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Hunter-Best [27]

2 years ago

11

The total number of math students and history students is 43. Find the number of students in each class if the number of history

students is 7 less than the number of math students.

1 answer:

olasank [31]2 years ago

8 0

Answer:

25 math 18 history

Step-by-step explanation:

Equations:

x+y=43

x-7=y

x+x-7=43

2x=50

X=25

25-7=y

y= 18

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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)

Sveta_85 [38]

Answer:

1. $-5x+3y+44=0$

2. $2x+y-2=0$

3. $2x+y-4=0$

Step-by-step explanation:

Standard form of a line is $Ax+By+C=0$ .

If a line passing through two points then the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope, i.e., $m=\dfrac{y_2-y_1}{x_2-x_1}$ .

1.

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

$y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)$

$y+3=\dfrac{-5}{-3}(x-7)$

$y+3=\dfrac{5}{3}(x-7)$

$3(y+3)=5(x-7)$

$3y+9=5x-35$

$-5x+3y+9+35=0$

$-5x+3y+44=0$

Therefore, the required equation is $-5x+3y+44=0$ .

2.

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to $2 x + y =-5$ .

Slope of the line : $m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2$

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

$y-2=-2(x-0)$

$y-2=-2x$

$2x+y-2=0$

Therefore, the required equation is $2x+y-2=0$ .

3.

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to $2x + y =-5$ .

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

$y-0=-2(x-2)$

$y=-2x+4$

$2x+y-4=0$

Therefore, the required equation is $2x+y-4=0$ .

5 0

2 years ago

If (2x,3y) =(8, 9),find x and y

solong [7]

Answer:

x = 4, y = 3

Step-by-step explanation:

Equating corresponding coordinates , gives

2x = 8 ( divide both sides by 2 )

x = 4

and

3y = 9 ( divide both sides by 3 )

y = 3

5 0

2 years ago

What transformation(s) is taking place i’ll mark u the brainliest if u help

Ray Of Light [21]

Answer:

Reflection, Translation, and possibly Rotation

6 0

3 years ago

A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financi

DochEvi [55]

Answer:

1.) 10000, -3, 1000 ; doesn't make sense

2.) 40000, 3, 40000 makes sense

3.) 32500, 1.5, 32500 makes sense

4.) [0,+ ∞ ]

Step-by-step explanation:

1.) r(-3) = 2500 - 3*5000=10000

2.) f(3) = 25000 + 3*5000 = 40000

3.) f(1.5) = 25000 +1.5*5000= 325000

4.) # of siblings must >= 0

3 0

2 years ago

The ratio of the measures of the sides of a triangle is 9:15:5. If the perimeter of the triangle is 130 feet, find the measures

Alex Ar [27]

5x + 9x +15x = 130
29x = 130
x = <span> <span> <span> 4.4827586207 </span> </span> </span>
So the triangle sides =
<span> <span> <span> 22.4137931034 </span> </span> </span>
<span> <span> <span> 40.3448275862 </span> </span> </span>
<span> <span> <span> 67.2413793103 </span> </span> </span>

5 0

3 years ago