Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.

Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”

Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”

Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”

Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”

Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem
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Answer:

7.07 miles/hour W 22° S.

Step-by-step explanation:

Given that the resultant velocity of the runner, [tex]v_r = 8[/tex] miles/hour due west.

Wind speed, [tex]v_w= 3[/tex] miles/hour N 28° W.

Assuming that the absolute velocity of the runner, [tex]v_a= x[/tex] miles/ hour W \alpha S as shown in the figure.

By using vector addition, [tex]\vec{v_r} = \vec {v_w} + \vec {v_a}[/tex] .

Now, from the figure,

[tex]|\vec {v_r}|=|\vec {v_w} |\sin{28°} + |\vec {v_a}| \cos \alpha \\\\\Rightarrow 8 = 3\sin{28°} + |\vec {v_a}| \cos \alpha \\\\\Rightarrow |\vec {v_a}| \cos \alpha =8-3\sin{28°} \cdots(i)[/tex]

And [tex]AC= |\vec {v_w} |\cos{28°} = |\vec {v_a}| \sin \alpha \\\\[/tex]

[tex]\Rightarrow |\vec {v_a}| \sin \alpha= 3\cos{28°} \cdots(ii)[/tex]

Dividing equation (ii) by equation (i), we have

[tex]\frac {|\vec {v_a}| \sin \alpha}{|\vec {v_a}| \cos \alpha}=\frac {3\cos{28°}}{8-3\sin{28°}} \\\\\Rightarrow \tan \alpha = 0.402 \\\\\Rightarrow \alpha = \tan ^{-1} (0.402)=22^{\circ} \\\\[/tex]

Putting the value of \alpha in equation (ii), we have

[tex]|\vec {v_a}| \sin {22^{\circ}}= 3\cos{28^{\circ}} \\\\\Rightarrow |\vec {v_a}| =(3\cos{28^{\circ}})/\sin {22^{\circ}} \\\\[/tex]

[tex]\Rightarrow |\vec {v_a}| = 7.07[/tex] miles/hour

Hence, the runner speed, without the effect of the wind, is 7.07 miles/hour W 22° S.

Answer:

-2

Step-by-step explanation:

Answer:

C. 28.26

May I have brainliest please? :)

Answer:

1

Step-by-step explanation:

First we need to find g (2) from g (2) = 2 ^ 2 to 4.

the result is 4, so f (4) asks, so f (4) = 4-3 = 1

Answer:

The answer is -3

Step-by-step explanation:

Slope means the rate of change of a line which is the letter m. Whenever you need to find slope remember this: m= y2-y1 over x2-x1.

(x1,y1)= (-3,7), ( x2, y2) = (0,-2) so the slope is -3.

It is either 6•9 to find the spaces or 54 spaces.

Answer:

[tex]\displaystyle y=\frac{7}{2}x-3[/tex]

Step-by-step explanation:

We wan to determine the equation of a line that passes through the point (2, 4) and is parallel to:

[tex]\displaystyle y=\frac{7}{2}x-5[/tex]

Since our new line is parallel to our equation, this means that the two lines have the same slope.

Therefore, the slope of our new line is also 7/2, the slope of the original.

Now, we can use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

So, we will substitute 7/2 for m.

Let's let our point (2, 4) be (x₁, y₁). Hence:

[tex]\displaystyle y-4=\frac{7}{2}(x-2)[/tex]

Solve for y. Distribute:

[tex]\displaystyle y-4=\frac{7}{2}x-7[/tex]

Add 4 to both sides.Therefore, our equation is:

[tex]\displaystyle y=\frac{7}{2}x-3[/tex]

Answer:

2 facturas de grasa.

12 facturas con dulce de leche

4 medialunas

Step-by-step explanation:

Una docena contiene 12 facturas y media docena contiene 6 facturas. Entonces Joaquin compro un total de 18 facturas (12+6). Si la novena parte (1/9) de las facturas son de grasa entonces solo multiplicamos esta fraccion por la totalidad de las facturas.

18 * (1/9) = 2 facturas de grasa.

La cantidad de facturas que tienen dulce de leche son dos tercios (2/3) de la totalidad. Entonces multiplicamos esta fracion for la totalidad.

18 * (2/3) = 12 facturas con dulce de leche

Por final, la cantidad de media lunas es el resto de las facturas, entonces descontamos las facturas de grasa y con dulce de leche de la totalidad para saber cuantas facturas son medialunas

18 - 2 - 12 = 4 medialunas

Answer:

Step-by-step explanation:

Given that 1/4 pounds = 1/8 gallons

We are to find the unit rate per gallon, hence we will say;

x pounds = 1 gallon

Equate both expression

1/4 pounds = 1/8 gallons

x pounds = 1 gallons

Cross multiply

1/8 * x = 1/4

divide both sides by 1/8

(1/8x)/(1/8) = (1/4)/(1/8)

x = 1/4 * 8/1

x = 1/4 * 8

x = 2 pounds

Hence the unit rate per gallon is 2 pounds per gallon

Her error was that he multiplied both values together to arrive at 1/32 instead of dividing as shown in the

Answer: 12

3×12=36

4×12=48

5×12=60

I hope this is good enough:

Answer:

11.45 + 57.25

Step-by-step explanation:

$68.70 is the correct answer because the question asks WHAT IS THE TOTAL COST FOR THE DINNER

The total cost he paid is $68.7

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part;

Given:

Bill for dinner is $57.25

20% tip was given

So, 20% on 57.25 is

=0.20 * 57.25

=11.45

Hence, total he paid = 57.25 +11.45 = 68.7

Learn more about percentage here:

https://brainly.com/question/13244100

#SPJ2

Answer:

pneumonoultramicroscopicsilicovolcanoconiosis is the word

Step-by-step explanation:

Answer:

[tex]=\frac{2a^4}{3bd}[/tex]

Step-by-step explanation:

Given expression is,

[tex]\frac{2ab^{-1}}{3a^{-3}d}[/tex]

Further simplify the expression by converting the negative exponents into positive.

[tex]b_1=\frac{1}{b}[/tex]

[tex]a^{-3}=\frac{1}{a^3}[/tex]

By substituting these terms in the given expression,

[tex]\frac{2ab^{-1}}{3a^{-3}d}=\frac{2a(\frac{1}{b})}{3(\frac{1}{a})^3d}[/tex]

         [tex]=\frac{\frac{2a}{b}}{\frac{3d}{a^3} }[/tex]

         [tex]=\frac{2a}{b}\times \frac{a^3}{3d}[/tex]

        [tex]=\frac{2a^4}{3bd}[/tex]

Answer:

thats hard dude why are you doing it

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

Answer:

add 10 which gives yoy 5x=10 divode by 5 that givdz u 2

Answer:

x = 2

Step-by-step explanation:

Answer:

1/14

Step-by-step explanation:

2/7 to 4 means 2/7 to 4/1

2/7 * 1/4

= 2/28

You can simplify by dividing the numerator and denominator

which will give you 1/14

Hope this help :)

Answer:

100 is the closest but that only leaves you with 63 not 630. It would have to be 1000.

Step-by-step explanation:

Explication étape par étape:

Soit la gratitude totale x

Montant reçu par le premier employé = 150 euros

Si le second reçoit 7/20 de la gratification, alors;

Deuxième reçoit = ​​7/20 × x

Si le troisième reçoit 5/28 de la gratification, alors

Le troisième reçoit 5/28 × x -

Si le quatrième reçoit le 9/35 de la gratification, alors;

Le quatrième reçoit 9/35 × x

Il faut ensuite calculer le pourboire total x.

Résumer tout le montant reçu

7x / 20 + 5x / 28 + 9x / 35 +150 = x

0,35x + 0,179x + 0,257x + 150 = x

0,786x + 150

x-0,786x = 150

0,214x = 150

x = 150 / 0,214

x = 700,9 euros

2) Pour obtenir le partage collecté par le premier, nous utiliserons l'expression

X × 700,9 = 150

x = 150 / 700,9

x ≈ 15/70

x≈ 3/14

D'où le premier a recueilli environ 3/14 de la gratification totale.

2) seconde collectée 0,35x

= 0,35 × 700

≈245 euros

Le troisième a recueilli 5/28 de x

Le troisième a collecté 5/28 × 700

= 3500/28

= 125 euros

Le quatrième a recueilli 9/35 de x

= 9/35 × 700

= 6300/35

≈ 180 euros

Answer:

Mya’s equation

Step-by-step explanation:

Given that:

Detergent left in bottle after a certain number of washes x

Dexter’s equation,

y= -1.6x+50

Mya’s equation,

y = 50(.75)x

y = Detergent left in bottle.

Given that amount of Detergent left is about 1/2 ounces = y

For Dexter’s equation,

y= -1.6x+50

0.5 = 1.6x + 50

0.5 - 50 = 1.6x

-45.5 = 1.6x

x = 28.4375

For Mya’s equation :

y = 50(0.75)x

0.5 = 37.5x

0.5 / 37.5 = x

0.0133333 = x

Hence, Mya’s equation

Answer:

y=-4/3x-5    y=7/6x-5

Step-by-step explanation:

That should be your answer I have already learn this so that should be right

Answer:

3x - 6b

Step-by-step explanation:

Answer:

y^6

Step-by-step explanation:

Answer:

the answer would be y^6

Answer:

$732.5

Step-by-step explanation:

Mae Ling earns a weekly salary of $365 which means salary per week is $365

Then plus a 7.5% commission on sales at a gift shop if she sold $4,900 worth of merchandise, which means additional

(0.075×4900)=367.5

The total she make will be

367.5+365

=$732.5

Therefore,she will make $732.5 in a work week if she sold $4,900 worth of merchandise

Answer:

The item is now 35$.

Step-by-step explanation:

First, find 65% of 100, which is 65. Then subtract the discount, or the "mark down" from 100. This gets you $35, so the item is $35 after the mark down.

Answer:

Two places to the left = 7.516

Step-by-step explanation:

Answer:

Step-by-step explanation:

751.6 ÷ 100 = 7.516

and that means that

the decimal point moves

two times to the right.

Hope this helps! <3

Answer: The slope is -1.

Answer:

Austin has the better average speed by 5 mph

Step-by-step explanation:

The slope of Dylan’s graph will his average speed

Let’s select two points on the graph to use

The slope can be calculated as;

m = (y2-y1)/(x2-x1)

m = (90-30)/(6-2)

m = 60/4

m = 15

So the equation for Dylan would be

d = 15t

This shows that Austin has a faster average speed by 5 mph

Answer:

There will be no common solution

Step-by-step explanation:

Given that the lines that represent the equations in the system of the two linear equations have equal slope but that their y-intercept are different, we have;

The two lines are parallel to each other

The two lines are different lines, given that they have different y-intercept

By definition of parallel lines, we have that the two lines representing the two equations will never meet, and therefore, both equations do not have a common solution which is a value that satisfies both equations

Therefore, the two equations in the linear system of equations, do not have a common solution

Answer:

yes

Step-by-step explanation:

they both equal to 2 pedestirans: 1 day

Answer: Yes.

Step-by-step explanation: By simplifying both ratios you get 2 pedestrians : 1 day.