The straight line 2x + 3y = 7 meets the curve
xy + 10 = 0 at the points P and Q. Calculate the
gradient of the curve at P and at Q.​

Answer:

y + 5 = 2(x - 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Point (3, -5)

Slope m = 2

Step 2: Write equation

Substitute in variables into the general form.

y + 5 = 2(x - 3)

Answer:

1/3

Step-by-step explanation:

slope is just change in y over change in x

on a graph this can be found by counting the change in units

look at the point at (-3,0)

find the change in y by starting at that point and counting up or down until you reach another point.

the next point (-4,-3) is three units down (change of -3)

now go back to the first point and count left or right until you reach the other point to get change of x

the other point is one unit left (change of -1)

change of y over change of x = -1/-3=1/3

Answer:

slope = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (- 3, 0) ← 2 points on the line

m = [tex]\frac{0-(-3)}{-3-(-4)}[/tex] = [tex]\frac{0+3}{-3+4}[/tex] = [tex]\frac{3}{1}[/tex] = 3

Answer:

585000Rs

Step-by-step explanation:

Area=l×b

Area =total cost/rate or rate ×area

Answer:

1,200 miles

Step-by-step explanation:

1/4 in = 100 miles

         |

There is 4/4 which makes 400 miles in 1 in.

        |

So 400*3=1,200

Answer: 6(2+2x+1y)

Step-by-step explanation:

i think that is the anwser

Answer:

Step-by-step explanation:

We have pairs (5, 2550) and (8, 3300)

Find the rate of change:

$250 is the amount added to savings account every month

Initial amount was:

Since the change is linear and we have y-intercept and slope, we can show the amount after x months as:

5+2+10 is what i thibnk the answer is

Answer:

6

Step-by-step explanation:

You can memorize these for the smaller shapes

for equilateral polygons:

triangle: 60

square: 90

pentagon: 108

hexagon: 120

Otherwise, I believe the formula is the total degrees in a polygon (s-2)*180 where s is the number of sides.

So the measure of each angle on average would be (s-2)*180/s.

There (s-2)*180/s = 120

180(s-2) = 120s

180s-360 = 120s

60s = 360

s = 6

Answer:

D: y=-2x+5

Step-by-step explanation:

Answer:

y=-2x+5

Step-by-step explanation:

The basic formula you go by for these problems is y=mx+b.

For this example, b is 5 and m is -2.

This would make the problem y=-2x+5

Answer:

1.

[tex]x < - \frac{5}{13} [/tex]

2.

[tex]x \geqslant - \frac{1}{5} [/tex]

Step-by-step explanation:

↷

[tex] - \frac{13}{16}x + \frac{3}{8} < \frac{11}{16} \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: - \frac{3}{8 } < - \frac{3}{8} }{ \frac{ - \frac{13}{16}x }{ - \frac{13}{16} } < \: \: \: \frac{ \frac { 5}{16} }{ - \frac{ 13}{16} } } \\ \\ x < \frac{ - 5}{ \: 13} [/tex]

↷

[tex] \frac{1}{3} \geqslant \frac{2}{9} - \frac{5}{9} x \\ \frac{ - \frac{ 2}{9} \geqslant - \frac{2}{9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ \frac{ \: \: \: \frac{1}{9}x }{ - \frac{ 5}{9} } \geqslant \frac{ - \frac{5}{9} }{ - \frac{5}{9} } } \\ \\ x \geqslant - \frac{1}{5} [/tex]

We know these triangles are congruent with the missing side, N would be equal to 15.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We know these triangles are congruent.

To find the missing side, N

ΔABC ≅ΔQRS

AC/QS = BC/RS

2/5 = 6/n

n = 6 x 5/2

n = 30/2

n = 15

Thus, the value of N is 15.

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Answer:

MQ = 16 units

Step-by-step explanation:

[tex]\frac{x}{14}[/tex] = [tex]\frac{9}{63}[/tex]

x = [tex]\frac{14*9}{63}[/tex] = 2

MQ = 14 + 2 = 16 units

Answer:

Step-by-step explanation:

ohh i seeee

Answer: 6:5

Step-by-step explanation:

Let each little rectangle have the dimensions a by b (where a is the length and longer than b, the width). We find that l=3a because there are 3 lengths of a along l at the top of the crate and that l=4b because there are 4 lengths of b along l at the bottom of the crate. In addition, w=2b+a because there are 2 lengths of b and one length of a along w. Therefore, we can find b and a in terms of l and plug them into w=2b+a to find w in terms of l:

l=4b

b=l/4

l=3a

a=l/3

w=2b+a

w=2(l/4)+(l/3)

w=l/2+l/3

w=5l/6

If w=5l/6, l:w=l/(5l/6)=l(6/5l)=6/5

The correct answer is 6:5.

Answer: [tex]\frac{8}{3}\ ft/s[/tex]

Step-by-step explanation:

Given

length of shadow =22 ft

height of woman =5.5 ft

speed of woman [tex]\frac{dy}{dt}=8\ ft/s[/tex]

from the figure, we can write

[tex]\frac{22}{x+y}=\frac{5.5}{x}[/tex]

at given instant

y=20 ft

so, using similar triangle properties

[tex]\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft[/tex]

Again we can write

[tex]\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}[/tex]

Answer:

[tex]x>0\:or\:x<0[/tex]

As seen in graph, there is an open circle on 0, and it goes out left and right.

Option C is correct option.

Step-by-step explanation:

We need to draw the graph for the solution of the open sentence [tex]|x| +3>3[/tex]

First we will solve the inequality: [tex]|x| +3>3[/tex]

Adding -3 on both sides

[tex]|x| +3-3>3-3\\|x| >0[/tex]

We know that [tex]If\:|x|>0,\:then\:x>0\:or\:x<0[/tex]

So, we have

[tex]x>0\:or\:x<0[/tex]

Now, the graph is attached in the figure below

As seen in graph, there is an open circle on 0, and it goes out left and right.

Option C is correct option.

Answer:

b

Step-by-step explanation:

i got it right oon plato

Answer:

it should be y= 5x + 5 or y= 15x + 5

Step-by-step explanation:

I had something similar like a week ago and I am 100% its one of those

Answer:

B

Step-by-step explanation:

21*8=168

29*168=$4,872.00

Answer:

yes

Step-by-step explanation:

Answer:

y =2

then u should put 2 in y = 3x -2 or y = -3x + 4

= y =3x - 2

= 2 = 3x - 2

= 2 + 2 = 3x

= 4 = 3x

=x = 4/3

Answer: x = 12

Step-by-step explanation:

(180 - 130) + (3x - 6) + (8x + 4) = 180

180 - 130 + 3x - 6 + 8x + 4 = 180

48 + 11x = 180

48 + 11x - 48 = 180 - 48

11x = 132

11x ÷ 11 = 132 ÷ 11

x = 12

The required value of variable "x" is 12 which is determined by the property of interior angles.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

We know that the linear pair of angles are adjacent angles the sum of their measures is 180°

Since the sum of all interior angles of the triangle = 180°

(180 - 130) + (3x - 6) + (8x + 4) = 180

180 - 130 + 3x - 6 + 8x + 4 = 180

Rearrange the terms of  variable "x" and combine them,

48 + 11x = 180

48 + 11x - 48 = 180 - 48

11x = 132

x = 132/11

x = 12

Therefore, the required value of variable "x" is 12.

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Answer:

Table 1

Step-by-step explanation:

Table represents a function because the Input does not repeat.

Answer:

the answer would be the first one

Step-by-step explanation:

Answer:

what do you mean?

Step-by-step explanation:

Answer:

103

Step-by-step explanation:

appears to be an arithmetic sequence question where sequence is 7, 13, 19 meaning the initial value is 7 and the common difference is 6 so we'll plug into this formula:

[tex]a_{17}[/tex] = 7 + (17 - 1) · 6

    = 7 + (16 · 6)

    = 7 + 96

'7' because that's the initial value

'6' because that the common difference

'17' because that's the position the question is asking

Answer:

I filled it in for you. Hope it helps xx

Answer:

-5x^3+8

Hope this helps

Answer:Takeyour time

Step-by-step explanation: