First, remember that:
log
a
(
b
⋅
c
)
=
log
a
(
b
)
+
log
a
(
c
)
Therefore, we can say that:
log
(
4
x
)
+
log
(
3
x
+
1
)
=
log
(
4
x
⋅
(
3
x
+
1
)
)
⇒
log
(
12
x
2
+
4
x
)
We now rewrite the equation:
log
(
12
x
2
+
4
x
)
=
3
Now remember that:
log
(
b
)
=
log
10
(
b
)
And that if
log
a
(
b
)
=
c
, then
b
=
a
c
Therefore, we can now simplify the equation.
log
(
12
x
2
+
4
x
)
=
3
=>
log
10
(
12
x
2
+
4
x
)
=
3
=>
(
12
x
2
+
4
x
)
=
10
3
=>
12
x
2
+
4
x
=
1000
=>
12
x
2
+
4
x
−
1000
=
0
Let's use the quadratic formula
−
b
±
√
b
2
−
4
(
a
)
(
c
)
2
(
a
)
We now know that:
x
=
−
4
±
√
4
2
−
4
(
12
)
(
−
1000
)
2
(
12
)
We can now solve for
x
.
=>
x
=
−
4
±
√
48016
24
=>
x
=
−
4
±
4
√
3001
24
=>
x
=
−
1
±
√
3001
6
=>
x
≈
8.964
,
9.197
Now, we see that when
x
<
0
, whatever solution we have will be extraneous.
Therefore,
x
≈
8.964
okay i think this big enough for yall
Answer:
b(side length) = 15 centimeters
Step-by-step explanation:
Given an assumed regular rectangular prism which has a height of 18, and volume of 4050 cubic centimeters.
We are also given the formula b = (v/18)^1/2 which is said to find the side length of the rectangular prism. Therefore, it is implied that b must be the side length. Since we know everything except the side length we can substitute the volume since we are already given the height in the formula derived from the problem.
b = (4050/18)^1/2
b = (225)^1/2
b = 15
___________
We should also know that the volume of a rectangular prism is defined as V = l × w × h, with l as the length, w as the width, and h as the height, given that b is the side length which is multiplied by the width and height to get 4050, the base must be a square. Since 4050 = 15 × w × 18
4050 = 270 × w
4050/270 = w
15 = w
w = 15.
A square base is when the length and width are equal. Therefore this value has to be true.
As 15 × 15 × 18 = 4050.
Same set up as the problem
to the left. Fill in the blanks.
25
39
Answer:
Step-by-step explanation:
Huh?
osana is tracking how many customers she can serve in a morning. She listed the number of customers served per hour in the following table: Hour (x) Number of Customers f(x) 1 3 2 5 3 7 Determine if these data represent a linear function or an exponential function, and give the common difference or ratio. This is a linear function because there is a common difference of 2. This is an exponential function because there is a common ratio of 2. This is a linear function because there is a common difference of 3. This is an exponential function because there is a common ratio of 3.
Answer: This is a Linear function because there is a common difference of 2.
Step-by-step explanation:
Answer:
Answer A) ;
✅This is a linear function because there is a common difference of 2.
Step-by-step explanation:
Because she listed the number of customers served per hour in the following table: Hour (x) Number of Customers f(x) 1 3 2 5 3 7
What is the X-INTERCEPT (x, 0) of the equation x - 3y = 7
Answer:
7
Step-by-step explanation:
When finding the x intercept you replace the y with 0 leaving only x=7
Answer:
7
Step-by-step explanation:
You find it the same way you find the y - intercept in y=mx+b.
Classify each of the following variables as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.
a. Number of students in a class of 35 who turn in a term paper before the due date.
b. Gender of the next baby born at a particular hospital.
c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop.
d. Thickness of the gelatin coating of a vitamin E capsule
e. Birth order classification (only child, firstborn, middle child, lastborn) of a math major
Answer:
a. Numerical (discrete).
b. Categorical.
c. Numerical (continuous).
d. Numerical (continuous).
e. Categorical.
Step-by-step explanation:
In Mathematics, a categorical data can be defined as a statistical data type that is used to group informations having the same attributes or characteristics. Some examples of a categorical data are age, gender, race, religion etc.
A numerical data can be defined as a data set that is expressed in numbers only or a data set consisting of numbers rather than words. A numerical data is also known as a quantitative data.
Basically, numerical data are classified into two (2) main categories and these are;
1. Discrete data: a discrete data is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.
2. Continuous data: a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous data.
a. Number of students in a class of 35 who turn in a term paper before the due date: this is a numerical data and it is discrete in nature because the number of possible values are finite or countable.
b. Gender of the next baby born at a particular hospital: this is a categorical data because it contains a nominal variable (gender).
c. Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.
d. Thickness of the gelatin coating of a vitamin E capsule: this is a numerical data and it is continuous in nature because the number of possible values are infinite or uncountable.
e. Birth order classification (only child, firstborn, middle child, lastborn) of a math major: this is a categorical data because it is used to categorize an information (birth order).
#7-11 given two parallel lines find the values of the variables requested below.
Answer:
what the heck
Step-by-step explanation:
It costs $520.00 to buy 4 ounces of gold. How much would it cost to buy six tenths of an ounce of gold?
6oz=$780.00
If it costs $520.00 for 4oz you first divide both numbers by 4 which should leave you with 1oz=$130.00 if you then multiply both sides by 6 you end up with your answer 6oz=$780.00
Answer:
around like 700,000
Step-by-step explanation:
If you can buy one jar of sun-dried tomatoes for $4, then how many can you buy with $20? Round to the nearest whole number, if needed.
Answer:
5
Step-by-step explanation:
If you can buy one for $4
20/4 = 5
you can buy 5 cans
Answer:
He can buy 5 jars of sun-dried tomatoes
Step-by-step explanation:
all you have to do is divide 4 and 20 so you get 5!
Solve.
2a + 3b = 5
b=a5
a = 4
b = -1
a = 4
b=1
Answer:
5 = 5 True
1 = 20 False
Step-by-step explanation:
help this question why s really hard
Answer:
12 2/3
Step-by-step explanation:
I'm too lazy to give an explanation. Hope this helped though.
Tomatoes and cucumbers were planted in the garden in the ratio 4:1 there if there 14 cucumber plants how many tomato plants are there
Answer:
56
Step-by-step explanation:
14 cucumbers multiplied by 4 is 56 tomatoes
The number of tomato plants is 56.
Important information:
Ratio of tomatoes and cucumbers is 4:1.Number of cucumbers is 14.Ratio:Let [tex]x[/tex] be the number of tomato plants. Then,
[tex]\dfrac{x}{14}=\dfrac{4}{1}[/tex]
On cross multiplication, we get
[tex]x\times 1=4\times 14[/tex]
[tex]x=56[/tex]
Therefore, the number of tomato plants is 56.
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I NEED HELP WITH THESE PLEASE?
Answer:
59
Step-by-step explanation:
Review the steps of the proof of the identity
At which step was an error made?
step 1
step 2
step 3
step 4
The solutions to the trigonometric equation [tex]cos(\frac{\pi}{4} - x) = \frac{\sqrt{2} }{2} \cdot sin(x)[/tex] are;
{π/2, 3·π/2}
What is a trigonometric equation?A trigonometric equation is an equation involving trigonometric functions with the input of the function, represented by a variable. specified equation is presented as follows;
[tex]cos(\frac{\pi}{4} - x) = \frac{\sqrt{2} }{2} \cdot sin(x)[/tex]
The subtraction formula for the trigonometric ratios of cosine can be presented as follows;
cos(A - B) = cos(A)·cos(B) + sin(A)·sin(B)
Therefore;
cos(π/4 - x) = cos(π/4)·cos(x) + sin(π/4)·sin(x)
sin(π/4) = √2/2
Therefore;
cos(π/4 - x) = cos(π/4)·cos(x) + (√2/2)·sin(x)
cos(π/4 - x) = (√2/2)·sin(x)
cos(π/4)·cos(x) + (√2/2)·sin(x) = (√2/2)·sin(x)
cos(π/4)·cos(x) = (√2/2)·sin(x) - (√2/2)·sin(x) = 0
cos(π/4)·cos(x) = 0
cos(x) = 0/cos(π/4) = 0
x = arccos(0) = π/2 + n·π
Where n is an integer, therefore the values of the angle between 0, and 2·π are;
x = π/2 + π × 0 = π/2 and x = π/2 + 1 × π = 3·π/2
x = π/2 and x = 3·π/2
The solutions of [tex]cos(\frac{\pi}{4} - x) =\frac{\sqrt{2} }{2} \cdot sin(x)[/tex] are; {π/2, 3·π/2}Learn more on trigonometric identities here: https://brainly.com/question/29297432
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point a is located at coordinates (-4,3) point d is the image of A after a reflection using the y-axis , then a translation two units to the right. what are the coordinates of point d ?
help Asap
Answer:
(6,3)
Step-by-step explanation:
If you reflect (-4,3) over the y-axis it is going to become (4,3).
Then, if you move it 2 units to the right, it becomes (6,3)
The coordinates of the point (-4,3) after reflection and translation will be ( 6, 3 ).
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the point (-4,3) is the image of A after a reflection using the y-axis, then a translation of two units to the right.
Reflection of point ( -4 , 3 ) ⇒ ( 4 , 3 )
A translation of two units to the right ⇒ ( 4 + 2, 3 ) ⇒ ( 6, 3 )
Therefore, the coordinates of the point (-4,3) after reflection and translation will be ( 6, 3 ).
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Solve for x: –5x+3=2x-1
Answer:
x=1.2
Step-by-step explanation: take -5x and devide it by 2x. then - 3 from -1. -3 devided by -2.5 then it equalls x=1.2
What is the place value of the 3 in the following number:
0.2738
Answer:
It is in the thousands place
Nathan plays Fortnite and has accumulated 380 solo wins over 2 days . His friend Debbie has 10 times fewer solo wins. How many solo wins does Debbie have?
Answer:
okay if nathan has 380 wins in 2 days that would mean debbie has 190 wins per day
Step-by-step explanation:
380 divide 2=190
Evaluate
2
a
4
+
5
b
3
when
a
=
4
and
b
=
−
5
Answer:
-113
Step-by-step explanation:
2a^4+5b^3 --> 2(4)^4+5(-5)^3= -113
not 100% on this since its hard to understand the original equation (I'm assuming that the numbers after the variables are exponents)
13 people take their driving test on the same day. 9 of them pass. What fraction of people didn’t pass?
Answer:
30.769230769231% or 4/13
Step-by-step explanation:
The fraction of people didn’t pass is 4/ 13.
We have,
Total number of people taking the test: 13
Number of people who passed: 9
So, the number of people who didn't pass
Number of people who didn't pass = Total number of people - Number of people who passed
Number of people who didn't pass = 13 - 9
Number of people who didn't pass = 4
So, the fraction of people didn’t pass
= 4/ 13.
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Given ABC = DEF
m
m
find m
9514 1404 393
Answer:
10
Step-by-step explanation:
Corresponding angles of congruent triangles are congruent.
angle B = angle E
3v +4 = 8v -6
10 = 5v
v = 2
Then the measure of angle B is
3v +4 = 3(2) +4 = 10 . . . measure of ∠B
Answer:
10
Step-by-step explanation:
I hope this helps and good luck
3 2/5 * 1 1/2=
please help asap
Answer: 5.1
Step-by-step explanation:
I don’t get it help
Answer:
I believe it would be → and →. These are considered rays (V and X) and they connect at W to form an angle.
Graph y = 1/x + 3 and identify the x-intercept
Answer:
x intercept is 6
y intercept is 3
Step-by-step explanation:
Please look at the image below for the question.
Write 68 447/1000 as a decimal number
Find the distance between the points.
(-1, -3) and (-1,0)
The distance is
Answer:
5.099
Step-by-step explanation:
Evaluate the expression when c=3 and y=-4. 8c-y
Answer:
28
Step-by-step explanation:
8c - y
8( 3) - (- 4)
24 + 4
28
Solve for x
(3x + 2)
71
A) 28
C) 24
B) 23
D) 34
3x=71-2
3x=69
x=69/3
x=23
I will give you brainliest.
1 euro is 1.07 dollars and £1 is 1.25 dollars how many euros are in £1
Answer:
1.18 i think
Step-by-step explanation: