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Solve System of Equations from Context
Sep 21, 5:21:12 AM
Gavin works as a salesperson at an electronics store and sells phones and phone accessories. Gavin earns a $12 commission for every phone he sells and a $3.50 commission for every accessory he sells. On a given day, Gavin made a total of $135 in commission and sold 12 more accessories than phones.
Determine the number of phones sold and the number of accessories sold.

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

27

900 jadi 3 -30 =27 100-1.000 =900

Answer:

100

Step-by-step explanation:

trust me

The largest place value of the numeric part of this quantity is 10 million.

Our entire number system is built around place value. This is the system in which the value of a number is determined by the position of its digits. The numbers 42,316 and 61,432 differ because the digits are in different positions.

Every digit in a number has a place value in mathematics. Place value is the value represented by a digit in a number based on its position in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. The place value of 7 in 7,432 is, however, 7 thousands or 7,000.

In the number, 12,345,000, the highest place value is 1 and it denotes 10 million.

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Answer:

0.23333333...

Step-by-step explanation:

X+2/3 = 9/10. X = 9/10 - 2/3 = 27/30 - 20/30 = 7/30 = 0.2333333...

Answer:

wow that's a lot lol

Step-by-step explanation:

i needthe points i'm ssrry

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

<95141404393>

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

Yes, 20:25 and 12:15 are in proportion.

Step-by-step explanation:

Since 20:25 can also be written as 4:5 (Multiples of 5).

And 12:15 can also be written as 4:5 (Multiples of 3).

Answer:

0.60

Step-by-step explanation:

3/5 is equal to 6/10 which as a decimal would be 0.60 or 0.6

The answer is 0.6

I hope I helped. Sorry, I did this quickly.

The area should be 47.5 CM.

Answer:

Step-by-step explanation:

The figure you see here is a trapezoid.

Area = \(\frac{(a + b)h}{2}\) = \(\frac{(6 + 13)(5)}{2}\) = \(\frac{(19)(5)}{2}\) = \(\frac{95}{2}\) = 47.5 cm

Answer:

40

Step-by-step explanation:

"The minimum number of hours is the distribution was 23."

So the lowest number of hours per week is 23

"The range was 17."

So from 23 we add 17 more hours to get the full range.

23 + 17 = 40

The maximum number of hours in the distribution is 40.

Answer:

The answer is option

3 and 4

Answer:

180 degrees, 120 degrees, 90 degrees

Step-by-step explanation:

each hour is 30 degrees.

at 6 o'clock the hands are straight, at 4 o'clock they make a 120 degree angle, and at 3 o'clock they make a right angle

Answer:

y= 4x-3

Step-by-step explanation:

y=mx+b

the 4 is your slope so you input it in place of the m, which basically tells you the pattern in witch the line goes. For this one it tells you to go right one and up 4 to get to each point: rise/run = 4/1

The -3 is your y-intercept aka b in the equation above. this tells you where the line will intercept the y-axis. in this case it would be (0,-3).

a helpful tip for doing the slope and plotting your points, first try to locate the intercept and do your rise and run from there.

Ex:

 y-inter : (0,-3)     rise/run : 4/1

(0+1, -3+4)  = (1,1)

(1+1,1+4) = (2, 5)

and so on you can also do it the opposite way to get the rest of your points

(0,-3)

(0-1,-3-4)=(-1,-7)

(-1-1,-7-4)=(-2, -11)

and so on.

Answer:

891.46

Step-by-step explanation:

"Nearest hundreth" refers to the second decimal place. You can remember this by knowing that 100 has two zeroes and a decimal place in the nearest hundredth has two numbers after the decimal.

We know that the answer is 891.46 because original decimal was .456. 6 is greater than 4, so it can be rounded to 10. The 1 is brought to the 5, making it 6. The 0 is not written. 0 is never included at the end of a decimal place.

Let t = time traveled at 51 mph

The total time is given as 3.5 hours

So (3.5- t )= time traveled at 62 mph

We are going to use the distance formula:

distance = speed* time

51t + 62(3.5-t) = 200.5

51t + 62*3.5 - 62*t = 200.5

51t + 217 - 62t = 200.5

Solve the equal terms

51t - 62t = 200.5 - 217

-11t = -16.5

t = -16.5/-11

t = 1.5

Then he took 1.5 at 51mph

and (3.5- t ) = (3.5-1.5) = 2h at 62 mph

To confirm these results, find the actual speed of each speed:

speed* time = distance

51*1.5 = 76.5miles

62*2. = 124 miles

76.5miles + 124 miles = 200.5miles

Answer:

Step-by-step explanation:

x² - 3x - 1 = 0

a = 1, b = -3, c = -1

x₁ = (3 + sqrt(-3² - 4(1(-1))))/(2(1))

x₁ = (3 + sqrt(9 + 4))/2

x₁ = (3 + sqrt(13))/2

x₁ = 3.302...

x₂ = (3 - sqrt(-3² - 4(1(-1))))/(2(1))

x₂ = (3 - sqrt(9 + 4))/2

x₂ = (3 - sqrt(13))/2

x₂ = -0.302...

Answer:

Step-by-step explanation:

Given the function y = e^x between the interval x = -2 and x =1, the average rate of change for the function will be the slope of the function expressed as m = Δy/Δx where;

Δy = f(b)-f(a) and Δx = b-a

m =  f(b)-f(a)/b-a where a and b is the interval [-2, 1]

m =  f(1)-f(-2)/1-(-2)

m = f(1)-f(-2)/3

Given the function f(x) = e^x,

at the end point x = b, f(1) = e^1; f(1) = e

at the end point x = a, f(-2) = e^-2; f(-2) = 1/e²

m = (e - 1/e²)/3

m = [(e³ - 1)/e²]/3

m = (e³ - 1)/e² * 1/3

m = (e³ - 1)/3e²

Hence, the average rate of change for the function at the interval [-2, 1] is  (e³ - 1)/3e²

Answer:

79

Step-by-step explanation:

So we have the function:

\(g(t)=t^2-2\)

To find g(9), substitute 9 for t. Thus:

\(g(9)=9^2-2\)

Square:

\(g(9)=81-2\)

Subtract:

\(g(9)=79\)

So, our answer is 79.

And we're done!

Step-by-step explanation:

For some side x, we are given two angles so let use law of sines

We don't know the angle opposite of the x side so we using the triangle interior property

\(120 + 51 + x = 180\)

\(x = 9\)

So the missing angle is 9.

The law of sines formula is that

\( \frac{a}{ \sin( \alpha ) } = \frac{b}{ \sin( \beta ) } \)

where a and b are side lengths.

And alpha, and Beta are angles that are OPPOSITE of the side lengths, a and b, respectively

Let a be 25,

therefore alpha is 120

Let b be x,

therefore beta is 9.

\( \frac{25}{ \sin(120) } = \frac{x}{ \sin(9) } \)

Solving for x.

\(25 \times \frac{ \sin(9) }{ \sin(120) } = x\)

\(x = 4.51587\)

Round if needed so our answer is

\(x = 4.5\)

Answer: 80%. Hope this helps, please consider making me Brainliest.

Step-by-step explanation:

To find the percentage, divide the sale cost by the original cost:

27.60/34.50

Let's multiply both sides by 10 to make the operation easier:

27.6/34.5 ( I eliminated the zero's because they kind of have no use) -->

276/345, now solve:

276/345 = 0.8

0.8 = 80%

The percentage is 80%.

Answer: (9,1)

Step-by-step explanation: This is because x (7) moves left and right, and y (0) moves up and down. the formula would be (x, y) --->(x+2, y+1)

Answer:

$0.01

Step-by-step explanation:

Convert gallons to ounces:

0.03125 Gallons of milk per serving

0.03125/2.48=0.0126008

Simplify:

0.01.

One portion costs 1 cent.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is:

5y^10

_____

7x^4

If this isnt the simplified version, you want im sorry

Answer:

\(\frac{5y^{10} }{7x^{4} }\)

Step-by-step explanation:

\(\frac{30x^{3}y^{2} }{42x^{7} y^{-8} }\)  to make \(y^{-8}\) positive we need to put it in the numerator (top)

\(\frac{30x^{3}y^{2}y^{8} }{42x^{7} }\)  Now I am going to write it in expanded form

\(\frac{2x3x5xxxyyyyyyyyyyyy}{2x3x7xxxxxxx}\)  If we cross out what we have on the bottom and the top, we will be left with our answer simplified.

\(\frac{5y^{10} }{7x^{4} }\)

The value of the determinants are

D=13

Dx =26

Dy =52

Dz =26

The determinant of a matrix is ​​a scalar value calculated for a given square matrix. Linear algebra deals with the determinant, it is calculated using the elements of a square matrix. It can be thought of as a scaling factor for the matrix transformation. Useful for solving a system of linear equations, calculating the inverse of a matrix, and numerical operations.

Given system is

x+ y-z= 4

3x+4y-3z=16

9x- 3y+4z=14

from the system the determinants become,

D=  1   1  -1

      3  4  -3

      9   -3  4

D= 1(16-9)-1(12+27)-1(-9-36)

   =7-39+45

   13

Dx=4   1  -1

      16  4  -3

      14   -3  4

   =26

Dy=1  4  -1

      3  16  -3

      9   14  4

   =52

Dz=1  1  4

      3  4  16

      9   -3  14

 =26

Hence, D=13, Dx=26, Dy=52, Dz=26

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Answer:1/3

Step-by-step explanation:

can you give branliest??

Answer: 1/3 Or 0.3333333

Step-by-step explanation:

Answer:

65 boletos.

Step-by-step explanation:

Sabemos que el precio para un niño es 6 dólares, y el precio para un adulto es 9,20 dólares. Además, el cine se vendió 146 boletos, y recibió 1135,20 dólares.

Vamos a resolver este problema con un sistema, usando 2 varibles.
No sabemos cuantos boletos de niño el cine vendió, entonces el cine vendió <<x>> boletos de niños. Tampoco sabemos cuantos boletos de adultos vendió, entonces vendió <<y>> boletos de adultos.

En total, vendió 146 boletos; el número de los boletos de niños con el número de los boletos de adultos es 146 boletos.

Usando las variables, x + y = 146 boletos.

Esta es una de las equaciones que necesitamos.

Porque todos los boletos de niños es 6 dólares, si el cine vendió <<x>> boletos, su total de ventas (de boletos de niños) es <<6x>> dólares.

Lo mismo es verdad para los boletos de adultos; todos los boletos de adultos es 9,20 dólares, entonces si vendió <<y>> boletos, el total de ventas de boletos de adultos es <<9,20y>> dólares.

En total, las ventas de los boletos de niños + las ventas de los boletos de adultos es 1135,20 dólares.

O, con variables, es 6x + 9,20y = 1135,20

Nuestra sistema es:

x + y = 146

6x + 9,20y = 1135,20

Ahora necesitamos resolver esta sistema.

Podemos usar la sustitución. Vamos a resolver una de las eqaciones para una variable, y después, usar el valor de esa variable para encontrar la solución para una de las variables, y después, usar  esa solución para encontrar la solución de la otra variable.

Podemos mover <<y>> al otro lado.

x + y = 146 => x = 146 - y

Ahora, podemos sustituir <<x>> para 146 - y en 6x + 9,20y = 1135,20

6(146-y) + 9,20y = 1135,20

Multiplica.

876 - 6y + 9,20y = 1135,20

Combina los términos que son los mismos.

876 + 3,20y = 1135,20

Mueva 876 al otro lado.

876 + 3,20y = 1135,20 => 3,20y = 259,20

Divide todo por  3,20.

3,20y/ 3,20 = 259,20/ 3,20

y = 81

Entonces, el cine vendió 81 boletos de adultos.

Recuerda, esta (81 boletos de adultos) no es lo que necesitamos. Necesitamos cuantos boletos de niños vendió.

Entonces, podemos substituir <<y>> con 81 en x = 146 - y. Recuerda que <<x>> es cuantos boletos de niños vendió.

x = 146 - y => x = 146 - 81 => 65

Entonces, el cine vendió 65 boletos de niños.

Answer:

Step-by-step explanation:

pls brainlest mee