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3 years ago

Which expression is equivalent to the expression shown?

Mathematics

1 answer:

Bess [88]3 years ago

5 0

Answer:

option 3

Step-by-step explanation:

$Formula : a^{-x} = \frac{1}{a^x}$

$3^7 \times 3^{-4} = 3^7 \times \frac{1}{3^4}$

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Sophia can walk 1.4 miles in 15 minutes. At this rate how far can she walk in an hour

spin [16.1K]

At this rate she can walk 5.6 miles because you need to multiply 1.4 by each 15 minutes until it gets to a hour so you get 5.6 miles

6 0

3 years ago

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A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 22 mi/h. Find the speed and direc

Minchanka [31]

Answer: The speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

Step-by-step explanation:

Since we have given that

Speed at which woman walks due west = 3 mi/hr

Speed at which ship moving due north = 22 mi/hr

Now it forms "Pythagorus theorem":

So, it becomes,

$H^2=B^2+P^2\\\\H^2=3^2+22^2\\\\H^2=9+484\\\\H^2=493\\\\H=\sqrt{493}\\H=22.20\ mi/hr$

And the direction of the woman relative to the surface of the water is given by

$\theta=\sin^{-1}x(\dfrac{3}{22.2})=7.76\approx 8^\circ$

Hence, the speed is 22.2 mi/hr and woman is 8° north relative to the surface of the water.

5 0

3 years ago

The low temperature on Monday was 16°F. On Tuesday, the low was 18°F cooler. On Wednesday, the low temperature was –4 times Tues

drek231 [11]

Answer:

$-4(16-18)$ , $[16 + (-18)](-4)$

Step-by-step explanation:

Given: The low temperature on Monday was 16°F. The low temperature on Tuesday was 18°F cooler. The low temperature on Wednesday was –4 times Tuesday’s temperature.

To find: expression that can be used to describe the low temperature on Wednesday

Solution:

Temperature on Monday = 16°F

So,

Temperature on Tuesday = $(16-18)\°F$

Temperature on Wednesday = $-4(16-18)\°F$

So, expression $-4(16-18)=(16-18)(-4)$ can be used to describe the low temperature on Wednesday.

Also,

$(16-18)(-4)=[16 + (-18)](-4)\,\,\left \{\because (a-b)=\left [ a+(-b) \right ] \right \}$

So, expression $[16 + (-18)](-4)$ also represent temperature on Wednesday.

3 0

3 years ago

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Mrs. Smith is shopping for a toy chest to go in her kids' playroom. She looks at the options shown.

AfilCa [17]

The volume of a cuboid toy chest is equal to their product of the length,

width, and height.

The correct option for the toy chest she should purchase is; Only toy chest A will provide the necessary storage space.

Reasons:

The dimensions of the toy chest are;

Toy chest A;

Length = 5 feet

Width = 4 feet

Height = 2 feet

Toy chest B;

Length = 4 feet

Width = 2 feet

Height = 4 feet

Volume of Toy chest A = 5 ft. × 4 ft. × 2 ft. = 40 ft.³

Volume of Toy chest B = 4 ft. × 2 ft. × 4 ft. = 32 ft.³

The volume of the toy chest Mrs. Smith needs = 35 ft.³

The toy chest Mrs. Smith should purchase is Toy chest A, that has a volume of 40 ft.³, which can store items that with a volume of 35 ft.³

The correct option is; Only toy chest A will provide the necessary storage space

Possible question options obtained from a similar question found online are;

Either toy chest have the storage space needed

Neither has the storage space needed

Only toy chest A

Only toy chest B

Learn more about calculating volumes of various shapes here:

brainly.com/question/3789826