LITERAL EQUATIONS: A literal equation is one consisting of all letters (or at least mostly letters). The Latin word literalis means "of or belonging to letters or writing," giving the term literal equations its meaning. We can solve literal equations the same way we solve any other equation. We just need to be told which variable (letter) we are solving for. To solve a - 2 = 5 for a, we would add two to each side of the equation. To solve b - r = z for b, we would add r to each side of the equation. What would the resulting solution be ? b = z - r z = b - r r = b - z b = r + z

Answer:

a) 30feet

b) 9.12feet

Step-by-step explanation:

a) Given the path of the ball is modeled by the equation y=-0.02(x-18)²+12​, where;

x is the​ ball's horizontal distance in feet from​ Amaya's position

y is the distance in feet from the ground to the ball.

The ball will be at the maximum height when dy/dx = 0

Differentiate the function:

dy/dx = 2(-0.02)(x-18)^(2-1)+0

dy/dx = -0.04(x-18)

Equate the resulting expression to zero and find x as shown;

-0.04(x-18) = 0

Open the parentheses

-0.04x+0.04(18) = 0

-0.04x+0.72 =0

-0.04x = -0.72

x = -0.72/-0.04

x = 18ft

Hence the ball is 18ft away from Amaya when it is at its maximum height

b) To get the balls height y when x = 30, we will substitute x = 30 into the equation given and calculate the value of y as shown:

y=-0.02(x-18)²+12

y = -0.02(30-18)²+12

y= -0.02(12)²+12

y = -0.02(144)+12

y = -2.88+12

y = 9.12 feet

Hence the Ball's height is 9.12feet when it crosses the net at x = 30.

Answer:

The value of the gift card = v = $40

The visit to the skate cost = $8

The number of visits = n

∴ n = the value of the gift card over the cost of one visit to the skate

∴ n = v/8 = 40/8 = 5

Step-by-step explanation:

The general function for relating the value of the gift card, v, in terms if the number of visits, n. ⇒⇒⇒   v = 8n

Answer:

$7.5 = 3 pounds

Step-by-step explanation:

1. If $5 is equal to 2 pounds of cherries, you want to find what 1 pound of cherries cost. You should divided 5 by 2 and 2 by 2 to find what 1 pound of cherries cot.

2. That means that 1 pound of cherries cost $2.5.

3. Now we want to find how much money 3 pounds cost, so you should multiply the 2.5 and the 1 by 3.

4. Now that gets you to $7.5 for 3 pounds of cherries.s

Answer: y = -2x + 7

Step-by-step explanation:

Answer:

y= -2x+7

Step-by-step explanation:

We need to keep y on one side of the equation.

2x+y= 7

=2x     -2x

y= -2x+7

Hope this helps!

Answer:

328 IF its 7,872 divided 24. If it 7,872 divided by 24 then it's 0.00304878049

Step-by-step explanation: Please mark as brainlest i really need to keep me motivated.

Answer:

z = 40° (V. O. A)

Now find x

40 + 25 + x = 180(A. S. P)

65 + x = 180

x = 180 - 65

x = 115°

Now find y

x = y (V. O. A)

Y = 115°

So angles are

X = 115°

Y = 115°

Z = 40°

Hope this helps, have a great day, have a wonderful weekend and stay safe!

Also Happy Halloween! :) :D :3

Answer:

If angle A is not acute, then the m angle A is not equal to 20

(3rd choice)

Answer:

Step-by-step explanation:

Use the quadratic formula

=

−

±

2

−

4

√

2

x

=

−

b

±

b

2

−

4

a

c

2

a

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

2

2

+

−

6

=

0

2

x

2

+

x

−

6

=

0

2x2+x−6=0

=

2

a

=

2

a=2

=

1

b

=

1

b=1

=

−

6

c

=

−

6

c=−6

=

−

1

±

1

2

−

4

⋅

2

(

−

6

)

√

2

⋅

2

x

=

−

1

±

1

2

−

4

⋅

2

(

−

6

)

2

⋅

2

x=2⋅2−1±12−4⋅2(−6)​​

Answer:

x = - 2, x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given

2x² + x - 6 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = + 1

The factors are + 4 and - 3

Use these factors to split the x- term

2x² + 4x - 3x - 6 = 0 ( factor the firs/second and third/fourth terms )

2x(x + 2) - 3(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

Answer:

The primes up to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. The sequence of gaps—the differences between each prime and the next—is 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2 and 4. The number 1 appears only once because all primes except for 2 are odd. The rest of the gaps are even numbers.

The conjecture which could be inferred from the sequence is that it is a list of prime numbers.

From the sequence given : 2, 3, 5, 7, 11, 13

All values in the sequence are prime numbers.

Prime numbers are numbers which have only two divisors which are 1 and the number itself.

Divisors of :

2 = 1 and 2

3 = 1 and 3

5 = 1 and 5

7 = 1 and 7

11 = 1 and 11

13 = 1 and 13

Hence, the conjecture which could be inferred from the sequence is that, the numbers are prime numbers.

Learn more : https://brainly.com/question/9315685

Answer: y=Mx+b

so y=-2/3x+5

Step-by-step explanation:

slope you go down 2 right 3, y int is (0,5)

9514 1404 393

Answer:

Step-by-step explanation:

The function has a positive leading coefficient (1/3) and is of odd degree (3). These conditions mean the sign of the end behavior of the function will match the sign of x.

  x → ∞, m(x) → ∞

  x → -∞, m(x) → -∞

Answer:

y+1= 1/4(x-4)

Step-by-step explanation:

y+1 = 1/4(x-4)

y+1 = 1/4x-1

y = 1/4x -2 -which is the equation of the line

Answer:

try 5 or 3, half of 6 is 3 may be the same angle

Answer:

carolina needs to buy at least 713 paintballs to get $10 off

Step-by-step explanation:

Entrance fee = $18

Fee per ball = $0.08

The field has a promotion that says, "Get $10 off if you spend $75 or more"

Let B represent the number of paintballs that Carolina buys.

18 + 0.08B ≥ 75

Subtract 18 from both sides

0.08B ≥ 75 - 18

0.08B ≥ 57

Divide both sides by 0.08

B ≥ 57 / 0.08

B ≥ 712.5

Approximately

B ≥ 713

carolina needs to buy at least 713 paintballs to get $10 off

Answer:

C

Step-by-step explanation:

Perpendicular lines have the exact opposite slope of the other equation.

So the slope will be x or 1x. Plug in

-8 = 1(4) + b (b represents y-intercept) like y=mx+b

-8 = 4 + b (subtract 4 on both sides)

-12 = b

The equation is y = x - 12

C

solve

y + 8 = x - 4 (subtract 8 on both sides)

y = x - 12

Answer:

Converse: if 5=x then x+2=7

Inverse: if x+2 doesnt = 7 then x isnt 5

Contrapositive: if x doesnt equal five then x plus two doesnt equal seven

Step-by-step explanation:

We just did this last week :)

Answer:

y = 5/2x + 1

Step-by-step explanation:

you are given (0,1) which means that the y intercept is 1.

Subsitute values in a linear equation:

y = mx + b

y = 5/2x + 1

Answer:

kind of an estimate but it is probably 220cm, if not then its 175cm, couldn't really see the bottom part of the window

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x = 2.4545... → (1)

100x = 245.4545... → (2)

Subtract (1) from (2) eliminating the repeating decimal

99x = 243 ( divide both sides by 99 )

x = [tex]\frac{243}{99}[/tex]

Answer:

500 ML

Step-by-step explanation:

for every 1 liter, it is 1,000ML

so 1 L / 2 is 500ML

and 500 on your beaker is located in between 600 and 400

Hope this helps :)

Answer:

the correct option is B

I hope my answer is helpful to you

please give me five star rating

Answer:

problem 9

x is 45 and y is 20

problem 10

x is 20 and y is 10

problem 11

x is 13 and y is 12

Answer:

Step-by-step explanation:

Answer:

Answer:

Dilations create similar figures because multiplying by the scale factor creates proportional sides while leaving the angle measure and the shape the same.

Step-by-step explanation: