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3 years ago

6

PLEASE HELP MATH QUESTION

1 answer:

Sholpan [36]3 years ago

8 0

Answer:

c is the answer

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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

PLEASE help me !!!! i dont know the exponent

Serggg [28]

Answer:

$24\sqrt[3]{x^{7}}$

Step-by-step explanation:

The exponent rule that applies to products like this is ...

... (a^b)(a^c) = a^(b+c)

In your problem, this is

... x^(1/3)·x^2 = x^(1/3 +2) = x^(1/3 +6/3) = x^(7/3)

This fractional exponent translates to the root of a power:

... = (x^7)^(1/3)

In typeset form, it is ...

$\sqrt[3]{x^{7}}$

You have already figured correctly that the coefficient is 3·8 = 24.

8 0

3 years ago

How can I find slope

Llana [10]

To find the slope of a line, you first chooses 2 points with known coordinates that belongs to the line. Let those points be A(x1,y1) and B(x2,y2) with x2>x1. You then divide the subtraction of their Ys as y2-y1 by the subtractions of their Xs as x2-x1 (the point with the higher x comes first, this is why x2>x1). And let the slope be m. m= (y2-y1) / (x2-x1). If the slope is positive, the line croissant and y2>y1. If the slope is negative, the line is decroissant and y1>y2. Hope this helps! :)

5 0

3 years ago

Solve and simplify to simplest form: 1 3/8 −(−7/8)

nydimaria [60]

Answer:5/4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In the system below, what is the sum of the x-coordinates of all solutions?

Ainat [17]

Answer:

The sum of the x-coordinates of all solutions is -2

Step-by-step explanation:

We are given system of equations as

$7x^2+3y^2=187$

$3y^2-7x=47$

Firstly, we will isolate x

$7x=3y^2-47$

$x=\frac{3y^2-47}{7}$

now, we can plug back in first equation

$7(\frac{3y^2-47}{7})^2+3y^2=187$

now, we can solve for y

$\frac{9y^4}{7}-\frac{261y^2}{7}+\frac{2209}{7}=187$

$\frac{9y^4}{7}-\frac{261y^2}{7}+\frac{2209}{7}-187=0$

$(y^2-25)(y^2-4)=0$

$y=-5,y=5,y=-2,y=2$

now, we can find x-values

At y=-5:

$x=\frac{3(-5)^2-47}{7}$

$x=4$

At y=5:

$x=\frac{3(5)^2-47}{7}$

$x=4$

At y=-2:

$x=\frac{3(-2)^2-47}{7}$

$x=-5$

At y=2:

$x=\frac{3(2)^2-47}{7}$

$x=-5$

now, we can add all x-coordinate solution values

$=4+4-5-5$

$=-2$

So,

the sum of the x-coordinates of all solutions is -2

4 0

3 years ago