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4 years ago

To solve 49^3x = 343^2x+1, write each side of the equation in terms of base ____

Mathematics

2 answers:

Vinil7 [7]4 years ago

7 0

The base is 7

Second question is (7^2)^3x=(7^3)^2x+1

3rd question is no solution

melamori03 [73]4 years ago

3 0

Create equivalent expressions in the equation that all have equal bases.72(3x)=73(2x+1)72(3x)=73(2x+1)Since the bases are the same, then two expressions are only equal if the exponents are also equal.2(3x)=3(2x+1)

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Work out the area of a circle whose diameter is equal to 14 cm.

Lera25 [3.4K]

Given:

The diameter of the circle = 14 cm

To find:

The area of the circle.

Solution:

We have,

Diameter of the circle = 14 cm

We know that the radius of the circle is half of its diameter. So,

$r=\dfrac{14}{2}$

$r=7\text{ cm}$

The area of a circle is:

$A=\pi r^2$

Substituting $\pi=\dfrac{22}{7}, r=7$ in the above formula, we get

$A=\dfrac{22}{7}\times (7)^2$

$A=22\times 7$

$A=154$

Therefore, the area of the circle is 154 square cm.

6 0

3 years ago

A circle has an area of 36 m2. What is the area of a 40 sector of this circle?

ruslelena [56]

The ratio of the area of the sector (S) to the area of the entire circle (C) is equal to the ratio of the angle subtended to form the sector (As) to the angle for the whole revolution (Ac)
S / C = As / Ac
Substituting the given,
S / 36 m² = 40 degrees / 360 degrees
Solving for S gives, S = 4. Thus, the area of the sector is 4 m².

6 0

3 years ago

Pls answer with formula. will rate 5.0

lara31 [8.8K]

Answer:

a) -19/60

Step-by-step explanation:

add 7/12 to -19/60 and you get 0.26 repeating.

4/15 is 0.26 repeating.

so yea hope this helped :)

6 0

3 years ago

Read 2 more answers

Evaluate, M squared + mtp if m=3, t=4 and p=7

navik [9.2K]

m square +84 is the answer

3 0

3 years ago

You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte

Mama L [17]

Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

$f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \, otherwise }} \right.$

a) We calculate the probability that you need less than 5 minutes to get up:

$P(x$

Therefore, the probability is P(x<5)=0.

b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.

E(X)=15.

c) We calculate the probability that you will need between 8 and 13 minutes:

$P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3$

Therefore, the probability is P(8<x<13)=0.3.

d) We calculate the probability that you will be late to each of the 9:30am classes next week:

$P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6$

You have 9:30am classes three times a week. So, we get:

$P=0.6^3=0.216$

Therefore, the probability is P=0.216.

e) We calculate the probability that you are late to at least one 9am class next week:

$P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1$

Therefore, the probability is P=1.

3 0

3 years ago