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2 years ago

9

At the beginning of the month,Kimberly had $65.78. Since then,she has received three payments of $32.50 from her babysitting job

. Kimberly did not spend any money,how much money does she have now?

2 answers:

ivann1987 [24]2 years ago

8 0

Answer:

98.28

Step-by-step explanation:

Alika [10]2 years ago

8 0

The answer is 98.28

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<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

What is the greatest common factor of the terms in the polynomial 4x^4-32x^3-60x^2?

jonny [76]

Answer:

$\mathrm{Factor}\:4x^4-32x^3-60x^2:\quad 4x^2\left(x^2-8x-15\right)\\$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^3=xx^2\\x^4=x^2x^2\\=4x^2x^2-32xx^2-60x^2\\\mathrm{Rewrite\:}60\mathrm{\:as\:}4\cdot \:15\\\mathrm{Rewrite\:}32\mathrm{\:as\:}4\cdot \:8\\=4x^2x^2-4\cdot \:8xx^2-4\cdot \:15x^2\\\mathrm{Factor\:out\:common\:term\:}4x^2\\=4x^2\left(x^2-8x-15\right)$

<em>Hope this helps and have a great day!!!</em>

<em> $Sofia$ </em>

4 0

3 years ago

PilotLPTM [1.2K]

Answer:

450 millilitres

Step-by-step explanation:

1) $\frac{1}{2}$ of the water is gone, so you need to divide 900 by 2 to see how much is left

900÷2 = 450

5 0

3 years ago

9) What 2 numbers have a total of 28 and a difference of 6?<br>

Vedmedyk [2.9K]

Answer:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Step-by-step explanation:

The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:

x + y = 28

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

Now solve equation B for x to get the revised equation B:

x - y = 6

x = 6 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 28

6 + y + y = 28

6 + 2y = 28

2y = 22

y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

x + y = 28

x + 11 = 28

X = 17

Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

8 0

3 years ago

Read 2 more answers

The formula to find the area of a rectangle is: area = length x width.

bezimeni [28]

Answer : E ; 105 square feet

Explanation : 7 x 15 = 105

7 0

3 years ago