Determine the vertex of the quadratic relation y=2(x+2)(x-6)

The constant of proportionality of the given graph is gotten as 4.

The constant of proportionality here is simply the slope of the graph.

Now, we will take two points and use their coordinates to find the slope from the formula;

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

Let us pick 2 points which are;

(1, 4) and (2, 8). Thus;

m = (8 - 4)/(2 - 1)

m = 4/1

m = 4

Thus, the constant of proportionality of the graph is gotten as 4.

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The distance apart of the two guy wire is 187.7 metres

The distance apart of the two wires can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Therefore,

tan 13 = 27 / x

x = 27 / tan 13 = 27 / 0.23086819112 = 117.391304348

tan 21 = 27 / y

y = 27 / tan 21

y = 70.338144115

Therefore,

distance apart of the guy wire = 117.391304348 + 70.338144115 = 187.728144115 = 187.7 metres

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Answer:

74.8 cm^2

Step-by-step explanation:

The figure is a parallelogram with base of 11cm and height of 6.8cm . To find the area, we multiply the base by the height to get 11 × 6.8 = 74.8 cm^2

The parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

The parent function is given as:

f(x) = x^2

The parabolas are given as:

y = f(x - 4), y = f(x + 3), y = f(x - 7), y = f(x + 2) and f = (x - 1/2)

The transformation from the parent function to each of the parabola is a horizontal translation.

This means that the y coordinate of their vertices are the same.

Arrange the parabolas starting from the left translations

y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

Hence, the parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

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The number of hours it would take to make 450 wackiest widgets is 4 hours 30 minutes.

The first step is to determine how many minutes it would take to make 1 widget.

Minutes it would take to make 1 widget ; 90 / 120 = 3 / 4 minutes

Number of minutes it would take to make 450 widgets: 3/4 x 450 = 270 minutes

Now convert minutes to hours : 270 / 60 = 4 hours 30 minutes

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The two rational expressions will be; (x + 2)/(x² - 36) and 1/(x² + 6x)

We want to determine the two rational expressions whose difference completes the equation.

The two rational expressions will be;

(x + 2)/(x² - 36) and 1/(x² + 6x)

Now, this can be proved as follows;

Step 2 [(x + 2)/(x² - 36)] - [1/(x² + 6)]

= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]

Step 3; By subtracting, we have;

[x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]

Step 4; By further simplification of step 3, we have;

[x² + x + 6]/[x(x-6)(x + 6)]

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Answer: [tex]33.56^{\circ}[/tex]

Step-by-step explanation:

[tex]\sin \alpha=\frac{\sqrt{11}}{6}}\\\\\alpha=\sin^{-1} \left(\frac{\sqrt{11}}{6}} \right)\\\\\alpha \approx 33.56^{\circ}[/tex]

Answer:

33.56

Step-by-step explanation:

Answer:

radius is 62.04

Step-by-step explanation:

use the formula V=

[tex] v= \frac{4}{3} \pi {r}^{3} [/tex]

Q6: A, Árbol

Q7: D, nube

Q8: C, Viento

Q9: B,

Q10: D, Cielo

Q11: D, Hablarian

Answer:

[-7, + ∞)    is domain

Step-by-step explanation:

Domain    is all of the 'x' values a function has

  this one goes from   -7 to + inf

Answer:

See below

Step-by-step explanation:

An invalid solution.

When you use the quadratic formula, for example, to  solve for 't', time, you will often find one of the values of 't' to be  NEGATIVE value for time.....this would be an extraneous solution.      

   Sometimes when working with LOG equations you may fin an answer which is negative.....you cannot have a LOG of a negative number...THAT solution would be EXTRANEOUS

 ETC

SO, always check your answers to see if they 'work' for your problem.

The value of the w is 130.95

We have given that,

[tex]\frac{w}{13.5}=9.7[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}13.5[/tex]

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

[tex]\frac{13.5w}{13.5}=9.7\cdot \:13.5[/tex]

[tex]w=130.95[/tex]

Therefore the value of the w is 130.95.

The questions seem incomplete the complete question is

Which student solved the equation StartFraction w Over 13.5 EndFraction = 9.7 correctly? Kwan's work. StartFraction w Over 13.5 EndFraction = 9.7. 9.7 times 13.5 = 130.95. Amala's work. StartFraction w Over 13.5 EndFraction = 9.7. 13.5 minus 9.7 = 3.8. Sid's work. StartFraction w Over 13.5 EndFraction = 9.7. 13.5 + 9.7 = 23.2. Joaquin's work. StartFraction w Over 13.5 EndFraction = 9.7. 9.7 divided by 13.5 = 0.72. Mark this and return.

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Answer:A

Step-by-step explanation: i dont kno you tell me

Answer:

The product is the difference of squares is [tex]$$\left(11-b\right)\left(11+b\right)=121-{{b}^2}$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(11-b)(11+b)=(11)^{2}-(b)^{2} \\&(11-b)(11+b)=121-b^{2}\end{aligned}$$[/tex]

The solution of the equation is union of  x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.

sin²x = cosx + 1

1 - cos²x = cosx + 1

cos²x + cosx = 0

cosx(cosx + 1) = 0

When cosx = 0

x = a(π/2) where a = 1,2,3......∞

When cosx = -1

x = n(π) where n = 1,3,5,7.......∞

Hence the solution of the equation will be the union of x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.

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Answer: Its A and A

Step-by-step explanation: I did the question

The first machine has added maximum 25 scoops of candies.

Given Machine 1 can add 46899 pieces of candies in the giant vat and machine 2 can add 13576 pieces of candies in the giant vat to form total supply of 600000.

let the number of scoops added by first machine be x and number of scoops added by second machine is y.

The equation will be as under:

46899x-13576y=600000

It can be solved logically. Because other machine is removing the candies from the giant vat so the value of 13576y is minimum 600000-13576=586424. Because it atleast withdrawn 1 scoop.

So the value of 46899x is maximum 1186424 which can bewhen the number of scoops is =1186424/46899=25 approximately.

Hence the number of scoops added by first machine is maximum  25.

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Question contains an error as the line related to left over 1 candy should be deleted.

Answer:

The answer is x= -15

Answer:

`18. x=9

19. x=4

20. x=25,5

21. x=3

22. x=3,5

23. x=10

Step-by-step explanation:

Answer:

The equation has the form Y= a + bX, where Y is the dependent variable (that's the variable that goes on the Y axis), X is the independent variable (i.e. it is plotted on the X axis), b is the slope of the line and a is the y-intercept.

Step-by-step explanation:

for more information check the above attachment

Answer:

38

Step-by-step explanation:

hope it helps good day.

Answer:

38 pencils and pens

Step-by-step explanation:

Given

Cost of pencil= $1.20

Cost of pen= $2.90

Difference in cost

= $2.90 -$1.20

= $1.70

Since she bought an equal number of pens and pencils, the additional amount of money spent on pens is due to the difference in price of a pen as compared to a pencil. Let one pen and one pencil be a set.

Number of sets

= $32.30 ÷$1.70

= 19

Since there are 19 sets,

total number of pencils and pen

= 19(2)

= 38

The next step Nolan should take is to find the average of the distances from the mean.

A measure of variance in a data set is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

The steps to find mean absolute deviation are:

Hence, The next step Nolan should take is to find the average of the distances from the mean.

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Answer:

x=-5, y=-2

Step-by-step explanation:

10x-9y=-32

2x-10y=10

(2x-10y)*5=10*5

10x-50y=50

(10x-9y)-(10x-50y)=-32-50

41y=-82

y=-82/2

y=-2

10x-9(-2)=-32

10x+18=-32

10x=-50

x=-5

The statement and reason that complete the flowchart proof are:

1. ∠BDE ≅ ∠BAC

2. Corresponding angles postulate.

The corresponding angles postulate states that two angles that correspond to each other are congruent angles.

In the given flowchart proof, ∠BDE and ∠BAC are corresponding angles, So, they are congruent by the corresponding angles postulate.

Therefore, the missing statement and reason are:

1. ∠BDE ≅ ∠BAC

2. Corresponding angles postulate.

The remaining part of the question is

"In ΔABC shown below, BD over BA equals BE over BC:

Triangle ABC with segment DE intersecting sides AB and BC respectively.

Top path, by Given the ratio of line segments BD to BA is equal to the ratio of line segments BE to BC. By Side Angle Side.

Which reason can be used to fill in the numbered blank space?"

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The set is expressed using inequalities; [tex]0 < x\leq 3[/tex], option D is correct.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.

The set be expressed using inequalities are;

[tex]0 < x\leq 3[/tex].

Thus, option D is correct.

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121.3 grams of caffeine is remaining in her blood

The given parameters are:

The amount of caffeine is calculated as:

A(t) = a(1 - r)^t

This gives

A(t) = 175 * (1 - 11.5%)^t

At 3 hours, we have:

A(3) = 175 * (1 - 11.5%)^3

Evaluate

A(3) = 121.3

Hence, 121.3 grams of caffeine is remaining in her blood

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The choice which is equivalent to; √(4-x²)/√(2-x) is; √(2-x).

According to the task content, it follows that the expression whose equivalent is to be determined can be evaluated as follows;

√(4-x²)/√(2-x) = √(4-x²)/(2-x)

Hence, the numerator can be evaluated by difference of two squares where;

(4-x²) = (2-x)(2+x)

Hence; we have; √(2-x)(2+x)/(2-x) = √(2-x).

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Answer:

sqrt 2+x

Step-by-step explanation:

Answer:

Hence, 3,40,000 can be expressed as [tex]$$3.4\times10^5$$[/tex]

Step-by-step explanation:

Step 1 of 1

Consider 3,40,000

3.4

So, 3.4 lies between 1 & 10

Now, Decimal has moved 5 places to left.

[tex]$3.4=10^{5}$[/tex]

So, 3,40,000=[tex]3.4 \times 10^{5}$[/tex]

The coordinates of the function will be T (x , y ) = (2 x, y + 5) ; Option B is the answer.

A function is a mathematical statement that relates an independent and a dependent variable .

An inverse of a function is given

T⁻¹ (x, y) :  (½x, y - 5)

 T(x, y)  : ?

As the inverse in given , to find the function , the reverse of all the transformation has to be done .

The x coordinate has been halved , so the original function will be double.

The y coordinate has  5 subtracted to it , so it will be added to the coordinate.

So the coordinates of the function will be

T (x , y ) = (2 x, y + 5)

Therefore Option B is the answer.

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Answer:

B. y = x + 2; y = 5

Step-by-step explanation:

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