Solve the following inequality:
-5.3 > 1 – 2(-5x - 1)
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Odd and even square numbers

As all even square numbers are divisible by 4, the even numbers of the form 4n + 2 are not square numbers. As all odd square numbers are of the form 4n + 1, the odd numbers of the form 4n + 3 are not square numbers.

Step-by-step explanation:

Answer:

[tex]f(x)=-0.5x+40[/tex]

Step-by-step explanation:

To solve this problem, we need to find the linear function. We know that the constant rate of change is -0.5° Celsius per minute. Also, after 60 minutes the temperature was 10° Celsius. So, we have a one point and the slope of the linear function, let's use the point-slope formula

[tex]y-y_{1} =m(x-x_{1} )\\y-10=-0.5(x-60)\\y=-0.5x+30+10\\y=-0.5x+40[/tex]

Where the y-intercept is at (0, 40).

Now, we have two points to graph the relation between minutes and Celsius degrees.

Therefore, the room's temperature as a function of time is

[tex]f(x)=-0.5x+40[/tex]

Its graph is attached.

Answer:

Put one of the dots 2 spaces obove 60 and the other dot 3 spaces above 50.

Step-by-step explanation:

Answer:

Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

Step-by-step explanation:

Let's rule out the options given one by one.

Option 1: Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.

This is not true, because 1.2 is a rate, it just means that the carrier can finish 1 house in a minute, and also have time to get started delivering to the second house. The total number of houses has to be a whole number, but the rate doesn't.

Option 2: Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.

This option is also incorrect. Delivering mail for 7.5 minutes just means 7 minutes and 30 seconds, which is definitely possible.

Option 3: Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

This option is correct. 1.2 is the rate of which the carrier delivers mail.

Option 4: Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.

This option is also incorrect. Although it is possible to deliver mail for 7.5 minutes, it is not the unit rate, it is the total amount of time it would take.

Answer:

Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

Step-by-step explanation:

Answer:

Edge = 2.5

Step-by-step explanation:

Answer:

Slope-intercept: y=3/4x+1

Sorry idk how to do general form

Step-by-step explanation:

Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.

The slope of this graph is 3/4, and the y-intercept is 1.

Answer:

Slope-intercept form: [tex]y=\frac{3}{4}x+1[/tex]

General form: [tex]-3/4x+y-1[/tex]

Step-by-step explanation:

Firstly, to get the slope intercept form, we need to find the slope and the y-intercept.  To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is [tex]\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}[/tex]. So, after we plug in those values we get in the two points, we can see that [tex]\frac{4-1}{4-0}[/tex], so the slope is [tex]\frac{3}{4}[/tex]. The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, [tex]mx+b[/tex], where m is the slope and b is the y-intercept, m is [tex]\frac{3}{4}[/tex] and b is 1. So, our final answer for the slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]. Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, [tex]y=\frac{3}{4}x+1[/tex], we can subtract y from both sides to get 0 on the left, like this: [tex]0=\frac{3}{4}x+1-y[/tex]. Then, we can rearrange the variables to general form: [tex]0=\frac{3}{4}x-y+1\\[/tex]. That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!

Answer:3a ?

Step-by-step explanation:

Answer:

✈️?

Step-by-step explanation:

Answer:

6 plus .1 plus .007

6 times 1 plus 1 times .1 plus 5 times .01

Step-by-step explanation:

Hope this helps

Answer:

Length of segment BD = 42 units

Step-by-step explanation:

Since C is the midpoint of AB,

Then segment AC = segment CD

Since B is the midpoint of BC,

Then the length of segment AB = Length of segment BC = 14 units

Length of AC = 2 × (14)

                      = 28 units

Length of AC = length of CD = 28 units

Length of segment BD = Length of BC + length of CD

                                      = 14 + 28

                                      = 42 units

Therefore, length of segment BD is 42 units.

Answer:

13

Step-by-step explanation:

Given: a*b=2a-3b

To find: 2*(-3)

Solution:

Numbers that are used for counting are known as natural numbers. Number along with the digit 0 are known as whole numbers.

In the question, [tex]*[/tex] is used to define relation between a and b as [tex]a*b=2a-3b[/tex]

To find 2*(-3), use the given condition: a*b=2a-3b

Put [tex]a=2,b=-3[/tex]

[tex]2*(-3)=2(2)-3(-3)=4+9=13[/tex]

Given that a*b = 2a-3b,then 2*(-3)=​ 13

The given binary operation is:

a*b = 2a  -  3b

Applying this binary operation to 2*(-3), we are going to substitute a = 2 and b = -3 into the binary operation a*b = 2a  -  3b

If a = 2 and b = -3:

2*(-3)  =  2(2)  -  3(-3)

2*(-3)  =  4   +  9

2*(-3)  =  13

Therefore, given that a*b = 2a-3b,then 2*(-3)=​ 13

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Answer:

9 pack their lunches

Step-by-step explanation:

Take the number of students and multiply by the fraction that pack their lunches

15 *3/5 =

15/5 * 3

3*3

9

Answer:

Step-by-step explanation:

In 5th hour remainder is 11,000 gal

Therefore at 4th hour 11,800 gal

At 3rd hour 12,600 gal

At 2nd hour 13,400 gal

at 1st hour 14,200 gal

Part B

At the beginning there is 15,000 gal

Before the draining began, the pool contained 14,200 gallons of water.

The water is being drained at a rate of 800 gallons per hour.

The function f(t) = 14,200 - (800t - 800)

Step-by-step explanation:

4 + (27 - 12 * 2) / 2

4 + (27 - 24) / 2

4 + 3/2

5 1/2

Answer:

5 1/2

Step-by-step explanation:

4 + (27 - 12 ∙ 2) ÷ 2=

4 + (27 - 24) ÷ 2=

4 + 3/2= 5 1/2

Answer:

25 minutes

Step-by-step explanation: 20 divided by 8 equals 2.5 so she take 2 and a half minutes per question. 2.5 plus 2.5 equals 5 so just add five minutes on her original time. 25 minutes

Answer:

25 minutes

Step-by-step explanation:

→You can set this problem up as a proportion, like so:

[tex]\frac{8}{10} =\frac{20}{x}[/tex]

→Cross multiply:

[tex]\frac{8x}{200}[/tex]

→Divide 200 by 8:

x = 25

Answer:

4x^2+10x-2=0

Step-by-step explanation:

So the total area of mirror: 2*3 = 6 ft sq

8-6 = 2 ft sq is the area of the frame

x is the thickness of the frame

so we have (2*x)*2+(3*x)*2+x*x*4= 2

4x+6x+4x^2=2

-> 4x^2+10x-2=0

Answer:

x=62.

Step-by-step explanation:

2x +4=128

2x=128-4

2x=124

x= 62

Step-by-step explanation:

-9x-4y=1....eq1

3x+3y=3.....eq2

multiply eq2 by 3

to get

9x+9y=9....eq3

add eq1 and 3

0+5y=10

5y=10

divide both sides by 5

y=2

substitute y=2 in to eq1

-9x-4(2)=1

-9x-8=1

grouping of like terms

-9x=1+8

-9x=9

divide both sides by -9

x= -1

now the answer is

x= -1, y=2

Answer:

24cm^2

Step-by-step explanation:

3cm times 8cm = 24cm^2

Answer:

A=b*h

Step-by-step explanation:

base=5

height=3

5*3=15

15 is the answer

Answer:

82

Step-by-step explanation:

49 - 3 + 9 times 8 divided by 2

Answer:

82

Step-by-step explanation:

49 -3 + 9*8/2

PEMDAS

Multiply and divide from left to right

49 -3 + 72/2

49 -3 + 36

Add and subtract from left to right

46 +36

82

Answer:

a) The equation of the parabola

                        [tex]y = \frac{-x^{2} }{4} +5[/tex]

Step-by-step explanation:

Explanation:-

Step(i):-

Given the directrix of the parabola y = 6

Focus of the parabola S(0,4)

The standard equation of the parabola

                  ( x- h)² = 4 a (y-k)

(h,k) is the vertex of the parabola

Axis of the parabola is parallel to y-axis

Given the directrix of the parabola y = 6

The directrix of the parabola y = k -a = 6

                                k-a =6 ...(i)

The focus of the parabola

                         S( h , K+a) = (0,4)

so   h = 0 and K+a =4

                          K+a =4 ....(ii)

Step(ii):-

Solving (i) and (ii) equations , we get

    Adding (i) and (ii) equations and we get

     K-a + k+a = 6 +4

               2 K = 10

                  K =5

Substitute   K =5 in equation (i)

             K -a =6

            5 -a =6

            5-6 =a

            a = -1

Step(iii):-

we have (h,k) =( 0,5)  and a = -1

The equation of the  parabola

                                 ( x- h)² = 4 a (y-k)

                                 ( x- 0)² = 4 (-1) (y-5)

                                x²  = -4 y + 20

                              -4 y =   x²  - 20

dividing '-4' on both sides, we get

                         [tex]y = \frac{x^{2} }{-4} +\frac{-20}{-4}[/tex]

                          [tex]y = \frac{-x^{2} }{4} +5[/tex]

Final answer:-

The equation of the parabola

                        [tex]y = \frac{-x^{2} }{4} +5[/tex]

Answer:

12

Step-by-step explanation:

n*30=360

n=360/30

n=12

Answer:

The answer is B 6.252

Step-by-step explanation:

Answer:

y = 4 - x/2

Step-by-step explanation:

Since the line passes through the points A(8,0) and B(4,6), we find that gradient of that lime m = (y₂ - y₁)/(x₂ - x₁) where (8,0) = (x₁, y₁) and (-4,6) = (x₂, y₂).

So, m = (6 - 0)/(-4 - 8) = 6/-12 = = -1/2.

Since the line passes through the point (0,4), the equation of the line is

m = (y - y₃)/(x - x₃) where (x₃, y₃) = (0,4)

So, -1/2 = (y - 4)/(x - 0)

            = (y - 4)/x

    -x/2 = y - 4

         y = 4 - x/2

which is the equation of the line.

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

6a

Sn = n/2 [2a + (n-1) d]

(2Sn)/ n = 2a + (n - 1) d

2a + (n-1) d = (2Sn)/n

(n-1) d = (2Sn - 2a)/n

[tex]d = \frac{2sn \: - 2a}{(n(n - 1))} [/tex]

[tex]d = \frac{2(sn - a)}{ {n}^{2} - n} [/tex]

6b

[tex]d = \frac{2(56 - 25)}{ {32}^{2} - 32} [/tex]

d = ¹/16

7a.

E = (mv²)/2 + mgh

E = m( v²/2 + gh)

E/m = v²/2 + gh

E/m - gh = v²/2

2(E/m - gh) = v²

so

[tex]v = \sqrt{2( \frac{e}{m} - gh)}[/tex]

7b.

[tex]v = \sqrt{2( \frac{4900}{20} - 9.8 \times 15)}[/tex]

v = 14 m/s

Answer:

Step-by-step explanation:

= 2- 6*7 + 18*3 - 14

=2-42+54-14

=2 + 12- 14

= 14-14

=0

Answer:

the ans is 0

Step-by-step explanation:

=2- 6*7 + 18*3 - 14

=2-42+54-14

=2 + 12- 14

= 14-14

=0

Answer: 10.99 + 1.25x

Step-by-step explanation:

The cost of a large pizza is $10.99 and each additional topping costs $1.25. The expression that can be used to calculate the cost of a pizza when x toppings are added will be:

Cost of pizza + (number of additional toppings × 1.25)

Since x toppings are included, this will be:

= 10.99 + (1.25 × x)

= 10.99 + 1.25x

Answer:

The explicit formula is Tn = 18[(2/3)^(n-1)]

Where n is the term we are looking for

Step-by-step explanation:

Here, we want to get an explicit formula to model the equation

Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12

F(3) = 2/3 * f(2) = 2/3 * 12 = 8

F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3

F(5) = 2/3 * 16/3 = 32/9

Thus, seeing how the equations are progressing, we can definitely see a pattern.

That is Tn = (2/3)^(n-1)(18)

Answer:

Answer in image.

Step-by-step explanation:

Answer:

The solution of the given two simultaneous equation

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The intersecting points of given two simultaneous equations are

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

Step-by-step explanation:

Explanation:-

Step(i):-

Given  simultaneous equation

        y  =  9-x    ...(i)

      y   = 2 x² +4 x+6 ..(ii)

Equating (i) and (ii) equations , we get

      9 -x =  2 x² +4 x+6

 ⇒    2 x² +4 x + 6- 9 +x =0

 ⇒  2 x² + 5 x - 3 =0

  ⇒ 2 x² +6 x -x -3 =0

⇒   2 x ( x +3) -1 ( x+3) =0

⇒    (2 x -1 ) ( x+3) =0

⇒    (2 x -1 ) = 0   and   ( x +3 ) =0

    [tex]2 x =1[/tex]    and   x = -3

      x = 1/2 and x =3

Step(ii):-

  x = 3  ⇒ y = 9 - 3 =6

   A( 3 ,6)

 [tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]

[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

Final answer:-

The intersecting points of two simultaneous equations are

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The solution of the given two simultaneous equation

A( 3 ,6)  and  [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]

The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

From the question,

We are to solve the given simultaneous equations

The given equations are

y = 9-x                ---------- (1)

y = 2x²+4x+6    ---------- (2)

Substitute equation (1) into equation (2)

y = 2x²+4x+6

That is

9-x = 2x²+4x+6

Simplifying, we get

0 = 2x² +4x +x +6 -9

0 = 2x² +5x -3

∴ 2x² +5x -3 = 0

Now, solving the quadratic equation

2x²+6x -x -3 = 0

Factorizing

2x(x+3) -1(x+3) = 0

Then, we get

(2x -1)(x+3) = 0

∴ 2x - 1 = 0 OR x + 3 = 0

2x = 1 OR x = -3

∴ x = 1/2 OR x = -3

Now, substitute the values of x into equation (1) to determine the values of y

y = 9-x

When x = 1/2

y = 9 - 1/2

y = 8 1/2

and when x = -3

y = 9 --3

y = 9+3

y = 12

Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)

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