UNIT TEST:
Basic Tools and Transformations - Part 1

The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.

Parabolae are defined by quadratic equations, that is, equations whose form is y = a · x² + b · x + c. The slope of a line tangent to a point of the curve is defined by a linear equation, that is, an equation of the form y = m · x + b. By derivative rules, the slope of the tangent line can be found by using the following expression:

m = 2 · a · x + b

Then, if we know that y = 2 · x² - 3 · x + 5 and x = 4, then the equation of the tangent line is:

Slope

m = 4 · x - 3

m = 4 · 4 - 3

m = 13

Intercept

b = y - m · x

y = 2 · 4² - 3 · 4 + 5

y = 32 - 12 + 5

y = 25

b = 25 - 13 · 4

b = 25 - 52

b = - 27

The equation of the line tangent to the parabola at x = 4 is y = 13 · x - 27. The tangent line has a slope of 13 and a intercept of - 27.

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Step-by-step explanation:

1)

the perimeter P

P = 2x + 2y = 80 m

the area A

A = x × y

2)

2x + 2y = 80

2y = 80 - 2x

y = 40 - x

and we use that in the equation for area

A = x × (40 - x) = 40x - x²

we find the maximum (or minimum) of a function by finding the 0s of the first derivative.

A' = 40 - 2x = 0

40 = 2x

x = 20

y = 40 - x = 40 - 20 = 20

and just to be sure :

if the second derivative at that point x is negative, we have a maximum, if it is positive, we have a minimum.

A'' = -2

so, it is negative for all x incl. x = 20.

therefore, we have a maximum.

the rectangle with perimeter of 80 m and the max. area is a square of 20 m side length.

Answer:

22.6796 kg.

Step-by-step explanation:

The answer is 22 i am sure about this

The equation of the line passing through points (-3,0) and (0,3) is y=x+3.

The equation of the line passing through two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula y-y₁=m(x-x₁)   ,  where m denotes the slope of the line .

from the given graph we can find that the line passes through the two points (-3,0) and (0,3)

we get the values , as x₁=-3 , x₂=0 and y₁=0 , y₂=3 .

Slope of the line can be calculated by using the formula ,

m=(y₂-y₁)/(x₂-x₁)

Substituting the values we get ,

m = (3-0)/(0+3)

m=3/3 = 1

Now substituting the values of x₁, x₂, y₁, y₂ and m in the formula of equation of line we get ,

y-0=1(x-(-3))

y-0=1(x+3)

y-0=x+3

y=x+3

Therefore , the equation of the line passing through points (-3,0) and (0,3) is y=x+3.

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Answer:

95=Xx9 +Yx2.50

Step-by-step explanation:

The inequalities graphically shows the given situation is 95 ≥  +2.50y + 18x. The graph is attached below.

If the equation or inequality contains variable terms, then there might be some values of those variables for that equation or inequality might be true. Such values are called solution to that equation or inequality.

Here Set of such values is called solution set to the considered equation or inequality.

We have been given that William and his children went into a restaurant where they sell hamburgers for $8 each and drinks for $2.50 each.

Since William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether.

If x represents the number of hamburgers purchased and y represents the number of drinks purchased then;

95 ≥  +2.50y + 18x

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Answer:

x = 2

Step-by-step explanation:

5x^2 - 20x + 20 = 0

5 (x^2 - 4x + 4) = 0

x^2 - 4x + 4 = 0

x             -2

x             -2

(x - 2)(x - 2) = 0

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

x - 2 = 0

x = 2

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

5x² - 20x + k = 0

k = - 5x² + 20x

k = - 5(2)² + 20(2)

k = -20 + 40

k = 20

Answer + Step-by-step explanation:

Consider the equation :

5x² - 20x + k = 0

∆ = b² − 4bc is the discriminant of the quadratic equation.

In our equation :

a = 5  ;  b= -20  ;  c = k

Then

∆ = (-20)² − 4×5×k

   = 20² − 20k

   = 20×(20 − k)   (Factoring)

The equation 5x² - 20x + k = 0 has exactly one real solution

if and only if  ∆ = 0.

Solving the equation ∆ = 0 :

∆ = 0

⇔ 20×(20 − k) = 0

⇔ (20 − k) = 0    (Zero product property)

⇔ k = 20

[tex]\displaystyle\\Answer:\ (-\frac{3}{13},-2\frac{6}{13} )[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\frac{3}{10} =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=\frac{x_1+\lambda x_2}{1+\lambda} }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=\frac{y_1+\lambda y_2}{1+\lambda} }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=\frac{-3+0.3*9}{1+0.3} \\\\x=\frac{-3+2.7}{1.3} \\\\x=\frac{-0.3}{1.3}\\\\ x=-\frac{0.3*10}{1.3*10}\\\\ x=-\frac{3}{13} \\\\[/tex]

[tex]\displaystyle\\y=\frac{-5+0.3*6}{1+0.3} \\\\y=\frac{-5+1.8}{1.3} \\\\y=\frac{-3.2}{1.3} \\\\y=-\frac{3.2*10}{1.3*10} \\\\y=-\frac{32}{13} \\\\y=-2\frac{6}{13} \\[/tex]

Answer:

Step-by-step explanation:

Answer:

find the value of 8x³-y³ if 2x-yand xy

=-1

The area of the Triangle is 7.8 cm².

The perimeter of the triangle is given to be 13cm.

As we know,

perimeter of triangle = sum of length of all sides of the triangle.

13cm = 4cm + 5cm + third side

third side = 4cm.

Hence two side of the triangle are equal to 4cm. We can say that this is an isosceles triangle, with the base length as 5cm and the other two equal sides of length 4cm.

Let say the base length is B and the other sides length is A.

So area of the isosceles triangle can be given by,

Area = 1/2 x B x √(A²-B²/4)

Area = 1/2 x 5 x √(4²-5²/4)

Area = 1/2 x 5 x √(16 - 25/4)

Area = 1/2 x 5 x 3.12

Area = 7.8 cm².

The area of the triangle is 7.8cm².

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Answer:

D

Step-by-step explanation:

I got it right!

Answer:

d

Step-by-step explanation:

took the test

Answer:

they all can't be divided

Answer:

The tip was 20.6% or 20.59% of the original bill

Step-by-step explanation:

Question: The bill for dinner was $77.12. You left $15.88 for the tip. What percentage of the original bill was the tip?

Step-by-step:

To find the percentage of how much a part ($15.88) is or a whole ($77.12), the formula of part = percentage * whole is used.

It is usually written as a = p*w

In this case, $15.88 is a and $77.12 is w.

so, 15.88 = p*77.12

However, we need to find p. To do so, we need to get p by itself. Divide 77.12 on both sides so that it cancels out on the right side.

15.88 divided by 77.12 is about 0.2059

We need to make the decimal a percentage by multiplying 100

0.2059 * 100 = 20.59%

You could probably round it up to 20.6% if you wanted to

Therefore, the tip was 20.6% or 20.59% of the original bill.

Answer:

Step-by-step explanation:

Solve parts of equation in order:

Brackets

Indices

Division

Multiplication

Addition

Subtraction

8 + 2 x 7 - 9 = 63

8 + (2 x 7) - 9  not = 63   (multiplication is the first thing that applies to this equation)

(8 + 14) - 9  not = 63

22 - 9 = 13

So the error would be it equals 13 not 63

Answer:

9 is supposed to be 7

Step-by-step explanation:

8 + 2 = 10

10 × 7 = 70

70 - 7 = 63

Answer:

y = x/7 + 31/7

or 7y = x + 31

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other so slope will be 1/7

m = 1/7, y = -4, x = 3

y = mx + b

-4 = 1/7(3) + b

b = 3/7 + 4

b = 3/7 + 28/7

b = 31/7

so

y = x/7 + 31/7

or 7y = x + 31

Step 1) : Based on the given conditions, formulate

[tex] \large\bf \longrightarrow \frac{510}{3000} [/tex]

Step 2) : Calculate

[tex] \bf \longrightarrow\frac{51 \cancel{0}}{{300 \cancel{0}} } \: = \frac{51 \div 3}{300 \div 3} = \frac{17}{100} [/tex]

Step 3) : Convert to percentage

[tex] \bf\longrightarrow{\frac{17}{100} = 0.17}[/tex]

Answer:

[tex] \large{ \boxed{ \star{ \tt \: answer : 14 \: units}}}[/tex]

Please see the attached picture for full solution!

-------- HappY LearninG <3 -----

Answer:

hi hhhhhhdhwjwheheheuhehegdhue

The numbers arranged in a sequence will be - ∛100² < - 4.67 < - 4.25 Both Victor and Sean are correct.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Victor thinks that negative 28 / 6 Is greater than negative ∛100². Sean thinks that 17 / 4 is greater.

The value of the number negative 28 / 6 will be - 4.67.

The value of the number negative ∛100² will be - 21.54.

And the value of the number negative 17/4 will be - 4.25.

The numbers are arranged in a sequence.

- ∛100² < - 4.67 < - 4.25

Both Victor and Sean are correct.

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Answer:

[tex] \sqrt[2]{?5} x25 \geqslant 6 - 9 + 88 = 2[/tex]

Answer:

f^-1(x)=(3/4)x

The vertical distance (Δ`y`) for the slope triangle as indicated is; (4-2) ; 2.

The horizontal distance (Δ`x`) for the slope triangle as indicated is; (4-0) ; 4.

According to the task content, it follows that the vertical and horizontal distance for the slope triangle in discuss are to be determined.

Hence, by observation, Δ`y` can be obtained on the graph from points 4 and 2; we have; 4-2 = 2.

Also, by observation, Δ`x` can be obtained on the graph from points 4 and 0; we have; 4-0 = 4.

Ultimately, the vertical and horizontal distances of the slope triangle are as indicated.

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Answer:

5mph=20 hours to do 100 miles with a bicycle

10mph=10 hours to do 100 miles with a bicycle

15mph=6hours 40minutes(maybe)to do 100miles with a bicycle

20mph=5 hours to do 100miles with a bicycle

25mph=4 hours to do 100 miles with a bicycle

the faster u go the time will decrease

the slower u go the time will increase

hope that helped I didn't really understand much

Answer:

nwm zycze powodzenia kolego drogi

Answer:

Step-by-step explanation:

Answer:

80,000 A

Step-by-step explanation:

it is under 85000 so it is rounding down to 80,000

Answer:

true

Step-by-step explanation:

Answer:

150 student now school gema plyar

3.5 * [tex]10^{9}[/tex] WATTS IS THE TOTAL OUTPUT OF THE STAR

Electrical power is the rate at which electrical energy transforms into another form, such as motion, heat, or an electromagnetic field. The capital P is frequently employed as a symbol representing authority. The universal unit is the watt, which is represented by the letter W. Utility circuits typically have a kilowatt (kW) indication, which is 1000 W.

Summarized Version:

1-The values of the solar constants were imparted to us by our planet, the first object in our solar system.

2-We therefore know the value of the solar constant for the given solar system, which consists of a planet and the star it orbits.

3-Therefore, if you assume that the orbit is circular, the radius of the orbit will be determined by multiplying the value of the solar constant by 10 to the power 11 m and the radius.

4-We can therefore state that the star's power output is simply equal to the solar constant times the orbit's area.

5-What. So, this is the star's power output for the particular solar system.

The second part of the inquiry now asks what the solar constant will be if the distance between the planet and the star is reduced to 75,000,000 km.

6-We also need to determine what the new solar constant for the solar system will be.

So, in this case, power is equal to area times the solar constant once more.

The solar constant, multiplied by four, multiplied by 3.14, multiplied by are here is 75 multiplied by 10 to the power nine full square, giving us 25.12 multiplied by 10 to the power 25, which is equivalent to that.

We can calculate the value of the solar constant as follows: 25.12 multiplied by 10 to the power of 25 split by four; 3.14 multiplied by 75 square; and 10 multiplied by10.

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Answer:

x - 17.95 = 71.80

Use the commutative property of addition

71.80 + 17.95 = 89.75

$89.75 was the original price.

Step-by-step explanation:

Hope it helps! =D

Answer:

y = 4/3x - 5

Step-by-step explanation:

y-intercept will be (0,-5)

so m = (y2-y1)/(x2-x1)

m = (-5 -7)/(0 - 9) = (-12)/(-9) = 4/3

Using m = 4/3, y = 7, x = 9

y = mx + b

7 = 4/3(9) + b

7 = 12 + b

b = -5

so

y = 4/3x - 5