Solve the equation 8y + 4x=5 for y. Oy=32x + 40 0 y = 40

While doing back to school shopping on tax-free weekend, Mrs. Michaels bought 2 packs of mechanical pencils and 3 binders for a

IRISSAK [1]

Answer:

$3.00

Step-by-step explanation:

Let p = the cost of a pack of pencils

and b = the cost of a binder

Then we have two simultaneous equations.

(1) 2p + 3b = 21.00

(2) 5p + 2b = 25.00

1. Multiply each equation by numbers to give one of the variables the same coefficient.

Multiply (1) by 2 and (2) by 3.This gives

(3) 4p + 6b = 42.00

(4) 15p + 6b = 75.00

2. Subtract (3) from (4)

This gives

(5) 11p = 33.00

3. Solve equation (5) for p

Divide each side by 11

p = 3.00

Each pack of pencils costs $3.00.

4 0

3 years ago

Starting with 195 grams of a radioactive isotope, how much will be left after 3 half-lives?

MrMuchimi

After one half-life: $\frac{1}{2}\times 195=97.5$ grams.

After two half-lives: $\frac{1}{2} \times 97.5=48.75$ grams.

After three half-lives: $\frac{1}{2} \times 48.75=24.375$ grams.

4 0

3 years ago

Complete the point-slope equation of the line through (3,6)(3,6) (3,6) left parenthesis, 3, comma, 6, right parenthesis and (5,−

Elanso [62]

Answer:

y = -7x + 27 is the point slope equation that passes through the two points

Step-by-step explanation:

Here, we want to write the equation of the line between (3,6) and (5,-8)

Mathematically, the equation of the line that passes through both points can be represented by ;

y = mx + c

where m is the slope and c is the y-intercept

Let’s find the slope m first;

Mathematically;

slope m = y2-y1/x2-x1

where (x1,y1) = (3,6) and (x2,y2) = (5,-8)

Substitute these values in the slope equation , we have the following;

m = (-8-6)/(5-3) = -14/2 = -7

So the equation becomes;

y = -7x + c

we still need the value of c

To get this, we can substitute any of the points in the equation, where x is the x coordinate of the point and y is the coordinate of the point.

Let’s use (3,6)

Thus we have;

6 = -7(3) + c

c = 6 + 21

c = 27

So the equation becomes;

y = -7x + 27

3 0

3 years ago

What is likely to have a mass of 1 gram

Gre4nikov [31]

Answer:

paperclip, thumbtack, or safety pin.

Step-by-step explanation:

I measured some.

4 0

3 years ago

Read 2 more answers

Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

..............................................................................................................................

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

..............................................................................................................................

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

................................................................................................................................

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

................................................................................................................................

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

................................................................................................................................

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

................................................................................................................................

Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

Solve the equation 8y + 4x=5 for y. Oy=32x + 40 0 y = 40 – 32x o y= J +3 5. o y=​

Solve the equation 8y + 4x=5 for y. Oy=32x + 40 0 y = 40 – 32x o y= J +3 5. o y=