Solving an exponential equation by using logarithms: Exact answers in logarithmic form

The actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.

Generally, a scale drawing is described as a drawing that has been reduced or enlarged from its original size to a specified scale.

For instance, the scale of the drawing of the original aquarium is ¹/16.  This implies that the length, width, and height have been scaled down to one-sixteenth of the original size.

Scale drawing = ¹/16 of the original aquarium

Length of the colored face = 2¹/₄ inches

The actual length of the colored face = 36 inches (2¹/₄ inches x 16)

Thus, the actual measurement of the length of the colored face of the aquarium is D. 36 inches by 14 inches.

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The volume of the composite fiqure as shown in the diagram above is 300 cm³.

A composite fiqure is a fiqure that can be divided into mor than one of the basic shapes.

Note: The composite fiqure is made up of two different cubiods

To calculate the volume of the composite fiqure, we use the formula below.

Formula:

Where:

Given:

Subsitute these values into equation 1

Hence, The volume of the composite fiqure as shown in the diagram above is 300 cm³.

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Explanation:

Take note that the x and y coordinate of this vector are the same.

This leads to a 45-45-90 reference triangle. If the vector was in the first quadrant (the northeast), then the answer would be 45 degrees.

However, we need to add on 180 so we get to the third quadrant instead where x and y are both negative. This gets us to 180+45 = 225 degrees

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If you wanted to use a calculator, then you would compute the value of [tex]\tan^{-1}(b/a)[/tex] where <a,b> is the vector in question.

Since a = b in this case, we have b/a = 1 and the arctangent of this is 45 degrees. The adjustment of adding on 180 still applies like from before.

Answer:

[tex]x = 0 \\ x = 4[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 4x = 0 \\ x(x - 4) = 0 \\ \\ x = 0 \\ \\ x - 4 = 0 \: - > x = 4[/tex]

Answer:

1.97 day; 1 day.

Step-by-step explanation:

0.07*100 = 7

31.91x - 7 = 70

70 - 7 = 63

31.91x = 63

63 / 31.91 = 1.97

Answer:

33

Step-by-step explanation:

35 take away 1 is 34 take away one more its 33

Considering that the powers of 7 follow a pattern, it is found that the last two digits of [tex]7^{1867}[/tex] are 43.

The last two digits of a power of 7 will always follow the following pattern: {07, 49, 43, 01}, which means that, for [tex]7^n[/tex], we have to look at the remainder of the division by 4:

In this problem, we have that n = 1867, and the remainder of the division of 1867 by 4 is of 3, hence the last two digits of [tex]7^{1867}[/tex] are 43.

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Answer:

Is this really college math?

He would have 8 slices of pizza

Step-by-step explanation:

8 * 4 = 32

32 / 4 = 8...

the number of slices John would have after distributing it among his friends.

8×4=32

32/4

= 8

John would have 8 slices of pizza.

Step-by-step explanation:

apothem : distance from the center of the object to the side(s).

area : 1/2 × perimeter × apothem

perimeter : 9 x side

perimeter = 9×15 in = 135 in

area = 1/2 × 135 × 20.6 = 1,390.5 in²

The perimeter and area of a nonagon with apothem of 20.6 inches and side of 15 inches are 135 inches and 1390.5 inches² respectively.

A nonagon is a polygon with 9 sides. The perimeter and area can be found as follows;

Perimeter = length of the whole sides

side length = 15 inches

P = 9 × 15

p = 135 inches

Area of a nonagon = 1 / 2 pa

where

Therefore,

apothem = a = 20.6 inches

area of the nonagon = 1 / 2 × 135 ×  20.6

area of the nonagon = 2781 / 2

area of the nonagon = 1390.5 inches²

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Answer:

y=mx+b. slopes.

Fiona's equation is y=-3x+30. She will have no money after buying 10 of her favorite drink. She starts with $30 and loses $3 each time. She loses at a slower rate than Chester.

Chester's equation is y=-5x+20. He will have no money after buying 4 of his favorite drink. He starts with $20 and loses $5 each time. He loses at a faster rate than Fiona.

Answer:

m = 4

(0, 1)

y = 4x + 1

Step-by-step explanation:

Slope using first two points (-2, 7) & (-1, -3):

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{-3+7}{-1+2} =\frac{4}{1}[/tex]

m = 4

Y-intercept, b: (0, 1)

Equation:

y = mx + b

y = 4x + 1

Answer:

You have to pay $3.50 up front before using the kayak

Let's complete

Rule following=4n

#2

The rule is 4n

#3

Let's see

Answer:

12

Step-by-step explanation:

5^2+b^2=13^2

25+b^2=169

169-25=144

b=12

(yes, this is also a triple)

Answer:

a) 8xy = (4)(2xy)

b) 15x⁴z = (5x²)(3x²z)

c) -12x³y³ = (3y³)(-4x³)

d) 8x-2y = (2)(4x-y)

Step-by-step explanation:

a) 8xy = (4)(2xy) for the right side to equal the left 2xy needs to be multiplied by 4 to equal 8xy

b) 15x⁴z = (5x²)(3x²z) you need to multiply 5x² by 3x²z to equal 15x⁴z.

5*3 = 15 and x²*x² = x⁴ so 15x⁴*z = 15x⁴z

c) -12x³y³ = (3y³)(-4x³) becuase -4*3 = -12 and x³*y³ equal x³y³

d) 8x - 2y = (2)(4x-y) when you multiply 2 by 4x-y it equals 8x-2y

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

f(x) = 6√7

Step-by-step explanation:

f{g(x)}=h(x)

f(7x+2)=6√7x+2

let y = 7x+2

x= (y-2)/7

f(x)= 6 √7(y-2)/7+2

Thus, f(x) =6√7

Answer:

[tex]Y=-\frac{1}{3} + 6[/tex]

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okay okay what is emoji aaaaa

Answer:

65 alojamiento

Step-by-step explanation:

Answer

i dont know i jus want the points

Step-by-step explanation:

Answer:

x=5

y=0

Step-by-step explanation:

Let's solve the system of equations through elimination

Solving by elimination is when you add or subtract one equation by the other to eliminate one variable

In this case, adding 3x and -3x would cancel each other out so we should add the equations

[tex]-3x + 7y = -15\\+(3x + 5y = 15)\\0+12y=0\\12y=0[/tex]

Now solve for y

Divide both sides by 12 to isolate y

[tex]12y=0\\\\\frac{12y}{12} =\frac{0}{12} \\\\y=0[/tex]

Now sub in the value of y into one of the original equations and solve for x

[tex]3x+5y=15\\3x+5(0)=15\\3x=15\\[/tex]

Divide both sides by 3 to isolate x

[tex]\frac{3x}{3} =\frac{15}{3} \\x=5[/tex]

Answer:

1

Step-by-step explanation:

Answer:

[tex]\fbox{ Option D ➫ \: 416 \: cm²}[/tex]

Step by step explanation:

Given:

height of prism h = 18 cm

length of base of triangle b = 10cm

height of triangle h' = 2 cm

side A of triangle = 5 cm

side B of triangle = 7 cm

To find:

Surface area of prism = ?

Solution:

[tex]Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{10} \times \not{2} \\ Area \: of \: base \: triangle = 10 \: {cm}^{2} [/tex]

[tex] \fbox{Area \: of \: base \: triangle \: (B) = 10 \: cm²}[/tex]

[tex]Perimeter \: of \: base \: triangle = Side A + Side B + base b \\ Perimeter \: of \: base \: triangle = 5 + 7 + 10 \: cm \\ Perimeter \: of \: base \: triangle = 22 \: cm[/tex]

[tex] \fbox{Perimeter \: of \: base \: triangle (p) \: = 22 \: cm}[/tex]

[tex]Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 10+ \: 22 \times 18 \\ Surface \: area \: of \: prism = 20 + 396\\ Surface \: area \: of \: prism = 416 \: {cm}^{2} [/tex]

[tex]\fbox{Surface \: area \: of \: prism = 416 \: cm²}[/tex]

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Answer:

D. 416 cm²

Step-by-step explanation:

Let S be the surface area of the prism

     B be the area of the base of the prism

     A be the lateral area of the prism

_______

formula :

S = 2B + A

__________

The base is a triangle ,then B the area of the base :

[tex]B=\frac{10 \times 2}{2}=10 \mathrm{~cm}^{2}[/tex]

_______

formula :

A = (Perimeter of the base) × (the height of the prism)

__________

then ,

[tex]\begin{aligned}A &=(10+5+7) \times 18 \\&=22 \times 18 \\&=396cm^2\end{aligned}[/tex]

Conclusion:

[tex]\begin{aligned}S &=2 B+A \\&=2 \times(10)+396 \\&=20+396 \\&=416 \mathrm{~cm}^{2}\end{aligned}[/tex]

Answer:

The final answer is 16.

Gd luck with your work! :)

Answer:

Step-by-step explanation:

Answer: y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

    First we will find the slope, then we will find the y-intercept.

    Slope is change in y over change in x:

[tex]\frac{-1-3}{2--1}=\frac{-4}{3}[/tex]

    Now we will solve for the y-intercept:

y = [tex]\frac{-4}{3}[/tex]x + b

(-1) = [tex]\frac{-4}{3}[/tex](2) + b

-1 = [tex]\frac{-8}{3}[/tex] + b

[tex]\frac{5}{3}[/tex] = b

b = [tex]\frac{5}{3}[/tex]

    Final equation:

y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]

Answer:

6 , 7 , 8 , 9...

Step-by-step explanation:

2x > 10

x > 5

then

x = 6 , 7 , 8, 9...

I think that I am right and also think this will helpful to you.....

Answer:

-y-1

Step-by-step explanation:

Answer:

value of missing angle is..57°

Step-by-step explanation:

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54° and 69°

the missing angle of the triangle.

let's consider the missing angle as n.

sum of interior angle of triangle= 180°

n+54°+69°= 180° (adding up to sum of interior angle of triangle)

n+123°= 180°

n= 180°-123°

n= 57°