The largest possible sum, less than 10, of two consecutive prime number is

[tex]\dfrac{x^2+7x+12}{x^2-x-12}\\\\=\dfrac{x^2 +3x+4x +12}{x^2 -4x+3x-12}\\\\=\dfrac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}\\\\=\dfrac{(x+4)(x+3)}{(x-4)(x+3)}\\\\=\dfrac{x+4}{x-4}\\\\\text{Restrictions:}~ x\neq 4 ,~ x\neq -3[/tex]

Let's see

[tex]\\ \rm\rightarrowtail x^2-2x=0[/tex]

[tex]\\ \rm\rightarrowtail x(x-2)=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x-2=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x=2[/tex]

[tex] \green{••••••••••••••••••••••} \blue{••••••••••••••••••••••••••}[/tex]

[tex] \sf {x^2 - 2x = 0} [/tex]

[tex] \sf {x ( x - 2) = 0} [/tex]

[tex] \sf {x = 0 \: or \: x-2 = 0} [/tex]

[tex] \sf \green{ {x = 0 \: or \: x = 2}} [/tex]

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Answer:

angle DCE

Angle DEC

Angle ABF

Step-by-step explanation:

you had the wrong order

Answer:

(-3, 0) and (1, 0)

(0, 4)

Step-by-step explanation:

x-intercept is the point where y = 0.

y-intercept is the point where x = 0.

or points ...

f(x) = y = -4×|x + 1| + 8

let's start with the y-intercept (x = 0)

y = -4×1 + 8 = -4 + 8 = 4

the y-intercept point (only 1 point) is (0, 4).

for x = 0 the absolute value function contains 0+1. and that is always +1.

the x-intercept(s) :

0 = -4×|x + 1| + 8 (dividing by -4)

0 = |x + 1| - 2

|x + 1| = 2

because of the absolute value we have 2 possibilities :

+(x + 1) = 2

x + 1 = 2

x = 1

and

-(x + 1) = 2

-x - 1 = 2

-x = 3

x = -3

so the points of x-intercept are (-3, 0) and (1, 0)

Answer:

Top left.

Step-by-step explanation:

Answer:

15 students in each bus.

Step-by-step explanation:

Subtract 10 from 100 and you get 90 then divide 90 by 6 and that gives you how many students in each bus

Answer:

multiply the top number then divide the bottom

Step-by-step explanation:

Answer:

the answer is 3040 and does

Answer:

I believe he sells each bar for .75 cents

Answer:

x = 8

y = 6

Step-by-step explanation:

First and foremost, it's an equilateral triangle, therefore all sides and angles are equal.

Knowing that the sum of angle in a triangle is 180°, therefore each angle is 60°.

Then equating (7x+4)° to 60, we have that,

7x+4=60

7x=60-4

7x=56

x=56÷7

x=8.

[tex]5^2 - \left(\dfrac 14 \right)^2= 25 - \dfrac{1}{16} = \dfrac{400-1}{16} = \dfrac{399}{16}=24\dfrac{15}{16}[/tex]

Answer:

$3.78

Step-by-step explanation:

30 dollars minus 7 dollars and 28 cents is twenty-two and seventy-two cents, then minus another eighteen and ninety-four cents, would end up at three dollars and seventy-eight cents.

Answer:

[tex]\boxed{\$3.78}[/tex]

Step-by-step explanation:

To find out how much money does Kaya have left, we need to subtract the total money spent from the total money brought to the mall.

In this problem, we can tell that Kaya brought $30 to the mall as stated in the question. Furthermore, the problem states that she spent $7.28 on food, and $18.94 on a necklace. This means that the sum of 7.28 and 18.94 is the money spent by Kaya.

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[tex]\$30 - (\$7.28 + \$18.94) = \text{Money remained}[/tex]

➡ [tex]\$30 - (\$26.22) = \text{Money remained}[/tex]

➡ [tex]\$30 - \$26.22 = \text{Money remained}[/tex]

➡ [tex]\bold{\underline{\$3.78} = Money \ remained}}[/tex]

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Answer:

The answer is 157 mm.

Step-by-step explanation:

Now,

C = πd

C = 3.14 × 50 mm

C = 157 mm

Thus, The circumference of the circle is 157 mm.

Answer:

$636.17

Step-by-step explanation:

       First, we need to find the volume of the ball. Then, we will solve for the cost of it.

       Volume of a sphere and solving for the area:

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(7.5)³

V ≈ 1767.15 in³

       Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.

1767.15 in³ * $0.36 = 636.174

       Money rounds to the hundredth place,

636.174 -> $636.17

          It will cost $636.17 to make one ball.

Answer:

Volume of a sphere = 4/3 Pi r³

if r = 7.5

= 4/3 pi 7.5³

= 4/3 pi 421.87

= 1687.5/3 pi

= 562.5 Pi

= 1767.15 in³

then

1767.15 x 0.36 = 636.17

if 1 in³ costs 0.36$

then 1767.15 in³ costs 636.17$

Answer:

6

Step-by-step explanation:

to find the perimeter of a trapezoid you add all the sides together

therefore we do it backwards

24-3-6-9=6

Solution :-

We know that perimeter is the sum of all sides, and here we have been provided with perimeter and the length of three sides. Now, we can assume the length of other side as any variable, say x. And develop a linear equation, and solve it. Thus,

A/Q,

→ 3yd + 6yd + 9yd + x = 24yd

→ 18yd + x = 24yd

→ x = 24yd - 18yd

→ x = 6yd

Thus, the length of the fourth side is 6yd.

Hope that helps :)

Answer:

I'm stuck on the same question

Step-by-step explanation:

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

Answer:

38.6 m

Step-by-step explanation:

Picture explanation

Hope this Helps!

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Answer:

38.6 m

Step-by-step explanation:

x+x + y * y = 2x + y²

Answer:

[tex]2x + y^{2}[/tex]

Step-by-step explanation:

[tex]\text{If a number is being added to itself, it is basically a number being multiplied by 2. }[/tex]

[tex]\rightarrow x + x[/tex]

[tex]\rightarrow \boxed{\bold{2x}}[/tex]

[tex]\text{If a number is being multiplied by itself, it is basically the number squared.}[/tex]

[tex]\rightarrow y \times y[/tex]

[tex]\rightarrow \boxed{\bold{y^{2}}}[/tex]

Thus, the simplified expression is 2x + y².

Answer:

20π

Step-by-step explanation:

Area = πr^2

100π = πr^2

solve for r and r = 10

circumference of a circle is 2πr

therefore 2π×10=20π in

The height of the right circular cylinder with volume of 500π cubic centimetre and radius of 5 centimetre is 20 cm.

volume = πr²h

where

Therefore,

volume = 500π cm³

r = 5 cm

Therefore,

volume of the cylinder = πr²h

500π = 5²πh

500π = 25πh

divide both sides by 25π

500π / 25π = 25πh / 25π

h = 20 cm

learn more on cylinder here: https://brainly.com/question/11083770

Answer:

A) 20 cm

Step-by-step explanation:

The little square on the angle means that the entire angle is 90 degrees

The larger angle is made up of two angles of measure 'x - 18' and 'x'

Let's put that into an equation form:

     (x - 18) + (x) = 90

        2x - 18 = 90

           2x = 108

            x  = 54

So x = 54

Hope that helps!

Answer:

The velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Acceleration is constantly [tex]6\; {\rm m\cdot s^{-2}}[/tex] (and thus is never [tex]0[/tex].)

Step-by-step explanation:

The distance between the particle and the initial position is the displacement of this particle. Let [tex]x(t)[/tex] denote the displacement (in meters) of this particle at time [tex]t[/tex] (in seconds.) The question states that [tex]x(t) = 3\, t^{2} + t[/tex].

Differentiate displacement [tex]x(t)[/tex] with respect to time [tex]t[/tex] to find the velocity [tex]v(t)[/tex] (in [tex]{\rm m \cdot s^{-1}}[/tex]) of this particle:

[tex]\begin{aligned}v(t) &= \frac{d}{d t}\left[x(t)\right] \\ &= \frac{d}{d t}\left[3\, t^{2} + t\right] \\ &= 6\, t + 1 \end{aligned}[/tex].

Set velocity to [tex]25\; {\rm m\cdot s^{-1}}[/tex] and solve for time [tex]t[/tex] (in seconds):

[tex]v(t) = 25[/tex].

[tex]6\, t + 1 = 25[/tex].

[tex]t = 4[/tex].

Thus, the velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Differentiate velocity [tex]v(t)[/tex] with respect to time [tex]t[/tex] to find the acceleration (in [tex]{\rm m\cdot s^{-2}}[/tex]) of this particle:

[tex]\begin{aligned}a(t) &= \frac{d}{d t}\left[v(t)\right] \\ &= \frac{d}{d t}\left[6\, t + 1\right] \\ &= 6\end{aligned}[/tex].

In other words, the acceleration of this particle is constantly equal to [tex]6\; {\rm m\cdot s^{-2}}[/tex]. Hence, the acceleration of this particle is never [tex]0[/tex].

Answer:

Step-by-step explanation:

from

3(7x +7) + 5x = 5(5x + 10)

21x+21+5x     = 25x + 50

26x + 21        = 25x + 50

26x-25x +21 = 50

1x+21            = 50

1x                 =50-21

            x      = 29

equal when x= 29

try to x> 29      such as 30  

3(7(30) +7) + 5(30)     ?    5(5(30) + 10)

1470    ?      800

so  greater than when x >29

finally  

less than when x<29

Answer:

When x = 29:   the expressions are equal

When x < 29:   3(7x + 7) + 5x is less than 5(5x + 10)

When x > 29:    3(7x + 7) + 5x is greater than 5(5x + 10)

Step-by-step explanation:

Given expressions:

Expand both expressions:

   3(7x + 7) + 5x

⇒ 21x + 21 + 5x

⇒ 26x + 21

   5(5x + 10)

⇒ 25x + 50

Equate the expanded expressions and solve for x

   26x + 21 = 25x + 50

⇒ 26x - 25x = 50 - 21

⇒ x = 29

Therefore, the expressions are equal when x = 29

When x < 29:    3(7x + 7) + 5x < 5(5x + 10)

When x > 29:    3(7x + 7) + 5x > 5(5x + 10)