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3 years ago

Calculate the value of P and of Q that satisfy the following simultaneous linear equations.

Mathematics

1 answer:

luda_lava [24]3 years ago

5 0

0.5p -3q =11
5p +6q =2

1) ×-2

--> 3. -p +6q =-22

2) - 3)

6p =24

p =4

sub into 2)

5(4) +6q =2

20 +6q =2

6q =2 -20 =-18

q=-3

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Someone help -2/5 x 1/4 x 1/5

kari74 [83]

Answer:

Lol i got u homie!

-0.02

(Sorry if that wasn't a fraction but hopefully this helps)

Step-by-step explanation:

7 0

3 years ago

Directions: Evaluate the solution 6) g(x) =- 2x + 5; Find g(-5) 6) in function notation?

harina [27]

Answer:

g(-5) = 15

Step-by-step explanation:

Put the value where the variable is and do the arithmetic.

g(-5) = -2(-5) +5 = 10 +5

g(-5) = 15

5 0

4 years ago

How many students were surveyed about their mode of transportation to school?

AlekseyPX

Answer:

Total number of students surveyed about their mode of transportation to school is 400.

Step-by-step explanation:

Here, given student who uses car as their mode of transport = 120 students

We have to find the total number of students who are surveyed.

Also, since complete circle represents 100% of data,

Total students who uses at least one mode of transport out of foot, bicycle, bus or car let it be x students.

Total percentage of students that uses bus, bicycle and on foot = (20 +15+35)% = 70%

Thus, percentage of students that uses car = 100 - 70 = 30%

Thus, 30 % of total students = 120

Mathematically, 30% of x = 120

Solving for x, we get,

$\frac{30}{100} \times x=120$

$\Rightarrow x=120 \times \frac{100}{30}$

$\Rightarrow x=400$

Thus, total number of students surveyed about their mode of transportation to school is 400.

8 0

3 years ago

PLEASE HELP GUYS i am struggling so much, two questions

ankoles [38]

Answer: the equation of the standard parabola

1) $(y-6)^2 = 4 (x-1)$

The equation of the standard parabola

2) (x+5)^2 = 16(y-2)

Step-by-step explanation:

Explanation

Parabola:-

The set of points in a plane whose distance from a fixed point and a constant ratio to their corresponding perpendicular distance from a fixed straight line is a conic.

Let S be a fixed point and l be a fixed straight line from any point P,the perpendicular PM is drawn to the line 'l'

The locus of P such that $\frac{SP}{PM} = constant$
The fixed point 'S' is called the Focus.
The fixed line'l 'is called the directrix of the conic
The constant ratio is known as the eccentricity, denoted by 'e'
If e=1 , the conic is called a parabola

1) Step 1 :-

Given the focus S = (2,6) and directrix is x=0

we know that $\frac{SP}{PM}=1$

now cross multiplication , we get

$SP = PM$

squaring on both sides,we get

$SP^{2} = PM^2$

step 2:-

now using distance formula is

$\sqrt(((x_{2}-x_{1})^2+(y_{2} -y_{1} )^2)$

Given S =(2,6) and P(x,y) be any point on parabola

$SP^2 = (x-2)^2+(y-6)^2$ ........(1)

Now using perpendicular distance formula

let P(x , y ) be any point on the parabola

$\frac{ax_{1}+by_{1}+c }{\sqrt{a^2+b^2} }$

Given the directrix is x =0 and P(x,y) be any point on parabola

$PM^2 = \frac{x^2}{\sqrt{1}^2 }$ ......(2)

equating equation(1) and equation (2), on simplification

we get $(x-2)^2+(y-6)^2 = x^2$ .....(3)

apply $(a-b)^2 = a^2+ b^2+2 ab$

now the equation (3) is

$(y-6)^2 = 4 x-4$

now the standard form of parabola is

$(y-k)^2 = 4 a(x-h)$

Final answer:-

$(y-6)^2 = 4 (x-1)$

2) Explanation:-

step 1:

Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)

here the given points of 'x'co- ordinates are equal

Therefore the axis AS is parallel to y- axis

now the standard equation of parabola

$(x-h)^2 = 4 a (y-k)$

now you have to find' a' value

Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)

The distance of $AS = \sqrt{(-5-(-5)^2+(2-6)^2}$

on simplification we get a =4

Final answer :-

the vertex (h,k) = (-5,2) and a=4

$(x-h)^2 = 4 a (y-k)$

The standard parabola is $(x+5)^2 = 16 (y-2)$

5 0

3 years ago

Use what you know about the properties to rewite each number sentence. Use mental math to find the sum. 0.6 + (0.4 + 0.9) = n an

dusya [7]

First Equation:

0.6 +(0.4+0.9) =n

Step 1: do parentheses first:

0.4+0.9 = 1.3

Step 2: Add 0.6 + 1.3

0.6 + 1.3 = 1.9

n= 1.9

Second Equation:

(1.57 + 0.75) + 0.25 + n

Step 1: do parentheses first:

1.57 + 0.75 = 2.50

Step 2: Add 2.50 + 0.25 = 2.75

Step 3: Add 2.75 and n = 2.75+n

Final Answer:

1.9 +2.75+n = 4.65 +n

Hope this helps!!

8 0

3 years ago