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Masja [62]
3 years ago
9

Translate the following problem into an equation: (1) together Jon and Amy spent $29 dollars on a birthday gift. (2) Jon spent $

5 more than Amy . : How much did each spend ? Explain
Mathematics
1 answer:
kolbaska11 [484]3 years ago
4 0
Let the money spent by John = y
and Amy=x

ATQ

x+y = $29

It is given that jon spend 5 more than Amy. SO he spend

x +5

x+y = $29
x+x+5=$29

2x = 29-5

2x= 24

x = 24/2 =12

So Amy spend $ 12 and Jon spend x+5 = 12+5 = $17
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Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )
Zina [86]

Answer:

\purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

Step-by-step explanation:

\cos( \alpha ) =  \frac{ \sqrt{6} }{6}  =  \frac{1}{ \sqrt{6} }  \\  \\  \therefore \:  \sin( \alpha )  =  \sqrt{1 -  { \cos}^{2} ( \alpha ) }  \\  \\  =  \sqrt{1 -  \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} }  \\  \\ =  \sqrt{1 -  {\frac{1}{ {6} }}}  \\  \\ =  \sqrt{ {\frac{6 - 1}{ {6} }}}   \\  \\  \red{\sin( \alpha ) =  \sqrt{ { \frac{5}{ {6} }}} } \\  \\  \tan( \alpha ) =  \frac{\sin( \alpha ) }{\cos( \alpha ) }  =  \sqrt{5}  \\  \\ \sin( \beta )  =  \frac{ \sqrt{2} }{4}  \\  \\  \implies \: \cos( \beta )  =   \sqrt{ \frac{7}{8} }  \\  \\ \tan( \beta )  =  \frac{\sin( \beta ) }{\cos( \beta ) } =  \frac{1}{ \sqrt{7} }   \\  \\  \tan( \alpha  -  \beta ) =  \frac{ \tan \alpha  -  \tan \beta }{1 +  \tan \alpha .  \tan \beta}  \\  \\  =  \frac{ \sqrt{5} -  \frac{1}{ \sqrt{7} }  }{1 +  \sqrt{5} . \frac{1}{ \sqrt{7} } }  \\  \\  =  \frac{ \sqrt{35} - 1 }{ \sqrt{7}  +  \sqrt{5} }  \\  \\  \purple{ \bold{ \tan( \alpha  -  \beta ) = 1.00701798}}

8 0
3 years ago
HELP!! let f be defined as shown. what is f^-1(-3)?
Assoli18 [71]

Answer:

F is the base or variable.

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Step-by-step explanation:

3 0
2 years ago
What is 8.6x+2.2(2x-5)=54
Alex787 [66]
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4 0
3 years ago
3. 'a' and 'b' are the intercepts made
Julli [10]

Given:

'a' and 'b' are the intercepts made  by a straight-line with the co- ordinate axes.

3a = b and the line  pass through the point (1, 3).

To find:

The equation of the line.

Solution:

The intercept form of a line is

\dfrac{x}{a}+\dfrac{y}{b}=1         ...(i)

where, a is x-intercept and b is y-intercept.

We have, 3a=b.

\dfrac{x}{a}+\dfrac{y}{3a}=1           ...(ii)

The line  pass through the point (1, 3). So, putting x=1 and y=3, we get

\dfrac{1}{a}+\dfrac{3}{3a}=1

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Multiply both sides by a.

2=a

The value of a is 2. So, x-intercept is 2.

Putting a=2 in b=3a, we get

b=3(2)

b=6

The value of b is 6. So, y-intercept is 6.

Putting a=2 and b=6 in (i), we get

\dfrac{x}{2}+\dfrac{y}{6}=1

Therefore, the equation of the required line in intercept form is \dfrac{x}{2}+\dfrac{y}{6}=1.

5 0
3 years ago
30. What is the solution to the system of equations?
sukhopar [10]

Answer:

x = 3

y = 0

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Step-by-step explanation:

a) 3x + 3y - z = 1

b) z = 8

c) -x -3y + 2z = 13

a) 3x + 3y - 8 = 1 (substitution)

a) 3x + 3y = 9

c) - x - 3y + 2(8) = 13 (substitution)

c) -x - 3y + 16 = 13

c) -x - 3y = -3

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= 2x = 6

x = 3

a) 3(3) + 3y - 8 = 1

9 + 3y - 8 = 1

y = (1 -9 + 8)/3

y = 0

5 0
3 years ago
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