Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution. Log(x-1)+log5x=2
Answers
Answer:
see attached
Step-by-step explanation:
We prefer to solve these by rewriting the equations to the form f(x) = 0, then having a graphing calculator show us the x-intercepts of f(x). This is illustrated in the second attachment.
__
The applicable rules of logarithms are ...
log(a) +log(b) = log(ab) . . . for logs of any baselog(a) = b ⇔ 10^b = aln(e^a) = alog(a) = log(b) ⇔ a = b . . . . for a > 0 and b > 0We can apply these rules to the given expressions to solve for x algebraically.
__
log(x-1) ...Taking antilogs, we have ...
(x -1)(5x) = 10^2 = 100
x(x -1) = 20 . . . . . . . . . . . divide by 5
x² -x -20 = 0 . . . . subtract 20, put in standard form
(x -5)(x +4) = 0 . . . . factor
x = 5 or x = -4 . . . . . . the latter is an extraneous solution
x = 5 only
__
ln(x +5) ...Taking antilogs, we have ...
x +5 = (x +1)(x -1)
x² -x -6 = 0 . . . . . . . subtract (x+5), write in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or x = -2 . . . . . . the latter is an extraneous solution
x = 3 only
__
e^x² ...Taking natural logarithms, we have ...
x² = 4x +5
x² -4x -5 = 0 . . . . . write in standard form
(x -5)(x +1) = 0 . . . . factor
x = 5 or x = -1 . . . . values that make the factors zero
__
log₄(5x² ...Taking antilogs, we have ...
5x² +2 = x +8
5x² -x -6 = 0 . . . . . write in standard form
(5x -6)(x +1) = 0 . . . . factor
x = 6/5 or x = -1 . . . . values that make the factors zero
_____
Additional comment
A solution is extraneous when it does not satisfy the original equation. Here, solutions are extraneous because they make the argument of the log function be negative in the original equation. The log function is not defined for negative arguments. (Actually, it gives complex values for negative arguments.)
We could have gone to the trouble to determine the applicable domain of each of the log equations. It is easier to (a) use a graphing calculator, or (b) test the solutions found.
Related Questions
HELP PLEASE!!!
The two-way table shows the number of students in a school who like painting and/or dance.
Like Painting
Do Not Like Painting
Like Dance
28
?
Do Not Like Dance
17
18
45
What is the missing number in the table?
016
023
033
079
Answers
Answer:
The total for liking and not liking painting is 51.
28 like painting, so to find the missing number subtract 28 from 51.
The missing number is 23
Peter has 96 stamps and Sam has 63. How many stamps should Sam give Peter so that Peter will have twice as many stamps as Sam? equation please
Answers
Answer:15
Step-by-step explanation:
96÷2=48
63-48=15
So Sam should give Peter 15 of his stamps so that Peter will have twice as many stamps as him.
Answer:
10 stamps
Step-by-step explanation:
Let n = the number of stamps Sam gives Peter.
63 - n is the number stamps Sam has after giving some of them to Peter.
Peter starts with 96 stamps.
After Sam gives Peter n stamps, Sam will have 96 + n stamps.
2(63 - n) = 96 + n
126 - 2n = 96 + n
-3n = -30
n = 10
Answer: 10 stamps
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r? (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14) (startfraction 3 over 3 5 endfraction) (negative 14 minus 2) 2 (startfraction 3 over 3 5 endfraction) (2 minus 14) 14 startfraction 3 over 3 5 endfraction (negative 14 minus 2) minus 2
Answers
The mathematical expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r is:
" (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14)" (Option A)
What is a mathematical expression?A mathematical expression is a statement that contains numbers, variables, functions, etc that are related to one another in a very logical way.
It can also be defined as a mathematical phrase that comprises:
NumbersVariables or both.Learn more about mathematical expression at:
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Answer:
A
Step-by-step explanation:
A right rectangular prism has a base area of 20 cm? and a height of 9. 2 cm.
Answers
Answer:
the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.
Step-by-step explanation: hopefully that is the correct and have a great day.
Todd bought g boxes of granola bars. There are 12 granola bars in each box. Write an expression that shows how many granola bars Todd bought.
Answers
The expression that shows the granola bars Todd bought is 12g.
What is an algebraic expression?The algebraic expression stands for the mixture of variables, coefficient, constant, or all three in a mathematical form where both sides are set equivalent to each other.
Given: Todd bought g boxes of granola bars.
There are 12 granola bars in each box.
Let g be the boxes of granola bars.
Therefore, the expression that shows the granola bars Todd bought is 12g.
To learn more about algebraic expression
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Help me please help me
Answers
Answer:
h=5/18
Step-by-step explanation:
Hi there!
If you try to solve 1/2-h=2/9 for h immediately, you will find that you cannot because the denominator is odd for 2/9. Multiply 2 for the numerator and the denominator to get 4/18. Now we have 1/2-h=4/18. Multiply the numerator and denominator by 9 to get 9/18-h=4/18. H=5/18.
Answer:
[tex]\boxed{h=\dfrac{5}{18}}[/tex]
Step-by-step explanation:
[tex]\textsf {$\dfrac{1}{2} - h$ = $\dfrac{2}{9}$}[/tex]
1. Subact [tex]\dfrac{1}{2}[/tex] from both sides:
[tex]\textsf {$\dfrac{1}{2} - h$ = $\dfrac{2}{9}$}\\\\\textsf {$\dfrac{1}{2}-\dfrac{1}{2} - h$ = $\dfrac{2}{9} -\dfrac{1}{2}$}\\\\\textsf {$-h$ = $\dfrac{4-9}{18}$}\\\\\textsf {$-h$ = $\dfrac{-5}{18}$}[/tex]
2. Divide both sides by -1
[tex]\textsf {$-h$ = $\dfrac{-5}{18}$}\\\div -1 \div-1\\\\ \boxed{h=\dfrac{5}{18}}[/tex]
Final answer: [tex]\boxed{h=\dfrac{5}{18}}[/tex]
Hope this helps!
If f(x) = x2 – 2x and g(x) = 6x 4, for which value of x does (f g)(x) = 0? –4 –2 2 4
Answers
The sum of function is a way of adding two or more functions together
The values of x for which f(g(x)) = 0 are -2/3 and -1/3
Sum of functionsThe sum of function is a way of adding two or more functions together
Given the following functions
f(x) = x² - 2x
g(x) = 6x + 4
f(g(x) = f(6x +4))
f(6x+4) = (6x+4)² - 2(6x+4)
(6x+4)² - 2(6x+4) = 0
(6x+4) = 0 and 6x+4-2 = 0
x = -2/3 and -1/3
Hence the values of x for which f(g(x)) = 0 are -2/3 and -1/3
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MARKING BRAINLIEST!
This is Poe’s most well-known poem, published in 1845, which quickly became famous. What words, lines, or features of the poem stand out to you? List three.
This is about “The raven”
Answers
Step-by-step explanation:
where is the figure and question
Simpifly : -5/6-7/-8+11/12–1/6+0- -7/16
Answers
Answer:
the chosen topic is not meant for use with this typ of problem try the examples below
Step-by-step explanation:
please help!! will mark brainiest to whoever gets it right!!
Answers
Answer:
x = 77
Step-by-step explanation:
x and 103 are same- side exterior angles and sum to 180°
x + 103 = 180 ( subtract 77 from both sides )
x = 77
3x∧2±6x±x±20 sole by factorization
Answers
Answer:
just look at the algebra formula and simplify to get your answer. Remember to use your powers well
can someone explain how to do this
im not very smart
Answers
Answer:
50.24sq units
Step-by-step explanation:
4^2=4x4
4x4=16
16x3.14=50.24
This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.
Answers
Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
Combine the polynomials
(z2 - 5z + 3) - (z2 – 13z + 12)
-
Please help the twos are squared
Answers
Answer:
i think its 8z-9 if im not wrong :)
Step-by-step explanation:
are all natural numbers also a rational number? (yes/no)
Answers
Answer:
Yes
Step-by-step explanation:
But not all rational numbers are natural numbers, so be careful of that.
Amazon stock has been rising for the past week. One stock was originally $6.75 , but the price has risen 135%. What is the new price?
Answers
Answer:
$15.86
Step-by-step explanation:
Which best describes the solutions to the inequality x greater than 10? 10 and every whole number greater than 10 a rational number infinitely close to 10 but greater than 10, and all other rational numbers greater than 10 11 and every whole number greater than 11 a rational number infinitely close to 10 but greater than 10, and all other whole numbers greater than 10
Answers
Answer:
option A infinite rational values of x greater than 500
Step-by-step explanation:
i just finished the quiz on edge
Lacey had $603 in her checking account. Then, she spent $252 from the account. How much money is left in Lacey's checking account?
Answers
Answer:
In this problem we are given the initial amount of money that Lacey has in her account and we are also given the amount of money that she has spent using that account. We are told to check how much money is left in her account and we can do this with a simple subtraction.
[tex]Initial\ Amount - Money\ Spent[/tex]
[tex]\$603-\$252[/tex]
[tex]\$351[/tex]
Therefore, our final answer is that Lacey has $351 left in her account.
Hope this helps! Let me know if you have any questions
Please answer the following for 50 points, if you get it right you can get brainly, Please hurry!
Answers
Answer:
3.2 and 3.92
Step-by-step explanation:
Find y.
Do not round your answer.
9 in
у
5 in
Х
19 in
y = [ ? ] in
=
Answers
Answer: 11.2
I found the answer in the comments and figured I should make it an answer, so it's easy to find:)
<3
what’s the circumference, to this problem ?
Answers
Answer:
= 20.7345115137
or
≈ 21
Step-by-step explanation:
Circumference = 2 x π x radius
Circumference = 2 x π x 3.3
hope this helps
have a good day
Answer:
The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex]. We can then input the value and we get that [tex]C=2*\pi*3.3[/tex] and as we solve it more the final answer that we get is [tex]C=20.735[/tex].
Hope this helps! Let me know if you have any questions
Use the distributive property to write an equivalent expression.
10(y-7z+1)
Answers
Answer:
10y - 70z + 10.
Step-by-step explanation:
10(y-7z+1) Multiply each term in the brackets by 10:
= 10y - 70z + 10
A cylindrical tank has diameter 3.2 m and length
12.7 m.
What is the surface area of the tank, to 1 decimal
place?
Answers
Answer:
143.8 m²
Explanation:
Surface Area of cylinder = 2πr(r + h)
Here given,
diameter: 3.2 mradius: d/2 = 3.2/2 = 1.6 mlength: 12.7mSurface Area of cylinder:
⇒ 2π(1.6)(1.6+ 12.7)
⇒ 174.2955 m²
⇒ 143.8 m² (rounded to nearest 1 decimal place)
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each description with the correct inequality.
(5x)2 ≤ 46,
(5x)2 ≥ 46,
x2 + 5x ≥ 46,
5x2 > 46,
x2 + 5x ≤ 46,
5x2 < 46,
The square of the product
of 5 and a number is
no less than 46.
arrowBoth
The product of 5 and the
square of a number is
greater than 46.
arrowBoth
The sum of the square of a
number and five times that
number is no more than 46.
Answers
Answer:
(5x)² ≥ 46
x² + 5x ≤ 46
5x² > 46
Step-by-step explanation:
Suppose number is x
1)The square of the product of 5 and a number is not less than 46.
Step 1
Product of 5
5x
Step 2
Square of the product of 5
(5x)²
Step 3
A number is not less than 46
(5x)² ≥ 46
2)The sum of square of a number and five times that number is no more than 46
Step 1
Square of a number
x²
Step 2
Five times that number
5x
Step 3
The sum
x² + 5x
Step 4
Is no more than 46
x² + 5x ≤ 46
3)The product of 5 and the square of a number is greater than 46
Step 1
The square of a number
x²
Step 2
The product of 5
5x²
Step 3
Is greater than 46
5x² > 46
Answer this question to get 10 pts!
Answers
A = 70x30 = 2100
B = 4x30 = 120
C = 9x70 = 630
D = 9x4 = 36
Total Area = 2100+120+630+36 = 2886
So 74x39=2886
B = 30 x 4 = 120
C = 9 x 70 = 630
D = 9 x 4 = 36
to find area use length x breadth
Given 184% what is the equivalent fraction and decimal in simplest form?
Answers
Step-by-step explanation:
184% = 46/25 = 1 21/25 as a fraction
Solve the system using linear combination. Show all work.
{9x + 4y = 28
{2x + 4y = 0
Answers
Answer:
(4,-2)
Step-by-step explanation:
What is linear combination?
Linear combination is the process of adding two equations to eliminate a variable so that we are able to solve for the other variable.
Here we are given the two equations 9x + 4y = 28 and 2x + 4y = 0. We can use linear combination to cancel out the two 4y terms leaving us with only x variables in which we can solve for.
Adding the two equations. (subtracting the second equation from the first) we really are subtracting the second equation from the first because if we were to add we would get 4y + 4y which wouldn't cancel out the terms therefore we would have to subtract the two equations to get 4y - 4y which cancels out the terms.
9x + 4y = 28
- (2x + 4y = 0)
==> remove parenthesis and apply negative sign
9x + 4y = 28
-2x - 4y = -0
----------------------
7x = 28
==> divide both sides by 7
x = 4
Finding the y value:
The solution is written as (x,y) meaning we also need the value of y. To find it we can plug in the value of x into one of the equations and then we can solve for y.
2x + 4y = 0
==> plug in x = 4
2(4) + 4y =0
==> multiply 2 and 4
8 + 4y = 0
==> subtract 8 from both sides
4y = -8
==> divide both sides by 4
y = -2
so we have x = 4 and y = -2
the solution of the equation would be (4,-2)
Checking our work
If our answer is correct we can plug in the values of x and y into both equations and the outcome will be valid ( or correct )
Equation 1 : 9x + 4y = 28
==> plug in x = 4 and y = -2
9(4) + 4(-2) = 28
==> multiply 9 and 4
36 + 4(-2) = 28
==> multiply 4 and -2
36 - 8 = 28
==> subtract 8 from 36
28 = 28
Equation 2 : 2x + 4y = 0
==> plug in x = 4 and y = -2
2(4) + 4(-2) = 0
==> multiply 2 and 4
8 + 4(-2) = 0
==> multiply 4 and -2
8 - 8 = 0
==. Subtract 8 from 8
0 = 0
Both are correct so our solution is correct!
Learn more about solving systems using linear combination here! : https://brainly.com/question/12691830
Step-by-Step Explanation:
Lets solve using Elimination Method.
9x + 4y = 28 (Eq. 1)
2x + 4y = 0 (Eq. 2)
Subtracting Eq. 2 from Eq. 1, we get :-
7x = 28
x = 28/7
=> x = 4
Therefore, x = 4
Substituting value of ‘x’ in Eq. 2 :-
2x + 4y = 0
2(4) + 4y = 0
8 + 4y = 0
4y = 0 - 8
4y = -8
y = -8/4
=> y = -2
Therefore, y = -2
What type of number is -5.41?
Choose all answers that apply:
A. Whole Number
B. Integer
C. Rational
D. Irrational
Answers
The type of number -5.41 is is an rational number.
What type of number is -5.41?A rational number is a number that can be expressed as a fraction of two integers. 5.41 can be expressed as -5.41 / 1000.
An integer and whole number is a number that does not have any fraction or decimal. -5.41 is a decimal number, thus it is not an integer and a whole number.
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Find three consecutive even integers such that the sum of 5 and the second is multiplied by -7, the result is 11 greater than 5 times the opposite of the third
Answers
Answer:
-20, -18, -16
Step-by-step explanation:
For consecutive integer problems, it often works well to let a variable represent the middle one (or their average value).
__
Here, we can let x represent the second integer. Then the first is (x-2), and the third is (x+2). The given relation can be written as ...
(5 +x)(-7) = 11 +5(-(x+2))
-35 -7x = 11 -5x -10 . . . . . . eliminate parentheses
-36 = 2x . . . . . . . . . add 7x -1
-18 = x . . . . . . . . divide by 2
The three integers are -20, -18, -16.
Tim, Ryan, and Joe are brothers. Their mom, Lisa gives them each a weekly allowance. Since Tim is older, she gives him 4 more dollars than Joe. Ryan is the youngest and receives 2 less dollars than Joe. Lisa gives a total of 20 dollars a week in allowance. With Joe receiving m dollars, which equation demonstrates the situation?
Answers
Answer:
m + (m+4) + (m-2) = 20 or 3m + 2 = 20
Step-by-step explanation: