Find the vertex form of y=(x+2)(x-3)

Answer:

4x - y = 7.

Step-by-step explanation:

We substitute for x and y and see if they fit.

4x - y = 7

4(2) - 1 = 7

So it is the first line.

Answer: First option.

Step-by-step explanation:

To find which line contains the point (2,1), we can substitute the coordinates into each equation of the line provided in the options:

First option:

[tex]4x-y=7\\4(2)-1=7\\7=7[/tex]

It contains the point (2,1)

Second option:

[tex]2x+5y=4\\2(2)+5(1)=4\\9\neq 4[/tex]

It does not contain the point (2,1)

Third option:

[tex]7x-y=15\\7(2)-1=15\\13\neq15[/tex]

It does not contain the point (2,1)

Fourth option:

[tex]x+5y=21\\2+5(1)=21\\7\neq 21[/tex]

 It does not contain the point (2,1)

Answer:  29/28

Step-by-step explanation:

To add fractions we have to calculate the Least Common Denominator of the denominators. Then we have to change each fraction (using equivalent fractions) to make their denominators the same as the Least Common Denominator. Then we can add (or subtract) the fractions.

LCD (4,7,2)= 4·7 = 28

1/4 = 7/28

2/7 = 4·2/28 = 8/28

1/2 = 14/28

Since the fractions have the same denominator we can add them

7/28 + 8/28 + 14/28 = (7+8+14)/28 = 29/28

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

d = 5 and a₁ = - 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

Given a₃ = 6, then

a₁ + 2d = 6 → (1)

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Given [tex]S_{12}[/tex] = 282, then

6 [ 2a₁ + 11d ] = 282 ( divide both sides by 6 )

2a₁ + 11d = 47 → (2)

We can now solve (1) and (2) for d and a₁

Multiply (1) by - 2

- 2a₁ - 4d = - 12 → (3)

Add (2) and (3) term by term

7d = 35 ( divide both sides by 7 )

d = 5

Substitute d = 5 in (1) and solve for a₁

a₁ + 10 = 6 ( subtract 10 from both sides )

a₁ = - 4

Answer:

Explanation:

That the discrepancy in diameter is more than 0.002 mm means that the difference between the measured diameter of a ball and the standard diameter is greater than 0.002.

That is:

So, the function is f(x) = |x - 42.67| > 0.002, where x and f(x) are in mm.

Answer:

First one is B f(x) = (42.67-x)

Second is 42.6668 mm, 42.673 (options b and d)

Hope this helps

Checked on edge

Answer:

= 9x³+ 0x²+0x -52....

Step-by-step explanation:

Descending powers means you start with highest power and then decrease.

In this expression the highest power is 3. We do not have any variable with power 2 and 1. So we will write it as:

9x³ -  52

= 9x³+ 0x²+0x -52....

Answer:

For [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656[/tex]

[tex]46,656 > 500,000[/tex]

Inequality is not met because [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

[tex]7^7=823,543[/tex]

[tex]823,543 > 500,000[/tex]

Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7

Inequality is met.

In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543[/tex]

Answer:

Smallest positive integer value for [tex]x^x>5000[/tex] is,

x = 7,

Largest negative integer value for [tex] x^{-x} >500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....

Case 1 : If x < 7,

[tex]x^x < 500000[/tex]

Case 2 : If x ≥ 7,

[tex]x^x > 500000[/tex]

Hence, smallest positive integer value of x is 7.

Now, if [tex]x^{-x}>500000[/tex]

∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....

Case 1 : if x is odd negative integer,

[tex]x^{-x} < 50000[/tex]

eg : -1, -3, -5, -7,...

Case 2 : If x is even negative integer then there are further two cases,

(i)  x is more than or equal to -6,

[tex]x^{-x} < 500000[/tex]

eg x = -6, -4, -2,

(ii) x is less than -8,

[tex]x^{-x} > 50000[/tex]

eg : x = -10, -12, -14,...

Hence, the largest negative integer value that will make [tex]x^{-x}> 500000[/tex] is x = -8.

Answer:

x=4

Step-by-step explanation:

AB + BC = AC

AB= 6x, BC= x-5, AC= 23

Substituting what we know

6x + x-5 = 23

Combine like terms

7x -5 = 23

Add 5 to each side

7x-5+5 =23+5

7x = 28

Divide each side by 7

7x/7 = 28/7

x=4

hey! the value of y is 57

Answer:

First Image: [tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Step-by-step explanation:

We have the following functions:

[tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in w weeks.

J(y)  = Number of weeks per year.

Since, J(y) is the number of weeks spent per year in painting, in order to calculate the paintings completed in a year we substitute w = J(y) in the above equation. So the equation becomes:

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

This composite function would represent number of paintings Jenny completes in a year.

p[J(y)] = 1/2 . J(y) + 1 or the first image is the correct answer!

I took the test and ended up getting it right.

Good luck! I hope you have an awesome day!

Answer:

2n-7

Step-by-step explanation:

"7 less than twice a number n"

is the same as

"7 less than (twice a number n)".

I put ( ) around that one part because I want you to focus on that part first.

Twice a number n means 2 times that number n or 2n.

So now we have

"7 less than 2n".

This means 2n-7.

Answer:

Step-by-step explanation:

[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\(x_1,\ y_1)-point\ on\ a\ line\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\======================================[/tex]

[tex]\text{We have the points:}\ (2,\ -2)\ \text{and}\ (1,\ -6).\\\\\text{Substitute:}\\\\m=\dfrac{-6-(-2)}{1-2}=\dfrac{-4}{-1}=4\\\\y-(-2)=4(x-2)\\\\y+2=4(x-2)[/tex]

For this case we must find an expression equivalent to[tex]6 ^ {- 3}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, we can rewrite the given expression as:

[tex]6 ^ {3} = \frac {1} {6 ^ 3}[/tex]

This is equivalent to:

[tex](\frac {1} {6}) ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer option is D. ( 1 / 6 ) ^ 3.

Step-by-step explanation:

We are given the following expression and we are to determine whether which of the given answer options is equivalent to this:

[tex] 6 ^ { - 3 } [/tex]

Rewriting this as a fraction to get:

[tex] \frac { 1 } { 6 ^ 3 } [/tex]

Therefore, the correct answer option is D. ( 1 / 6 ) ^ 3.

Answer:

The correct option is A. The given statement is true.

Step-by-step explanation:

Given statement: If A and B are two points in the plane , the perpendicular bisector of AB is the set of all points equidistant from A and B.

Let a line is perpendicular bisector of AB at point D and C be a random point of perpendicular bisector.

In triangle ACD and BCD,

[tex]AD=BD[/tex]                          (Definition of perpendicular bisector)

[tex]\angle ADC=\angle BDC[/tex]                          (Definition of perpendicular bisector)

[tex]DC=DC[/tex]                       (Reflexive property)

By SAS postulate of congruence,

[tex]\triangle ACD\cong \triangle BCD[/tex]

The corresponding parts of congruent triangles are congruent.

[tex]AC\cong BC[/tex]               (CPCTC)

[tex]AC=BC[/tex]

The distance between A to C and B to C are same. So, the set of all points on perpendicular bisector are equidistant from A and B.

The given statement is true. Therefore the correct option is A.

Final answer:

The statement is True because the perpendicular bisector is defined as the line that divides a line segment into two equal parts at its midpoint and is perpendicular to the segment, making all points on it equidistant from both endpoints of the segment.

Explanation:

The statement 'If A and B are two points in the plane, the perpendicular bisector of AB is the set of all points equidistant from A and B' is True. The definition of a perpendicular bisector is that it is a line which is perpendicular to another line segment (AB in this case) and divides it into two equal parts at its midpoint. Therefore, any point on the perpendicular bisector is equidistant from points A and B, which is a direct consequence of the definition.

This is further supported by Theorem 11, which states that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities makes equal angles with them and is bisected at right angles by a third perpendicular erected midway between them, ensuring that any point on this third perpendicular (the perpendicular bisector) is equidistant from A and B.

Answer:

$10d

Step-by-step explanation:

The unit price is $d per pound. It is a dollar amount divided by the number of pounds. If you multiply the unit price by pounds, then the units work out like this:

$/lb * lb = $

When you multiply the unit price in dollars per lb by lb, you get dollars.

In your case:

$d/lb * 10 lb = $10d

That value of the nuts is $10d.

Answer:

sqrt( 146)

Step-by-step explanation:

To find the distance between two points, we use the formula

d = sqrt( ( y2-y1)^2 + (x2-x1)^2)

Where (x1,y1) and (x2,y2) are the two points.

(–9, 0) and (2, 5).

Substituting into the equation

d = sqrt( (5-0)^2 + (2- -9)^2)

d = sqrt( ( 5^2 + (2+9)^2)

      sqrt( ( 5^2 + (11)^2)

   = sqrt( 25+121)

  = sqrt( 146)

The distance between the two points is sqrt(74)

Final answer:

The distance between the points (–9, 0) and (2, 5) in the Cartesian plane is approximately [tex]\sqrt{146}[/tex] units.

Explanation:

To find the distance between two points in the Cartesian plane, we can use the distance formula.

The distance formula is:

distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}[/tex]

Using the given points (–9, 0) and (2, 5), we can plug in the values:

distance = [tex]\sqrt{((2 - (-9))^2 + (5 - 0)^2)}[/tex]

distance = [tex]\sqrt{((11)^2 + (5)^2)}[/tex]

distance = [tex]\sqrt{(121 + 25)}[/tex]

distance = [tex]\sqrt{146}[/tex]

So, the distance between the points (–9, 0) and (2, 5) is approximately [tex]\sqrt{146}[/tex] units.

Answer:

1.3 repeating or 4/3

Step-by-step explanation:

if you take 24 and divide it by 18 this is the answer you receive

Answer:

C.

Step-by-step explanation:

If Erin has 9 more shells than Jamie, then 27 minus 9 would be equivalent to the amount of shells Jamie has.

This can be represented by:

[tex]27-9=j[/tex]

Which can be rewritten as:

[tex]27=j+9[/tex]

by adding 9 to both sides.

To solve, subtract 9 from 27.

[tex]27-9=18[/tex]

Jamie has collected 18 shells.

Answer:

C. 27=j+9; Jamie collected 18 shells.

Step-by-step explanation:

First, you do is switch sides.

[tex]\displaystyle j+9=27[/tex]

Then, you subtract 9 from both sides.

[tex]\displaystyle j+9-9=27-9[/tex]

Simplify, to find the answer.

[tex]\displaystyle 27-9=18[/tex]

Therefore, Jamie got collected of 18 shells.

[tex]\huge \boxed{18}[/tex], which is our answer.

The correct answer is C.

Answer:

[tex]7 \times {3}^{n - 1} [/tex]

Step-by-step explanation:

using form:

[tex]a \times {r}^{n - 1} [/tex]

where a: starting number

where r: common ratio (in this case each next term is 3 times previous term)

The nth term of the sequence 7, 21, 63, 189,... is given by the explicit rule an = 7 × 3(n-1), which applies to a geometric sequence with a common ratio of 3.

To find an explicit rule for the nth term of the sequence 7, 21, 63, 189,..., we notice that each term is three times the previous term. This indicates that the sequence is geometric with a common ratio of 3. The first term of the sequence (a1) is 7.

To find the nth term of a geometric sequence, the formula is an = a1 × r(n-1) where r is the common ratio. Plugging in the values for our sequence, we get the nth term as an = 7 × 3(n-1).

This gives us the explicit rule for the nth term of the given sequence, which allows us to calculate any term in the sequence based on its position, n.

Where an represents the nth term of the sequence and an-1 represents the previous term.

For example, if we want to find the 5th term of the sequence, we can use the formula:

a5 = a4 * 3 = 189 * 3 = 567

Answer:  24/4=D

Step-by-step explanation:

24LEGS/4LEGS=6DOGS

Answer:

4d=24

Step-by-step explanation:

4(dogs)=24 legs

so the answer is 6 dogs (in case you need it)

[tex]h(6)=3\cdot6-4=14[/tex]

Answer:

a. 14 is your answer.

Step-by-step explanation:

h(x) = 3x - 4

h(6) = ?

Plug in 6 for x: x = 6

h(6) = 3(6) - 4

Remember to follow PEMDAS. First, multiply, then subtract:

h(6) = (3 * 6) - 4

h(6) = (18) - 4

Simplify:

h(6) = 18 - 4

h(6) = 14

a. 14 is your answer.

~

Only statement B is true, so you would select that as the answer.

We can check if statement A is true by finding the ratio of cows to all animals, which we do by finding the total number of animals, 5 + 3 + 2 + 6 = 16.

Then we can say that the ratio of cows to all animals is 2:16, which simplifies to 1:8, so statement A is false.

Statement B is just another way of saying that the ratio of rabbits to all animals is 3:8, so we can see if this is true by finding the ratio of rabbits to all animals. There are 6 rabbits, so it would be 6:16, which simplifies to 3:8. This means that statement B is true.

I hope this helps! Let me know if you have any questions :)

Answer: 359 ft

Step-by-step explanation:

Whenever you have a problem like this, you must first make an assumption that the building (in this case the lighthouse) is perpendicular to the ground (or sea).  This allows you to create a right triangle (see attached image).

The angle of depression is the angle from an imaginary perpendicular line passing through the top of the building.  Since that imaginary line is parallel to the ground (or sea), you can use alternate interior angles to place that angle in the triangle.

NOTE: BOTH angle of elevation and angle of depression are placed in the lower corner of the triangle. Don't let the names confuse you!

Now you can use trigonometry to solve ....

In the given problem, we have the side OPPOSITE of the given angle (24°) and need the side ADJACENT to the angle, so we will use tan to solve for x.

[tex]tan\ \theta=\dfrac{opposite}{adjacent}\\\\\\tan\ 24^o=\dfrac{160}{x}\\\\\\\rightarrow x=\dfrac{160}{tan\ 24^o}\\\\\\\rightarrow x=359.4\\\\\\\rightarrow x\approx 359[/tex]

Answer:

Step-by-step explanation:

x=1, y=-1

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

y = 2x² - 6x + 3 → (1)

y = x - 2 → (2)

Since both equations express y in terms of x we can equate the right sides, that is

2x² - 6x + 3 = x - 2 ( subtract x - 2 from both sides )

2x² - 7x + 5 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 5 = 10 and sum = - 7

The factors are - 2 and - 5

Use these factors to split the x- term

2x² - 2x - 5x + 5 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) - 5(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x - 5) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]

Substitute these values into (2) for corresponding values of y

x = 1 : y = 1 - 2 = - 1 ⇒ (1, - 1)

x = [tex]\frac{5}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] - 2 = [tex]\frac{1}{2}[/tex]

Solutions are (1, - 1) and ( [tex]\frac{5}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Answer:

x^2  +  y^2  = 4

Step-by-step explanation:

The center-radius form (formally called the standard form) of a circle is

(x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.

So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:

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

Let's simplify:

x^2  +  y^2   = 4

[tex]\large\boxed{59\,\text{years old}}[/tex]

In this question, it's asking you to figure how old the oldest person in the company is.

To solve this, we would need to gather some important information from the question.

Important information:

With the information above, we can get closer to our answer.

We need some prior knowledge to solve this. The "range" is the highest number subtracted by the lowest number.

This means that the the 22 was already subtracted to get 37.

What we would do is reverse to solution and add 22 to 37 to get our highest number (oldest person).

[tex]37+22=59[/tex]

When you add them together, you should get 59.

This means that the oldest person in the company is 59 years old.

Answer:

Age of oldest person = 59 years

Step-by-step explanation:

Points to remember

Range of a data set is the difference between smaller value and larger value value in the set.

It is given that, the youngest person in the company is 22 years old. The range of ages is 37 years.

To find the age of oldest person

Range = 37 years

Youngest age =  22 years

Range = oldest age  - youngest age

oldest age = range + youngest age

 = 37 + 22

 = 59

Age of oldest person = 59 years

Answer:

(4,3)

Step-by-step explanation:

asoming 4 is x and 5 is y down 2 turns 5 into 3

Start at the point (4,5). Moving 2 units down decreases the y-coordinate by 2, thus bringing you to the new point (4,3). Draw a graph to visualize this better.

In the context of a grid in Mathematics, the first quadrant is where both x and y coordinates are positive. The given point starts at (4,5). If you move 2 units down, it means you are reducing the y-coordinate by 2 units. So, starting at (4,5) and moving 2 units down would land you at a new point, which will be (4,3).

To visualize this, you may want to draw a graph on an x-y axis and plot the points (4,5) and (4,3) to see how the position change looks.

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Answer:

all her patients patients with no cavities

patients younger than 18

every patient with braces

Step-by-step explanation:

when a sample is selected in a manner that some elements, in this case patients, of population have higher or lower probability of sampling then that sample is biased.

From given case, all the following are biased samples

all her patients patients with no cavities

patients younger than 18

every patient with braces

because they are non-random sample of a population in which all other elements were not equally likely to be chosen!

The dentist should avoid biased sampling methods.

The biased samples in this case would be:

1. All her patients: This would only include the dentist's current patients, which may not be representative of the entire population.
2. Patients with no cavities: This would only include a specific subset of patients who do not have cavities, which may not be representative of the entire population.
3. Patients younger than 18: This would only include patients below the age of 18, which may not be representative of the entire population.

It is important to have a random and representative sample in order to make accurate conclusions about the population's flossing habits.

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Answer:

The one that is not equivalent is 7x^3

Step-by-step explanation:

7x^3= 7 * x*x*x

4x+3x = 7x = 7*x

(4+3)x = (7)x = 7*x

7x= 7*x

Answer:

7x^3

Step-by-step explanation:

All of the following are equivalent except 7x^3.

7x^3 = 7x^3

4x+3x = 7x

(4+3)x = 7x

7x = 7x

Answer:

The shaped is being reflected.

Answer: Reflection

Step-by-step explanation:

When we look at the picture, the two rectangles QRST and Q'R'S'T' appears as the mirror images of each other , also the corresponding sides and angles are congruent.

The transformation that create a mirror image of the figure is known as reflection. It is a rigid transformation because it produces congruent shapes.

Therefore, the transformation maps rectangle QRST to rectangle Q'R'S'T' is reflection.