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3 years ago

4^4x-5= 8^3x-4 solve

1 answer:

8 0

$4^{4x-5}=8^{3x-4}\\\\(2^2)^{4x-5}=(2^3)^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-5)}=2^{3(3x-4)}\iff2(4x-5)=3(3x-4)\qquad\text{use distributive property}\\\\(2)(4x)+(2)(-5)=(3)(3x)+(3)(-4)\\\\8x-10=9x-12\qquad\text{add 10 to both sides}\\\\8x=9x-2\qquad\text{subtract 9x from both sides}\\\\-x=-2\to \boxed{x=2}$

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Anna [14]

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3 years ago

QUESTION 5 The lengths of the legs of a right triangle are 9 cm and 40 cm. What is the length of the hypotenuse? 41 cm 65 cm 49

GREYUIT [131]

Using Pythagoras' Theorem

$c {}^{2} = 9^{2} + {40}^{2}$
$c = \sqrt{81 + 1600 }$
$c = 41$

So, the answer is 41 cm.
C refers to the hypotenuse

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3 years ago

Read 2 more answers

The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation

labwork [276]

Answer:

Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

$\text{Radius = }\dfrac{\text{Diameter}}{2}$

$\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}$

The equation for circle given the center and radius, can be represented as:

$(x-a)^{2}+ (y-b)^{2} = r^{2}$

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

$(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq$

$(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0$

Hence, Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

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3 years ago

Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks hi

Lostsunrise [7]

We need to write equation for both mandy and bill on how many books they read depending on how many months passed.

Mandy's equation:
16 + 2x

she starts with 16 read books and she reads 2 books each month which is in total 2*x where x is number of months

Bill's equation:
4x
because from table we can see he is reading 4 new books each month.

now we need to make those 2 equations equal to eachother and solve for x because we want to see after how many months both will read the same that is why we set them equal.

16 + 2x = 4x
16 = 2x
x = 8

That means that in december he will catch her (if i counted months correctly :) )

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3 years ago

Find perimeter for a trapezoid

Reil [10]

In this example, we are asked to find the perimeter of the trapezoid. The perimeter of a figure is the distance around the figure.

To find the perimeter of the trapezoid, all we have to do is add the lengths of the sides. In this case, we would add 3 + 5 + 3 + 9 = 20 cm.

Therefore, the perimeter of the trapezoid is 20 cm

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3 years ago