The graph of f(x) = x² is shown.
Compare the graph of f(x) with the graph of d(x) = x² - 27.

The least distance from point P to line l is approximately equal to 3.536 units.

There are several ways to calculate the least distance, in this case we decided to use the approach based on vectors and projections. First, we generate two auxiliary vectors:

Vector parallel to the line l

[tex]\overrightarrow {AB} = (5, 1) - (2, 4)[/tex]

[tex]\overrightarrow{AB} = (3, - 3)[/tex]

A vector from one point on the line l to the point P

[tex]\overrightarrow{AP} = (1, 1) - (2, 4)[/tex]

[tex]\overrightarrow {AP} = (- 1, - 3)[/tex]

Now we proceed to find the vector distance by using the following vectorial formula:

[tex]\vec d = \frac{\overrightarrow{AP} \,\bullet\, \overrightarrow {AB}}{\overrightarrow {AB} \,\bullet \,\overrightarrow {AB}} \cdot \overrightarrow{AB} - \overrightarrow {AP}[/tex]

[tex]\vec d = \frac{(-1)\cdot (3) + (- 3) \cdot (- 3)}{3^{2}+ (-3)^{2}} \cdot (3, - 3) - (-1, - 3)[/tex]

[tex]\vec d = - \frac{1}{6}\cdot (3, - 3) - (- 1, - 3)[/tex]

[tex]\vec d = \left(-\frac{1}{2}, \frac{1}{2} \right) + (1, 3)[/tex]

[tex]\vec d = \left(\frac{1}{2}, \frac{7}{2} \right)[/tex]

The magnitude of the vector distance is determined by Pythagorean theorem:

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{7}{2} \right)^{2}}[/tex]

d ≈ 3.536

The least distance from point P to line l is approximately equal to 3.536 units.

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The different statements and reasons to prove that −3(x + 8) = −21 are as detailed below.

Statement 1; −3(x + 8) = −21

Reason 1; Given

Statement 2; −3(x + 8)/-3 = −21/-3

Reason 2; Division property of Equality

Statement 3; x + 8 - 8 = 7 - 8

Reason 3; Subtraction Property of Equality

Statement 4; x = -1

Reason 4; Given

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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

Answer:

The answer is C. U=3x and V=2y^3

Step-by-step explanation:

3x*3x=9x^2

2y^3*-2y^3=-4y^6

Other variables cancel each other out

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:

100% on edge 2022!

The congruence property that shows that  if ΔABC ≅ ΔDEF, then  ΔDEF ≅ ΔABC is; A: Reflexive Property

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Now, since we are told that ΔABC is congruent to ΔDEF, then it means that by the reflexive property of congruence we can equally say that ΔDEF are congruent to angles of ΔABC

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Answer:

radius is 62.04

Step-by-step explanation:

use the formula V=

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

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

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 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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24.85

Step-by-step explanation:

First find the square root of 8.2 and subtract from the square root of 7.5. Multiply 3.5 by 0.71, the answer you get divide it by the answer you get after finding the square root.

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]

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:

not a function because it doesn't pass the vertical line test

Step-by-step explanation:

even though they have different y coordinates they still don't pass the test

Answer: Its A and A

Step-by-step explanation: I did the question

A scenario that would best model the graph on Holly, her home, and school is:

As Holly was heading to school, she felt uneasy and had to wait for 10 mins to catch her breath.

After doing so, she then continued to school which was 6 miles from her home. When she got there, she went to the nurse's office.

She waited in school for 15 minutes and was then told to go home to rest and recuperate. She then made the journey back home in a car and arrived in 10 minutes.

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The number of sides the regular polygon has is: B. 8.

A polygon with an n-side have a sum of interior angles which can be determined using the formula: (n - 2)180, where n is the number of sides of the regular polygon.

Thus, to find the measure of each interior angle of the polygon, we have: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given the following information about the regular polygon:

Interior angle of the regular polygon = 135 degrees.

Plug this into the given formula for finding the interior angle of a polygon:

135 = (n - 2)180/n

Multiply n by both sides of the equation

135 × n = (n - 2)180/n × n

135n = (n - 2)180

Open the bracket

135n = 180n - 360

Subtract both sides by 180n

135n - 180n = 180n - 360 - 180n

-45n = -360

Divide both sides by -45

-45n/-45 = -360/-45

n = 8

Thus, the number of sides that the regular polygon has is: B. 8 sides.

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Q6: A, Árbol

Q7: D, nube

Q8: C, Viento

Q9: B,

Q10: D, Cielo

Q11: D, Hablarian

I think factorizing everything you can first will make the simplification ... well, simpler.

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x(x+7)}{(x+7)(x+9)}[/tex]

The factors of [tex]x+7[/tex] in the second rational expression cancel:

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \div \dfrac{x}{x+9}[/tex]

Now, use the property

[tex]\dfrac ab \div \dfrac cd = \dfrac ab \times \dfrac dc[/tex]

(this is the property of multiplication having to do with multiplicative inverse, or "inverting the divisor" as the question calls it) to write

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \dfrac{x(x-3)}{(x+4)(x+9)} \times \dfrac{x+9}x[/tex]

and we see some more cancellation, namely of the factors of [tex]x[/tex] and [tex]x+9[/tex].

[tex]\dfrac{x^2 - 3x}{x^2 + 13x + 36} \div \dfrac{x^2+7x}{x^2+16x+63} = \boxed{\dfrac{x-3}{x+4}}[/tex]

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:

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 equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

We have:

x = -2 and x = 2

Rewrite as:

x + 2 = 0 and x - 2 = 0

Multiply both equations

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

This gives

x^2 - 4 = 0 --- option (a)

Add 4 to both sides

x^2 = 4

Multiply by 4

4x^2 = 16 --- option (d)

Hence, the equations that are true for x = -2 and x = 2 are (a) x^2 - 4 = 0 and (d) 4x^2 = 16

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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

The true statement about this information is that: A. It is both a relation and a function.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population.

In this context, we can infer and logically deduce that the true statement about this information collected by Jen is that it's both a relation and a function because it indicates a relationship between two variables.

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Answer:

It is both a relation and a function.

Step-by-step explanation:

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:

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.

Answer:

5 weeks

Step-by-step explanation:

We know that she works at a rate of $12 an hour, she also works 20 hours a week.

The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.

$240 - $34 = $206.

$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.

$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.