A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?

Answer:

[tex]26[/tex] and [tex]28[/tex].

Step-by-step explanation:

Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].

The square of the smaller integer would be [tex]x^{2}[/tex].

Five times the larger integer would be [tex]5\, (x + 2)[/tex].

Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].

The value of this expression should be equal to [tex]536[/tex]. In other words:

[tex]x^{2} - 5\, (x + 2) = 536[/tex].

Rewrite and simplify this quadratic equation:

[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].

Apply the quadratic formula to find possible values of [tex]x[/tex]:

[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].

[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].

Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.

Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].

Answer:

(2,-12)

Step-by-step explanation:

Correct equations:

  8x+y=4

 -2x-8=y

------------------

Rearrange the first equation:

8x+y=4

y=4-8x

Now use this value of y in the second equation:

-2x-8=y

-2x-8=4-8x

6x = 12

x = 2

When x = 2:

y=4-8x

y=4-8(2)

y = -12

(2,-12)

--

One can also graph the two equations and find the point they intersect.  See the attached graph.

The fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

Slope of a line = change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given the following points:

(4, 9) and (0, 5)

Slope of the line would be:

Slope = (5 - 9)/(0 - 4)

Slope = (-4)/(-4)

Slope = 1

Therefore, the fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

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Answer:

I think √8

Step-by-step explanation:

an integer to the power of 2

Answer:

184

Step-by-step explanation:

80% of 230

0.8x230

8×23

=184

Answer:

Your answer would be:
13.25

128 books in use + 84 books in the collection box =212 reference books on the shelf

212 books / 16 shelves =13.25 per shelf

Logically the answer 13.25 wouldn't make sense because you can't put a 25th of a book on a shelf, so that means you will need to put the "0.25 book" away. Technically your answer would be 13. Due to the question, however, it would be 13.25.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

1222 ft^2

Step-by-step explanation:

2(13x9) + 2(5x12) + 2(4.5x9) + 2(9x11) + 2(19x11) + (19x9)

Answer:

120 marbles

Step-by-step explanation:

we can find the answer by dividing the volume of the cylinder by the volume of the marble.

V of a cylinder is

pi×r^2×h = 1280pi

V of marble is

4/3 × pi × r^3

V is 32/3 pi

so final answer is 1280pi ÷ (32/3 × pi)

ANSWER IS 120 MARBLES

Answer:

(0,4) (0,7) (-2,4)

Step-by-step explanation:

The line x=1 is a vertical line that passes through the point (1,0). So we then place the new triangle at equal distance from the line.

I hope this helps!

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Answer:

i think you have to multiply

the answer is- 28.512

Step-by-step explanation:

i dont know if this is right im sorry but i think it is

Answer:

9

Step-by-step explanation:

6      x

-   =   -

8      12

the relationship from 8 to 12 is divided by.666666666666

So, we do the same for 6

We get 9.

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Answer:

1.c

2.a

3.d

4.e

5.f

6.b

Answer:

-14x + 6 (option D)

Step-by-step explanation:

To solve the given equation, you first need to distribute the negative 3.

So, you need to multiply

(4x)(-3)  ;  (-2)(-3)

(4x)(-3)= -12x

(-2)(-3)= 6

So, your new, distributed, equation would be:

-12x + 6 - 2x

If we combine like terms (-12x - 2x), our new equation will be:

-14x + 6

Answer:

9. (a) 1/4

   (b) remove 3 alphabet cards

   (c)  add 4 number cards

10.  1/8

Step-by-step explanation:

Question 9

Given:

⇒ total number of cards = 8 + 10 + 6 = 24 cards

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

(a) P(picture card) = 6/24 = 1/4

(b) P(alphabet card) = 10/24 = 5/12

If we remove 3 alphabet cards from the box

⇒ number of alphabet cards = 10 - 3 = 7

⇒ total number of cards = 24 - 3 = 21

Therefore, P(alphabet card) = 7/21 = 1/3

(c)  P(number card) = 8/24 = 1/3

If we add 4 number cards to the box:

⇒ number of number cards = 8 + 4 = 12

⇒ total number of cards = 24 + 4 = 28

Therefore, P(number card) = 12/28 = 3/7

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Question 10

Given:

⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²

As PR = SD = 4cm

Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²

P(point lies in ΔSDR) = 8/128 = 1/16

P(point lies in ΔPRQ) = 8/128 = 1/16

P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8

The value of 0.36 when converted to a fraction in the simplest form is 9/25.

Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.

From example, let's convert 0.36 to a fraction on its simplest form. This will be:

0.36 = 36/100 = 9/25

In conclusion, 0.36 is 9/25 in the simplest form.

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Answer: A, C, F

Step-by-step explanation:

Answer:

716

Step-by-step explanation:

Triangle = bh / 2

24 x 14 = 336, you should divide by 2 but there is 2 of them (front and back) so cancels out. 10 x 24 is 240 and cancels for same reason. 336 + 240 = 576. 14 x 10 = 140 and 576 + 140 = 716

Answer:

976 cm^2

Step-by-step explanation:

area of triangle is 1/2 times base times height

notice we have two triangles

so 14 * 24 * 0.5 is 168

168 times 2 is 336

now we have a rectangle on the bottom so its area is base times height

14 times 10 is 140

and now we have two rectangles on either side

25 times 10 is 250

250 times 2 is 500

500+140+336

976 cm^2

Answer:

Step-by-step explanation:

To make a guess as to the volume, it may be easier to guess in cups rather than centimeters or inches. One may visualize that a 12 ounce soda can is about 1.5 cups. This is equivalent to 354.88 cubic centimeters or 21.656 cubic inches.

Observe the division shown

To divide 2 by 9 Carl added a .0 on right of dividend and 0. on the right of quiotent .

Remainder recieved is 2 again

So these steps gonna repeating

The answer be like 0.222222..

Let's assume that all hours she worked were the first 35 hours of the week.

She would've made £22.80 x 35 = £798

So, she would've made 981.54 - 798 = 183.54 less than the actual amount

She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.

So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours

So in total, she worked for 35 + 7 = 42(hours).

Answer:

42 hours

We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.

981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.

and 35 plus 7 = 42 :)

Answer:

4x/(x+1)(x2+x+6)

Step-by-step explanation:

Answer:

The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4

Step-by-step explanation:

Answer:

2 m/s or 7.2 km/h

Step-by-step explanation:

Time = 50 seconds

Distance = 100 meters

Velocity = distance/time = 100/50 = 2 m/s or 7.2 km/h

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[tex] \large \purple { \rm{ To \: find \: speed \: we \: use↦}}[/tex]

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[tex] \large \rm{s = \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = \cancel \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = 2 m/s \: or \: 7.2km/h }[/tex]

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Answer:

x - 7 [tex]\leq[/tex] -28

Step-by-step explanation:

I guarantee you that this is correct. It's pretty simple to understand.

Please mark Brainliest. :)

Answer:

396 cm²

Step-by-step explanation:

    Let us break this shape into two parts.

    The left part:

27 cm² * 10 cm² = 270 cm²

    The right part:

24 cm² - 10 cm² = 14 cm²

14 cm² * 9 cm² = 126 cm²

    Total area:

270 cm² + 126 cm² = 396 cm²

Answer:

70

Step-by-step explanation:

20x(1+150%)

28x(1+1.5)

28x2.5

70

Use the formula shown:

6^2 + 2.5^ = c^2

36 + 6.25 = c^2

42.25 = c^2

Take the square root of both sides:

c = 13/2 as a fraction or 2.5495 as a decimal (round off as needed)

Answer:

2n= 53

and you divide both sides by 2

2n/2 =53/2

2 divided by 2 is 1 and 53 divided 2 is 26.5

n= 26.5

in the II Quadrant, let's recall that the adjacent side or cosine is negative whilst the opposite side or sine is positive, thus

[tex]tan(\theta )=-\sqrt{\cfrac{19}{17}}\implies tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{19}}}{\underset{adjacent}{-\sqrt{17}}}\impliedby \qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]c=\sqrt{(-\sqrt{17})^2~~ + ~~(\sqrt{19})^2}\implies c=\sqrt{17+19}\implies c=\sqrt{36}\implies c=6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{17}}}{\underset{hypotenuse}{6}}~\hfill[/tex]