How to constructed a square polygon

Answer:

3.75.

Step-by-step explanation:

Substitute x = 1/2 into x^2 + 3.5:

(1/2)^2 + 3.5

= 1/4 + 3.5

= 3.75.

Answer:

Step-by-step explanation:

[tex]\text{Put the value of}\ x=\dfrac{1}{2}=0.5\ \text{to the expression}\ x^2+3.5:\\\\0.5^2+3.5=0.25+3.5=3.75[/tex]

Answer:

1 = 2

3 = 14

10 = 56

Step-by-step explanation:

y = 6x - 4

y = 6 - 4

y = 18 - 4

y = 60 - 4

Step-by-step explanation:

In first there is 2

ln second there is 14

ln third there is 56

I hope this is right answer!

The complete table of values for the equation y = x/4 is

x   4   2  9

y  1   1/2  9/4

From the question, we have the following parameters that can be used in our computation:

y = x/4

The missing y values are at x = 4, 2 and x = 9

Substitute the known values in the above equation, so, we have the following representation

y = 1/4 * 4 = 1

y = 1/4 * 2 = 1/2

y = 1/4 * 9 = 9/4

So, the missing values are 1, 1/2 and 9/4

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Final answer:

The rule 'y = X/4' describes division of X by 4 to find Y. The student completes the table by dividing each X value by 4 to find the corresponding Y values, providing an organized data set.

Explanation:

The student is asking about the operation indicated by the rule y = X/4, which involves division. The fraction bar signifies division. Given this rule, we can complete the table for y when x-values are provided.

For x = 4: y = 4/4 = 1

For x = 2: y = 2/4 = 0.5

For x = 9: y = 9/4 = 2.25

To organize the data in the table, you simply divide the x-value by 4 to find the corresponding y-value.

Answer:

18/20 or 9/10

Step-by-step explanation:

The list shows the amount of hours each student USED the computer.

Wherever we see a "0", that means he/she DID NOT USE computer.

There are 2 "zeroes", so 2 didnt use out of 20, so number of student who DID USE is 20 - 2 = 18

To find ratio of total number of students who used to the total number surveyed, it is going to be:

18/20 or 9/10

Answer:

Ratio would be 9 : 10

Step-by-step explanation:

Liliana surveyed 20 students that how many hours they spend on their computers each week.

The results are as follows

8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21

In the above results 2 students did not use computers out of 20 students.

Therefore, The total number of students who used their computers = 20 - 2 = 18

So the ratio would be 18 : 20 or 9 : 10

Answer:

see explanation

Step-by-step explanation:

Given

8x + 5y = 10 ← solve for x by subtracting 5y from both sides

8x = 10 - 5y ( divide both sides by 8 )

x = [tex]\frac{10-5y}{8}[/tex]

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

Solve for y by subtracting 8x from both sides

5y = 10 - 8x ( divide both sides by 5 )

y = [tex]\frac{10-8x}{5}[/tex]

Answer:

The correct answer would be 34

Step-by-step explanation:

When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.

Answer:

(5x+4)(5x-4)

Step-by-step explanation:

The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.

The expression is a difference of two squares whose factors are generally

(a-b)(a+b)

√25x² is 5x

√16 is 4

Therefore the product required is (5x+4)(5x-4)

25x²-16 is equivalent to (5x+4)(5x-4)

Answer:

∠A, ∠B, ∠C

Step-by-step explanation:

In a triangle the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side, therefore:

∠A < ∠B < ∠C

Answer:

a,b,c

Step-by-step explanation:

The angle opposite the longest side has the largest angle measure, the angle opposite the shortest side has the most small angle measure etc.

Since BC is the shortest line, the angle opposite will have the smallest measure, this is ∠a.

CA is in the middle with length this means that the angle opposite of it will have an angle measure in between that of the other angle measures.  This is ∠b

AB has the longest length, therefore, the angle opposite it will have the largest measure, this is ∠c

Answer:-12

Step-by-step explanation:

Z-3x=

=3-3(5)

=3-15

=-12

Answer:

-12

Step-by-step explanation:

3 - 3(5)

3 -15 = -12

the answer to the question

Step-by-step explanation:

range is all the y values

{y|y=-9, -3, 0, 5, 7}

The range of a function are all the ys included in the graph. In this case that would be:

(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)

Remember to order it from least to greatest:

{yly = -9, -3, 0,5,7}

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

9 < n < 21

Step-by-step explanation:

15-6 < n < 15+6

9 < n<21

We are limited by the other two sides of the triangle

It can be no smaller than the other two sides subtracted and no larger than the other two sides added

Answer:

[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]

Step-by-step explanation:

[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]

[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]

Answer:

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

[tex]y-3.5=-1.25x[/tex]

Step-by-step explanation:

step 1

Find the slope of the linear equation

with the points (-2,6) and (2,1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{1-6}{2+2}[/tex]

[tex]m=-\frac{5}{4}[/tex]

step 2

Find the equation of the line into point slope form

The equation of the line in slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{5}{4}[/tex]

1) with the point (-2,6)

substitute

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

2) with the point (2,1)

substitute

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

3) with the point (0,3.5)

substitute

[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]

[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]

Answer:

A, D, E

Step-by-step explanation:

Answer:

A''(1,-1) B''(3,2) C''(3,2)

Step-by-step explanation:

A(−5,0) B(−3,3) C(−3,0)

reflection over x=-2

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1

after reflections, the perpendicular distance will be 6,2,2, and the points will be at

A'(1,0) B'(−1,3) C'(−1,0)

again  reflection over x=1

Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2

after reflections, the perpendicular distance will be 0,4,4 and the points will be at

A''(1,-1) B''(3,2) C''(3,2)!

Answer:

Option C is correct.

Step-by-step explanation:

If we look at the table,

The amount of Principal of Month 13 is $325.82

The amount of Principal of Month 14 is $328.19

The amount of Principal of Month 15 is $330.57

So, the amount of principal is increasing every month.

Rest of the options seems incorrect.

So, Option C The amount applied to the principal is increasing each month.

is correct.

Answer:

The answer is C

Step-by-step explanation:

I got the right answer on the test in e2020

In order to find all the types of sweatshirts, we simply have to multiply all the numbers by all the factors.

3 colors * 2 different styles * 3 different sizes = 18 different types of sweatshirts

The total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

The student council is selling sweatshirts with the school name and shirts come in three different colours, two different styles and three different sizes.

Total number of different sweatshirts = 3×2×3

= 18

Thus, the total of 18 different types of sweatshirts are available if shirts come in three different colours, two different styles and three different sizes.

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For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]

So, we have:

[tex]x + 2 <5\\x <5-2\\x <3[/tex]

The solutions are given by all strict minor numbers to 3.

[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]

The solutions are given by all the major strict numbers to 1.

If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].

The intersection is given by [tex]1 <x <3[/tex]

Answer:

 The solution interval is (1,3)

Answer:

Option C) b=6

Step-by-step explanation:

we know that

If two linear equations of a system of equations have an infinite of solutions, then both equations are identical

we have

[tex]y=6x-b[/tex] -----> equation A

[tex]-3x+(1/2)y=-3[/tex]

Multiply by 2 both sides

[tex]-6x+y=-6[/tex]

Adds 6x both sides

[tex]y=6x-6[/tex] ------> equation B

equate equation A and equation B

[tex]6x-b=6x-6[/tex]

solve for b

[tex]b=6[/tex]

Answer:

5 boxes

Step-by-step explanation:

Given:

Total crayons : 98

Capacity of each box : 24

Number of boxes of 24 crayons needed to hold 98 crayons,

= 98 ÷ 24

= 4.08 boxes.

However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.

4.08 rounded up to next whole number = 5

Hence he will need 5 boxes to hold all 98 crayons

Answer:

5x. 5x. 5x. 5x. 5x. 4x. 4x. 4x

Step-by-step explanation:

Just seperate all of the numbers out. Because 5x is raised to the fifth it is being multiplied by itself 5 times, the same goes for 4.

Firstly see what they are in mixed fraction form:

[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]

therefore, 7 9/7 is equal to 58/7

[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]

For this case we must factor the following equation:

[tex]x ^ 2 + x-6 = 0[/tex]

We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2

So, we have to:

[tex](x + 3) (x-2) = 0[/tex]

The roots are:

[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]

ANswer:

[tex](x + 3) (x-2) = 0[/tex]

The solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.

The statement that the graph of [tex]\( 2x^2 + 8 = 0 \)[/tex] does not cross the x-axis is correct, as the graph of this equation represents a parabola that opens upwards and is centered above the x-axis, meaning it has no real roots.

To find the solutions for the equation [tex]\( 2x^2 + 8 = 0 \)[/tex], we can start by isolating [tex]\( x^2 \):[/tex]

[tex]\[ 2x^2 = -8 \][/tex]

Dividing both sides by 2:

[tex]\[ x^2 = -4 \][/tex]

Now, to solve for ( x ), we take the square root of both sides:

[tex]\[ x = \pm \sqrt{-4} \][/tex]

[tex]\[ x = \pm 2i \][/tex]

So, the solutions to the equation [tex]\( 2x^2 + 8 = 0 \)[/tex] are complex numbers [tex]\( x = 2i \) and \( x = -2i \), where \( i \)[/tex] is the imaginary unit.

These are the roots of the equation, even though they do not lie on the real number line.

Hence, while there are no real solutions, there are indeed complex solutions for the given function.

Answer:

[tex]y = \sqrt{x - 16} [/tex]

Step-by-step explanation:

[tex]y = {x}^{2} + 16[/tex]

[tex]x = {y}^{2} + 16[/tex]

[tex]x - 16 = {y}^{2} [/tex]

[tex] \sqrt{x - 16} = y[/tex]

Answer:

f^-1 (x) = ±sqrt(x-16)

Step-by-step explanation:

To find the inverse of a function, exchange x and y and solve for y

y=x^2+16

Exchange x and y

x = y^2 +16

Then solve for y

Subtract 16 from each side

x-16 = y^2 +16-16

x-16 = y^2

Take the square root of each side

±sqrt(x-16) = sqrt(y^2)

±sqrt(x-16) = y

The inverse

f^-1 (x) = ±sqrt(x-16)

Answer:

Third choice

Step-by-step explanation:

They are asking us to find the inverse of y=5x. To do this you just switch x and y and then remake y the subject of the equation (solve for y.)

y=5x

x=5y (I switch x and y)

x/5=y ( I divided both sides by 5)

Then you just replace y with the f^-1(x) thing

f^-1(x)=x/5

or

f^-1(x)=1/5x

If f(x) = 5x, then the inverse of the function, f⁻¹(x) is x/5.

Given that :

f(x) = 5x

Let y = f(x).

So, y = 5x

Now, interchange the values for x and y.

Then,

x = 5y

Now, solve for y.

Divide both sides of the equation by 5.

x/5 = y

So, the inverse of the function is x/5.

Hence f⁻¹(x) = x/5.

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Answer:

195

Step-by-step explanation:

9 times 10 is 90 and 7 times 15 is 105  

so 105+90=195

Answer:

195 cm

Step-by-step explanation:

The area of ABCD is 195 cm.

Multiply the sides together:

9 ⋅ 10 = 90

7 ⋅ 15 = 105

Add them together:

105 + 90 = 195

Therefore, the area of ABCD is 195 cm.

[tex]\tt x^3+4x^2+8x+32\\\\=x^2(x+4)+8(x+4)\\\\=\boxed{\tt(x+4)(x^2+8)}[/tex]

Answer:

(x+4)(x^2+8)

Step-by-step explanation:

x^3 + 4x^2 + 8x + 32

We will factor by grouping

Factor out an x^2 from the first two terms and an 8 from the last two terms

x^2 (x+4) + 8(x+4)

Now we can factor out an (x+4)

(x+4)(x^2+8)

Answer:

26.6 degrees

Step-by-step explanation:

Use the converting formula:

(-3°C × 9/5) + 32 = 26.6°F

-3 degrees to Fahrenheit would be 26.6

The formula is attached in the image below

-3 × 1.8 = -5.4

-5.4 + 32 = 26.6

Answer:

35

Step-by-step explanation:

92-5+4-3=35

Answer with explanation:

A function is said to attain maximum in the interval , if you consider any two points on the curve suppose (a,b) and (c,d)

if , c>a

Then , f(d) > f(a).

A function is said to attain minimum in the interval,

if ,c>a

Then,f(d)< f(a).

A function can have more than one relative Maximum and more than one relative Minimum.

The function whose graph is given here has following Characteristics

    •Two relative minima

     •Two relative maxima

is True .

Answer:

Table B

Vertex is (3,-5)

Step-by-step explanation:

We are given with an equation of a parabola [tex]y=x^2-6x+4[/tex]

Let is convert it into standard form of a parabola

[tex]y=x^2-6x+4[/tex]

adding and subtracting 9 in the right hand side of the =

[tex]y=x^2-6x+9-9+4[/tex]

[tex]y=x^2-2\times 3\times x+ 3^2-9+4[/tex]

the first three terms of the right hand side forms the expression of square of difference

[tex]a^2-2 \times a \times b+b^2 = (a-b)^2[/tex]

Hence

[tex]y=(x-3)^2-5[/tex]

adding 5 on both sides we get

[tex](y+5)=(x-3)^2[/tex]

Comparing it with the standard equation of a parabola

[tex]X^2=4\times \frac{1}{4} \times Y[/tex]

where [tex]X=x-3[/tex] and [tex]Y=y+5[/tex]

The vertex of [tex]X^2=4\times \frac{1}{4} \times Y[/tex] will be (0,0)

and thus vertex of

[tex](y+5)=(x-3)^2[/tex] will be (3,-5)

Hence the Table B is our right answer