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4 years ago

Evaluate each expression if a=2,6=-3,c=-1, and d=4. 2d-a ———- b

Mathematics

1 answer:

Volgvan4 years ago

4 0

2(4)-(2) / -3 = -2
2•4 is 8 - 2 is 6, 6 divided by -3 is -2.

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Find <img src="https://tex.z-dn.net/?f=a_%7B1%7D" id="TexFormula1" title="a_{1}" alt="a_{1}" align="absmiddle" class="latex-form

yKpoI14uk [10]

Answer:

$\displaystyle a_{1} = 108$

Step-by-step explanation:

we are given

the sum,common difference and nth term of a geometric sequence

we want to figure out the first term

recall geometric sequence

$\displaystyle S_{ \text{n}} = \frac{ a_{1}(1 - {r}^{n} )}{1 - r}$

we are given that

$S_n=189$
$r=\dfrac{1}{2}$
$n=3$

thus substitute:

$\displaystyle 189= \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{1 - \frac{1}{2} }$

to figure out $a_1$ we need to figure out the equation

simplify denominator:

$\displaystyle \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2} } = 189$

simplify square:

$\displaystyle \frac{ a_{1}(1 - {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2} } = 189$

simplify substraction:

$\displaystyle \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2} } = 189$

simplify complex fraction:

$\displaystyle a_{1} (\frac{7}{8} ) \div { \frac{1}{2} } = 189$

calculate reciprocal:

$\displaystyle a_{1} \frac{7}{8} \times 2 = 189$

reduce fraction:

$\displaystyle a_{1} \frac{7}{4} \ = 189$

multiply both sides by 4/7:

$\displaystyle a_{1} \frac{7}{4} \times \frac{4}{7} \ = 189 \times \frac{4}{7}$

reduce fraction:

$\displaystyle a_{1} = 27\times 4$

simplify multiplication:

$\displaystyle a_{1} = 108$

hence,

$\displaystyle a_{1} = 108$

4 0

3 years ago

The fifth graders at Westwood elementary are planning a barbecue to raise money for a local charity. The principal will donate $

erma4kov [3.2K]

The principal will donate 1.50 for every dollar the fifth graders raise

6 0

3 years ago

Read 2 more answers

X^2-3x=0 zero product property

stellarik [79]

Answer:

x1 = 0

x2 = 3

Step-by-step explanation:

${x}^{2} - 3x = 0$

If that's the right equation we can now just simplify it a bit.

$x \times x - 3 \times x = 0$

Cause now it becomes obvious that we can break out x and make it into a parenthesis:

$x(x - 3) = 0$

And now there's two possibilities for what x could be. Either, x is 0:

$0(0 - 3) = 0$

Or, the parenthesis is 0, which means that x is 3 (because 3-3=0) :

$x(3 - 3) = 0$

So x has two answers:

x1 = 0

x2 = 3

At least I hope this was what you were looking for

3 0

3 years ago

Given that a minute hand travels through 360°in an hour, how many degrees does it turn in only 23 minutes?

8_murik_8 [283]

let's recall that a circle has a total of 360°, so a circular clock has 60 minutes, and if we divide those 360° into 60 even intervals, that'd be 360/60 or 6° per minute.

so since 1 minute is 6°, then 23 minutes is just 23 * 6 degrees.

8 0

3 years ago

Read 2 more answers

What is 765903 rounded to the nearest thousand

Dominik [7]

765,000 should be the correct answer

3 0

4 years ago

Read 2 more answers