Compare the two numbers. Use > or < .
16, √16

The compound inequality in this problem is represented by:

y > -(x + 2)² + 6.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (-2,6), hence:

h = -2, k = 6.

y = a(x + 2)² + 6.

When x = 0, y = 2, hence we use it to find a as follows:

2 = 4a + 6

a = -1.

Hence:

y = -(x + 2)² + 6.

The inequality is the interior of the parabola, hence values greater, and the parabola is dashed, hence it is an open interval and the inequality is given by:

y > -(x + 2)² + 6.

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Answer:

Step-by-step explanation:

80¢ is your answer because Derek paid $3.20 for a pack of 4 Gatorade so you would have to divide $3.20 by 4 which will be 80¢

So your answer would be 80¢ per bottle.

The equation in point-slope form of the line having the slope m=-2 and the given point (-6,-7) is y+7=-2(x+6)

Given,

The slope = -2

The point = (-6,-7)

We know the point slope form [tex]y-y_{1}=m(x-x_{1})[/tex]

Substitute the values in the equation

y-(-7)=-2(x-(-6))

y+7=-2(x+6)

Hence, the equation in point-slope form of the line having the slope m=-2 and the given point (-6,-7) is y+7=-2(x+6)

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Answer:

Je vous souhaite le Bonjour dominical,

Step-by-step explanation:

Si tu veux une réponse:
soit tu postes ce devoir dans la matière French

soit tu postes le problème sur le site nosdevoirs.fr

f(2)=6*2²-7*2=24-14=10

f(-3)=6*(-3)²-7*(-3)=54+21=75

The slope of the equation is 5 for the coordinates (-3,5) and (4,5).

Locate two points along the chosen line and find their coordinates.

Find the y-coordinate difference between these two sites (rise).

Find the x-coordinate difference between these two sites (run). Subtract the difference in y-coordinates from the difference in x-coordinates (rise/run or slope).

The slope calculation formula is -

m = y2 - y1 / x2 - x1

Given points are -

(-3,5) and (4,5)

Now, putting the values in equation,

m = 5-5 / 4+3

m = o

As slope is 0, this implies,

the equation of line is y = 5

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Answer:0.02 mol/L

Step-by-step explanation:

Given: pH = 1.7

Required: [H+]

Equation: pH = -log [H+]

Solution:

Take the antilog of both sides

[H+] = antilog(-pH)

Antilog(-pH) is equal to 10^-pH. Therefore

[H+] = 10^-pH

Solve for [H+]

[H+] = 10^-1.7

Answer: [H+] = 0.02 mol/L

Step-by-step explanation:

least value is q

greatest value is n-q

close to zero is q-n

45,90,180,360, .... is a geometric sequence. The next two terms are 720, 1440.

In an arithmetic sequence, the difference between two subsequent terms is constant. This difference between two subsequent terms is usually called common difference (d), and its value is:

d = a(n) - a(n-1)

Where a(n) is the nth term and a(n-1) is the (n-1)-th term.

In a geometric sequence, the ratio (r) between two subsequent terms is constant.  

r = a(n)/a(n-1)

The given sequence is: 45,90,180,360, .....

We can check that:

(90 - 45) is not equal to (180 - 90) and to (360 - 180)

So, there is no common difference in the given sequence.

Let us now check the ratio:

90/45 = 180/90 = 360/180 = 2

The ratio between two subsequent terms is constant, that is 2. Therefore, we can conclude that the given sequence is a geometric sequence with a(1) = 45 and r = 2.

In a geometric sequence, the next term is obtained by multiplying the current term by its ratio.

Hence, the next two terms are calculated as:

360 x 2 = 720

720 x 2 = 1440

or 720, 1440.

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Answer: 46 inches

Step-by-step explanation: the larger piece is 92 inches 92+46=138

Answer:

3 1/9

Change 2/3 to 6/9. Add 6/9 + 4/9 to get 10/9. Make a mixed number, 1 1/9. Add 2, 3 1/9.

Answer: 1.6,1.8,2.5,6.7,6.9,7.5

Step-by-step explanation:

Step-by-step explanation:

1.6 1.8 2.5 6.7 6.9 7.5

was that really all ? I don't see any trap in these numbers, so this is straight forward.

The ratio of pencils to all the item on the desk is 1 : 10

According to Gary,

    Number of pencils on the desk = 4

    Number of markers on the desk = 12

   Number of crayons on the desk = 24

Total number of item son the desk = 4 + 12+ 24

                                                             = 40

The ratio of pencils to all the item is given as = (number of pencils)/(total number of items)

                                                                                = 4/40

                                                                                = 1/10

                       Which in ratio can be written as 1 : 10

Thus the ratio of pencils to all the item is 1 : 10  

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Your answer would be the second one.

We know that adding [tex]\frac{1}{2}[/tex] to x gives us 4, as that's provided by the question.

So [tex]4=x+\frac{1}{2}[/tex]. Now, to find x, simply subtract [tex]\frac{1}{2}[/tex] from 4 to give us x, which gives us [tex]3\frac{1}{2}[/tex].

Part (a)

The horizontal part of the rectangle goes from m = -1 to n = 4. This is a distance of 5 units because |m-n| = |-1-4| = 5

The height is some unknown variable h

It must multiply with the base (5) to get an area of 1

base*height = area

5h = 1

h = 1/5

h = 0.2

========================================================

Part (b)

x = dismissal time minutes after class

Something like x = 2 means he dismisses class 2 minutes after the bell, while x = -1 is him dismissing class 1 minute early before the bell.

The phrasing "within 1 minute" means that x is between p = -1 and q = 1. So we can say [tex]-1 \le x \le 1[/tex]

This is a span of 2 units because |p-q| = |-1-1| = 2. Divide this over the entire horizontal span: 2/5 = 0.4

Exactly 40% of the time the teacher lets his class out within one minute of the scheduled end time.

Answer:

We can use the point-slope form of the equation of a line to find the equation that passes through the points (3, 5) and (6, 7).

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1, y1) is one of the points on the line and m is the slope of the line.

First, we need to find the slope of the line using the two given points. The slope formula is:

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

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

Plugging in the values we know, we get:

m = (7 - 5) / (6 - 3) = 2 / 3

So the slope of the line is 2/3.

Now we can use one of the given points and the slope to write the equation of the line in point-slope form. We'll use the first point, (3, 5).

y - 5 = (2/3)(x - 3)

This is the equation of the line in point-slope form.

If we want to write it in slope-intercept form (y = mx + b), we can simplify:

y - 5 = (2/3)x - 2

y = (2/3)x + 3

So the equation of the line that passes through the points (3, 5) and (6, 7) is y = (2/3)x + 3.

Answer:

k = -10

Step-by-step explanation:

1) Because of the division of the left side of the equation by 2, multiply both sides of the equation by 2, which means you now have :

-8 - 3k = 22

2) Now, add eight to both sides. Your equation now looks like this:

-8 + 8 - 3k = 22 + 8

3) Simplify.

-3k = 30

4) You now have k = -10

The function is neither an even function nor an odd function

The function is given as

g(x) = x + x^2

Calculate g(-x)

So, we have

g(-x) = -x + (-x)^2

Evaluate

g(-x) = -x + x^2

Calculate -g(x)

So, we have

-g(x) = -x - x^2

In the above computations;

g(x) does not equal g(-x) and -g(x)

Hence, the function is neither an even function nor an odd function

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The number of students that Fairview High School have in 2006 is 1615 students.

This is a question of percentages.

Given that:-

The number of students in Jefferson High School had in 2000 are 1125.

The number of students in Jefferson High School had in 2005 are 1425.

The number of students in Fairview High School had in 2000 are 1275.

It is given in the question that the student body of Fairview High school grew at the same rate as Jefferson High School.

We have to find the number of students in Fairview High School in 2006.

Rate at which the number of students grew at the  Jefferson High School =

[(1425-1125)/1125]*100 = (300/1125)*100 = 26 (2/3) % or 80/3 %

Let the number of students in the Fairview High School in 2005 be x.

Hence,

80/3 = [(x-1275)/1275]*100

x = 1615

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Answer:

Distance: 4√41

Midpoint: (2, 3)

Step-by-step explanation:

A: (-6, 13) B: (10, -7)

    (x₁, y₁)       (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(10 - (-6))² + (-7 - 13)²

d = √(16)² + (-20)²

d = √256 + 400

d = √656

d = √16 × 41

d = 4√41

midpoint:

(x₁ + x₂)    (y₁ + y₂)

---------- , ------------

    2            2

(-6 + 10)   (13 + (-7))

---------- , ------------

    2            2

   4             6

---------- , ------------

    2            2

Midpoint = (2, 3)

I hope this helps!

Answer:

The Answer is y=-6

The required value of constant of variation, k does not exist for which x and y vary directly..

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Given relation is  y + 3 = -3 x

y = -3 x - 3

y = -3(x + 1)

Comparing with equation 1, we get that y does not vary directly for any value of k.

Hence, the required value of constant of variation is does not exist.

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Answer:

In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.

Step-by-step explanation:

in easy language it's Transformations. Transformation means to change. Hence, a geometric transformation would mean to make some changes in any given geometric shape.

The two numbers other than 1 and 1 are 2 and 3 finally get the 34 means 7 th term in the sequence.

The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.

from the question

Let take the first term as 2.

and second term as 3.

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 + 34 = 55

34 + 55 = 89

The Fibonacci sequence includes the numbers 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.

Sum=2+3+ 5 + 8 +13 + 21+

34+55+89+144 = 374 is what we get when we add up the numbers in the series.

The first ten Fibonacci numbers sum is 374.

now divided the sum by 11.

374/11 = 34.

so,to get the 34 means 7 th term in the sequence.

Hence, the two numbers other than 1 and 1 are 2 and 3. finally get the 34 means 7 th term in the sequence.

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an=a1+d(n−1)  is the explicit and a recursive formula for each sequence .

See the pattern

-32-(-20) = -12

-20-(-8) = -12

-8-4 = -12

By this the explicit and a recursive formula for each sequence is  an=a1+d(n−1).

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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The fraction converted to an improper fraction is 11/3

An improper fraction can be defined as a type of fraction whose numerator is equal to or is greater than its denominator.

Examples of improper fractions are;

5/ 3, 8/2 , 11/ 7, 20/ 5, 4/ 1, 2/ 2, 5/ 3

Given the fraction;

3 2/3; this is a mixed fraction

To convert to improper fraction, we take the steps

Multiply the whole number by the denominator;

= 3 × 3 = 9

Add the value to the numerator

= 9 + 2 = 11

Divide by the denominator

= 11/ 3

Thus, the fraction 3 2/3 converted to an improper fraction is 11/3

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We can conclude that triangle ΔPQR ≇ ΔXYZ.

So,

Given: P(-3,-3), Q(-5,1), R(-2,6), X(2,-6), Y(3,3), Z(5,-1)

To find if ΔPQR ≅ ΔXYZ

So, ΔPQR ≇ ΔXYZ.

Therefore, ΔPQR ≇ ΔXYZ.

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Answer:

x = 7

Step-by-step explanation:

➟ x² = 49

in order to find the value of x will have to take square root of both side

➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]

Calculate

➟ [tex] \sf \: x = 7[/tex]

Answer:

1) 140°

2) 40°

3) 140°

4) 40°

5) 140°

6) 40°

7) 140°

Step-by-step explanation:

1) Angles on a straight line = 180°

180° - 40° = 140°

2) Angle 3 is Vertically opposite to Angle 1

So they are the same Angle

3) Angle 4 is Vertically opposite to Angle 2

So they are the same Angle

4) Angle 5 is corresponding to Angle 1

So they are the same angle

5) Angle 6 is corresponding to Angle 2

So they are the same angle

6) Angle 7 is corresponding to Angle 3

So they are the same angle

7) Angle 7 is corresponding to Angle 4

So they are the same angle