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grigory [225]
3 years ago
8

Simplify the expression. Write your answer using only positive exponents:7^6 x 7 x 7^-4

Mathematics
1 answer:
svetoff [14.1K]3 years ago
5 0
The problem is asking you to simplify the exponents.  When you multiply two or more powers with the same base, the exponents can be added and subtracted.  In this case, the base is 7.

7^6*7*7^{-4}

7 can also be written as 7^1.

7^6*7^1*7^{-4} = 7 ^{(6+1-4)} = 7^3

The answer would be 7³ if you kept the exponent, or 343 if you simplified further.
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Triangle PQR lies in the xy-plane, and the coordinates of vertex Q are (2, –3). Triangle PQR is rotated 180° clockwise about the
trasher [3.6K]

Answer:

(2,3)

Step-by-step explanation:

We are given that triangle PQR lies in the xy-plane, and coordinates of Q are (2,-3).

Triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R',

We have to find the coordinates of Q'.

The coordinates of Q(2,-3).

180 degree clockwise  rotation about the origin  then transformation rule

(x,y)\rightarrow (-x,-y)

The coordinates (2,-3) change into (-2,3) after 180 degree clockwise rotation about origin.

Reflect across y- axis the transformation rule

(x,y)\rightarrow (-x,y)

Therefore, when reflect across y- axis then the coordinates (-2,3) change into (2,3).

Hence, the coordinates of Q(2,3).

5 0
3 years ago
An investment firm wants to create a billboard that displays an enlarged $1,000,000 bill. The actual size of the bill is 2.61 in
Mandarinka [93]

We know how wide the billboard will be. Therefore, to know how much the original image should be enlarged, you must divide the final width of the billboard between the current width of the invoice.

We know both data, then we perform the operation:

48 feet /6.14 inches = 7.81 feet / inches .


Therefore the correct answer is option D. 1″ = 7.81′

For the bill to cover the billboard, the bill must be expanded by a factor of 7.81 feet long per inch long that has the original image.

3 0
3 years ago
Keiko received an $80 gift card for a coffee store. She used it in buying some coffee that cost $8.04 per pound. After buying th
Kryger [21]

Answer:

6 pounds of coffee.

Step-by-step explanation:

First, we determine how much money she spent. 80-31.76 = 48.24

Next, we divide the money spent by the price per unit. 48.24/8.04=6

Therefore, she bought 6 pounds of coffee.

3 0
3 years ago
Read 2 more answers
The perimeter of the rectangle below is 46 units. Find the length of side RS. Write your answer without variables.
inessss [21]

Answer:

30 units

Step-by-step explanation:

6 0
3 years ago
Find gradient <br><br>xe^y + 4 ln y = x² at (1, 1)​
cricket20 [7]

xe^y+4\ln y=x^2

Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).

\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}

\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x

\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x

e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x

Solve for d<em>y</em>/d<em>x</em> :

e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x

\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}

If <em>y</em> ≠ 0, we can write

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}

At the point (1, 1), the derivative is

\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}

4 0
3 years ago
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