By recognizing the relationship between Exponentiation and logarithms, we can transform the given expression into a more concise and equivalent form.
To rewrite the expression 3 log(5) in the form log(c), we can use the logarithmic property that states log(a^b) = b log(a). Applying this property, we have:
3 log(5) = log(5^3)
Simplifying further, we find that 5^3 is equal to 125:
3 log(5) = log(125)
Therefore, we can rewrite 3 log(5) as log(125).
In summary, the expression 3 log(5) can be rewritten as log(125) using the logarithmic property. It is important to understand logarithmic properties and their application to manipulate and simplify expressions involving logarithms. By recognizing the relationship between exponentiation and logarithms, we can transform the given expression into a more concise and equivalent form.
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A sphere has a radius of 4. what is the volume of the sphere? show your answer in terms of pi. I've been stuck on this for 4 days and I can't get it.
Answer:
ok let me help
Step-by-step explanation:
v=268.08 sooo
r(radius) which is 4
v=4/3 n r³ =4/3×n×4³ = 268.08
Answer:
(256/3)π or 85.33π
Step-by-step explanation:
The equation for volume of a sphere is 4/3πr^3 where r = the radius
So the volume of the sphere in terms of pi would be
4/3(π)(4)^3
(4/3)(64)π
4 x 64 = 256
256/3 = 85.33
In terms of pi the answer is (256/3)π or 85.33π
HELP! ITS EASY BUT I CANT DO IT!! Find the volume of a rectangular prism with length = 8.4mm, width = 3.5mm and height = 5.6mm. Length = 8.4mm
Answer:
164.64
Step-by-step explanation:
you just have to multiply
8.4 x 3.5= 29.4 then you do 29.4 x 5.6 = 164.64
Fill in the blank so that the ratios are equivalent. : 6 and 7:2
Answer:
x = 21
Step-by-step explanation:
x : 6 = 7 : 2
x/6 = 7/2
x/6 = 21/6
x = 21
Which of the followers scatter plots could have a trend line with an equation of 2x+5
Answer:
answer is c because of the y intercept . . so the y intercept is postive and goes through the orgin
Step-by-step explanation:
Help me please it’s due right now
Answer:
1. -3/2
2. 8
Step-by-step explanation:
Plug the number in with x to find the answer, then solve using PEMDAS as normal.
A postulate is something in geometry that must be proven true before you can use it.
Answer:
Statements Reasons
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Given
∠ADB and ∠CDB are right angles Given
ΔADB and ΔCDB are right triangles definition of right triangles
BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ reflexive property
ΔADB≅ΔCDB HL≅
AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ CPCTC (corresponding parts of congurent triangles must be congurent)
Step-by-step explanation:
Most of the geometry concepts and theorems that are learned in high school today were first discovered and proved by mathematicians such as Euclid thousands of years ago. Given that these geometry concepts and theorems have been known to be true for thousands of years, why is it important that you learn how to prove them for yourself?
Theorems and Proofs
In geometry, a postulate is a statement that is assumed to be true based on basic geometric principles. An example of a postulate is the statement “through any two points is exactly one line”. A long time ago, postulates were the ideas that were thought to be so obviously true they did not require a proof. A theorem is a mathematical statement that can and must be proven to be true. You've heard the word theorem before when you learned about the Pythagorean Theorem. Much of your future work in geometry will involve learning different theorems and proving they are true.
What does it mean to “prove” something? In the past you have often been asked to “justify your answer” or “explain your reasoning”. This is because it is important to be able to show your thinking to others so that ideally they can follow it and agree that you must be right. A proof is just a formal way of justifying your answer. In a proof your goal is to use given information and facts that everyone agrees are true to show that a new statement must also be true.
Suppose you are given the picture below and asked to prove that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯. This means that you need to give a convincing mathematical argument as to why the line segments MUST be congruent.
Here is an example of a paragraph-style proof. This is similar to a detailed explanation you might have given in the past.
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ because it is marked in the diagram. Also, ∠ADB and ∠CDB are both right angles because it is marked in the diagram. This means that △ADB and △CDB are right triangles because right triangles are triangles with right angles. Both triangles contain segment BD¯¯¯¯¯¯¯¯. BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ because of the reflexive property that any segment is congruent to itself. △ADB≅△CDB by HL≅ because they are right triangles with a pair of congruent legs and congruent hypotenuses. AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ because they are corresponding segments and corresponding parts of congruent triangles must be congruent.
There are two key components of any proof -- statements and reasons.
The statements are the claims that you are making throughout your proof that lead to what you are ultimately trying to prove is true. Statements are written in red throughout the previous proof.
The reasons are the reasons you give for why the statements must be true. Reasons are written in blue throughout the previous proof. If you don't give reasons, your proof is not convincing and so is not complete.
When writing a proof, your job is to make everything as clear as possible, because you need other people to be able to understand and believe your proof. Skipping steps and using complicated words is not helpful!
There are many different styles for writing proofs. In American high schools, a style of proof called the two-column proof has traditionally been the most common (see Example 3). In college and beyond, paragraph proofs are common. An example of a style of proof that is more visual is a flow diagram proof (see Example 4). No matter what style is used, the key components of statements and reasons must be present. You should be familiar with different styles of proof, but ultimately can use whichever style you prefer.
Learning to write proofs can be difficult. One of the best ways to learn is to study examples to get a sense for what proofs look like.
Answer:
False
Step-by-step explanation:
It doesn't need to be proven in order to be used. We can just assume the postulate is true.
ASAP! What is the surface area of the solid?
14 square inches
20 square inches
24 square inches
32 square inches
Answer:
I think is is 14 square inches.
Step-by-step explanation:
2 plus 2 plus 5 plus 5 = 14
I don't know if this is right.
not times because 2 time 2 times 5 times 5 equals 100. there is no 100 . divide is not working and subtract is not working so add. I hoke this is correct and helps.
Please help due today
Answer:
1) unlikely 1/8 12.5%
2) equally likely 4/8 50%
3) likely 5/8 62.5%
4)impossible 0/10 0%
5) unlikely 3/8 37.5%
The measures of the angles of a triangle are shown in the figure below. Solve for x.
39
(9x-3)
Answer:
23.56
Step-by-step explanation:
i thin if not then 13,67
2. The dimensions of a triangular pyramid are shown on the figure below. The height of the pyramid is
15 inches. What is the volume in cubic inches?
11
16 in
20 in
25.6 in
Answer:
he should be in 11 inches
A line has equation 2x + y=20 and a curve has equation y=a+
18/x-3, where a is a constant.
Find the set of values of a for which the line does not intersect the curve
Answer:
we have two equations:
2*x + y = 20
y = a + 18/x - 3
We want to find the values of a such that the graphs of the equations do not intersect.
The first step is to isolate y in the first equation.
now we get:
y = 20 - 2*x
Then we have the system of equations:
y = 20 - 2*x
y = a + 18/x - 3
If the line intersects the curve at a point (x, y), then at that point both functions have the same value of y, then:
20 - 2*x = y = a + 18/x- 3
We want to find a value of such that this does not happen.
Let's solve that equation and see what we can find.
20 - 2*x = a + 18/x - 3
20 + 3 = a + 18/x + 2*x
23 = a + 18/x + 2*x
(23 - a) = 18/x + 2*x
if we multiply all values by x, we get:
(23 - a)*x = 18 + 2*x^2
Then we have a quadratic equation, we can write this as:
2*x^2 - (23 - a)*x + 18 = 0
Now, remember that if the determinant of the quadratic function is smaller than zero, then the function does not have any real solution, then we need to find a such that the determinant of this quadratic equation is smaller than zero.
Remember that for a quadratic equation:
a*x^2 + b*x + c = 0 is:
b^2 - 4*a*c
In this case, the determinant is:
(-(23 - a))^2 - 4*2*18
(23 - a)^2 - 144
And this must be smaller than zero, then:
(23 - a)^2 - 144 < 0
23^2 - 2*23*a + a^2 - 144 < 0
529 - 46*a + a^2 - 144 < 0
a^2 - 46*a + 385 < 0
Notice that the function has a positive leading coefficient, then the arms of the function go upwards, then the region of the function that is smaller than zero is the values of a that are between both roots of a.
Then we need to solve:
a^2 - 46*a + 385 = 0
We can use the Bhaskara's equation to find the roots, the roots are given by:
[tex]a = \frac{-(-46) +- \sqrt{(-46)^2 - 4*1*385} }{2*1} = \frac{46 +-24}{2}[/tex]
Then the two roots are:
a₁ = (46 + 24)/2 = 35
a₂ = (46 - 24)/2 = 11
Then for all the values of a suc that:
11 < a < 35
The line does not intersect the curve.
I want you to do a linear and exponential model for Yakima's Population. Use the DATA below: in 1990 => P0 = 64792 in 2010 => P20 = 91646 A) Find the linear model of population growth. B) Predict the population for 2050. C) Find the exponential model of population growth. D) Predict the population for 2050. E) Which one seems more realistic?
Answer:
(a) [tex]P(x) = 1342.7x + 64792[/tex]
(b) [tex]P(60) = 145354[/tex]
(c) [tex]P(x) = 64792 *1.0175^x[/tex]
(d) [tex]P(60) = 183491[/tex]
(e) The exponential model is more realistic
Step-by-step explanation:
Given
[tex]1990 ==> P_0 =64792[/tex]
[tex]2010 ==> P_{20} =91646[/tex]
Solving (a): The linear model of the population growth
First, we calculate the slope of the function.
[tex]m = \frac{P_{20} - P_0}{20 - 0}[/tex]
[tex]m = \frac{91646 - 64792}{20 - 0}[/tex]
[tex]m = \frac{26854}{20}[/tex]
[tex]m = 1342.7[/tex]
The linear equation is then calculated using:
[tex]P(x) - P_0 = m(x - x_0)[/tex]
[tex]P(x) - 64792 = 1342.7(x - 0)[/tex]
[tex]P(x) - 64792 = 1342.7(x)[/tex]
[tex]P(x) - 64792 = 1342.7x[/tex]
Make P(x) the subject
[tex]P(x) = 1342.7x + 64792[/tex]
Solving (b): The population in 2050
First, calculate x:
[tex]x = 2050 - 1990[/tex]
[tex]x = 60[/tex]
Substitute 60 for x in [tex]P(x) = 1342.7x + 64792[/tex]
[tex]P(60) = 1342.7 * 60 + 64792[/tex]
[tex]P(60) = 80562 + 64792[/tex]
[tex]P(60) = 145354[/tex]
The population in 2050 is 145354
Solving (c): The exponential model of the population growth
An exponential model is:
[tex]y = ab^x[/tex]
In this case, it is:
[tex]P(x) = P_0 * b^x[/tex]
For x = 20, we have:
[tex]P(20) = P_0 * b^{20[/tex]
Substitute values for P(20) and P0
[tex]91646 = 64792 * b^{20[/tex]
Divide both sides by 64792
[tex]\frac{91646 }{64792} = \frac{64792 * b^{20}}{64792}[/tex]
[tex]\frac{91646 }{64792} = b^{20}[/tex]
[tex]1.41446474873 = b^{20}[/tex]
Take the 20th root of both sides
[tex]\sqrt[20]{1.41446474873} = b[/tex]
[tex]b = \sqrt[20]{1.41446474873}[/tex]
[tex]b = 1.0175[/tex]
So, the model is:
[tex]P(x) = P_0 * b^x[/tex]
[tex]P(x) = 64792 *1.0175^x[/tex]
Solving (d): The population in 2050
First, calculate x:
[tex]x = 2050 - 1990[/tex]
[tex]x = 60[/tex]
Substitute 60 for x in [tex]P(x) = 64792 *1.0175^x[/tex]
[tex]P(60) = 64792 *1.0175^{60[/tex]
[tex]P(60) = 64792 *2.832[/tex]
[tex]P(60) = 183490.944[/tex]
[tex]P(60) = 183491[/tex] ---- approximated
(e) The most realistic model
The exponential model is more realistic. This is so because:
The linear model grows at a constant linear rate which means that, every year a certain amount of individuals is added to the society. However, this is not always so because it is almost impossible to for growth rate to be constant
A curve in the exponential model shows that the addition of individuals in the society every year is not always constant.
The number in front of a variable or term is called a .
Answer:
Coefficient. For example, in the term -3x, -3 serves as the coefficient of x.
The number in front of a variable or term is called a coefficient.
The coefficient represents the numerical factor by which the variable or term is multiplied. In an algebraic expression, the coefficient is the number that appears directly in front of the variable.
For example, in the expression 5x, the coefficient of x is 5. Similarly, in the expression 3y², the coefficient of y² is 3. The coefficient helps determine the magnitude or scale of the variable or term within the expression.
Therefore, the number in front of a variable or term is called a coefficient.
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find the
value of
x if
3^x=3^2020+3^2017/3^2017+3^14
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Plz solve this question
Find the measure of unknown angles
Answer:
1360
Step-by-step explanation:
I know because I get all a's but then again I might be wrong I didn't take my time so sorry
Answer:
x = 110°
Step-by-step explanation:
∠ QRS = ∠ YRT = 110° ( vertically opposite angles )
∠ PQR = 180° - 120° = 60° ( adjacent angles )
The sum of the interior angles of a quadrilateral = 360°
Sum the angles and equate to 360°, that is
110 + 60 + x + 80 = 360
250° + x = 360° ( subtract 250° from both sides )
x = 110°
what value of x is quadrilateral CDEF a parallelogram
Answer:
x = 2
Step-by-step explanation:
CDEF is a parallelogram.
CE and FD are its diagonals.
Diagonals of a parallelogram bisects each other.
Therefore,
10x - 5 = 4x + 7
10x - 4x = 7 + 5
6x = 12
x = 12/6
x = 2
Thus, for x = 2, CDEF is a parallelogram.
In the quadrilateral CDEF, the value of x is 2.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Quadrilateral CDEF is a parallelogram.
Here, CE and FD are its diagonals.
We know that;
Diagonals of a parallelogram bisects each other.
Therefore, We can formulate;
⇒ 4x + 7 = 10x - 5
Solve for x as;
⇒ 7 + 5 = 10x - 4x
⇒ 12 = 6x
⇒ x = 12/6
⇒ x = 2
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please help mee
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.
Answer:
9x+15, and I used the distributive property
Step-by-step explanation:
Answer:
distributive property
9x+15
Step-by-step explanation:
The distributive property is whenever you have () and distribute until you have zero of these ()
The equivalent expression simply means write this equation differently.
EXPRESA EN METROS :
A= 3 km 8 hm 5 dam
B= 8 dam 5 m 7 cm
C= 1 m 4 dm 6 cm 7mm
Answer:b
Step-by-step explanation:
PLEASE HELP! GIVING POINTS :)!
Which situation would be represented by the integer -8? A hole 8 feet deep. An 8-yard pass. You earn $8. A temperature of 8°F.
Answer:
A
Step-by-step explanation:
another helluva boss meme
could u help me that would be really nice i have been going trow a hard time
Answer:
38
Step-by-step explanation:
38 / -2 = -19
-19 + 7 = -12
A computer store bought a program at $10 and sold it at a selling price of $12 find the percent makup
Answer:
20%
Step-by-step explanation:
12-10=2
changed ÷ original x 100
2 ÷ 10 x 100
=20%
1.Given point (-6, -3) and a slope of 4, write an equation in point-slope form.
a.y - 3 = 4(x - 6)
c.y + 3 = 4(x + 6)
b.y + 3 = 4(x - 6)
d.y - 3 = 4(x + 6)
2. Given point (-3, -5) and a slope of 2, write an equation in point-slope form.
a.y + 5 = 2(x - 3)
c.y + 5 = 2(x + 3)
b.y - 5 = 2(x - 3)
d.y - 5 = 2(x + 3)
Step-by-step explanation:
1) c
2) c
use the value of slope and the coordinates and substitute in the equation of line.
Bonjour, je bloque sur un exercice de mon DM pouvez vous m'aider s'il vous plaît ? Voici l'énoncé : Ce tremplin a la forme de la parabole de la fonction carré dans un repère orthonormé (unité : 1m). Il est haut de 0,5 m d'un côté et de 2m de l'autre. Calculer sa largeur l en m et arrondir au dixième. Merci d'avance.
What's the slope of the line
Answer:
-1/2
Step-by-step explanation:
first point is 1,-4
second point is 5,-6
Slope is y2-y1/x2-x1
-6 - -4 / 5 - 1
-2/ 4
-1/2
A 133.5 kg crate, sliding on the floor, is brought to a stop by a 54.5 N force. What is the deceleration of the crate?
Answer:
0.40m/s^2
Step-by-step explanation:
Given data
Mass= 133.5kg
Force F= 54.5N
The expression for the force acting is
F=ma
substitute
54.5=133.5*a
]Divide both sides by 133.5
a= 54.5/133.5
a= 0.40 m/s^2
Hence the acceleration is 0.40m/s^2
Chris needs to recover his drumhead. The drumhead's circumference is 40.82 inches. What is the area of the drumhead that needs to be covered? 1. 6.5 to the power of 2 (inches) 2. 132.67 to the power of 2 (inches) 3. 128.17 to the power of 2 (inches) 4. 64.09 to the power of 2 (inches)
Answer: 132.67 to the power of 2 (inches)
Step-by-step explanation:
The circumference of a circle is given as 2πr. Therefore, in his case,
2πr = 40.82
2 × 3.142 × r = 40.82
6.284r = 40.82
radius = 40.82/6.284
radius = 6.5 inches
Area will now be:
= πr²
= 3.142 × 6.5²
= 3.142 × 42.25
= 132.75 inches²
Therefore, the closest answer will be 132.67 to the power of 2 (inches).
Can someone help me with this please .
Answer:
4
Step-by-step explanation:
78
Jennifer and Ashley went to the store. Jennifer bought 1.2
pounds of apples. Ashley bought 0.75 pound of grapes. How
many pounds of fruit did they buy in all? Make sure to write your equation to receive credit.
Answer:
1.2+0.75=1.95 pounds
Step-by-step explanation:
please help me on this will give you brainliest
Answer:
1.41 x 10 to the 7th power
Step-by-step explanation:
3 x 10 to the fifth is 300000
300000 x 47 = 14100000 in 47 seconds
14100000 = 1.41 x 10 to the 7th power
Hope that helps!
Answer:
1.41*10^7 or 14,100,000
Step-by-step explanation:
3*10^5*47=1.41*10^7