Write an equation of
the line that passes
through (7, 10) and
is perpendicular to the
line y =
x-9.
Equation:
2

The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.

From the question, we have

2x -3+x>x+1

⇒3x-3>x+1

Subtract x from both sides, we get

⇒3x-3-x>x+1-x

⇒2x-3>1

⇒2x>4

⇒ x > 2

The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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The numbers of hours per week teenagers spend playing a sport or outdoor game is 2.4 or 2[tex]\frac{1}{15}[/tex] hours.

What is Averaging?

This refers to the mean value, which is equal to the ratio of all the numbers added and divided by the number of a given set of values present in the set of values.

Average= x₁+x₂+x₃+x₄..........xn

                        n

Where,

x₁+x₂+x₃+x₄..........xn = Given set of values

                             n= Number of a given set of values

From the question:

The number of hour per week spent playing a port or a game outdoors:

3; 2; 0; 6; 3; 3; 3; 1; 1; 2

number of teenagers,n =10

Average= 3+ 2+ 0+ 6+3+3+3+ 1+ 1+2

                                  10

               =2.4 or 2[tex]\frac{1}{15}[/tex] hours.

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The lengths of the sides of the rectangular field in order to minimize the cost will be length = 6000 feet and width = 4000 feet  .

In the question ,

it is given that ,

the area that farmer need to fence = 24 million square feet

let the length of  field be [tex]=[/tex]"x"   and

let the width  of rectangular field be  [tex]=[/tex]"y"  .

So , the area of the rectangular field = x.y = 24

So , y = 24/x  .

given that the field is divided into half ,

So , the required fencing will be

S = 2x + 3y

Substituting y = 24/x in the equation,

we get ,

S = 2x + 3(24/x)

S = 2 + 72/x

Differentiating the equation "S [tex]=[/tex] 2 [tex]+[/tex] 72/x" with respect to "x" ,

dS/dx = 2 - 72/x²

to minimize the cost of fencing , we equate ds/dx to 0 ,

we get

2 - 72/x² = 0

x² = 36 million feet

x² = 36000000

x = 6000 feet

and y = 24/x = 24million/6000

= 24000000/6000

= 4000 feet

Therefore , The length of the rectangular field is 6000 feet and the width of the rectangular field is 4000 feet .

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If ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1), the measure of x will be 29°.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),

Complementary angles are those where the sum of the two angles is 90 degrees. In other words, two angles are considered complementary if they combine to form a right angle. The two angles are said to complement one another in this context.

Since ∠EFH and ∠HFI are complementary angles,

∠EFH + ∠HFI = 90

(2x + 2)+ (x+1) =90

3x+3=90

x+1=30

x=29°

Thus, if ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)°  and ∠HFI= (x+1),the measure of x will be 29°.

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Answer:

angle a = 74 degrees

angle b = 106 degrees

angle c = 106 degrees

angle d = 65 degrees

angle e = 65 degrees

Step-by-step explanation:

Angle a:

the Alternate Interior Angles Theorem makes angle a equal to 74 degrees

Angle b:

First find angle c, and angle b is equal to angle c because angle b and c are Corresponding angles

Angle c:

angle c = 180 degrees - 74 degrees

angle c = 106 degrees

Angle d:

angle d corresponds with 65 degrees, therefore the are the same.

Angle e:

angle d and e are opposite angles, therefore they are the same.

Answer:

enter a function and from there you approximate hope it helps

Answer:

Yes.

Step-by-step explanation:

if 6s=24, s = 4 because 6 x 4 = 24

so

6s divided by 6 = 24 divided by 6 because 6 x s = 24

SOO

24 divided by 6 = 24 divided by 6

Answer: T= 1

Step-by-step explanation:

So, lets think about the information we are given.

Sammy earns 23,400 in a given year.

In a year, he works 52 weeks.

Per week, he works 30 hours.

Find hours -> find pay.

To find hours, multiply number of weeks by hours

52 * 30 = 1560

He works 1560 hours per year.

To find hourly income, divide total money per year by hours per year.  He makes 15 dollars per hour.

Find $ per week.

Hourly rate by hours per week

15 * 30 =450 per week

Hope this helps :)

Answer:

Sami had an hourly pay rate of $15 an hour

Step-by-step explanation:

Multiply 52 by 30 and you get 1,560, this is the total number of hours sami worked in a year.

If Sami made $23,400 in one year and worked 1,560 hours, you divide the total amount of hours work and total amount of money made to get an hourly pay rate of $15 an hour.

The statement “A teacher compares the pretests and posttest scores of students” is an example of matched pairs design.

Given data;

A teacher contrasts the results of her class's standardized test with the entire country's results. An instructor contrasts the results of the students' pre-and post-tests. A teacher computes the average grade received by students on two tests and checks to see if it is greater than 80%. An instructor contrasts the results of students who were taught using a computer-based method with those of post-students whose students ought to use a more conventional approach.

⇒

The statement “A teacher compares the pretests and posttest scores of student” using here would be approach-test because the sample “the students’ scores” are being compared with the two different treatments” and pretest and posttest scores.

A matched pairs design is demonstrated with the sentence "A teacher compares the pretests and posttest scores of students."

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Answer:

34

Step-by-step explanation:

Triangle is an isosceles triangle, where two angles are the same. BA=BC

Answer:34

Step-by-step explanation:

its an isosceles triangle because two sides are equal

If in a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, The probability of choosing a boy or an A student 4 / 5

From the question, we have the following data

Total number of students = 25

The total number of boys = 14

The students that are A male students = 6

Then we would have probability of having an A male student to be:

Total boys + A male students / total

= 14 + 6 / 25

= 4 / 5

Hence the probability is 4 / 5

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1353 numbers of minutes he has used his phone in a month.

What do you mean by algebraic expression?

In mathematics, an algebraic expression is an expression composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by exponents that are rational numbers).

Algebraic equations are equations that contain only algebraic expressions.

Algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual value. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.

It is given that Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use.

Let m be the additional minutes

Then charge for additional minutes is $0.07m

Now , it is also given that least he has been charged in a month is

$121.71.

⇒ 0.07m + 27 = 121.71

⇒ 0.07m = 121.71 - 27

⇒ 0.07m = 94.71

⇒ m = 94.71/0.07 = 1353

Therefore, 1353 numbers of minutes he has used his phone in a month.

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Answer:

The highest power of a variable in a function is known as its degree.

Step-by-step explanation:

Examples:

x + 5 is 1st degree, since x is to the power of 1.

5[tex]x^{3}[/tex] + 3x + 5 is 3rd degree.

[tex]x^{21}[/tex] +99 is 21st degree.

192.5  the length of the longest side of triangle DEF .

What do you mean by congruent?

Triangle ABC ~ Triangle DEF.

SO, both triangle sides are equal .

7/17.5 = 9/22.5  = 11/x

1/17.5 = 11/x

x = 11 * 17.5

x = 192.5

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The correct answer is:  " 4096 x⁶ " .

Step-by-step explanation:

Given:   [(4x)³] ² ;  Simplify.

Method 1)
Note the following multiplication property of exponents:
    ⇒ (aᵇ)ᶜ  = a⁽ᵇ*ᶜ⁾  ;

As such:

   [ [(4x)³] ²  = (4x)⁽²ˣ³⁾ = (4x)⁶ ;

Now; note the following property of exponents:
   (ab)ᶜ  = aᶜ * bᶜ  ;

As such:  (4x)⁶ = 4⁶ * x⁶ ;

Now; we can simplify 4⁶  ;  by using a calculator:
  →  4⁶  = 4096 ;

Or:  4⁶  =  4 * 4 * 4 * 4 * 4 * 4 ;

            =  (4 * 4) * 4 * 4 * 4 * 4 ;

            = 16 * 4 * 4 * 4 * 4 * ) ;

            = (16 * 4) * 4 * 4 * 4 ;

            =  64 * 4 * 4 * 4 ;  

            =   (64 * 4) * 4 * 4 ;

            =   (126 * 4) * 4    

            =  (256) * 4 ;

            =  4096 .
_______

or:   4⁶  = 4 * 4 * 4 * 4 * 4 * 4 ;

             =  (4 * 4) * (4 * 4) * (4 * 4) ;

             = 16 * 16 * 16 ;

             =  (16 * 16) * 16 ;

             = (256) * 16 ,   =  4096.

_______
So:       [(4x)³] ²  =  4⁶  *  x⁶  =  4096 x⁶ ;
_______
Method 2) Given: [(4x)³] ² ;

 (4x)³     =  4x * 4x * 4x ;

 [(4x)³]²  =  (4x * 4x * 4x)²

              = (4x * 4x * 4x) * (4x * 4x * 4x) ;

              =    (4 * 4 * 4 * x * x * x * 4 * 4 * 4 * x * x * x ;

              =   4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

 ⇒ (4 * 4 * 4 * 4 * 4 * 4)  = 4⁶  = 4096 ; (see Method 1 above).
 ⇒ (x * x *  x * x * x * x)  = x⁶ ;

                      ⇒  [(4x)³] ² =  4⁶ * x⁶ =  4096 x⁶ ;
_______
Method 3)
 [(4x)³] ²  = (4x)⁽²ˣ³⁾  = (4x)⁶ ;

      (4x)⁶ = 4x * 4x * 4x * 4x * 4x * 4x ;

              = 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;

              = (4 * 4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x) ;

⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; [see Method 1 above].
⇒  (x * x * x * x * x * x)  = x⁶ ;

                      ⇒   [(4x)³] ² =  4⁶ * x⁶ =  4096 x⁶ .

_______
The correct answer is:  " 4096 x⁶ " .

_______
Hope this is helpful.

  Best wishes in your academic endeavors!
_______

Answer:

Simplify (4x to the power of 3) power of 2

Step-by-step explanation:

The school I go to tells me to do this:

(4x^3)^2

(4x^3)(4x^3)

(4)(4) - 16

(x^3)(x^3) - x^6 bc you add the exponents

16x^6 which is correct bc my teacher has checked us on that before in class bc we have had equations like that ^_^

The statement that best compares the graph of G(x) with the graph of F(x) is the graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units to the left.

According to the question,

We have the following information:

F(x) = x² and G(x) = -1/4 (x+7)²

Now, the graph of G(x) will be the graph of F(x) but there will be certain changes in the graph according to its function.

Now, in this function, 7 is added to x then it means that it will shift 7 units to left.

There is a negative sign before the function which says that is flipped over the x-axis.

Now, the factor 1/4 in the multiplication says that it has been compressed.

Hence, the correct option is D.

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An equation for the constant of proportionality is (b) y = kx

From the question, we have the options to represent the given parameters

An equation that represents a constant of proportion passes through the origin

So, we have the following points

(x, y) = (0, 0) and (x, y)

The slope (k) is then calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

k = (y - 0)/(x - 0)

Evaluate the difference

k = y/x

Make y the subject

y = kx

Hence, the constant of proportionality has an equation of (b) y = kx

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Answer:

4/9

Step-by-step explanation:

Area of a triangle is 1/2*base*height

1/2*2/3*4/3 = 8/18 = 4/9

Answer:

a is right (prime number is always a even number)

Answer:

A.

a prime number may be an even or an odd number

The equation can be proved by taking Pythagorean Triplets into consideration, therefore 5^{2} + 12^{2} = 13^{2}

What are Pythagorean Triplets?

The "Pythagorean Triple" is a collection of three positive numbers, a, b, and c, that satisfy the following rule:

a^{2} + b^{2} = c^{2}

From the figure two in the attached image it can be very well observed that 5,12 and 13 are making a pythagorean triplets, therefore it can be said 5^{2} + 12^{2} = 13^{2}

Hence Proved.

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Since in the question we reject the alternative hypothesis hence type II error occurs.

What is Type I error?

When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.

What is Type II error?

Type II errors take place when you fail to reject the null hypothesis even though it is untrue.

The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.

Hence, this is a Type II error.

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Answer:

3.82%

Step-by-step explanation:

17.5 miles is the runner training distance in the tenth week.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The first​ week, she runs 4 miles during each training session

Each​ week, she increases her distance by 1.5 miles.

4,5.5,7,8.5....

The given sequence is a Arithmetic sequence, a is the first term and d is common difference

a=4,d=5.5

We need to find the distance in the tenth week.

n=10

aₙ=a+(n-1)d

a₁₀=4+(10-1)(1.5)

a₁₀=4+9(1.5)=4+13.5=17.5

Hence 17.5 is the runner training distance in the tenth week.

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In the tenth week, the runner will run 17.5 miles.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, A runner is training for a marathon.

The first​ week, she runs 4 miles during each training session.

Here a₁ = 4.

Each​ week, she increases her distance by 1.5 miles.

d = 1.5

We know the nth term of an AP is aₙ = a₁ + (n - 1)d.

∴ In tenth week which is a₁₀ the runner will run,

a₁₀ = a₁ + (10 - 1)×1.5

a₁₀ = 4 + 9(1.5).

a₁₀ = 4 + 13.5.

a₁₀ = 17.5 miles.

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The value is 5/2 and 35/2 pounds.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.

Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.

The ratios of  the given table

Table 10,

[tex]\begin{aligned}&\Rightarrow \frac{5}{3}=\frac{1}{x} \\&\Rightarrow x=\frac{3}{5} \\&\Rightarrow \frac{5}{3}=\frac{12}{x}=\frac{12+3}{15} \\&\Rightarrow x=\frac{12}{5}\end{aligned}[/tex]

Table 9,

[tex]\begin{aligned}&\frac{10}{4}=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{1} \\&x=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{7} \\&x=\frac{35}{2}\end{aligned}[/tex]

[tex]\begin{array}{rccc}\text { 9) pounds } & 10 & \frac{5}{2} & \frac{35}{2} \\\text { Weeks } & 4 & 1 & 7 \\\text { 10) tons } & 5 & 1 & 12 \\\text { days } & 3 & \frac{3}{5} & \frac{12}{5}\end{array}[/tex]

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The value of the fraction 28/63 in the simplest form is 4/9.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, we want to reduce 28/63 yo the simplest term. This will be illustrated thus:

= 28/63

= (7 × 4) / (9 × 7)

= 4 / 9

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[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}} \implies \cfrac{-18}{1 +8} \implies \cfrac{ -18 }{ 9 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-8)}) \implies y -8 = - 2 ( x +8) \\\\\\ y-8=-2x-16\implies {\Large \begin{array}{llll} y=-2x-8 \end{array}}[/tex]