Pls help !!!!
A video game designer places an anthill at the origin of a coordinate plane. A red ant
leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the
anthill and moves along a straight line to (1, -1). Next, the red ant moves to (2, 2), while
the black ant moves to (-2,-2). Then the red ant moves to (3, 3), while the black ant
moves to (-3, -3), and so on. Complete the explanation of why the red ant and the black
ant are always the same distance from the anthill,
At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The
red ant's distance from the anthill is . The black ant's coordinates may be written
as (-a, -a) and the black ant's distance from the anthill is . This shows that at
any given moment, both ants are
units from the anthill.

The answers for 13 and 14 are attached in the file.

The value of y from the given equation is 8. Hence, proved.

The given equation is (2y-1)/(-3) = -5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

12. (2y-1)/(-3) = -5

⇒ 2y-1=15 (Cross multiply -3 to -5)

⇒ 2y=16 (Transpose -1 to RHS)

⇒ y=8 (Transpose 2 to RHS)

13. 2x+30=-4(5x-2)

⇒ 2x+30=-20x+8 (Multiply -4 into the bracket)

⇒ 2x+20x=8-30 (Transpose like terms LHS and constant terms to RHS)

⇒ 22x=-22

⇒ x=-1 (Transpose 22 to RHS)

14. 18x-2(3x+1)=5x-16

⇒ 18x-6x-2=5x-16 (Multiply -2 into the bracket)

⇒ 12x-2=5x-16 (Subtract like terms on LHS)

⇒ 12x-5x=-16+2 (Transpose like terms LHS and constant terms to RHS)

⇒ 7x=-14

⇒ x=-2 (Transpose 7 to RHS)

The value of y from the given equation is 8. Hence, proved.

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Answer:

2 11/12 cups of flour

Step-by-step explanation:

well 2 recipes is 2 1/2 cups of flour

1/3 is 1/3 x 1 1/4= 1/3 + 1/12= 5/12

so 2 11/12 cups of flour

Step-by-step explanation:

A proof that square root of 2 is irrational. ... An equation x² = a, and the principal square root ... The number under the radical sign is called the radicand. ... the given square numbers, each product of square numbers is equal to what square ... are relatively prime -- and it will be impossible to divide n· n into m· m and get 2.

Answer: The Answer is N = 5

Step-by-step explanation:

The reason is that 76 + n and 2n + 26. 5 can work for both of them. 76 + 5 = 81 which is a rational number and 2 * 5  + 26 = 36 which is also a rational number.

Answer:

respect , structure

Step-by-step explanation:

If a person has a high level of self-discipline, that means they are very responsible and self-controlled.

They work hard without being asked to, and they stop themselves from getting addicted to things, and they don't do anything bad.

♡ Hope this helped! ♡

❀ 0ranges ❀

Answer:  x = 2/5 in fraction form

In decimal form, the answer is x = 0.4

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

Work Shown:

2/3 = two thirds

2/3 + (1/3)x = 2x  is the equation you're given

Multiply every term by 3 so that we clear out the fractions

3*(2/3) + 3*(1/3)x = 3*2x

2 + x = 6x

From here, we solve for x

2 + x = 6x

2+x-x = 6x-x .... subtract x from both sides

2 = 5x

5x = 2

5x/5 = 2/5 ... divide both sides by 5

x = 2/5

x = 0.4

The solution of the expression is,

⇒ x = 0.4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

''Two thirds plus one third times x equals two times x.''

Now, We can simplify as;

⇒ 2/3 + 1/3x = 2x

Solve for x as;

⇒ 2/3 = 2x - 1/3x

⇒ 2/3 = 5x/3

⇒ 2 = 5x

⇒ x = 2/5

⇒ x = 0.4

Thus, The solution of the expression is,

⇒ x = 0.4

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Answer:

-40/2 is equal to -20

Step-by-step explanation:

still dont kno what n w z r means

Answer:

y = 4x + 9/4

Step-by-step explanation:

4x − y − 3 = 0

y = 4x − 3

The slope of the line is 4.

The slope of the tangent line is:

f(x) = x − x²

f'(x) = 1 − 2x

Setting the slope equal to 4:

4 = 1 − 2x

2x = -3

x = -3/2

The point on f(x) is:

f(-3/2) = -3/2 − (-3/2)²

f(-3/2) = -3/2 − 9/4

f(-3/2) = -15/4

Using point-slope form:

y − (-15/4) = 4 (x − (-3/2))

y + 15/4 = 4 (x + 3/2)

y + 15/4 = 4x + 6

y = 4x + 9/4

Answer:

y = 3

Step-by-step explanation:

To solve this equation, we will use conventional algebraic techniques as illustrated below.

3(y + 5) = 8y Distribute the 3.

3y + 15 = 8y Subtract 3y from both sides.

15 = 5y Rearrange the equation so the variable is on the left.

5y = 15 Divide by 5 on both sides.

y = 3

Answer:

Step-by-step explanation:

[tex]3\left(y+5\right)=8y\\[/tex]

Expand

[tex]\mathrm{Expand\:}3\left(y+5\right):\quad 3y+15\\\\=3y+15=8y[/tex]

Subtract 15 from both sides

[tex]3y+15-15=8y-15[/tex]

Simplify

[tex]3y=8y-15[/tex]

Subtract 8y from both sides

[tex]3y-8y=8y-15-8y[/tex]

Simplify

[tex]-5y=-15[/tex]

Divide both sides by -5

[tex]\frac{-5y}{-5}=\frac{-15}{-5}[/tex]

Simplify

[tex]y =3[/tex]

Answer:

Hey there!

Using conversion factors we get-

72 km/h=20 m/s

108 km/h=30 m/s

Let me know if this helps :)

Answer:

36cm²

Step-by-step explanation:

From the sketched diagram of the Quadrilateral above, we have two triangles that are joined together, ∆PQR and ∆PSR

Both triangles are right angled triangles.

Step 1

We solve for ∆PQR

When solving for the sides of a right angled triangle, if two sides are given, we solve for the third sides using Pythagoras Theorem

Pythagoras Theorem =

c² = a² + b²

Where c = Longest side

For ∆PQR,

/PQ/ = 3 cm = a

/QR/ = 4 cm = b

/PR/ = c ??

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5cm

/PS/ = 5cm

We find the Area of this triangle using Heron's formula

= √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

s = 3 + 4 + 5/2

= 12/2

s = 6

Area of the ∆PQR = √6(6 - 3)(6 - 4)(6 - 5)

= √6 × 3 × 2 × 1

= √36

= 6cm²

Area of the ∆PQR

Step 2

We solve for ∆PSR. Just like in Step 1, we solve for third side not given using Pythagoras Theorem

/PS/ = 13cm = c

/PR/ = 5cm = a

/SR/ = ?? = b

c² = a² + b²

13² = 5² + b²

b² = 13² - 5²

b² = 169 - 25

b² = 144

b = √144

b = 12cm

/SR/ = 12cm

We find the Area of this triangle using Heron's formula

= √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

s = 5 + 12 + 13/2

= 30/2

s = 15

Area of the ∆PSR = √15(15 - 5)(15 - 12)(15 - 13)

= √15 × 10 × 3 × 2

= √900

= 30cm²

Area of the ∆PSR = 30 cm²

Step 3

We find the Area of the Quadrilateral

Area of the Quadrilateral (PQRS)= Area of ∆PQR + Area of ∆PSR

= 6cm² + 30cm²

= 36cm²

Therefore the Area of the Quadrilateral PQRS = 36cm²

Answer:

Step-by-step explanation:

If we let d represent the number of dimes, then d+8 represents the number of quarters. The total number of coins is the sum of the numbers of each:

  d +(d +8) = 20 . . . . . matches choice d

Collecting terms, we have ...

  2d +8 = 20

  d +4 = 10 . . . . . divide by 2

  d = 6 . . . . . . . . subtract 4

The kid has 6 dimes and 14 quarters. (matches choice b)

Answer:

C. 408.268

Step-by-step explanation:

4080.2679 to be rounded to the nearest thousandth

Count 3 digits after the decimal sign.

Discount the 4th digit after the decimal sign and since it is 9>5, add 1 to the previous digit: 7+1= 8

Correct option is C

Answer:

(x+2)(x+4)=x^2+6x+8

Step-by-step explanation:

first you foil (x+2)(x+4) and you get x^2, 2x+4x+8

then combine like terms and you get x^2+6x+8

Answer:

(x+2)(x+4) = x*x + x*4 + 2*x + 2*4

                = x² + 4x + 2x + 8

                = x² + 6x + 8

Answer:

Step-by-step explanation:

You have shared only one graph, that of a quadratic function with vertex at (0, 0) and an equation based upon y = ax^2, where a is a constant coefficient.

Please go back to the source of  your question and describe the other graphs that were given to you.

The graph that shows a straight line is the linear function.

Answer:

The point of intersection is (6, 8). This indicates that in 6 days, asteroid A and B will collide at a point that is 8 million miles away from asteroid A's current position and 12 million miles away from asteroid B's current position.

Answer:

The point of intersection of the two lines is (6, 8). The x-value means that the two asteroids will collide in 6 days. The y-value means that they will collide 8 million miles away from where asteroid A is now located.

Step-by-step explanation:

Exact answer from edmentum.

Answer:

2(1 - x)

twice = 2

difference = subtraction

1

number = x

The algebraic expressions for Twice the difference of 1 and a number is:

2(1 - x)

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

We have:

Twice the difference of 1 and a number

Let x represent the number.

Let's write algebraic expression now:

The difference of 1 and a number is: 1 - x

Twice the difference of 1 and a number will be:

2 * (1 - x) = 2(1 - x)

Therefore, twice the difference of 1 and a number is 2(1 - x)

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Answer:

35/40

Step-by-step explanation:

7/8, with the given denominator 40

So how do we get 8, to turn into 40?

Simple multiplication.

8x5 = 40, and whatever we multiply times the denominator, we multiply for the numerator.

So

7x5 = 35

The answer should be 35/40

Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

Firstly we have to take variables to L.H.S and numbers to R.H.S

[tex]13n + 5n = - 8 + 16 \\ 18n = 8 \\ n = \frac{8}{18} \\ n = \frac{4}{9} [/tex]

Hope it helps

Answer:

False

Step-by-step explanation:

Geometric series have ratios.

The ratio here is 2.

So the next term should be -8.

Answer and Step-by-step explanation:

The computation of the class width for a frequency is shown below:

Class width is

[tex]= \frac{Range}{Number\ of\ class} \\\\ = \frac{96 - 20}{7}[/tex]

= 10.86

= 11

Now the class limits for a frequency table

Particulars      Lower class limit to upper class limit

First class          20 - 30

Second class    31 - 41

Third class        42 - 52

Fourth class      53 - 63

Fifth class         64  74

Six class           75 - 85

Seventh class   86 - 96

The class width for a frequency table with seven classes is 10.86.

The class limits for a frequency table with seven classes are;

Particulars      Lower class limit to upper class limit

First-class          20 - 30

Second class    31 - 41

Third class        42 - 52

Fourth class      53 - 63

Fifth class         64  74

Six class           75 - 85

Seventh class   86 - 96

A data set with whole numbers has a low value of 20 and a high value of 96.

1. The class width for a frequency table with seven classes is;

[tex]\rm Frequency = \dfrac{Highest \ term - lowest\ term }{Class}\\\\ Frequency = \dfrac{96-20}{7}\\\\ Frequency = \dfrac{76}{7}\\\\ Frequency =10.86[/tex]

The class width for a frequency table with seven classes is 10.86.

2. The class limits for a frequency table with seven classes are;

Particulars      Lower class limit to upper class limit

First-class          20 - 30

Second class    31 - 41

Third class        42 - 52

Fourth class      53 - 63

Fifth class         64  74

Six class           75 - 85

Seventh class   86 - 96

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Answer:

z = 13.75 * 0.8 = 11 ( two nonzero digits )  

Step-by-step explanation:

An equation that has two decimal places multiplied by a number with one decimal place can be written as

z = x*y

where x can be = 13.75

and y = 0.8

therefore : z = 13.75 * 0.8 = 11 ( two nonzero digits )  

Answer:

Inverse property of multiplication

Step-by-step explanation:

Servings = total amount / serving size

Servings = 5 / 3/4

When dividing by a fraction, reverse the fraction and multiply:

= 5 x 4/3

= 20/3

= 6 2/3 servings

Answer: 6 servings

Step-by-step explanation:

3/4+3/4+3/4+3/4+3/4+3/4=4.5

if you add 3/4 then it will be  5.25 so basically 5 tablespoons

it is 6 full servings

Answer:

The base of -5 raise to 7 is -5 and its exponent is 7. The base-9/7 raise to the power of 6 is -9/7 and it's exponent is 6.

Step-by-step explanation:

Answer:

The base of -5 raise to 7 is -5 and its exponent is 7. The base-9/7 raise to the power of 6 is -9/7 and it's exponent is 6.

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

You plug in both numbers for the corresponding letters

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Prime Factor of 84:

84

84 divides by 2 84 = 42 x 2

84 = 2 x 42

42 divides by 2 42 = 21 x 2

42 = 2 x 2 x 21

21 divides by 3 21 = 7 x 3

21 = 2 x 2 x 3 x 7

2, 3, 7 is a prime number, therefore no further factorization is possible = 2 x 2 x 3 x 7

~~~~~~~~~~~~~~~~~~~~~~

Prime Factor of 98:

98

98 divides by 2 98 = 49 x 2

98 = 2 x 49

49 divides by 7 49 = 7 x 7

49 = 2 x 7 x 7

2, 7 is a prime number, therefore no further factorization is possible = 2 x 7 x 7

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

q = 27

I hope this helps!

Answer: q=27

Step-by-step explanation:

Given

5(34-10)-5q=-15

Combine like term in the parentheses

5×24-5q=-15

Combine like term by multiplication

120-5q=-15

Subtract 120 on both sides (subtraction property of equality)

120-5q-120=-15-120

-5q=-135

Divide -5 on both sides (division property of equality)

-5/-5 q=-135/-5

q=27

Hope this helps!! :)

Please let me know if you have any question

Answer:

Step-by-step explanation:

+(+) Two like signs become a positive sign 3+(+2) = 3 + 2 = 5

−(−) 6−(−3) = 6 + 3 = 9

+(−) Two unlike signs become a negative sign 7+(−2) = 7 − 2 = 5

−(+) 8−(+2) = 8 − 2 = 6

Answer:

It is an equation, and the answer is [tex]h = -3[/tex]

Step-by-step explanation:

We have a variable that's equal to a term, so this is an equation.

To solve this, we want to isolate h on one side.

[tex]h - (-5) = 2[/tex]

Subtracting a negative is the same thing as adding a positive:

[tex]h + 5 = 2[/tex]

Now we can subtract 5 from both sides to isolate h.

[tex]h + 5 - 5 = 2-5\\\\h = -3[/tex]

Hope this helped!

Answer:2 2/2

Step-by-step explanation: