1. Which logarithm bases can you use to solve for x in the exponential equation 4^3+x= 25 ? (Select all that apply.)
log base 10
log base x
log base 4
log base 25
Answers
The logarithm bases can you use to solve for x in the exponential equation [tex]4^{3+x}[/tex]= 25 is log base 4. So, option 3 is correct.
What is meant by exponential equation?Finding the slope (m) and y-intercept (b) of a line's graph will allow us to build a linear function with the formula y=mx+ b. We may build an exponential function of the form y=a+ bx given an exponential curve graph by locating the common ratio (b) and y-intercept (a) on the graph. If your function has the formula y = a + b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.
Given equation is [tex]4^{3+x}[/tex]= 25
Applying logarithm with base 4 to both sides.
log [tex]4^{3+x}[/tex]=log 25
(3+x)log 4=log25/log 4
3+x=log 25/log 4
x=(log 25/log4)-3
So, we use log base 4.
Hence, option 3 is correct.
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Related Questions
8.121 Round 8.121 to the nearest tenth.
Answers
Formulas are NOT used to solve a real-world problem of converting inches to feet.
O True
O False
Answers
hope you have a great day
Can you help me find this answer?
Answers
Step-by-step explanation:
These two angles are same side corresponding interior angles so they are equal to each other
[tex]5x + 20 = 120[/tex]
[tex]5x = 100[/tex]
[tex]x = 20[/tex]
Summer Swim charges a $45 membership fee and $3.50 each time you visit their pool. Super Swimmers charges $6.50 each time you visit their pool with no membership fee.
a. For what number of visits will both swim clubs charge the same amount? Justify your answer using mathematics.
visits:____
b. You anticipate that you will visit the pool about 32 times this summer. Which Swim Club should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
(Type Summer Swim or Super Swimmers) :______
Answers
Answer:
A) 15
B) Summer Swim
Step-by-step explanation:
How to solve problem "A":
45+3.50x =6.50x
Take 3.50 from each side.
6.50-3.50=3
45=3x
Now you divide 45 divided by 3.
45/3=15
So after 15 visits, you'll be charged the same amount.
6.50 (15)=97.5
3.50 (15)+45= 97.5
So it's definitely correct.
_________________________________________________________
How to solve problem "B":
All we have to do is plug 32 into "x"
Equation 1: 45+3.50(32)= 157
Equation 2: 6.50 (32)=208
So equation 1 definitely is cheaper. So it's the Summer Swim that's cheaper
I hope this helps!!!
What is the following product? rootindex 3 startroot 5 endroot times startroot 2 endroot.
Answers
The product of the given irrational number ∛5 × √2 is equal to
option b. [tex]\sqrt[6]{200}[/tex]
As given in the question,
Given irrational numbers are:
∛5 × √2
Take the least common multiple of 3 and 2
Least common multiple of 3 and 2 is 6.
∛5 = [tex]5^{2 \times\frac{1}{2}\times \frac{1}{3} }[/tex]
= [tex]\sqrt[6]{5^2}[/tex]
= [tex]\sqrt[6]{25}[/tex]
√2 = [tex]2^{3 \times\frac{1}{3}\times \frac{1}{2} }[/tex]
=[tex]\sqrt[6]{2^3}[/tex]
= [tex]\sqrt[6]{8}[/tex]
Product of ∛5 × √2 is given by:
∛5 × √2 = [tex]\sqrt[6]{25} \times \sqrt[6]{8}[/tex]
= [tex]\sqrt[6]{25 \times 8}[/tex]
= [tex]\sqrt[6]{200}[/tex]
Therefore, the product of the given irrational number is equal to [tex]\sqrt[6]{200}[/tex] .
The complete question is:
What is the following product?
∛5 × √2
a. [tex]\sqrt[6]{10}[/tex]
b. [tex]\sqrt[6]{200}[/tex]
c. [tex]\sqrt[6]{500}[/tex]
d. [tex]\sqrt[6]{10000}[/tex]
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Woof Woof Dog School offers dog training classes. This session, there are 7 puppies
enrolled in classes for every 4 adult dogs enrolled.
Pick the diagram that models the ratio in the story.
puppies
adults
puppies
adults
If there are 42 more puppies than adult dogs enrolled in classes this session, how many dogs
are enrolled altogether?
dogs
Answers
The diagram that models the ratio in the story is the first diagram.
Puppies = Seven green boxes.
Adults = Four violet boxes.
There are 66 dogs enrolled together.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of puppies = 7
Number of adult dogs = 4
This can be written as,
7 puppies = 4 adult dogs
Multiply 6 on both sides.
42 puppies = 24 adult dogs
Now,
The total number of enrolled dogs.
42 + 24 = 66 dogs
Thus,
The ratio that models the story is the first diagram.
The total number of enrolled dogs is 66.
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help i really need this answer please
Tim lives 2/3 as far from school as Felipe. Felipe walks to school and then walks to
Tim's house after school. What expression represents the total distance
Felipe walked?
Answers
Answer: x + 2/3(x)
Step-by-step explanation:
x = distance F walks to school
2/3(x) = distance T walks to school
Felipe walks first to school, then walks to Tim's house, so total distance Felipe walks: x + 2/3(x)
A car drives down a road in such a way that its velocity (in m/s) at time t (seconds) is v(t)=2t1/2+1. Find the car's average velocity (in m/s) between t=4 and t=8
Answers
Average velocity of the car as calculated from the given data is 6m/s.
The average velocity is calculated by dividing the total distance travelled by the whole time that has passed. Given the velocity as a function of time, you may integrate the velocity function from t = 4 to t = 8 to determine the total distance travelled.
The opposite of taking a derivative is to integrate; in other words, the function I get when I take a derivative is 2t1/2 + 1. Assuming you are aware of how to do that If not, you can input the aforementioned integral into your TI-84 to obtain the result.
The integral turns out to be
(4/3)t^3/2 + 4t so x(t)
= (4/3)t3/2 + 4t and x(8) - x(4)
= (4/3)(8)3/2 + 4(8) - [(4/3)(4)3/2 + 4(4)]
= 24 meters
The distance travelled in total was 24 meter and it took 4 seconds (8-4) to do it, so the average velocity is 24 /4 = 6 m/s.
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the following are the amount of time, in minutes, that it took a random sample of 20 technicians to perform a certain task: 18.1 20.3 18.3 15.6 22.5 16.8 17.6 16.9 18.2 17.0 19.3 16.5 19.5 18.6 20.0 18.8 19.1 17.5 18.5 18.0 assuming that the sample came from a symmetric continuous distribution, use the sign test at the 0.05 level of significance to test the null hypothesis that the mean of the population is 19.4 against a 2-sided alternative. perform the test using: (a) the binomial distribution; (b) the normal approximation to the binomial distribution.
Answers
The normal approximation to the binomial distribution is C ( n , r ) * p^r * q^n - r .
a )
the binomial distribution .
Null hypothesis H0: μ = 19.4
Alternative hypotheses H1: μ ≠ 19.4
19.4 with minus sign, we get
n = 20, x = 4 and n/2 = 10
Here x < n/2
Therefore, from table the computed P-Value is.
b )
the normal approximation to the binomial distribution ,
P = 2P(X ≤ 4 when θ = 1/2 )
= 2 (0.0059)
= 0.0118
Hence the P value, 0.0118, is less than 0.05, the null hypothesis must be rejected, and we conclude that the mean of the population is not 19.4 minutes.
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PLSS HELP ASAP!! 30 PTS
Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3).
Which statement about triangle ABC is true?
Answers
Answer:
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
Step-by-step explanation:
What is the area of this composite figure?
10 ft
10 ft
6 ft
2 ft
Answers
Answer:
88 ft^2
Step-by-step explanation:
we can make this a full 10 by 10 rectangle and find the area
10x10
100
And now we subtract the 6 by 2 triangle area that we added
6x2
12
100-12
88 ft^2
Hopes this helps please mark brainliest
Answer:
Answer = 88 ft²
Step-by-step explanation:
Step 1: Divide the composite shape into two separate parrellagrams
1. Dimensions of shape 1: Length is 10 ft, and width is 4 ft
2. Dimensions of shape 2: Length is 8 ft, and width is 6 ft
Step 2: Multiply the length by the height of each shape
Area = lw
3. Area of shape 1: 10 ft ∙ 4 ft = 40 ft²
4. Area of shape 2: 8 ft ∙ 6 ft = 48 ft²
Step 3: Add both areas together to get the total area of the composite shape
5. 40 ft² + 48 ft² = 88 ft²
Hence, the total area of this composite figure is 88 ft²
(f)-3 =9 and g(-3) =2 find (f+g)(-3)
Answers
The value of f(-3) + g(-3) Or (f + g)(-3) is 11.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(-3) is 9 and g(-3) is 2.
We know f(x) + g(x) = (f + g)(x).
∴ (f + g)(-3) = 9 + 2.
(f + g)(-3) = 11.
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Use synthetic division to solve (×3 + 1) = (X - 1). What is the quotient?
Answers
The required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient.
Use the divisor and find x :
x - 1 = 0 add 1
x= 1
Now we'll divide with the number one:
Take the coefficients from the terms in front of them.
Make careful to include 0's for x² and x since all terms must be included.
set it up with a 1 in a box:
1| 1 0 0 1 bring the first number down
____________
1 multiply the boxed number by the first number and add it to the second number
1| 1 0 0 1
____+1_____ repeat with the rest of the terms
1 1
1| 1 0 0 1
___+1_+1_+1
1 1 1 2
When you're finished, use the new numbers to build an equation that begins with a term that has one fewer degree than the previous equation.
Because there is a remnant, divide it by the original divisor.
final answer:
x² + x + 1 + (2/ x -1)
Thus, the required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.
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Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet. The enclosed area of the Alamo Mission was 480 feet long and 160 wide.
What should the length of the enclosed area of the scale model be in inches?
Answers
Which of the following equations is NOT a form of a linear equation?
y = mx + b
y- y₁ = m (x − x₁)
Ax+By = C
y= ax² + bx + c-
y = kx
Answers
Answer:
the third onei
Step-by-step explanation:
it describes a quadratic equation/
Reason a linear equation will not have an exponent. This is a parabola.
y=mx+b is y intercept form of linear equation
y-y1 = m (x-x1) is point slope form of linear eq.
Ax + By = C is standard form of linear eq.
❌y=ax^2 + bc + c- is not linear, its a parabola
y = kx is constant of proportionality, is linear
Which graph is defined by f(x) = x² + 5|x| + 6?
O A.
OB.
O C.
O D.
graph A
graph B
graph C
graph D
Answers
The attached graph is defined by f(x) = x² + 5|x| + 6.
What is the graph function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.
We have,
y = x² + 5|x| + 6
we know,
|x|² = x² use this ,
y = |x|² + 5|x| + 6
Steps for drawing y = |x|² + 5|x| + 6
step1 :- first draw y = x² + 5x + 6, this graph is quadratic equation .
step2:- Leave the part of y=x² + 5x + 6 right side to the y-axis and also take its image with respect to the y-axis as a plane mirror.
step3 :- now remove the part of y = x² + 5x + 6 to left side from y - axis .
now your graph is ready
you can see in the figure attached.
Hence, the attached graph is defined by f(x) = x² + 5|x| + 6.
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Characterize the slope of the line in the graph
Answers
it must be A because it's is going down word
Answer:
Slope is negative
Step-by-step explanation:
from one point to the next, it goes down 1 (-1) and over 4 (4)
or, from one point it goes left 4 (-4) and up 1 (1) just depending on how tou look at it.
1.) in the number 4658.21987 what digit is in the hundredths place
2.) in the number 4716.054321 what digit is in the ten-thousands place
Answers
Answer:
1)1
2)3
Step-by-step explanation:
Have a look at some tables online
2) the ten-thousands place is empty so the value is zero
the ten-thousandths place has a 3
9. You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
Answers
Answer:
$560.30 & $60.30
Step-by-step explanation:
A = $560.30
A = P + I where
P (principal) = $500.00
I (interest) = $60.30
Given that ∠X≅∠D, and DE≅XW, what is the third congruence needed to prove that ΔXWY≅ΔDEC by ASA?
A
∠Y≅∠C
B
∠Y≅∠E
C
∠W≅∠C
D
∠W≅∠E
Answers
Answer:
(A) ∠Y ≅ ∠C.
Step-by-step explanation:
To prove that two triangles are congruent by ASA (Angle-Side-Angle), you need to show that two angles in one triangle are congruent to two corresponding angles in the other triangle, and that the side between the two angles is congruent to the corresponding side in the other triangle.
Given that ∠X ≅ ∠D and ∠DE ≅ ∠XW, the third congruence needed to prove that ΔXWY ≅ ΔDEC by ASA is:
(A) ∠Y ≅ ∠C
This is because ∠Y and ∠C are the corresponding angles in the two triangles that have not been shown to be congruent.
So the answer is (A) ∠Y ≅ ∠C.
Tell me if this helped :)
A cell phone carrier charges a monthly fee of $20 and also charges customers $0.05 per text message. The function C(t)+0.05t+20 represents the cost of C, per month based on t text messages in a month.
Which best describes the domain of the function?
All real numbers
All real numbers that are multiples of 0.05
All whole numbers
All whole numbers for 0 to 20
Answers
Answer:500
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form.
Answers
You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).
you are given points (-6 , 3) and (6 , 1). Find slope:
slope = change in y / change in x
slope = (3 - 1) / (-6 - 6)
slope = 2/-12
slope = -1/6
slope-intercept form: y = mx + b where m = slope and b = y intercept.
y = -1/6x + 2
what is 24 in scientific notation
Answers
Answer:
2.4 × 101
Step-by-step explanation:
that is 24 in scientific notation
Answer:
24 * 10^1
Step-by-step explanation:
Hope this helps. :)
Write an equation for the line.
Answers
Answer:
y = 2x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0-(-2)}{1-0}[/tex] = [tex]\frac{0+2}{1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = 2x - 2 ← equation of line
Answer:
y = 2x - 2
Step-by-step explanation:
The equation y = mx + b is a standard form of a linear equation in one variable. It represents a straight line on a graph
In this equation, y is the dependent variable, which is the variable that is being measured or predicted. The independent variable is x, which is the input or cause in the relationship.
The coefficient m is the slope of the line, which tells you the rate of change between the two variables. It represents how much the value of y changes for each unit change in the value of x. A positive slope means that the line goes up as you move from left to right, while a negative slope means that the line goes down.
- Our slope is positive
- slope (m) = rise / run = 2/1 = 2
The constant b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0.
- Our y-intercept is -2
m is 2 and b is -2, the equation y = 2x - 2 represents a line with a slope of 2 and a y-intercept of -2. This means that for every 1 unit increase in the value of x, the value of y increases by 2 units, and the line crosses the y-axis at the point (0, -2).
You make $10 an hour babysitting and $20 an hour lifeguarding. You need to make at least $120 next week to buy a concert ticket. You can work at most 10 hours a week. Use y for number of hours babysitting and x for hours lifeguarding
Answers
Answer:
5 hours lifeguarding and two hours babysitting.
Step-by-step explanation:
5(20) = 100
10(2) = 20
100 + 20 = 120
i think of a number,multiply it by 3,add 4 and square the result
Answers
The algebraic expression is (3X + 4)²
What is word problem?Word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
From the question
To express the worded problem algebraically using X as your unknown
To express the worded problem algebraically using X as your unknown
The number is X
Now if we multiply the number X by 3 we get 3X
When we add 4 with 3X we get 3X + 4
Finally the squaring the result 3X + 4 we get (3X + 4)²
Hence the required algebraic expression for the worded problem is (3X + 4)²
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Harper spent at least 40 minutes drawing on Friday. She spent 20 minutes more on Friday than on Monday. How many minutes could harbor have spent drawing on Monday, m?
(Make equation with inequality)
Answers
Answer:153000394836295938
Step-by-step explanation:
;)
Online there is an item that usually costs $20 is advertised as being 25% off.
What is the discount?
What is the sale price of the item?
Answers
Answer: The discount is 25% * $20 = $5.
The sale price of the item is $20 - $5 = $15.
Joanna's tree starts at 4 feet tall and
grows 15% each year. What is the tree's
height after 12 years?
Answers
The height of the tree after 12 years is 21.401 feet.
How to predict the height of the tree
In this problem we find the case of a tree that grows exponentially, the height of the tree is defined by the following formula:
h = a · (1 + r / 100)ⁿ
Where:
a - Initial height of the tree, in feet.r - Increase rate, in percentage.n - Number of periods, in years.If we know that a = 4 ft, r = 15 and n = 12, then the final height of the tree is:
h = 4 · (1 + 15 / 100)¹²
h = 21.401
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A local dry cleaner interviewed 10 candidates for the positions of cashier, washer, salesperson, and delivery driver. How many ways can they fill the 4 positions?
A. 14
B. 210
C. 5,040
D. 151,200
Answers
Answer:
How many ways can they fill the 4 positions?
The Answer is B. 210
Answer: b. 210
Step-by-step explanation: