Apply the 45º-45º-90º Triangle Theorem to find the length of a leg of a right triangle if the length of the hypotenuse is 8{x} inches.

The equations best verifies the reasonableness of the solution will be log₃ 2187 = 7 and log₃ (3⁷) = 7. Then the correct options are A and E.

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The equation is given below.

log₃ x = 7

Take anti-log on both side, then we have

x = 3⁷

x = 2187

Then the equation is satisfied by 2187. Then we have

log₃ 2187 = 7

  log₃ (3⁷) = 7

Then the correct options are A and E.

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Answer:

zeros and AoS

Step-by-step explanation:

zeros, x = (1 , -7)

AoS:x =-1

Answer:

10

Step-by-step explanation:

he can buy 10 because 7×10=70

Answer:

10

Step-by-step explanation:

Answer:

A.)  g (x) = f (x) - 2

Step-by-step explanation:

The first thing we are going to do in this case is to take into account the following definition.

Translations are transformations that change the position of the graph of a function.

The general shape of the graph of a function is moved up, down, to the right or to the left.

The translations are considered rigid transformations. Now we will see how these are performed.

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

To graph y = f (x) -k, move the graph of k units down.

Using the definition we conclude that:

g (x) = f (x) - 4

Two exponential functions, fand g, are shown in the figure, where g is a transformation of f, g (x) = f (x) - 4 equation shows transformation of f. The correct option is A.

A mathematical function of the form [tex]f(x) = a^x[/tex], where an is a positive constant and x is the input variable, is an exponential function.

The characteristic curve of exponential functions rises or falls rapidly depending on whether an is greater or less than 1.

To determine the transformation of f which gives g, we need to examine how f has been transformed to obtain g.

Looking at the graph, we can see that g is a vertical shift of f. Specifically, g is obtained by shifting f downward by 2 units. Therefore, we need a rule that subtracts 2 from f (x) to get g (x).

Out of the given options, the only one that matches this description is:

g (x) = f (x) - 4

Option A subtracts 4 from f (x), which is not what we observe in the graph. Option B uses an incorrect format and is also subtracting 4 from  f (x).

Option C adds 4 to x, which would result in a horizontal shift, not a vertical shift.

Therefore, the correct answer is A g (x) = f (x) - 2.

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Answer:

120.8

Step-by-step explanation:

1510divide15.10x8%=120.8

Answer:

11=x

Step-by-step explanation:

since the lines are parallel the distances between each section of line is proportional to each other.

5/6=(x-1)/12

multiply both sides by 12

12(5/6)=(x-1)12/12

10=(x-1)

add 1 to both sides

10+1=x-1+1

11=x

I hope that helps :)

Answer:

a) (tri)ABC ~ (tri)CDE

b) AA

Step-by-step explanation:

a) Given in the question (the triangles are similar)

b) AA similarity is found by the vertical angle at <ACB and <DCE and the marked angles at <D and <A.

Answer:

Use this formula to solve SA= [tex]\frac{1}{2}[/tex] p (l) + B

Step-by-step explanation:

p= perimeter of base

l= slant height  (2.8)

B= Base

Answer:

This is your work so i cant do it but I can give you a hint divide both the numerator and deomonator to get simplified form

Step-by-step explanation:

Answer:

ericyikaimiao said she/he is right

Answer:

The first answer is no

two varying quantities are said to be in a relation of proportionality you can't divide 50 into 6 and get a proportional number

The second answer is yes because they are all equal and make a straight line

Step-by-step explanation:

Answer:

MONKE

Step-by-step explanation:

MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE MONKE

-BOB THE MF BUILDER WAS HERE

Answer:

The answer is

90 degrees the first one is I don't know about the rest sorry

Step-by-step explanation:

Answer:

b) 50

Step-by-step explanation:

750/15 = 50

Answer:

Step-by-step explanation:

Givens

y2 = - 4

y1 = - 8

x2 = - 3

x1 = - 2

==========

Equation

m = (y2 - y1) / (x2 - x1)

m = (-4 - - 8) / (-3 - - 2)

m = 4 / - 1

m = - 4

Answer:

(1, -4)

Step-by-step explanation:

(-3, -4) >> (x1, y1)

(-2, -8) >> (x2, y2)

(y2 - y1)           -8 - (-4) = -4

----------- >>>

(x2 - x1)           -2 - (-3) = 1

x always goes first in a coordinate, so

(1, -4)

Hope this helped ;)

Answer:

A. Banana to grape this should be right

Answer:

Daniel is 8 years old now.

Step-by-step explanation:

From the word problem we can make the following two equations:

Let "K" be Kevin's age now and let "D" be Daniel's age now, then...

K = 3D

K - 4 = 5(D - 4)

Now we substate the value of K, and get...

K - 4 = 5(D - 4)

3D - 4 = 5(D - 4)

3D - 4 = 5D - 20

3D - 5D = - 20 + 4

- 2D = - 16

D = 8

Therefore Daniel is 8 years old now.

Answer:

x=4

Step-by-step explanation:

on edge

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

When you raise a number with an exponent, there comes a result.

Lets say you get[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]

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Answer:

Hi! Your answer is down below!

Step-by-step explanation:

Hope this helps!

Have a nice day <3

Answer:

57.2243187

Step-by-step explanation:

it would be way too long to explain

Answer:

3000=3000*0.02t

3000/60=t

t=50 yrs

Step-by-step explanation:

Step-by-step explanation:

Hence the value of x is 70.14cm.

Answer:

A

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer: 20 cups

Step-by-step explanation:

Question would like to know the number of cups that Jada poured juice into.

If each cup got 0.45 litres, the number of cups that Jada poured drinks into would be the total amount of juice poured divided by the quantity per cup:

= Total juice poured / Quantity per cup

= 9 litres/ 0.45 litres per cup

= 20 cups

Answer:

y - 1 = 3/2(x - 6)

Step-by-step explanation:

First, we need to find the slope of the given equation. Without a graph, the easiest way to do this is by isolating y.

2x + 3y = 18

3y = -2x + 18        (Subtract 2x from both sides)

y = -2/3x + 6        (Divide both sides by 3)

The slope is -2/3. Perpendicular lines have opposite reciprocal slopes, so a line perpendicular to this one would need to have a slope of 3/2. We're given a point for this line, so we can write the equation for it in point-slope form.

Point-Slope Form: [tex]y - y_{1}=m (x-x_{1})[/tex]

y - 1 = 3/2(x - 6)

If necessary, this can also be written in slope-intercept form by solving for y.

Answer:

1. = 1 because any numbers to the power 0 is one

2. = 1/64

3.= b^15 base same power added up

Answer:

31 cm

Step-by-step explanation:

A rectangle has 4 sides.

27 cm + 4 cm = 31 cm.

The perimeter is 31 cm.

If you are confused, to find perimeter you add all the sides up. That is why I added 1 + 1 + 1 + 1 / 4.

For inches or a different measure I recommend just converting it. You never mentioned the measure so I decided with cm.

Answer:

35

Step-by-step explanation:

just because i saw a guy who commented on first answer

Answer:

Two possible combinations are;

1) 200 single and 30 couples

2) 150 single and 57 couples

Step-by-step explanation:

The given parameter in the question are;

The cost of ticket per person = $5

The cost of tickets per couple = $8

The minimum worth of tickets to be sold = $1,200

The maximum number of students that can fit in the gym = 500

Let 'x' represent the number of single persons that attend the dance and let 'y' represent the number of couple that attend, we have;

5·x + 8·y ≥ 1,200

x + y ≤ 500

Making 'y' the subject of both equations gives;

y ≥ 150 - 5·x/8

y ≤ 500 - x

From the graph of the inequalities created with Microsoft Excel, we have;

When x = 200, and y = 30, we get;

5 × 200 + 8 × 30 = 1240 > 1200

200 + 30 × 2 = 460 < 500

We also have;

x = 150, and y = 57, we get

Equating both values of 'y', we get;

5 × 150 + 8 × 57 = 1206 > 1200

150 + 57 × 2 = 264 < 500

Therefore, from the acceptable region in the graph, we have the following two possible combinations

1) 200 single and 30 couples

2) 150 single and 57 couples

Answer:

Sine

Step-by-step explanation:

Using the acronym SOHCAHTOA, we can see that Sine (S) should be used.

SOH represents Sine, Opposite, Hypotenuse.

Since we are only given the opposite side and hypotenuse, the sine ratio should be used, which is opposite / hypotenuse

So, sine will be used.