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3 years ago

If a person ran 32 kilometers at a rate of 8 kilometers/hr, how long did he run?

Mathematics

2 answers:

Alchen [17]3 years ago

8 0

Answer:

u use speed triangle so 32/8=4

so he travelled 4 hours

MARK AS BRAINLIEST

Andrews [41]3 years ago

5 0

Answer:

4 hours

Step-by-step explanation:

1hr=8 kilometers

2=16 kilometers

3=24 kilometers

4=32 kilometers

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Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 3

maxonik [38]

Answer:

$\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}$

Step-by-step explanation:

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}$

$a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}$

$b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22$

6 0

3 years ago

Skippy has a total of $10,000 to split between two investments. One account offers 4% simple interest, and the other account off

ki77a [65]

Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest

<em><u>Solution:</u></em>

Given that Skippy has a total of $10,000 to split between two investments

One account offers 4% simple interest, and the other account offers 8% simple interest

Total interest earned = 500

Number of years = 1

Let the principal with rate of interest 4 % is x

So the principal for rate of interest 8 % is 10000 - x

Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest

Simple interest is given as:

$S.I = \frac{pnr}{100}$

Where "p" is the principal and "r" is the rate of interest and "n" is the number of years

Therefore,

$\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}$

$500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500$

Therefore skippy should invest $ 7500 in account offering 4 % interest

And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest

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3 years ago

A team from the high school went on a science-and-math quiz show. The science questions were worth 1 point and the math question

Troyanec [42]

Answer:

5 math and 3 Science

Step-by-step explanation:

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3 years ago

Pleaseeee answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!

djverab [1.8K]

It’s 132 have a nice day

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