Find the equation of a line that passes through the point (-3,-1) and has a gradient of -2. Leave your answer in the form y = m x + c

Check the picture below.

If [m] represents the greatest possible length of line segment AD, and [p] represents the least possible length of line segment AD, than the value of [m - p] will be 2.84.

        where : [m] → is slope of line and [c] → is the y - intercept

We have in a plane, the lengths of line segments AB, BC, and CD are 3, 5, and 1.

Using the Pythagoras theorem, the length of side AC will be -

AC² = AB² + BC²

AC² = 9 + 25

AC² = 34

AC = √34

Also, we can write, the sum of two sides of a triangle is greater than the third side. So, in triangle ACD, we can write -

1 + √34 > AD

AD + √34 > 1

AD + 1 > √34

AD[min] = √34 - 1 = 4.84

AD[max] = √34 + 1 = 6.84

So -

m - p = 2.84

Therefore, if [m] represents the greatest possible length of line segment AD, and [p] represents the least possible length of line segment AD, than the value of [m - p] will be 2.84.

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Answer:

Here you go

Step-by-step explanation:

Answer:

---------------------------------------------

discount = 1/5

so after the discount we will pay 4/5 of the shirt

Answer: 8 I’m order to meet goal

Step-by-step explanation: 25-9=16 16-8=8

Explanation:

The diameter of the semicircle is 6 inches, which divides in half to the radius of r = 3 inches.

Add the two sub-areas to get the total area.

14.13 + 21 = 35.13 square inches

This answer is approximate since pi = 3.14 is approximate.

The Margin of error is 0.3 when assuming a 90% confidence level.

It is given that among 320 randomly selected airline travelers, the mean number of hours spent traveling per year is 24 hours and the standard deviation is 2.9.

It is required to find the margin of error when the confidence level is 90%.

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

[tex]\rm MOE= Z_{score}\times\frac{s}{\sqrt{n}}[/tex]

Where  [tex]\rm Z_{score}[/tex] is the z score at the confidence interval

             s is the standard deviation

             n is the number of samples.

We have in the question:

[tex]\rm Z_{score}[/tex] at 90% confidence interval = 1.645 (From the Z score table)

s = 2.9

n = 320

Put the above values in the formula, we get:

[tex]\rm MOE= 1.645\times\frac{2.9}{\sqrt{320}}[/tex]

MOE = 0.2666

Rounding the nearest tenth:

MOE = 0.3

Thus, The Margin of error is 0.3 when assuming a 90% confidence level.

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Answer:

0.3

Step-by-step explanation:

edg

Answer:

294mm

Step-by-step explanation:

The surface area of each side is 7mm x 7mm. 7•7 = 49

There are 6 sides on a cube, so just multiply 49 times 6.

49•6= 294 mm

Answer:

D, [tex]\frac{1}{2}x-3[/tex]

Step-by-step explanation:

Remember order of operations: parentheses first, then exponents, then multiplication/division, and finally addition/subtraction.

In this case, since there is no way to further simplify the parentheses, we can leave them be. But the negative sign in front of the parentheses is like multiplying it by -1. It needs to be distributed into the parentheses like so:

[tex]-(\frac{1}{4}x+5)=-\frac{1}{4}x-5[/tex]

We can now substitute that into the expression:

[tex]\frac{3}{4}x+2-\frac{1}{4}x-5[/tex]

From here, we can combine like terms:

[tex]\frac{2}{4}x-3[/tex]

And finally, we can simplify 2/4 to get:

[tex]\frac{1}{2}x-3[/tex]

Answer:

1) -100

2) Your laptop would lose value faster

3) Your laptop would lose value slower

4) Your laptop's value increases as time goes on

5) It is a horizontal line

6) the laptop's value doesn't change over time

7) A vertical line

Step-by-step explanation:

1) the slope of the line is -100. You can figure this out by doing rise/run

2) If the line were steeper, the laptop would lose more value each year, meaning that the laptop would lose it's value faster

3) If the line were less steep, the laptop would lose less value over each year, so it's value would decrease slower.

4) If the slope was positive, that means that the laptop would be gaining value as the time increases or goes by

5) A slope of zero has a rise over run of 0/something, meaning that the rise or change in y should be equal to zero. This can only occur in a horizontal line.

6) If the y-value doesn't change, that means that the value isn't changing as time goes by.

7) A line with an undefined slope has a rise over run of something/0 and it's undefined because anything divided by 0 is undefined. In this situation, the run, or change in x is 0, and this can only occur in a vertical line

Answer:

The value of discriminant is -7.

Explanation:

The given equation is,

x^2+x+2=0x

2

+x+2=0

The standard form of the quadratic equation is,

ax^2+bx+c=0ax

2

+bx+c=0

By comparing the given equation with the standard equation we get,

a = 1, b = 1 and c = 2.

The Formula for discriminant is,

D=b^2-4acD=b

2

−4ac

Substitute a = 1, b = 1 and c = 2,

D=1^2-4(1)(2)D=1

2

−4(1)(2)

D=1-8D=1−8

D=-7D=−7

Therefore, the -7 is the value of the discriminant.

Step-by-step explanation:

# Jerry Don is here#

Answer:

-7

Step-by-step explanation:

took the test

Answer: smaller number = 5, bigger number = 8

Step-by-step explanation:

Let x represent the smaller number

and y represent the bigger number.

The sum of 2 times the smaller number and 3 times the bigger number is 34.

EQ1: 2x + 3y = 34

Two times the bigger number is subtracted from 5 times the smaller number is 9.

EQ2: 5x - 2y = 9

Solve the system of equations using the Elimination method:

EQ1: 2x + 3y = 34      →   2(2x + 3y = 34)     →   4x + 6y = 68

EQ2: 5x - 2y = 9       →    3(5x - 2y = 9 )      →   15x - 6y = 27

                                                                         19x         = 95

                                                                      ÷19            ÷19

                                                                                  x =  5

Substitute x = 5 into either equation to solve for y:

EQ2: 5x - 2y = 9

      5(5) - 2y = 9

        25 - 2y = 9

              -2y = -16  

                  y =  8

The smaller number (x) is 5 and the bigger number (y) is 8.

[tex] \huge\fbox { \: smaller \: no. = 5}\ \\ \huge\fbox { \: bigger \: no. = 8} \: [/tex]

Here,We'll assume the smaller no. as x & the bigger one as y

Now,

ATQ,

(sum of two times the smaller number and three times the bigger number is 34.)

(Two times the bigger number is subtracted from the five times the smaller one)

Now,

we'll apply the elimination method to find The value of the variables↷

Here,

Let's equalize the variable ,'x'

[tex]To \: equalize \: the \: variable,[/tex]

[tex]We \: need \: to \: multiply \: the \: first \: equation \\ \: by \: 5 \: and \: the \: second \: one \: by \: 2↴ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]5(2x + 3y = 34) \\ \: \: \: = > 10x + 15y = 170......(3) \\ \\ 2(5x - 2y = 9) \\ = > 10x - 4y = 18 ......(4)\\ \\ [/tex]

Since Now our variable'x' is equalize in Both of the equations (10x),

We'll subtract the Equation 4 From Equation 3rd so that we can find out the Value of y

[tex] \: \: \: \: \: \: \: 10x + 15y = 170 \\ \: \ - 10x - 4y = 18 \\ \: \: - - - - - - - - \\ 0 + 19y = 152 \\ \: \: \: - - - - - - - - \\ 19y = 152 \\ \frac{19y}{19} = \frac{152}{19} \\ \huge\fbox{y = 8} [/tex]

Now,

By plugging the Value of y in any of the equation,we can find the Value of x.

Here,

We'll plug the value of y into the equation 2↴

[tex]5x - 2(8) = 9 \\ 5x - 16 = 9 \\ 5x - 16 + 16 = 9 + 16 \\ 5x = 25 \\ \frac{5x}{5} = \frac{25}{5} \\ \huge\fbox{x = 5} [/tex]

Hence, the Value of the smaller number = 5

and the value of the bigger one = 8

[tex] \small\mid{ \underline{ \overline{ \tt \: －ɪƭ'ꜱ \: ʙᴙᴜᴛᴀʟ \: σʋʇ \: ɦэŗǝ~}} \mid} [/tex]

Answer:

30,370 feet

Step-by-step explanation:

Given that,

Mt. Everest is a little over 29,000 feet above sea level, and the shore of the Dead Sea is about 1,370 feet below sea level.

We need to find the approximate difference in elevation between the two points.

29,000 feet is above sea level and 1,370 feet is below sea level i.e. both elevations are in opposite direction.

Difference = 29,000 - (-1,370 )

= 30,370 feet

Hence, the difference in elevation between the two points is 30,370 feet.

Answer:30,370 feet

Step-by-step explanation:

[tex]\\ \rm\rightarrowtail 2x^2-9x+8=0[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{9\pm\sqrt{81-64}}{4}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{9\pm\sqrt{27}}{4}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{9\pm3\sqrt{3}}{4}[/tex]

The height of the prism that's depicted in the water tank will be 8m.

The area of the base of the triangular prism will be calculated thus:

= 1/2 × 4 × 9

= 18m²

The volume of water removed from the rectangular tank will be:

= (6 × 6) × 4

= 144m³

Therefore, the height will be calculated thus:

18 × h = 144

18h = 144

h = 144/18

h = 8m

Therefore, the height is 8m.

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Answer:

2,5,5,5

Step-by-step explanation:

50×5=2×5×5×5

Using an exponential function, it is found that the value of Yong's investment account after 7 years is given by:

(C) $2363

It is modeled by:

[tex]y = ab^x[/tex]

In which:

Her account was worth $2000 initially, and it increases by 10%, percent every 4 years, hence, it is modeled by:

[tex]y(t) = 2000(1.1)^{\frac{t}{4}}[/tex]

After 7 years, the amount is:

[tex]y(7) = 2000(1.1)^{\frac{7}{4}} = 2363[/tex]

Hence option C is correct.

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Answer:

The area is 5x

Step-by-step explanation:

1) a = lw (starter equation)

2) a= 5x (substiute x in for the width, and 5 in for the length)

Answer:

5x^2

Step-by-step explanation:

[tex]Solution \\

Here \\ \hookrightarrow \: length(l) = x \: units \\ \hookrightarrow \: breadth(b) = 5 \: units \\\hookrightarrow \: area = l \times b \\ \hookrightarrow \: area = x \: units \times 5 \: units \\ \hookrightarrow \: area = 5 {x}^{2} [/tex]

Answer:

2x +6

Step-by-step explanation:

if you are given a question like this u will leave it like that because maybe the question is wrong

Answer:

70

Step-by-step explanation:

From the question given above, the following data were obtained:

TU = 8x + 11

UV = 12x – 1

Next, we shall determine the value of x.

From the question:

U is the midpoint. This means that TU and UV are equal i.e

TU = UV

With the above idea in mind, we shall determine the value of x as follow:

TU = UV

TU = 8x + 11

UV = 12x – 1

8x + 11 = 12x – 1

Collect like terms

11 + 1 = 12x – 8x

12 = 4x

Divide both side by the coefficient of x i.e 4

x = 12/4

x = 3

Next, we shall determine the length of TU and UV. This can be obtained as follow:

TU = 8x + 11

x = 3

TU = 8(3) + 11

TU = 24 + 11

TU = 35

UV = 12x – 1

x = 3

UV = 12(3) – 1

UV = 36 – 1

UV = 35

Finally we shall determine the length of TV. This can be obtained as follow:

TV = TU + UV

TU = 35

UV = 35

TV = 35 + 35

TV = 70

Therefore, the distance between my house and grandma's house is 70.

NOTE: Assume the distance is measured in kilometer (km)

This means that I will travel 70 km from grandma's house to my house.

Answer:

The midpoint is (4, 3).

Step-by-step explanation:

to get the midpoint (x1+x2/2, y1+y2/2)

(0+8/2, 0+6/2)

(4, 3)

Answer:

The value of the car will be $2,363.19 after 14 years

Step-by-step explanation:

The rule of depreciating is  

[tex]A=p(1-r)^{t}[/tex] , where

∵ A new car is purchased for 18000 dollars

∴ P = 18,000  

∵ It depreciates at a rate of 13.5% per year

∴ r = 13.5% = 13.5/100 = 0.135  

∵ We need to find how much it will be worth after 14 years

∴ t = 14

→ Substitute all of these values in the rule above to find A  

∵  [tex]A=18000(1-0.135)^{14}[/tex]

→ Use your calculator to find the answer  

∴ A = 2,363.186569

→ Round it to the nearest cent (2d.p.)

∴ A = 2,363.19

∴ The value of the car will be $2,363.19 after 14 years.

Step-by-step explanation:

°c to °F = (°c × 9/5) + 32

= ( 37.2 × 9/5) + 32

= 66.96 + 32

= 98.96 °F

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The slope is 2

Step-by-step explanation:

Gradient = rise/run

= 2/1

Hope this helps!

Answer:

m = 2

Step-by-step explanation:

(40, 10) and (50, 30)

20/10= 2

Answer:

[tex]y = 5x + 3[/tex]  

I hope this helps!

Answer:

Both are equations, one is linear, one is not linear boom

Step-by-step explanation: