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4 years ago

10^x • 100^2x = 1000^5. Step by Step

1 answer:

4 0

Step one: set the base of each term to be the same (10)
(10ˣ)(10²)²ˣ = (10³)⁵
(10ˣ) (10⁴ˣ)= (10¹⁵)
10⁵ˣ = 10¹⁵
Because the indices are the same we can equate the two.
5x = 15
x = 3

Check 10⁵ˣ³ = 10¹⁵ 10¹⁵=10¹⁵

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It takes an ant farm 6 days to consume 3/8 of an apple. (Show all work) At that rate, in how many days will the ant farm cons

Lana71 [14]

Answer: 48 days

Step-by-step explanation:

Given

Ant takes 6 days to consume $\dfrac{3}{8}$ of an apple

Using unitary method

$6\ \text{days}\rightarrow \quad \frac{3}{8}\ \text{of an apple}\\\\1\ \text{apple takes}\rightarrow \quad \frac{8}{3}\times 6=16\ \text{days}\\\\3\ \text{apples take}\rightarrow\quad 16\times3=48\ \text{days}$

6 0

3 years ago

PLEASE HELP 100 POINTS!!!!!!

horrorfan [7]

Answer:

A) See attached for graph.

B) (-3, 0) (0, 0) (18, 0)

C) (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.

Given piecewise function:

$g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}$

Therefore, the function has two definitions:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

$g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}$

When <u>graphing</u> piecewise functions:

Use an open circle where the value of x is <u>not included</u> in the interval.
Use a closed circle where the value of x is <u>included</u> in the interval.
Use an arrow to show that the function <u>continues indefinitely</u>.

<u>First piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=(3)^3-9(3)=0 \implies (3,0)$

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

<u>Second piece of function</u>

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)$

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the <u>first piece</u> of the function to zero and solve for x:

$\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}$

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the <u>second piece</u> to zero and solve for x:

$\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}$

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation: (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0

2 years ago

another rectangle has length and width in the ratio of 3:2. If the length is increased by eight and the width is increased by 50

Andreyy89

Answer:

Area of the new rectangle = 148.8 cm square

Step-by-step explanation:

Let x be the dimensions of the rectangle then the

Perimeter of the Original rectangle= 2(L+B)

= 2 ( 3x+2x) = 2(5x)= 10xcm

If the length is increased by eight the new length would be 3x+ 8

and width would be 2x+x= 3x after 50 % increase

Perimeter of the new rectangle= 2(L+B)

= 2 ( 3x+8 +3x)

= 2 (6x+8)

= 12x + 16

Ratio of the new perimeter to the original perimeter is

New perimeter : Original perimeter

8 : 5

12x+ 16 : 10x cm

80x= 60x + 16

20x= 16

x= 16/20= 4/5

Putting the value of length and breadth in place of x

Area of the new rectangle = L*B = 3 * (4/5) +8 *3(4/5)=

= 12+ 40/5 * 12/5

= 62/5* 12/5

= 744/5

= 148.8 cm square

8 0

4 years ago

Does anyone know this or how to do it?

Pavlova-9 [17]

Copy and paste into search bar and it shoudl come up

7 0

3 years ago

I need you guys to check if im correct! if not, show me step by step explanations

tamaranim1 [39]

● Answer:

b) 24 cm

● Step-by-step explanation:

l + 4 = 2w => l = 2w - 4

5w + 6 = P => 5w + 6 = 2w + 2l

5w + 6 = 2w + 2(2w - 4)

5w + 6 = 2w + 4w - 8

6 + 8 = 6w - 5w

w = 14

l = 2x14 - 4

l = 28 - 4

l = 24 cm

7 0

4 years ago

Read 2 more answers