The side of an equilateral triangle is given as 8 cm, correct to the nearest centimetre. What is the least possible length of its perimeter?​

Answer:

Step-by-step explanation:

Comment

Do the most mechanical part first. Moving 1 unit left will mean that x becomes (x + 1). It is anti intuative, but that is the correct answer.

So far what you have is y = a(x + 1)^2

The reason that you want to do it this way is any answer with a minus sign is wrong which eliminates A and B

When you stretch the parabola, a becomes 5 so now you have another part of the puzzle. and the equation becomes

y = 5(x +  1)^2

The 5 goes on the outside of the brackets which eliminates D

When you reflect this over the x axis, you invert the parabola which means you turn it upside down. The sign in front of the 5 becomes a minus.

Answer

y = - 5(x + 1)^2 or C.

Answer:

0(x-4)

Step-by-step explanation:

in my working system i mean just when i try on the place of 4 any number can be inserted

$5x-7=13x+17$,here both gives -22 as a result so

$6(x-4)$=6x-24 and to give the same result or 0

$6(x-4)$=0(x-any number )

Answer:

-x - 3

Step-by-step explanation:

1) Distribute

(3x+3)-(4x+6)

3x + 3 - 4x - 6

2) Subtract the numbers

3x + 3 - 4x - 6

3x - 3 - 4x

3) Combine like terms

3x - 3 - 4x

-x - 3

The mistake she had done is she should have reversed the inequality as per the division property of inequality.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The inequality is:

500 − 30x  ≥  200 −500 −500 −30x  ≥  −300 x  ≥  10

Given:

Jamie had $500 in her savings account.

She wants to have at least $200 left in the account at the end of the school year.

The inequality she had done is

500 − 30x  ≥  200 −500 −500 −30x  ≥  −300 x  ≥  10

But when she was dividing she should have reversed the inequality as per the division property of inequality.

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The simplified expression is 5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6.

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Given:

(5[tex]x^{4}[/tex] - 9x³ + 7x -1) + ( -8[tex]x^{4}[/tex]+ 4x² - 3x + 2) - ( -4x³ + 5x -1) (2x - 7)

Now,

5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 - ( -4x³ + 5x -1) (2x - 7)

=5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2-(-8[tex]x^{4}[/tex]+28x³ +10x² - 35x -2x +7

= 5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 +8[tex]x^{4}[/tex]- 28x³  - 10x² + 35x + 2x - 7

=  5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6

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To calculate the area that Marcus needs to paint we must calculate the area of the window and subtract it from the total area of the wall.

To calculate the area of a rectangular wall we must use the following formula:

Where a is the length of the height, and b is the length of the width.

Next, we need to calculate the area of the window. If it is a square or rectangular window we use the same formula "area = a × b".

If the window is circular we use this formula:

Once we know the area of the wall and the area of the window, we subtract the area of the window from the area of the wall and we will know what is the total area that Marcus must paint.

Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.

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The range of the function will be all values that are greater than 17 that is y > 17

The range of a function is the dependent variable of the function for which it exists,

Given the linear function

y = 8x + 1

If the value of x is 2, hence;

y = 8(2) + 1

y = 17

Hence the range of the function will be all values that are greater than 17 that is y > 17

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Answer: 3
________________________________
initial value = starting value when x is 0

as you can see when x is 0 y is 3

so your initial value is 3

________________________________

Hoped this helped.

Answer:

d

Step-by-step explanation:

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

The graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.

For the line crossing the negative x-axis

Using the coordinate points (-4, 2) and (-2, -4)

Slope = -6/2

Slope = -3

2 = -3(-4) + b
2 - 12 = b

b = -10

The equation of the line will be y = -3x-10

For the line crossing the negative y-axis

Using the coordinate points (-2, -4) and  (2,-2)

Slope = 2/4

Slope = 1/2

-2 = 1/2(2) + b
-2 - 1 = b

b = -3

The equation of the line will be y = -1/2x-3

For the line crossing the positive x-axis

Using the coordinate points (2, -2) and (3, 0)

Slope = 2/1

Slope = 2

0 = 2(3) + b
0 - 6 = b

b = -6

The equation of the line will be y = 2x-6

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

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Answer:

see explanation

Step-by-step explanation:

the domain is the set of x- coordinates from the ordered pairs , that is

domain : { - 7, - 3, 0, 5 }

the range is the set of y- coordinates from the ordered pairs, that is

range : { - 2, 1, 2, 5 }

Solution: 8p+44

Detailed explanation:

First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.

[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]

To make life easier let's just put the p's next to each other.

[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]

Now let's add the p's

[tex]---\mapsto\boldsymbol{8p+44}[/tex]

Voila! There's our answer!

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Hope I helped! Best wishes.

Reach far. Aim high. Dream big.

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Answer:

[tex]\frac{4}{60}[/tex] = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Is that a log with the base of   3√(2)  ?

If so....my calculator says the answer is   4

Let's see if we can do it w/ou the calculator:

3 sqrt(2)^x = 324 =  3^4 * 2^2     Now 'LOG' both sides:

x log (3 sqrt 2)  =   log (3^4 *2^2)  =  4 log ( 3 * 2^(2/4)) = 4 log (3 sqrt2)

                       now divide both sides by log (3 sqrt2 )

  x = 4        (If I did the math correctly ! )  

The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given:

genera form of an exponential function is  y=aeᵇˣ

Now, equation for f(x) is

f(x) = [tex]e^{(log \;2)x} -2[/tex]

Similarly, graph for g(x) is

g(x) = [tex]-3e^{(log \;2)x} +6[/tex]

Comparing the two function a relation can  be establish

g(x) = -3[f(x)]

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Answer:

shifted to the left two units
g(x)=-f(x+2)

Step-by-step explanation:

Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is  exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).

Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!

Answer:

let the remaining sides be X and Y

perimeter = X + Y + 13

24 = X + Y + 13

11 = X + Y ---(1).

Area = 1/2 * base * height

24 = 1/2 * X * Y

XY = 48.-----(2)

solving eq 1 and 2

X + Y = 11

XY = 48

Xy + y² = 11y

Xy = 48

y²= 11y - 48

y² -11y + 48 = 0

no real solution of this equation.

Answer:

Step-by-step explanation:

the triangle is NOT a 3–4–5 or multiple,

so it is not a right triangle or your data is wrong.

Answer:

216

Step-by-step explanation:

You are rolling three die three times

a die has six sides

to obtain the sample space

we would have to multiply 6 x 6  x 6

which could account for the three roles which would be equivalent to the sample space

6^3

The direct distance form A to C is represented by the inequality

AC < 40 yards.

A triangle is a polygon with three sides , three vertices and three angles.

It is given that

Distance form point A to B is 15 yards

Distance form point B to C is 25 yards.

Distance AC = ?

In a Triangle the sum of two sides is always greater than the third side.

Therefore

AC < 15 +25

AC < 40 yards.

Therefore the direct distance form A to C is represented by the inequality AC < 40 yards.

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Answer:

2.15%

Step-by-step explanation:

If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.

Z-score:

550-400/2=3

500-400/2=2

Probability:

3 (from the Z-table) is .9987

2 (from the Z-table) is .9772

.9987-.9772= .0215

.0215 as a percentage is 2.15%

Mean: 400

Standard deviation: 50

Check to see if 500 and 550 fall within the standard deviations:

400+2(50) =500

400+3(50) =550

These values lie between the 2nd and 3rd deviations, so

the value is 0.0235

Percentage: 2.35%

Hope it helps!

Answer:

B) 2y² - y - 6 = 0

Given following:

Insert equation 1 into 2:

Put in second

Answer:

Step-by-step explanation:

Hi, let me help you out.

First I'm going to turn the verbal phrase into an algebraic phrase...

21+n=37. here n is the unknown number

Next, I believe you need to find what n equals.

This can be done by subtracting 21 from both sides.

n=37-21

n=16

Thus the number we need is 16.

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The answers are mentioned below.

Acceleration is the change of speed with respect to time.

It is given that ,

The mass of the person is 50kg

Weight is 490 N

He has boarded an elevator with a bathroom scale.

1. The elevator is going down at constant speed , Force = 0N as acceleration is zero , The reading is 50kg.

2. The elevator is going up an slowing down . The magnitude of the acceleration is 4.9 m/sq.s , Force = mass * acceleration = 50 * 4.9 = 245N acting upward but the net force will be acting downward.

490 - 245 =  145N , reading 14.79 kg.

3.The elevator is free falling with an acceleration of 9.8m/sq.s force 0 N , as the gravitational force is pulling you down and the scale pushes up with the same force , Reading is 0 kg.

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Answer:

0.75

Step-by-step explanation:

slope is the coeffecient of x when the equation is in the order yb= mx + b

3x - 4y = 7

-4y = 7 - 3x

4y = 3x - 7

y = (3x - 7) / 4

y = 3x / 4 - 7 / 4

slope = 3/4

Answer:

choice C

Step-by-step explanation:

x could be any number except -1.

Cause for x=-1 the denominator becomes undefined.

Answer:

A dashed line down V on the (0,0) with the shading inside the V.

Step-by-step explanation:

- graph of y = -|x| is an upside down V

- less than sign means that there is dashed lines only

- plug in an x-value to determine whether the graph is shaded within the V or outside

Answer:

The answer is A

Answer:

[tex]\fbox {B. CA}[/tex]

Step-by-step explanation:

Picture the line segment :

⇒ A ---------------- C ------------------ B

Then :

⇒ CA + CB = AB