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2 years ago

The speed of light in a vacuum is 29,980,000,000

Mathematics

2 answers:

Flura [38]2 years ago

6 0

Answer:

B. 2.998 x 10¹⁰

Step-by-step explanation:

Given :

29,980,000,000

Steps in solving :

Take the zeros after the last non-zero digit as a power of 10.
Take the non-zero part (in the part) and put a decimal point after between the thousands and hundreds place, and shift the remaining powers of 10 to the previously grouped part.
Adjust further if needed to match an answer.

Solving :

29,980,000,000
2,998 x 10⁷
2.998 x 10³ x 10⁷
2.998 x 10¹⁰

sweet [91]2 years ago

4 0

Answer:

$\huge\boxed{\sf 2.998 \times 10^{10}}$

Step-by-step explanation:

Given number:

29,980,000,000

Rules:

Move the decimal point after the first non-zero digit. (after 2)
Here, we will move the decimal point 10 places to the left to move it after the first non-zero digit.
Since we move the decimal point 10 places, we will write the number as a multiple of 10¹⁰ (10 being the exponent).

The number will become:

2.998 × 10¹⁰

$\rule[225]{225}{2}$

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15. Sensei's Judo Club has a competition for

marta [7]

Answer:

6 grapples

Step-by-step explanation:

x = number of wins

y = number of ties

y = 15 - x

48 = 5x + 2y

48 = 5x + 2(15 - x)

48 = 5x + 30 - 2x

48 = 3x + 30

18 = 3x

x = 6

3 0

3 years ago

Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

The sum of two numbers is 62 the smaller number is 6 less than the larer number what are the numbers

muminat

X= larger number
x-6= smaller number

x + (x - 6)= 62
combine like terms

2x - 6= 62
add 6 to both sides

2x= 68
divide both sides by 2

x= 34 larger number

SMALLER NUMBER
x - 6= 34 - 6= 28

ANSWER: The smaller number is 28 and the larger number is 34.

Hope this helps! :)

5 0

3 years ago

Can anyone help me ? I just need the numbers

Nimfa-mama [501]

Answer:

(-6, 0) and (0, 1.5)

Step-by-step explanation:

The equation of the line in pint slope form is expressed as;

y-y0= m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given

m = 1/4

(x0, y0) = (6,3)

Substitute into the formula;

y - 3 = 1/4(x-6)

4(y-3) = x - 6

4y - 12 = x-6

4y - x = -6+12

4y - x = 6

x = 4y - 6

To get the points to plot, we will find the x and y-intercept of the resulting expression.

For the x-intercept,

at y = 0

x = 4(0) - 6

x = -6

Hence the x-intercept is at (-6, 0)

For the y-intercept,

at x = 0

0 = 4y - 6

4y = 6

y = 6/4

y = 3/2

y = 1.5

Hence the y-intercept is at (0, 1.5)

Hence the required points to plot to get the required line are (-6, 0) and (0, 1.5)

7 0

3 years ago

Pedro said, "On summer vacation, I spent 3 1/2 weeks with my uncle and two weeks more with my friend than with my uncle." How ma

ladessa [460]

Answer:

Pedro spent 9 weeks with his uncle and his friend.

Step-by-step explanation:

First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:

$3\frac{1}{2}$ 2