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8_murik_8 [283]
2 years ago
13

Ingrid spends $120 on car repairs. Which integer represents the amount of money Ingrid must earn in order to create a zero pair?

Mathematics
2 answers:
Julli [10]2 years ago
8 0

Answer: -120

Step-by-step explanation:

this would be the answer because if you take a positive and add it to a negative you get zero if their the additive inverse of the number.

valentina_108 [34]2 years ago
4 0

Answer:

C. 120

Step-by-step explanation:

Zero pair is a pair of numbers whose sum is zero, e.g. +5, -5. Assigning a negative value to expenditures, Ingrid spent money represents $-120. From the definition, it is deduced that $120 make the zero pair in this case. So, she must earn $120.

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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9
Naddika [18.5K]

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

y=A\sin[\omega(x-\alpha)]+C

where, A =  amplitude; \omega=\dfrac{2\pi}{period} ,  α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= C=\dfrac{73+97}{2}=85   [midline is average of upper and lower limit.]

A=  97-85 = 12

Phase shift: \alpha=10

Period = 24 hours;

\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}

Substitute all values in sinusoidal function, we get

y=12\sin[\dfrac{\pi}{12}(x-10)]+85

Put y= 82, we get

82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03

Hence, After about 9.03 hours the temperature first reach 82 degrees.

3 0
3 years ago
(Giving Branliest)
REY [17]

Answer:

106.68 cm

Step-by-step explanation:

Change ft to inches

3.5 ft * 12 inches / 1 ft = 42 inches

Change inches to cm

42 inches * 2.54 cm/ inch =106.68 cm

8 0
3 years ago
Read 2 more answers
Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative? A coordina
IrinaK [193]

Answer:

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

Step-by-step explanation:

Ax + By = C, where A = 0, B is positive, and C is negative

By= C or y= C/B which is negative

Since A is zero and C is negative, the line is parallel to x- axis and has negative value for y, so it is a horizontal line below zero

---------------

A coordinate plane with a vertical line passing through (1, negative 4), (1, 0) and (1, 4).

  • no, the line is horizontal

A coordinate plane with a vertical line passing through (negative 2, negative 4), (negative 2, 0) and (negative 2, 4).

  • no, the line is horizontal

A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (negative 4, 4).

  • no, the y-values should be negative

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

  • yes, this is horizontal line below zero
8 0
3 years ago
Read 2 more answers
You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0
3 years ago
HELP ASAP GIVING BRANLIST 100 POINTS!!
musickatia [10]

Rate of change = difference in y over difference in x.

Rate of change = (33-20)/(3-1) = 13/2

Rate of change = (48-33) /(5-3) = 15/2

The rates are not the same so it isn’t linear.

The rate of change for x=3 and x = 5 is greater.

6 0
3 years ago
Read 2 more answers
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