I need to simplify the complex fraction.​

Answer:

d

Step-by-step explanation:

The train traveled for a distance of 300 miles

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the train be S = 60 miles per hour

The time taken by the train to reach the destination = 5 hours

So ,

The distance traveled by the train = Speed of the train x Time taken

                                                         = 60 x 5

                                                         = 300 miles

Therefore , the distance traveled by the train is 300 miles

Hence , The train traveled for a distance of 300 miles

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Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x - 5y = 6

5y = 2x - 6

y = 2/5x - 6/5

y-intercept is -6/5

x-intercept is when you say that y = 0

and so 6/5 = 2/5x

x = 6/2 = 3

Answer:

Step-by-step explanation:

a. It is a decay function as number of population is decreasing over time

b. f(n) = 33500*((100 - 2.5)/100)^n = 33500*(0.975)^n

c. In year 2025, n = (2025 - 1995)/10 = 3

f(3) = 33500*(0.975)^3 = 31100 rounded up

Answer:

C. 27

Step-by-step explanation:

((4x + 5) + 10)*10 = (21 + 9)*9 (two secants intersecting)

(4x + 5 + 10)*10 = (30)*9

(4x + 15)*10 = 270

40x + 150 = 270

40x = 270 - 150 (subtraction property of equality)

40x = 120

Divide both sides by 40

40x/40 = 120/40

x = 3

✔️QS = (4x + 5) + 10

Plug in the value of x

QS = 4(3) + 5 + 10

QS = 12 + 5 + 10

QS = 27

Answer:

y=5/2x+2

Step-by-step explanation:

rearrage equation: y=5/2x-7

new slope is same: y=5/2x+b

substitue point (-2,-3):

-3=5/2(-2)+b

-3=-5+b

-3+5=b

2=b

Answer:

x = 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

-2(5x - 5.5) + 8 = -9x + 2 - (-5)

Step 2: Solve for x

Answer:

The stake is 80√3 ft or 138.56ft away

Step-by-step explanation:

let the distance from the stake to the foot of the tower=x

tan(60°)=x/80

x=80tan(60°)

x=80√3 ft

The distance of the stake from the foot of the tower is 46.189 feet.

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle of depression is 60°

60° is the angle from the stake to the top of the tower due to alternative angles,

height of tower = 80 feet

let the distance of the stake from tower be x

using tangent to find the distance,

tanФ = perpendicular/base

perpendicular = 80 feet

base = x

Ф = 60°

tan60 = √3

tan60 = 80/x

x = 80/1.732

x =  4.189 feet

hence stake is 46.189 feet from the tower.

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Answer:

3 2/3

Step-by-step explanation:

Use a calculator please

Answer:

[tex]m=-4[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (5, 6)

Point (7, -2)

Step 2: Find slope m

Answer:

2nd and 4th options are correct

Step-by-step explanation:

Here, let’s work with the number of tablespoon of lemon juice

From the question ;

2 servings = 1/2 tea spoon

So 4 servings = 2 * 1/2 = 1 tea spoon

Let us convert this to table spoon

3 teaspoon = 1 table spoon

1 teaspoon = x table spoon

3 * x = 1

x = 1/3 tablespoon

As we can see, this is not any part of the options

Let us check for 6 servings

6 servings = 3 * 1/2 = 1.5 tea spoon

From the question;

3 tsp = 1 tbsp

1.5 tsp = x tbsp

x * 3 = 1.5

x = 1.5/3

x = 1/2 tbsp

As we can see, second option is correct

second part

we are working with vinegar

For 2 servings = 2 tbsp of vinegar

4 servings = 2 * 2 = 4 tbsp of vinegar

From the question

2 tbsp = 1/8 cup

4 tbsp = x cup

x = (4 * 1/8)/2 = 1/2/2 = 1/4 cup

For 6 servings

= 3 * 2 = 6 tbsp

From the question;

2 tbsp = 1/8 cup

6 tbsp = x cup

2 * x = 6 * 1/8

x = 6 * 1/8 * 1/2

x = 3/8 cups of vinegar

So therefore, options 4 and 2 are correct

Answer:

a) 70 azulejos

b) 37500 litros

c) 37.5m³

Step-by-step explanation:

A piscina tem 5 m de comprimento, 3 m de largura e 2,5 m de profundidade.

Comprimento = 5m

Largura = 3m

Profundidade (altura) = 2,5 m

Calcular:

a) A quantidade de ladrilhos necessária para cobrir a piscina

Isso é calculado como a área de superfície da votação

A = 2 (wl + hl + hw)

A = 2 × (3 × 5 + 2.5 × 5 +2.5 × 3)

A = 70 m²

Observe que:

1 m² = 1 azulejo

70 m² = 70 azulejos

b) A quantidade de água que pode caber na piscina.

1 m³ = 1000 litres

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

1 m³ = 1000 litros

37.5m³ =

37.5 × 1000 litros

= 37500 litros

c) seu volume em m³

O volume de uma piscina = Comprimento × Largura × Altura

= 5m × 3m × 2.5m

= 37.5m³

Answer:

Please check the explanation.

Step-by-step explanation:

Given the points

Finding the slope between (2, 17), (4, 7)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(2,\:17\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)[/tex]

[tex]m=\frac{7-17}{4-2}[/tex]

[tex]m=-5[/tex]

We know the Point-Slope Form of the line equation is

[tex]y-y_1=m\left(x-x_1\right)[/tex]

Here:

substituting the values m = -5 and the point (2, 17) in the Point-Slope Form

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - 17 = -5 (x-2)[/tex]

Thus, the answer Point-Slope Form is

[tex]y - 17 = -5 (x-2)[/tex]

It can be further simplified to write into the Slope-Intercept Form

[tex]y - 17 = -5 (x-2)[/tex]

y-17 = -5x+10

y = -5x+10+17

y = -5x+27

Thus, the answer in the Slope-Intercept Form (y=mx+b)

y = -5x+27         ∵Slope-Intercept Form → y=mx+b

Answer:

2

Step-by-step explanation:

5 bottles = 10 dollars

divide by 5 to get 1 bottle

now divide 10 by 5 that will be 2

2$ for 1 bottle

Answer:

x = 24

y = 10

z = 17

Explanation:

It's long to explain, so heres a picture of how solved each. hope this helps!! :)

Answer:

Discriminant = 100

Number of solutions = 2

Type of solution = Real and Unique

Rational or Irrational: Rational

Step-by-step explanation:

Given the quadratic expression;

[tex]2x^2 - 28x= - 48 \\[/tex]

Rewrite in standard form

[tex]2x^2 - 28x+ 48= 0 \\[/tex]

Divide through by 2;

[tex]x^2 - 14x + 24 = 0[/tex]

From the expression;

a = 1, b = -14 c = 24

Discriminant determines the nature of the root of the quadratic equation;

Discriminant D = b² - 4ac

Substitute the given values;

D = (-14)² - 4(1)(24)

D = 196 - 96

D = 100

Since the discriminant is greater than zero this means that the solution will be real and unique values.

Get the number of solutions;

Using the formula;

x = -b±√D/2a

x = -(-14)±√100/2(1)

x = 14±10/2

x = 14+10/2 and 14-10/2

x = 24/2 and 4/2

x = 12 and 2

Hence the equation has 2 solutions.

The solutions are rational since we can write then as a ratio of two integers

Answer:

Y intercept is 12 x intercept is -4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

huh??? I'm confused lol

Answer:

what do u mean???

Step-by-step explanation:

Answer:

7) 480 m³

8) 84 ft³

Step-by-step explanation:

7) 8 x 6 x 4 = 192

12 x 6x 4 = 288

192 + 288 = 480

8) 6 x 4 x 2 = 48

6 x 3 x 2 = 36

36 + 48 = 84

Answer:

The number of Potatoes remaining is = 150

Step-by-step explanation:

From the information given above,

On first day of the week (Sunday),

Total potato = 800

The number used include:

Monday = 380

Tuesday = 270

Total potato used = Monday + Tuesday

= 380 + 270 = 650

Remaining Potato = 800 - 650 = 150

Answer: a definition of an equation can be defined as a mathematical statement consisting of an equal symbol between two expressions that have the same value.

Step-by-step explanation:

Answer:

the fist one

Step-by-step explanation:

Hope it helps

x=6 , y = 4

Step-by-step explanation:

( x-2,6)=(4,Y+2)

this means; (x-2) &( 4) stands for" x "axis.

and( 6 )& (y+2) stands for y axis.

So, we can say( x-2)=X1 & (4)=X2 , (6)=Y1 & (y+2)=Y2

then; to Solve The Equation we use The Formula: X1=X2 for "X" And Y1=Y2 for "Y".

Solution: for "X" ; X1=X2

x-2= 4

x=4+2

x=6

For "Y" ; Y1=Y2

6 = y+2

y=6-2

y=4

finally check ; ( (x-2),6) = (4,(y+2) )

(6-2),6 = (4,(4+2) )

( (4),6) = (4,(6) )

(4,6) = (4,6)

so, X1 =X2 ; 4 = 4

Y1 = Y2 ; 6 = 6

Answer:

for anyone who needs it: the answer was C.

Step-by-step explanation:

i got it correct on plato test

Answer: First step would be to do whatever is inside the parentheses.

Step-by-step explanation:

PEMDAS