If Nicholas is located at (–3, 2), what is the distance to get to the grocery store?

The ratio of the width to the length of a rectangle is 3:7. The shorter side is 9 inches long. What is the longer side and also

photoshop1234 [79]

shorter side : longer side = 3 : 7

Equate 3 parts tp 9 inches:

3 parts = 9 inches

Find 1 part:

1 part = 9 ÷ 3 = 3 inches

Find 7 parts:

7 parts = 3 x 7 = 21 inches

Area = Length x Width = 21 x 9 = 189 in²

Answer: The longer side is 21in and the area is 189 in²

3 0

3 years ago

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What is 6.7 x (-2.3) round to the nearest hundredth

Vaselesa [24]

Your answer would be -15.41. If you ever need any other kind of help, just ask me.

6 0

3 years ago

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Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

Find the missing side . round the the nearest tenth

lys-0071 [83]

$S\frac{O}{H} C\frac{A}{H} T\frac{O}{A}$

$Sin=\frac{Opposite}{Hypotenuse} Cos=\frac{Adjacent}{Hypotenuse} Tan=\frac{Opposite}{Adjacent}$

7) You have the opposite. You need the adjacent.

$Tan=\frac{Opposite}{Adjacent}$

$Tan57=\frac{12}{x}$

$x=\frac{12}{Tan57}$

x = 7.79289... =

8) You have the hypotenuse. You need the Opposite.

$Sin=\frac{x}{Hypotenuse}$

$Sin37=\frac{x}{13}$

x = sin37 × 13

x = 7.8235... =

9) You have the hypotenuse. You need the opposite.

$Sin=\frac{x}{Hypotenuse}$

$Sin59=\frac{x}{11}$

x = sin59 × 11

x = 9.4288.... =

10) You have the hypotenuse. You need the opposite.

$Sin=\frac{x}{Hypotenuse}$

$Sin53=\frac{x}{11}$

x = sin53 × 11

x = 8.7459.... =

7 0

3 years ago

The original price of a plane ticket was reduced by $150. if p=the ticket’s original price in dollars, which algebraic expressio

mariarad [96]

Answer:

Reduced price = $ ( p - 150)

Step-by-step explanation:

Let the original price of plane ticket be $p

Price reduced in plane ticket = $150

So the amount actually need to pay for a plane ticket will be given by:

Actual reduced price of plane ticket = $p - $150

i.e Algebraic expression for reduced price is:

Reduced price = $ (p - 150)

3 0

3 years ago