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Elina [12.6K]
3 years ago
7

Miguel wants to buy a new stereo that costs $320. He has $40 in March, $80 in April, and $120 in May. If this pattern continues,

in what month will he be able to buy the stereo
a.September
b.October
c.November
d.December
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
8 0
March, April, and May correspond to 3,4, and 5th months.  Each month the amount of money he saves increases by $40, so this is a constant rate of change, or constant velocity, which means that this is a linear equation.  Let y=the amount of money he has and x=the month number and model it with the line of form y=mx+b, where m=slope, or rate, and b=y-intercept...

y=40x+b, we know that he has $40 on the third month (February) so:

40=40(3)+b

40=120+b

-80=b so the equation is:

y=40x-80  (note that the domain is x=[3, +oo) only for the function to have meaining)

Now you want to know when he has $320...

320=40x-80  

400=40x

10=x

So he will have $320 on the 10th month, which is October.
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3 years ago
Rectangle STUV has square PQRS removed, leaving an area of 92 m^2. Side PT is 4 m in length and side RV is 8m in length
Andrei [34K]

Answer:

117 m^{2}

Step-by-step explanation:

First think of the square that was removed.  All 4 sides are equal but you don't know the length so lets gives them the variable X.

So to find the area of the rectangle, insert those variables into the area equation for a rectangle.

(RV + (X) ) (PT +(X)) = rectangle area

Now you are given what the area is if you remove the square.  So subtract the the square's area from the equation above and set it equal to the size they told you.

(RV + (X)) (PT + (X))  - [(X)(X)] = 92m^{2}

      rectangle          -  square  =  remaining area

Now plug in the numbers you know and solve for X.

(8 + X) (4 + X) - ((X)(X)) = 92    

Use FOIL to multiply the first part of the equation (first, outer, inner, last)

32 + 8x + 4x + x^{2} -  x^{2}  =  92

32 + 12x = 92

12x = 60

x = 5

So now you know the size of the square.  Each side is 5m.  So add 5m onto the top of the rectangle and onto the side.  The top is 13m and the side is 9m.  The area of the rectangle is the length times the height to 13 x 9 which is 117 m^{2}

6 0
2 years ago
WHAT IS THE MEASURE OF ANGLE F?
MArishka [77]

Answer:

Hello! answer: 25

Step-by-step explanation:

x = 56 because... 56 - 31 = 25 56 + 43 = 99 and x = 56 so 56 + 25 + 99 = 180 Hope that helps!

5 0
3 years ago
Jayden is running laps at track practice. The track is 25 kilometers around. Jayden runs 1 lap in 2 minutes. How many minutes do
givi [52]

Answer:

0.08 minutes for a kilometer.

Step-by-step explanation:

If the track is 25 kilometers, and he runs 25 kilometers in 2 minutes, he runs a kilometer in 2÷25 minutes or 0.08 minutes which is 4.8 seconds.

I'm pretty sure the track isn't 25 kilometer or he can't run a lap in 2 minutes. But if so, the answer is 0.08 minutes.

8 0
3 years ago
To prove that δdef ≅ δdgf by sas, what additional information is needed? ∠def ≅ ∠ dgf ∠dfe ≅ ∠ dfg de ≅ dg dg ≅ gf.
snow_lady [41]

Reflection:

Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG.

Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.

The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.

So According to the above statement,

GF ≅ FE (: given)

DF is the common side to triangles DEF and DFG.

DFG is the included side.

Thus ∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)

Learn more about Reflection on:

brainly.com/question/26494295

#SPJ4

5 0
2 years ago
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