focus =  (-1,0)

3) The equation of the directrix is

Directrix

x = 1

Step-by-step explanation:

The general equation for this parabola is

y^2 = 4px

Problem 1

Find the value of p.

We are told that the equation of the problem is

y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because

y^2 = 4(-1)x = -4x

This means that p = -1

Problem 2

Find the focus

To find the focus we can see the equations attached below for the focus, vertex and directrix.

In these case, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x =>

x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus

((4ac -b^2  + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>

(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus =  (-1,0)

Problem 3

Find the directrix

The equation is

x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix

x = 1

Answer: P is -1

Focus is (-1,0)

Directrix is X= 1

Answer:

f(4) = 4

Step-by-step explanation:

F(x)=1/4•2^x

Let x = 4

F(4)=1/4•2^4

      = 1/4 * 2^4

      = 1/4 *16

      = 4

Answer: f(4) = 4

Step-by-step explanation:

f(x) = 1/4 . 2^x

To find f(4) we simply replace x by 4 in the above equation;

f(4) =1/4 . 2^4

f(4) = 1/4 . 16

f(4) = 16/4

f(4) = 4

Therefore f(4) is equal to 4

Translating the half to symbols would be 1/2. Therefore, your answer is 1/2(n)

Hope this helps!

Answer:

1/2n

Step-by-step explanation:

half of n

of means multiply

1/2 * n

n/2

Answer:   [tex]\bold{\dfrac{1}{19}}[/tex]

Step-by-step explanation:

Let x represent the quantity of yellow cubes

Yellow: x

Blue: three times yellow --> 3x

Green: five times blue --> 5(3x) = 15x

Yellow + Blue + Green = Total cubes

    x      +   3x  +    15x   =       19x

[tex]Probability=\dfrac{yellow}{total}=\dfrac{x}{19x}=\large\boxed{\dfrac{1}{19}}[/tex]

The probability of Sarah taking out a yellow cube from the bag is 0.7 or 5/7.

The fraction of favorable outcomes of an event to the total number of outcomes of the event is said to be the probability. The fraction can also be written in the simplest form.

P(E)= n(E)/n(S) where E -event, n(E) - favorable outcomes and n(S) is the total outcomes.

It is given that a bag contains blue cubes, yellow cubes, and green cubes.

Consider the number of blue cubes = n

So, the number of yellow cubes = 3 times as many as blue cubes

                                                     = 3n

Then, 5 times as many as green cubes = blue cubes

⇒ number of green cubes = n/5

Then the total number of cubes in the bag

= n + 3n + n/5

⇒ [5n + 15n + n]/5

⇒ 21n/5

Then the probability of taking out a yellow cube = (possible outcomes of a yellow cube)/(total number of cubes)

⇒ [tex]\frac{(3n)}{(21n/5)}[/tex]

⇒ 15n/21n

⇒ 5/7

∴ The probability of taking out a yellow cube = 5/7 = 0.7.

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Answer:

D

Step-by-step explanation:

A difference of squares is represented in general as

a² - b²

Both variables have an even power (2) → a

There are only two terms → b

Answer:

a= -6

Step-by-step explanation:

Given

a=2+3a+10

In order to find the value of a, we have to isolate a on a single side of the equation

So,

subtracting 3a from both sides

a-3a = 2+10+3a-3a

=>a-3a=12

=> -2a = 12

Dividing both sides by -2

=> -2a/-2 = 12/-2

=> a = -6

The value of a in the given equation is -6 ..

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2.  Thus, f(-2.2) = 1.

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2. Thus, f(-2.2) = 1.

Answer:

3*5=15

15 is your answer

ANSWER

15 square units.

EXPLANATION

Each box is 1 square units.

When we count the number of boxes we obtain 15 boxes.

This implies that the area of the rectangle is 15 square units.

Alternatively, we can observe that:

The rectangle is a 3 by 5 rectangle.

So the area is

[tex]3 \times 5 = 15 \: units \: square[/tex]

The rectangle is 15 units square.

Answer:

x²+y²=16

Step-by-step explanation:

the general equation for a circle is given as :

(x−h)²+(y−k)²=r²

where (h, k) is the coordinate of the center of the circle and r is the radius

in this case h=0, k=0 and r = 4

equation becomes

x²+y²=4²

or

x²+y²=16

Answer: Last option.

Step-by-step explanation:

The equation of a circle in Center-radius form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the center is at the point (h,k) and "r" is the radius.

If the center of this circle is at the origin, means that:

[tex]h=0\\k=0[/tex]

Since the radius is 4, then:

[tex]r=4[/tex]

Now we need to substitute these values into the equation of the circle.

[tex](x-0)^2+(y-0)^2=(4)^2[/tex]

Simplifying the equation, we get:

[tex]x^2+y^2=16[/tex]

This matches with the last option.

Answer:

sin(arccos(-4/√25)) = 0.6

Step-by-step explanation:

The expression you want to evaluate is

sin(arccos(-4/√25))

= sin(arccos(-4/5))

We place this expression into a calculator and get the result

arccos(-4/5) = 2.498 rads = 143.1°

then

sin(143.1°) = 3/5

sin(143.1°) = 0.6

sin(arccos(-4/√25)) = 0.6

Answer: It is!!!!!!!!

Answer:

The correct option is C.

Step-by-step explanation:

The standard form of a parabola is

[tex]y=ax^2+bx+c[/tex]

The table of values represents the coordinate pairs of the parabola. It means the graph of the parabola must be passes through these coordinate pairs.

From the given table it is clear that the parabola passes through the points (0.5,21), (1,34) and (1.5,39).

[tex]21=a(0.5)^2+b(0.5)+c[/tex]

[tex]21=0.25a+0.5b+c[/tex]             .... (1)

[tex]34=a(1)^2+b(1)+c[/tex]

[tex]34=a+b+c[/tex]                      .... (2)

[tex]39=x(1.5)^2+y(1.5)+z[/tex]

[tex]39=2.15a+1.5b+c[/tex]            .... (3)

On solving (1), (2) and (3), we get

[tex]a=-16, b=50,c=0[/tex]

The equation of parabola is

[tex]y=-16x^2+50x+0[/tex]

[tex]y=-16x^2+50x[/tex]

The graph of parabola is shown below. It is same as graph in option C.

Therefore the correct option is C.

Answer:

13. 23/4

14. 13/2

15. 6 and 1/2

16. 2 and 7/12

Answer:

13. 23/4

14. 13/2

15. [tex]6\frac{1}{2}[/tex]

16. [tex]2 \frac{7}{12}[/tex]

Step-by-step explanation:

13) 5×4=20

    20+3=23

    [tex]\frac{23}{4}[/tex]

14) 2×6=12

     12+1=13

     [tex]\frac{13}{2}[/tex]

15 an 16 divide

Answer:

Explanation:

In order to calculate the variance and standard deviation of a set of data, you first must calculate the mean.

Mean = average = μ = ∑ values / (number of data)

Hence, the mean of our data set is:

Now you can calcuate the variance using the formula.

For a data set (which is all your population and not a sample) the formula is:

That is:

The standard deviation, S.D., is the square root of the variance:

Answer:

Variance = 8732.24 and standard deviation = 93.45

Step-by-step explanation:

We have to calculate the variance and standard deviation of the data set

3,832, 3,779, 3,655, 3,642, 3,579

First we calculate the mean of the data

Mean = [tex]\frac{(3,832+3,779+3,655+3,642+3,579)}{5}[/tex]

         = [tex]\frac{18487}{5}[/tex]

         = 3697.4

Now we calculate the variance by subtracting the mean from value of data set and square it.

3832 - 3697.4 = 134.6² =  18,117.16

3779 - 3697.4 = 81.6² = 6,658.56

3655 - 3697.4 = -42.4² = 1,797.76

3642 - 3697.4 = -55.4 = 3069.16

3579 - 3697.4 = -118.4 = 14,018.56

Add up the squared result and take the mean

=  [tex]\frac{(18117.16+6658.56+1797.76+3069.16+14018.56)}{5}[/tex]

=  [tex]\frac{43661.2}{5}[/tex]

Variance = 8732.24

To calculate standard deviation, we take the square root of the variance = [tex]\sqrt{8732.24}[/tex]

Standard deviation = 93.44645526 ≈ 93.45

Variance = 8732.24 and standard deviation = 93.45

Answer:

7.1 inches

Step-by-step explanation:

An Isosceles right triangle is one with two sides equal and the angles equal too.The angles in this case are 45°

For this question, to get the hypotenuse, you apply the Pythagorean relationship where the legs will be represented by a and b where as the hypotenuse will be represented by c.

[tex]a^2+b^2=c^2\\[/tex]

Given;

One leg = 5 inches, but you know that in this triangle, the two sides are equal, hence the other side/leg is 5 inches.

Lets take one side of the triangle as a=5 inches

The other side as b=5 inches

The hypotenuse as c=?

Apply the expression;

[tex]a^2+b^2=c^2\\\\5^2+5^2=c^2\\\\25+25=c^2\\\\50=c^2\\\\c=\sqrt{50} =7.071[/tex]

To the nearest tenth 7.071 = 7.1 inches

Answer:

C.(10x^2-4) - (7x^2+3)

In option C,

(10x^2-4) - (7x^2+3) = 10x^2 - 4 - 7x^2 - 3 = 3x^2 - 7

⇒ Option C is correct

Answer:

0

Step-by-step explanation:

(93)10 - 930=

930 - 930=

0

Answer:

The turning point is (2,8)

Step-by-step explanation:

we know that

The general equation of the substance's temperature is equal to

[tex]T(x)=(x-h)^{3}+k[/tex]

where

(h,k) is the vertex (turning point)

In this problem we have

[tex]T(x)=(x-2)^{3}+8[/tex]

so

(h,k)=(2,8)

therefore

The turning point is (2,8)

Answer: 7 boxes of carrots, 9 boxes of potatoes, 18 boxes total

Step-by-step explanation:

75 -68=7 boxes of carrots

80-71=9 boxes of potatoes

For this case we have:

x: Represents the number of carrot boxes

y: Represents the number of boxes of potatoes

Initially we have:

[tex]x = 75\\y = 80[/tex]

If you sold 68 boxes of carrot we have:

[tex]x = 75-68 = 7[/tex]

If you sold 71 boxes of potatoes, we have:

[tex]y = 80-71 = 9[/tex]

The number of boxes I take home is given by:[tex]x + y = 7 + 9 = 16[/tex]

ANswer:

7 boxes of carrots left

There are 9 boxes of potatoes left

A total of 16 boxes remain

Answer:

15+25d=t

Step-by-step explanation:

the initial value is 15 it increases(+) by 25 to each kilometer(distance=d) of depth.

The equation that models the relationship between distance d in kilometers and temperature t in degrees Celsius is t = 25d + 15. This means that for each kilometer increase in depth, the temperature increases by 25 degrees Celsius in addition to the initial 15 degrees Celsius surface temperature.

The relationship between the variables, distance (d) and temperature (t), is described as a linear function. Given that the surface temperature is 15 degrees Celsius and it increases by 25 degrees Celsius with every kilometer, the mathematical model is expressed as:

t = 25d + 15

In this equation, t represents the temperature and d is the distance from the surface in kilometers. This implies that for every kilometer increase in depth, the temperature increases by 25 degrees Celsius on top of the initial 15 degrees Celsius surface temperature.

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For this case we must find the GCF of the following expression:

[tex]24y ^ 8 + 6y ^ 6[/tex]

By definition, the largest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. We find the factors of each number:

24: 1,2,3,4,6,8,12,24

6: 1,2,3,6

Thus, the GCF of both numbers is 6

The GCF of the expression is: [tex]6y ^ 6[/tex]

Answer:

[tex]6y ^ 6[/tex]

Answer:

[tex]<CGF = 130[/tex]

Step-by-step explanation:

A triangle adds up to 180.

180 - 50 = 130

Since both of the missing angles are congruent each of the missing angles is 65 degrees.

130/2 = 65

As per the exterior angle theorem, the measure of the exterior angle is determined by the sum of the opposite interior angles.

65 + 65 = 130

So, the measure of [tex]<CGF = 130[/tex]

Answer:

The correct answer is last option  

10

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here  (x1, y1) = R(0, 0)  and (x2, y2)  = S(6, 8)

Distance, RS = √[(x2 - x1)² + (y2 - y1)²]

 = √[(6 - 0)² + (8 - 0)²]

 = √[6² + 8²]

 = √[36 + 64]

 = √100

 = 10

Therefore the correct answer is last option  10

Answer:

A. (1,-2)

B. (-3,6)

Step-by-step explanation:

we know that

If two vectors are orthogonal, then the dot product ( or scalar product) of the vectors is equal to zero

so

Let

a (x1,y1)  and b(x2,y2)

The dot product is equal to

a.b=(x1*x2+y1*y2)

Verify each case

case A) (2,1) with (1,-2)

(2,1).(1,-2)=(2)*(1)+(1)(-2)=2-2=0

therefore

(1,-2) is orthogonal to the given vector

case B) (2,1) with (-3,6)

(2,1).(-3,6)=(2)*(-3)+(1)(6)=-6+6=0

therefore

(-3,6) is orthogonal to the given vector

case C) (2,1) with (1,2)

(2,1).(1,2)=(2)*(1)+(1)(2)=2+2=4

therefore

(1,2) is not orthogonal to the given vector

case D) (2,1) with (-2,3)

(2,1).(-2,3)=(2)*(-2)+(1)(3)=-4+3=-1

therefore

(-2,3) is not orthogonal to the given vector

Answer: B, D, E

On EDGE

Step-by-step explanation:

Answer:

a)  [tex]240\degree[/tex]

b) [tex]\frac{15\pi}{4}[/tex]

Step-by-step explanation:

Coterminal angles have the same terminal sides in standard position.

a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range.

 [tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].

In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.

b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.

We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.

[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]