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2 years ago

The product of 5 and 2 less than triple a number equals the product of 7 and 8 more than twice the number. What is the number?

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

5 0

Answer:Hi,

Let the number be x

Twice the number is 2x

Five less than twice the number is 2x-5, which is given as 9

Therefore, 2x-5 = 9

or, 2x = 9+5

or, 2x = 14

or x=7

Thus the number is 7.

Cheers

Step-by-step explanation:

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Let f(x) = (5)^x+1 .Evaluate f (-3) without using a calculator

rewona [7]

Answer:

$f\left(-3\right)=\frac{126}{125}$

Step-by-step explanation:

Given

$f\left(x\right)\:=\:\left(5\right)^x+1$

Putting x = -3 to find f(-3)

$f\left(-3\right)\:=\:\left(5\right)^{\left(-3\right)}+1$

$5^{-3}=\frac{1}{125}$ ∵ $\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$f\left(-3\right)=\frac{1}{125}+1$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot \:125}{125}$

$f\left(-3\right)=\frac{1\cdot \:\:125}{125}+\frac{1}{125}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$f\left(-3\right)=\frac{1\cdot \:\:125+1}{125}$

$f\left(-3\right)=\frac{126}{125}$ ∵ $1\cdot \:125+1=126$

Thus,

$f\left(-3\right)=\frac{126}{125}$

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3 years ago

The largest side of a triangle is six more units than the smallest side. The third side is twice the smallest side. If the perim

svetlana [45]

Equation: x + x + 6 = 2x = 25
smallest side is 4.75 units
largest size is 4.75 + 6 = 10.75 units
3rd side is 2(4.75)= 9.5 units

smallest side is x
largest size is x + 6
3rd side is 2x
-----------------------------------
4x + 6 = 25
-6 -6
4x = 19
 4 4

x = 4.75 is the smallest side

smallest side is 4.75 units
largest size is 4.75 + 6 = 10.75 units
3rd side is 2(4.75)= 9.5 units

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