Answer:
The solution is x = 2 and x = 4
Step-by-step explanation:
Let us revise some rules in logarithmic function:
[tex]log_{a}(x)+log_{a}(y)=log_{a}(xy)[/tex]The logarithmic function is the inverse of the exponential function [tex]log_{b}(c)=a[/tex] is the inverse of [tex]b^{a}=c[/tex]Let us solve the question
∵ [tex]log_{2}(x)+log_{2}(6-x)=3[/tex]
→ By using the first rule above
∴ [tex]log_{2}(x)(6-x)=3[/tex]
→ Multiply x by (6 - x)
∵ x(6 - x) = x(6) - x(x) = 6x - x²
∴ [tex]log_{2}(6x-x^{2})=3[/tex]
→ Change the logarithmic function to exponential function using
the second rule above
∴ [tex]2^{3}=(6x-x^{2})[/tex]
∵ 2³ = 8
∴ 8 = 6x - x²
→ Add x² to both sides
∴ x² + 8 = 6x
→ Subtract 6x from both sides
∴ x² - 6x + 8 = 0
→ Factorize it into 2 brackets
∴ (x - 2)(x - 4) = 0
→ Equate each factor by 0 to find the values of x
∵ x - 2 = 0
→ Add 2 to both sides
∴ x = 2
∵ x - 4 = 0
→ Add 4 to both sides
∴ x = 4
∴ The values of x are 2 and 4
∴ The solution of the equation is x = 2 and x = 4
is the line liner?
someone help i need this to pass
Answer:
yes
Step-by-step explanation:
What is the slope of the linear function y= - 5/3 - x
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 3 .
Step-by-step explanation:
brainliest please
A motorist drives at a constant rate of 60 kph. If his destination is 240 kilometers away from his
starting point, how many hours will it take him to reach the destination? Write a rule that best describes
the problem and draw its graph using any method.
Answer:
4 hours
Step-by-step explanation:
240/60=4
The rule that best describes the problem is time = 240/60.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A motorist drives at a constant rate of 60 kph and his destination is 240 kilometers away from his starting point.
We know, Distance = time×speed.
time = distance/speed.
time = 240/60.
time = 4 hours.
speed×time = distance.
60t = 240.
60x = 240. (x = t).
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ2
rationalise the denominator 20 over root 2
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{20}{\sqrt{2} }[/tex]
To rationalise the denominator multiply the numerator and denominator by [tex]\sqrt{2}[/tex], that is
[tex]\frac{20(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]
= [tex]\frac{20\sqrt{2} }{2}[/tex]
= 10[tex]\sqrt{2}[/tex]
combine like terms to create an equivalent expression 6(1/2 w - 3/4)
.
A baker is making cakes for a party. She uses 2 1/4 cups of flour for each cake. If she has 11 cups of flour, how many cakes can she make?
1. Find f(3) for
the function
below.
f(x) = 4^x
Answer:
64
Step-by-step explanation:
f(x) = 4^x,
When x = 3,
=> f(3) = 4^3
= 4 * 4 * 4
= 64
Answer:
f(3) = 64
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x) , that is
f(3) = 4³ = 64
Please help this test is overdue and I really need to finish it I’ll do brainliest
A. -2 +23 = 21 C
B. -2 x 3 = -6 C
A grocery delivery service has 22 members. Each member pays monthly dues of $12.80
on the first day of the month,9 members paid
their dues. The remaining members paid
their dues on the third day of the month. How much
money was
collected in dues on the
(third days of the month?
A.115.20
B.232
C.166.40
D.131.84
Answer:
C
Step-by-step explanation:
If 9 members paid on the first day, this means they did not pay on the third day
The remaining people (everyone but the 9) paid on the third day
Therefore we must subtract to find out how many members paid on the third day
22 - 9 = 13
Each of the 13 members paid $12.80 which means we must multiply
13 × 12.80 = 166.40
In total, the grocery store collected $166.40 on the third day of the month
BD = 8 and AB = 4 Find AD
Answer:
AD is 12
Step-by-step explanation:
Answer:
AD=12
Step-by-step explanation:
AB=4
BD=8
AD=AB+BD
AD=4+8
AD=12
Hope this helps :)
What is the relationship between angles 1, 2, and 3?
Answer:
The angles opposite each other when two lines cross. In the figure, the 1 and 3 are vertically opposite angles and they are always equals. Same goes for angles 2 and 4. The angles in matching corners when two lines are crossed by another line, called the transversal.
Step-by-step explanation:
1. Complementary Angles
Definition
Complementary angles are two positive angles whose sum is 90 degrees.
Examples
For example, complementary angles can be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two acute angles, like ∠MNP and ∠EFG, whose sum is equal to 90 degrees. Both of these graphics represent pairs of complementary angles.
complementary angles example
Complementary Angles Example
2. Supplementary Angles
Definition
Supplementary angles are two positive angles whose sum is 180 degrees.
Examples
For example, supplementary angles may be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two angles, like ∠MNP and ∠KLR, whose sum is equal to 180 degrees. Both of these graphics represent pairs of supplementary angles.
supplementary angles example
Supplementary Angles Example
What is important to note is that both complementary and supplementary angles don’t always have to be adjacent angles.
3. Adjacent Angles
Definition
Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points.
Examples
Angles 1 and 2 are adjacent angles because they share a common side.
adjacent angles examples
Adjacent Angles Examples
And as Math is Fun so nicely points out, a straightforward way to remember Complementary and Supplementary measures is to think:
C is for Corner of a Right Angle (90 degrees)
S is for Straight Angle (180 degrees)
Now it’s time to talk about my two favorite angle-pair relationships: Linear Pair and Vertical Angles.
4. Linear Pair
Definition
A linear pair is precisely what its name indicates. It is a pair of angles sitting on a line! In fact, a linear pair forms supplementary angles.
Why?
Because, we know that the measure of a straight angle is 180 degrees, so a linear pair of angles must also add up to 180 degrees.
Examples
∠ABD and ∠CBD form a linear pair and are also supplementary angles, where ∠1 + ∠2 = 180 degrees.
linear pair example
Linear Pair Example
5. Vertical Angles
Definition
Vertical angles are two nonadjacent angles formed by two intersecting lines or opposite rays.
Huh?
Think of the letter X. These two intersecting lines form two sets of vertical angles (opposite angles). And more importantly, these vertical angles are congruent.
Examples
In the accompanying graphic, we see two intersecting lines, where ∠1 and ∠3 are vertical angles and are congruent. And ∠2 and ∠4 are vertical angles and are also congruent.
vertical angles examples
Vertical Angles Examples
Together we are going to use our knowledge of Angle Addition, Adjacent Angles, Complementary and Supplementary Angles, as well as Linear Pair and Vertical Angles to find the values of unknown measures.
Angle Relationships – Lesson & Examples (Video)
32 min
Introduction to Angle Pair Relationships
00:00:15 – Overview of Complementary, Supplementary, Adjacent, and Vertical Angles and Linear Pair
Exclusive Content for Member’s Only
00:06:29 – Use the diagram to solve for the unknown angle measures (Examples #1-8)
00:19:05 – Find the measure of each variable involving Linear Pair and Vertical Angles (Examples #9-12)
Practice Problems with Step-by-Step Solutions
Chapter Tests with Video Solutions
The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
Given that,
To determine the relationship between angles 1, 2, and 3.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Angles 1 and 2 are remote interior angles while angle 3 is a remote exterior angle. So there is a property of a triangle in that the sum of the remote interior angles is equal to the remote exterior angle.
∠1 +∠2 = ∠3.
Thus, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ2
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.M. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.2 gallons. What is the average rate of flow of the gasoline into the gas tank?
Answer:
2.55gallons.minStep-by-step explanation:
given that the initial time before pumping is 3:40 p.M.
after pumping the time reads 3:44, hence he use 4 min to fill his tank
time taken=4 min
also given is that had pumped 10.2 gallons
the capacity of tank= 10.2gallon
Then the average rate of pump is
average rate= capacity of tank/time taken
average rate= 10.2/4min
average rate=2.55gallons.min
On a coordinate plane, a triangle has points D (negative 2.5, 5), E (0, negative 1), and F (negative 5, negative 1).
What is the y-coordinate of point D after a translation of (x, y) → (x + 6, y – 4)?
D′(3.5,___ )
Answer:
D = (3.5,1)
Step-by-step explanation:
(-2.5,5) is given
you must do (x+6,y-4)
x y
(-2.5,5)
-2.5+6=3.5
x=3.5
5-4=1
y=1
(3.5,1)
Answer:
(3.5, 1)
Step-by-step explanation:
edg 2021
can anyone answer this?
Answer:
it is J
Step-by-step explanation:
Alex has twice as much money as Jennifer. Jennifer has $6 less than Shannon. Together they have $54. How much money does each have?
Answer:
Alex has twice as much money as Jennifer.
a = 2j
Jennifer has $6 less than Shannon.
j = s-6
j+6 = s
All together the three friends have $54.
a + j + s = 54
Replace a and s
2j + j + (j+6) = 54
4j = 54 - 6
4j = 48
j = 48/4
j = 12
Jennifer has $12
Alex= 2*12 = $24
Shannon = 24+12+s = 54
= 36+s = 54
s = 18
Shannon has $18
Does 1 2 and 5 make a right triangle
Answer:
Yes.
Step-by-step explanation:
If the catetes are 5 and 12, then the hypotenuse is 13, and it is a special right triangle.
ASAP please answer correctly is answered right I will mark brainliest.
Answer:
x=9
Step-by-step explanation:
Relationship B has a greater rate than Relationship A. This graph represents Relationship A.
Which equations could represent Relationship B?
Select each correct answer.
A.y = 1.4x
B.y=12x
C.y = 2.2x
D.y = 3x
Please help me ffuufgigjgjfufjdjfjckcmdhsndjf
Answer:
1/16
Step-by-step explanation:
I usually provide explanations, but I'm pretty sure you need an answer fast. Tell me if you need an explanation!
Answer:
1/16
Step-by-step explanation:
please mark me brainliest
Explain how you could determine whether
21
3
120
12
and 7
9 have the same decimal
equivalent. Use vocabulary words in your explanation.
Step-by-step explanation:
ghsusvzbsisieb ujdidjd ki kdjd jarq. id dhdb
The area of a rectangle is x^2 - 6x - 7 with a width of x - 7. What is the lenght?
[tex] {x}^{2} - 6x - 7 = (x - 7)(x + 1) \\ [/tex]
[tex]width = (x - 7)[/tex]
So
[tex]length = (x + 1)[/tex]
Just it...
So we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
POINTS!! I NEED HELP WITH THIS, WILL GIVE BRAINLIEST TO BEST ANSWER
Answer: A
Figure A is a counterexample because they are vertical angles that equal 180°, which makes the statement false.
plz mark brainliest
A high school football team scores a total of 42 points by scoring touchdowns and field goals. Suppose each field goal is worth 3 points and each touchdown is worth 7 points.
a. Let x represent the number of field goals and y represent the number of touchdowns. Write an equation that models the total points scored in the game.
b. Identify and interpret the x- and y-intercepts.
Answer:
a) 3x+7y
Step-by-step explanation:
Sorry I don't know the answer to question B
Hope this helps
The equation models the total points scored in the game as 42 = 3x + 7y, and the x-intercept and y-intercept are 14 and 6.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A high school football team scores a total of 42 points by scoring touchdowns and field goals.
From the data given in the question:
42 = 3x + 7y
Here x represents the number of field goals and y represents the number of touchdowns.
For x-intercept:
Plug y = 0
3x = 42
x = 14
For y-intercept:
Plug x = 0
7y = 42
y = 6
Thus, the equation models the total points scored in the game as 42 = 3x + 7y, and the x-intercept and y-intercept are 14 and 6.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
I need help on this one too please and thank you
Gavin and Ethan are training for a race. Last week, Gavin ran 7 kilometers, and Ethan ran twice as far as Gavin. What is the total distance that Gavin and Ethan ran last week? Express your answer in meters.
If Ethan ran twice as far as Gavin then he ran 14 kilometers. 7*2=14. And then you add 7 to 14 which gives you 21. so they ran a total of 21 kilometers
The total distance that Gavin and Ethan ran last week is 21000 meters.
Given that, Gavin and Ethan are training for a race.
What is total?A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.
Last week, Gavin ran 7 kilometers, and Ethan ran twice as far as Gavin.
Number of kilometers Ethan ran =2×7
= 14 kilometers
= 14×1000
= 14,000 meters
Now, 7 kilometers = 7000 meters
Total =14000+7000
= 21000 meters
Therefore, the total distance that Gavin and Ethan ran last week is 21000 meters.
Learn more about the total here:
https://brainly.com/question/15842940.
#SPJ2
A piece of cable 1/2 cm long weighs 25 grams. What will a 1 1/2cm length of the same cable weigh?
Answer:
75 grams
Step-by-step explanation:
1/2 cm = 25 grams
(1 1/2) /( 1/2) = 3 times as much
1 1/2 cm = 3 x 25 75 grams
PLZ HELP It’s due soon
Answer:
30
Step-by-step explanation:
Answer:
Oh thats easy its $30
Step-by-step explanation:
so for 2 icecreams it costs $6
so if u divide them it would become 1 icecream for $3 so
10 times 3 will be $30
Which is not a pair of congruent angles in the diagram below?
angles BCD and BAD
angles ABD and BDC
angles BDA and DBC
angles ABD and BAD
:)
Answer:
angles ABD and BAD
Answer:
angles ABD and BAD
Step-by-step explanation:
The graph below represents the total shipping cost of x items for four different companies.
Shipping Charges
A graph has number of items on the x-axis and shipping cost in dollars on the y-axis. Line W goes through points (0, 5) and (2, 13). Line U goes through (0, 12) and (3, 16). Line Y goes through (0, 10) and (2, 12). Line Z goes through (0, 0) and (2, 4).
Which list places the companies in order from the steepest slope to the least steep slope?
W, Z, U, Y
U, Y, W, Z
W, Z, Y, U
U, Y, Z, W
Answer:
Steepest to most gentle: W, Z, U, Y
Step-by-step explanation:
Answer: WZUY
Step-by-step explanation: On Edgenuity!!!!!!!!!!!
Need help pls Need it