What is the quotient of 3,968 ÷ 32?

The correct statement about the given function is: The function is increasing for all real values of x where x < –4.

In this question, we have been given the graph of the function

f(x) = -(x + 6)(x + 2)

According to description of the graph of given function f(x), the graph of function is a parabola and on a coordinate plane, a parabola opens down.

Also, the parabola goes through (-6, 0), has a vertex at (-4, 4), and goes through (-2, 0).

We need to find to the correct statement about the function.

f(x) = -(x + 6)(x + 2)

The function is increasing until it reaches the vertex x = -4.  

The function will decrease after the vertex, so after x = -4 function decreases.

increasing: -∞ < x < -4

decreasing : -4 < x < ∞

Therefore, the correct statement about the given function is: The function is increasing for all real values of x where x < –4.

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Answer: \(4m^{6}\)

Step-by-step explanation:

\(\frac{8.4m^{9} n^{5} }{2.1m^{3}n^{5}}\)

Dividing exponents is the same as subtracting the exponents, so

\(\frac{m^{9}}{m^{3}} =m^{9-3}=m^{6}\)

\(\frac{n^{5}}{n^{5}} =n^{5-5}=n^{0}=1\)

So now our equation looks like

\(\frac{8.4m^{6}}{2.1}\)

Now we can divide the numbers

8.4/2.1 = 4

So your final answer is \(4m^{6}\)

The series appears to be     166, 199, 232, 265, 298, 331

With examples, define sequence?

A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.

                                      In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.

The last number of the common difference must end in 3

And this must be a 2 digit number

So....the first number must end in 6

The the 4th number must be 265

So..... the 5th number  must end in 8

And the last digit  of the last term must end in  1  [ and begin with 3 ]

Putting all this together  we have that

265  + 2d  =  331

2d  = 66   ⇒  d = 33

So  the first term must be  265 - 3 (66)  =  166

the series appears to be     166, 199, 232, 265, 298, 331

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Answer:

A≈78.54cm²

Step-by-step explanation:

Solution

A=πr2=π·52≈78.53982cm²

Answer:

Step-by-step explanation:

\(\[\displaystyle\sum_{n=-2, n~par}^{86}(2n+1)=-3+1+5+~.~.~.~+169+173\\\\n=-2,~0,~2,~4,.~.~.,~86\]\)

The perimeter and area of the rectangle with given vertices are  24 units and the area is 27 square units.

To find the perimeter and area of the rectangle with the given vertices, we can use the distance formula and the formula for rectangle area.

First, let's find the lengths of the sides using the distance formula:

Side AB: √[(x₂ - x₁)² + (y₂ - y₁)²]

         = √[(5 - 5)² + (-3 - 6)²]

         = √[0² + (-9)²]

         = √81

         = 9

Side BC: √[(x₂ - x₁)² + (y₂ - y₁)²]

         = √[(2 - 5)² + (-3 - (-3))²]

         = √[-3² + 0²]

         = √9

         = 3

Now, we can calculate the perimeter by adding the lengths of all four sides:

Perimeter = AB + BC + CD + DA

         = 9 + 3 + 9 + 3

         = 24

To find the area of the rectangle, we can use the formula:

Area = Length × Width

The length of the rectangle is AB = 9 and the width is BC = 3.

Area = 9 × 3

        = 27

Therefore, the perimeter of the rectangle is 24 units and the area is 27 square units.

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The three numbers are 10, 20, and 40.'

Let's assign variables to each number:

According to the problem, the sum of these three numbers is 70:

x + y + z = 70

Now, we can substitute the expressions for y and z in terms of x:

x + 2x + 2(2x) = 70

Combine the terms:

x + 2x + 4x = 70

7x = 70

Now, divide by 7 to find the value of x:

x = 70 / 7

x = 10

Now that we have the value of x, we can find the values of y and z:

y = 2x = 2(10) = 20

z = 2y = 2(20) = 40

So, the three numbers are 10, 20, and 40.

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The question in English is

The sum of 3 numbers is 70, the second number is twice the first and the third is twice the second.

Answer:

See below

Step-by-step explanation:

1. Reflection by a factor of (-3) and vertical shift down -12 units

2. Vertical shift up by 4 units and reflection by a factor of (-3)

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:

x=-2,x=-10

Step-by-step explanation:

x²+12x=-20

add both sides (12/2)^2 ,i.e.,36

x+2+12x+36=-20+36

(x+6)²=16=4²

x+6=±4

either x+6=4

x=4-6

x=-2

or x+6=-4

x=-4-6

x=-10

In this exercise we have to use the knowledge of equations to calculate the value that X can obtain, in this way we find that:

\(x=-2\\x=-10\)

Given the initial equation as:

\(x^2+12x=-20\)

We will have to add on both sides of the equation the value of 36, so we find that:

\(x^2+12x+36=-20+36\\(x+6)^2=16=4^2\\x+6=\±4\)

As every quadratic equation we find two possible values ​​for X and we will have to test them, so:

\(x+6=4\\x=4-6\\x=-2\)

\(x+6=-4\\x=-4-6\\x=-10\)

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Answer:

I dont get itt

Step-by-step explanation:

Answer:

11/18

Step-by-step explanation:

let n represent the number to be found

simplify the ratio on the right by multiplying both parts by 3

we now have

n/11 =11/18  ( cross-multiply )

18n = 11 ( divide both sides by 18 )

n = 11/18

Answer: Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(5,−2),(−3,−10)

Equation Form:

x=5,y=−2x=5,y=-2

x=−3,y=−10x=-3,y=-10

Maybe want something different then here:

X intercepts- (7,0)

Y intercepts- (0, -7)

The value of the given problem by using box method is 2546.

Multiplication computations involving numbers greater than ten can be simplified using the grid method, sometimes referred to as the box method, which is also known as the method of boxes. Making a table with the first factor's place values along the top and the second factor's place values down the left is how you multiply two numbers using the box approach. Place values are multiplied, and their products are added to the table. Clear up the table. In arithmetic, there is an alternative to the lengthy, error-prone classical multiplication approach: the box method. Multiplication of two or more digits is made easier with the use of the box approach.

X       60        7

30    1800    210

8       480      56

Therefore, 1800+480+210+56=2546

Therefore, the value of the given problem by using box method is 2546.

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Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer: $3.10 per gallon

Step-by-step explanation: 9.30 divided by 3

Answer:

$3.10 is the answer

Step-by-step explanation:

To find Unit rate you do whole to part. So you divide the whole to the part. In this expression the whole is $9.30 and the part would be per gallon or $3 when you divide 9.30 by 3 it should give you 3.10 or 3.1 which is the same thing.

the intersection points are (1, 7) and (4, 13), So the correct option is A.

To see that, we need to see when the two equations:

y = -x²+7x+1

y = 2x + 5

Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.

y = -x²+7x+1

y = 2x + 5

We can rewrite:

-x²+7x+1 = y =  2x + 5

Then we can solve this for x:

-x²+7x+1 =  2x + 5

x² - 5x + 4 = 0

This is just a quadratic equation, the solutions are:

\(x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}\)

So we have two values of x:

The correspondent values of y are:

y = 2*(4) + 5 = 13

y = 2*(1) + 5 = 7

Then the intersection points are (1, 7) and (4, 13)

Then the correct option is A. The dog will catch the frisbee.

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Hence, He had to pay $ 18.11 for the tip on a restaurant bill.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Josiah ate dinner at a restaurant and his bill was $15.75,

He wanted to leave  15% tip,

Then He had to pay,

=15.75+15 % of 15.75

=15.75 + 0.15*15.75

=18.11

Hence, He had to pay $ 18.11 for tip on the restaurant bill.

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the equation of the line is

y = -3x + 6

slope is m = -3

as we know that for parallel lines, the slope is always equal.

so the slope of the new line is also m = -3

it is also passing through (-4,9)

so the equation of the line i s

m= -3

so the answer is y = -3x - 3

Step-by-step explanation:

Find the x- and y-intercepts of the graph of x+10y=20.

x intercept when y = 0:

x + 10y = 20

x + 10(0) = 20

x = 20

or in point format: (20 , 0)

y intercept when x = 0:

x + 10y = 20

0 + 10y = 20

10y = 20

10y/10 = 20/10

y = 2

or in point format: (0 , 2)

The expression given as -8+19+8 has a value of 19

From the question, the expression is given as

-8+19+8

Rewrite the expression properly

This is rewritten as follows

-8 + 19 + 8

Collect the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 8 - 8 + 19

Evaluate the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 0 + 19

Finally. we add 0 and 19

So, we have the following equation

-8 + 19 + 8 =  19

Hence, the valye of the expression is 19

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The obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

In mathematics, the addition, subtraction, division, and multiplication of built-in expressions can also be used to specify arithmetic operations.

The expression which is given in the question is below

⇒ -8 + 19 + 8

Rearrange similar terms in the above expression,

⇒ 8 - 8 + 19

Apply the subtraction operation,

⇒ 0 + 19

Apply the addition operation to get the answer,

⇒ 19

Hence, the obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

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Answer:

143 degrees

Step-by-step explanation:

First find angle ACB which is 180-83=97

Then angle ABC which is 180-134=46

Then angle CAB (97+46)-180=37

Finally angle HAB 180-37=143

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

Explanations:

Problem 10

The order of the toppings doesn't matter. All that matter is the group itself. We'll use the combination formula nCr = (n!)/(r!*(n-r)!) where n = 12 and r = 3 in this case.

So,

nCr = (n!)/(r!*(n-r)!)

12C3 = (12!)/(3!*(12-3)!)

12C3 = (12!)/(3!*9!)

12C3 = (12*11*10*9!)/(3!*9!)

12C3 = (12*11*10)/(3*2*1)

12C3 = 1320/6

12C3 = 220

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

Problem 11

Like with problem 10, the order doesn't matter. This is assuming that each member on any given team has the same rank as any other member.

If you used the nCr combination formula, with n = 9 and r = 5, you should get the answer 126

Here's another way to get that answer.

There are 9*8*7*6*5 = 15120 different permutations. If order mattered, then we'd go for this value instead of 126

Within any group of five people, there are 5! = 120 different ways to arrange them. So we must divide that 15120 figure by 120 to get the correct value of 126 combinations

15120/120 = 126

Note the connection between nCr and nPr, namely,

nCr = (nPr)/(r!)

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

Problem 12

Now this is where order matters, because the positions in basketball are different (eg: a point guard differs from a center).

We have 13 choices for the first position, 12 for the second, and so on until we reach 13-r+1 = 13-5+1 = 9 as the number of choices for that last slot.

So we'll have 13*12*11*10*9 = 154,440 different permutations

Now if the condition that "each player can play any position" isn't the case, then the answer would very likely be different. This is because for the center position, for instance, we wouldn't have 13 choices but rather however many choices we have at center. To make the problem simpler however, your teacher is stating that any player can play at any slot. Realistically, the answer would be far less than 154,440

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

Problem 13

We have 6 applications for the 2 math positions. Order doesn't matter. That means we'll have 6C2 = 15 different ways to pick the math people. Use the nCr formula mentioned in problem 10. Since we'll use this value later, let's make x = 15.

There are 2 people applying for the chemistry teaching position, meaning there are 2 ways to fill this slot. We could compute 2C1 = 2, but that's a bit overkill in my opinion. Let y = 2 so we can use it later.

Similarly, there are 10 applicants for the Spanish teacher position, leading to 10 ways to get this position filled. You could compute 10C1 = 10 if you wanted to. Let z = 10 so we can use it later.

Once we figured out those x,y,z values, we multiply them together to get our final answer: x*y*z = 15*2*10 = 30*10 = 300

There are 300 different ways to select 2 math teachers, a chemistry teacher, and a Spanish teacher from a pool of 6 math applicants, 2 chemistry applicants, and 10 Spanish teacher applicants.

Answer:

x = 2, x = -8

Step-by-step explanation:

Since the equation equals 0, you know either (x-2) or (x+8) has to equal 0.

This means x = 2, and x = -8

Hope this helps!

The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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The value of the expression 2f(-3) - f( 4) is 23

Note that function are expressions explaining the relationship between two variables.

From the information given, we have that;

f(x) = 3x² - x + 5

To determine the f(-3), substitute the values, we get;

f(-3) = 3(-3)² - (-3) + 5

expand the bracket

f(-3) = 27 + 3 + 5

Add the values

f(-3) = 35

Then, f(4),

f(4) = 3(4)² - 4 + 5

f(4) = 48 - 1

f(4) = 47

Then,

2f(-3) - f(4)

70 - 47

23

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To be congrent two figures need to have corresponding sides with the same measure.

Non-rigid motion or transformations are those that change the structure of a figure

Rigid motion or transformations are those than doesn't change the structure of a figure.

If you compare the figures you can identify the correspondig points:

W and M

U and N

S and K

T and J