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2 years ago

Which graph best represents -5y = -6x + 15

Mathematics

1 answer:

frutty [35]2 years ago

3 0

Answer: Option c.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the equation:

$-5y = -6x + 15$

Solve for "y" in order to write in Slope-Intercept form:

$y = \frac{-6}{-5}x + \frac{15}{-5}\\\\y = \frac{6}{5}x -3$

Now you can identify that that the slope and the y-intercept are:

$m=\frac{6}{5}\\\\b=-3$

A posive slope means that the the line moves upward from left to right.

With this information, you can conclude that the the graph that best represents the given equation is the graph shown in the Option c.

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In a certain month, Oscar sells 6 cars more than Jackie. If together they sell 30 cars, how many cars did Jackie sell?

diamong [38]

Answer:

Jackie sold 12 cars.

Step-by-step explanation:

If we call the number of cars Oscar sold O, and the number of cars Jackie sold J, we can say the following:

O = J + 6

As Oscar sold 6 cars more than Jackie.

Together, they sold 30 cars.

O + J = 30

Since we know that:

O = J + 6

... we can put this into our previous equation.

O + J = 30

(J + 6) + J = 30

J + J + 6 = 30

2 * J + 6 = 30

Subtract 6 from both sides:

2 * J = 24

Divide both sides by 2:

J = 24 / 2

J = 12

Jackie sold 12 cars.

8 0

2 years ago

Read 2 more answers

Quadrilateral QRST is similar to quadrilateral EDGF. What's the scale factor from EDGF to QRST

mart [117]

Answer:

C. $\frac{6}{5}$

Step-by-step explanation:

The ratio of the corresponding sides of a polygon is said to be equal. The ratio gives us the scale factor.

Therefore, assuming that quadrilateral QRST was the original polygon that was scaled up to give a similar polygon, EDGF, the scale factor would be expressed as $\frac{42}{35}$

The scale factor = $\frac{42}{35} = \frac{6*7}{5*7} = \frac{6}{5}$

5 0

2 years ago

22.Lenin is preparing dinner plates. He has 12 pieces of chicken and 16 rolls. If he wants to make all the plates identicalwitho

Nitella [24]

Answer: The greatest number of plates Lenin can prepare = 4

and there will be 3 chickens and 4 rolls in each plate.

Step-by-step explanation:

Given: Lenin is preparing dinner plates. He has 12 pieces of chicken and 16 rolls.

To make all the plates identical without any food left over, the greatest number of plates Lenin can prepare = G.C.D.(12,16)=4

The number of pieces of chicken in each plate = $\dfrac{12}{4}=3$

The number of pieces of rolls in each plate = $\dfrac{16}{4}=4$

So, the greatest number of plates Lenin can prepare = 4

and there will be 3 chickens and 4 rolls in each plate.

7 0

2 years ago

Imaginá que tenés 125 dados cúbicos del mismo tamaño ¿Cuantos dados de altura tiene el cubo de mayor tamaño que podés armar apil

kumpel [21]

Answer:

(i) Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

Step-by-step explanation:

(i) Sabemos por la Geometría Euclídea del Espacio que un cubo es un sólido regular con 6 caras cuadradas y longitudes iguales. Cada dado tiene un volumen de 1 dado cúbico y 125 dados dan un volumen total de 125 dados cúbicos.

El volumen de un cubo está dado por la siguiente fórmula:

$V = L^{3}$

Donde:

$L$ - Longitud de la arista, medida en dados.

$V$ - Volumen del cubo, medido en dados cúbicos.

Ahora, necesitamos despejar la longitud de la arista para calcular la altura máxima posible:

$L = \sqrt[3]{V}$

Dado que $V = 125\,dados^{3}$ , encontramos que la altura del cubo de mayor tamaño sería:

$L =\sqrt[3]{125\,dados^{3}}$

$L = 5\,dados$

Debemos apilar 5 dados para construir el cubo de mayor tamaño.

(ii) El área cuadrada formada por cubos está determinada por la siguiente fórmula:

$A = L^{2}$

Donde:

$L$ - Longitud de arista, medida en dados.

$A$ - Área, medida en dados cuadrados.

Puesto que la longitud de arista se basa en un conjunto discreto, esto es, el número de dados disponibles, debemos encontrar el valor máximo de $L$ tal que no supere 125 y de un área entera. Es decir:

$L \leq 125\,dados$

Si cada cubo tiene un área de 1 dado cuadrado, entonces un cuadrado conformado por 125 dados tiene un área total de 125 dados cuadrados. Entonces:

$L^{2}< 125\,dados^{2}$

Esto nos lleva a decir que:

$L < 11.180\,dados$

Entonces, la longitud máxima del cuadrado con la mayor cantidad de cubos posible es de 11 dados. El número total requerido de cubos es el cuadrado de esa cifra, es decir:

$n = (11\,dados)^{2}$

$n = 121\,dados$

Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.

4 0

2 years ago

1. There are 125 juniors at the high school.How many ways can they elect a

valentinak56 [21]

Answer: 1. 1,906,500

2. 840

Step-by-step explanation:

1. Given: There are 125 juniors at the high school.

Total positions = 3 [president,vice president, and secretary]

Then, Number of ways to elect a president,vice president, and secretary( which is in order) out of 125 juniors = $^{125}P_{3}=\dfrac{125!}{(125-3)!}$ [Using permutations]

$=\dfrac{125!}{122!}\\\\=\dfrac{125\times124\times123\times122!!}{122!}\\\\=125\times124\times123\\\\=1906500$

Hence, Required ways =1906500

(2) Given word : "RHOMBUS"

Total letters= 7

By permutation, the umber of 4-letter arrangements = $^7P_4=\dfrac{7!}{(7-4)!}=\dfrac{7!}{3!}$

$=\dfrac{7\times6\times5\times4\times3!}{3!}\\\\= 7\times6\times5\times4\\\\=840$

Hence, required ways = 840

7 0

2 years ago