[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]3(x + 4) = 123 \\ 3x + 12 = 123 \\ 3x = 123 - 12 \\ 3x = 111 \\ x = \frac{111}{3} \\ x = 37[/tex]
=> The answer is 37.
Answer:
X=37
Step-by-step explanation:
3(x+4)=123
3x+12=123
3x=123-12
3x=111
3x/3 =111/3
x=37
Which one of the following options is true when considering the expansion of
the binomial expression (x + y)6?
A. The first term of the expansion of (x + y)^6 is x3y3.
B. The coefficients of the expansion of (x + y) are: 1,6, 15, 15, 6, 1.
c. The expansion of (x + y)^6 will yield 7 terms.
D. The sum of the exponents of each term of the expansion of
(x + y)^6 is 5
Answer:
c The expansion of (x + y)^6 will yield 7 terms
Step-by-step explanation:
(x + y)^6 =
x^6 +6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6
so its a no on A
its a no on B because its missing a 20
its a yes on c
its a no on d because the sum is 6
so c
write an expression for 15 divided by a number
show your work
Answer:
15/X
Step-by-step explanation:
a number divided by 15
15/X
solve the logarithmic equation
[tex] log_{6}(2x - 6) + log_{6}x = 2[/tex]
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \log_6(2x-6)+\log_6x=2[/tex]
Recall the property:
[tex]\displaystyle \log_bx+\log_by=\log_b(xy)[/tex]
Hence:
[tex]\log_6(x(2x-6))=2[/tex]
Next, recall that by the definition of logarithms:
[tex]\displaystyle \log_b(a)=c\text{ if and only if } b^c=a[/tex]
Therefore:
[tex]6^2=x(2x-6)[/tex]
Solve for x. Simplify and distribute:
[tex]36=2x^2-6x[/tex]
We can divide both sides by two:
[tex]x^2-3x=18[/tex]
Subtract 18 from both sides:
[tex]x^2-3x-18=0[/tex]
Factor:
[tex](x-6)(x+3)=0[/tex]
Zero Product Property:
[tex]x-6=0\text{ or } x+3=0[/tex]
Solve for each case. Hence:
[tex]x=6\text{ or } x=-3[/tex]
Next, we must check the solutions for extraneous solutions. To do so, we can simply substitute the solutions back into the original equations and examine its validity.
Checking x = 6:
[tex]\displaystyle \begin{aligned} \log_{6}(2(6)-6)+\log_{6}6&\stackrel{?}{=} 2 \\ \\ \log_6(12-6)+(1)&\stackrel{?}{=}2 \\ \\ \log_6(6)+1&\stackrel{?}{=}2 \\ \\ 1+1=2&\stackrel{\checkmark}{=}2\end{aligned}[/tex]
Hence, x = 6 is indeed a solution.
Checking x = -3:
[tex]\displaystyle\begin{aligned} \log_6(2(-3)-6) + \underbrace{\log_6-3}_{\text{und.}} &\stackrel{?}{=} 2\\ \\ \end{aligned}[/tex]
Since the second term is undefined, x = -3 is not a solution.
Therefore, our only solution is x = 6.
Answer:
x = 6
Step-by-step explanation:
The given logarithmic equation is ,
[tex]\implies log_{6}(2x - 6) + log_{6}x = 2[/tex]
We can notice that the bases of both logarithm is same . So we can use a property of log as ,
[tex]\bf \to log_a b + log_a c = log_a {( ac)} [/tex]
So we can simplify the LHS and write it as ,
[tex]\implies log_{6} \{ x ( 2x - 6 )\} = 2 [/tex]
Now simplify out x(2x - 6 ) . We get ,
[tex]\implies log_6 ( 2x^2 - 6x ) = 2 [/tex]
Again , we know that ,
[tex]\bf \to log_a b = c , a^c = b [/tex]
Using this we have ,
[tex]\implies 2x^2 - 6x = 6^2 \\\\\implies 2x^2 - 6x -36 = 0 [/tex]
Now simplify the quadratic equation ,
[tex]\implies x^2 - 3x - 18 = 0 \\\\\implies x^2 -6x + 3x -18=0\\\\\implies x( x -6) +3( x - 6 ) = 0 \\\\\implies (x-6)(x+3) = 0 \\\\\implies x = 6 , -3 [/tex]
Since logarithms are not defined for negative numbers or zero , therefore ,
[tex]\implies 2x - 6 > 0 \\\\\implies x > 3 [/tex]
Therefore the equation is not defined at x = -3 . Hence the possible value of x is 6 .
[tex]\implies \underline{\underline{ x \quad = \quad 6 }}[/tex]
y =2/3x + 20
when x = 21
Answer:
34
Step-by-step explanation:
First we need to do 2/3*21, which equals 14 as 3 and 21 can be simplified to 1 and 7. 7 * 2/1= 14. Then we add the 20 to 14, 20+14= 34
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{y = \dfrac{2}{3}x + 20}[/tex]
[tex]\mathsf{y =\dfrac{2}{3}(21) + 20}[/tex]
[tex]\mathsf{\dfrac{2}{3}(21) + 20 = y }[/tex]
[tex]\mathsf{\dfrac{2}{3}(21)=\bf14}[/tex]
[tex]\mathsf{14 + 20 = y}[/tex]
[tex]\mathsf{14 + 20 = \bf 34}[/tex]
[tex]\huge\checkmark\boxed{\huge\textsf{y = 34}}\huge\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf y = 34}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\huge\text{Amphitrite1040:)}[/tex]
Find the domain and range for each of the relations described by the sets of
ordered pairs below.
4. (-1, 2), (2, 51), (1,3), (8, 22), (9,51)
Domain:
Range:
Answers:
Domain = {-1, 2, 1, 8, 9}
Range = {2, 51, 3, 22}
==================================
Explanation:
The domain is the set of allowed inputs of a function. So it's the set of possible x values. We simply list the x coordinates of each point to form the domain.
The range is the set of possible y values or y outputs. So we simply list the y coordinates of the points. We toss out any duplicates. Since order doesn't matter in a set, we can have the values listed any way we want.
Side notes:
This is a function since we don't have any repeated x values between any of the points. This graph passes the vertical line test.This function is not one-to-one because we have y = 51 correspond to multiple x values (x = 2 and x = 9 simultaneously). This graph fails the horizontal line test.Solve the system of equations.
−5x−3y−9=0
4x−18y−54=0
y=? x=?
Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)
6 *( −5x−3y−9=0 )
Eq. 3) -30x -18y =54
subtract Eq. 2 from Eq. 3 :)
-30x -18y =54
-( 4x−18y=54)
-34x = 0
so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,
then:
-5x = 9 +3y
x = - 9/5 + (-3/5)y
now plug that into Eq. 2
4( - 9/5 + (-3/5)y ) - 18y = 54
-36/5 + (-12/5)y -18y = 54
(-12/5)y - (90/5)y = 54+36/5
-(102/5)*y =270/5+36/5
-(102/5)y = 306/5
y = (-5/102)*(306/5)
y = -306/102
y = -3
then plug in for either equation
-5x-3( -3) = 9
-5x + 9 = 9
-5x = 0
x = 0
now we have the full answer
check it by plugging in both x and y into the 2nd equation
4(0) - 18(-3) = 54
54= 54
this seems good
i need help trying to solve this question to the nearest tenth of a degree
Please help me with this
Answer:
x = 23
Step-by-step explanation:
if line j is parallel to line k then
5x + 9 + 33 + x = 180 add like terms
6x + 42 = 180 subtract 42 from both sides
6x = 138 divide both sides by 6
x = 23
Question 4 Multiple Choice Worth 4 points)
(01.02 LC)
What is the solution for the equation 6x - 8 = 4x?
Answer:
Algebra
Step-by-step explanation:
(+) it's the same thing btw6x -8 = 4x
(collect like terms) meaning the numbers with x go over the " = " sign
making it = -8 = 4x -6x
the signs change when it crosses over so it becomes that
-8 = -2x
-8 ÷ -2 = 4 (cause - ÷ by - is + )
Can somebody please help meee
Answer:
Top one: y= 3/1+2
bottom: y= -1/1+4
Summer school math problem
Hello!
4/18 = 6/27 ?
4 × 27 = 18 × 6
108 = 18 × 6
108 = 108 => 4/18 = 6/27
4/6 = 16/36 ?
4 × 36 = 6 × 16
144 = 6 × 16
144 ≠ 96 => 4/6 ≠ 16/36
3/4 = 9/12 ?
3 × 12 = 4 × 9
36 = 4 × 9
36 = 36 => 3/4 = 9/12
5/9 = 8/12 ?
5 × 12 = 9 × 8
60 = 9 × 8
60 ≠ 72 => 5/9 ≠ 8/12
Good luck! :)
What is the scale factor from abc to xyz?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C
The scale factor will be equal to 1 / 5. the correct option is C.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,
Scale factor = Original size / dilated size
Scale factor = XY / AB
Scale factor = 9 / 45
Scale factor = 1 / 5
Therefore, the scale factor will be equal to 1 / 5. the correct option is C.
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solve |5x+30|=10x ......
Answer:
Option A
Step-by-step explanation:
We need to solve out ,
[tex]\implies |5x + 30| = 10x [/tex]
We can write it as ,
[tex]\implies 5x + 30 = \pm 10x [/tex]
On simplyfing further,
[tex]\implies 5x + 30 = 10x \quad or \quad 5x +30=-10x [/tex]
On solving the above equation , we will get ,
[tex]\implies \boxed{ x = 6,-2}[/tex]
Now we know that the value of modulus is never negative so when we will put x is equal to 2 on the RHS we will get -20 which is not possible . Therefore , the extraneous root is -2 .
Option A is correct .
A claim is reviewed for MOHS surgery on the foot that was performed in 1 stage with 6 tissue blocks. The claim was reported with 17311, 17312-51, 17312-51. Is this correct
Answer:
17311, 17315
Step-by-step explanation:
Explanation,
Mohs surgery, also known as chemosurgery, created by a general surgeon, Dr. Frederic E. Mohs, is performed to remove complex or ill-defined cutaneous malignancy.List Of CPT Codes For Mohs Surgery
CPT Code 17311 and CPT Code 17313 are the base codes for the range of this surgery. CPT Code 17312, CPT Code 17314, and CPT Code 17315 are the add-on codes for this range.
Description Of CPT Code 17311
Moh’s micrographic technique, including removal of all gross tumor, surgical excision to tissue specimens, mapping, color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stain(s) (eg. Hematoxylin and eosin, toluidine blue), head, neck, hands, feet genitalia, or any location with surgery directly involving muscle, cartilage, bone, tendon, major nerves, or vessels; first stage, up to 5 tissue blocksDescription Of CPT Code 17315 (addon)
CPT Code 17315 may be used to report each block after the first 5 blocks for any single-stage.
Moh’s micrographic technique, including removal of all gross tumor, surgical excision of tissue specimens, mapping color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stains(s) (eg. Hematoxylin and eosin, toluidine blue), each additional block after the first 5 tissue blocks, any stage (List separately in addition to code for primary procedure)Extras
Description Of CPT Code 17312 (addon)
Each additional stage after the first stage, up to 5 tissue blocks (List separately in addition to code for primary procedure)
Description of CPT Code 17313
Moh’s micrographic technique, including removal of all gross tumor, surgical excision of tissue specimens, mapping, color coding of specimens, microscopic examination of specimens by the surgeon, and histopathologic preparation including routine stains(s) (eg. Hematoxylin and eosin, toluidine blue), of the trunk, arms, or legs; first stage, up to 5 tissue blocks
Description Of CPT Code 17314 (addon)
Each additional stage after the first stage, up to 5 tissue blocks (List separately in addition to code for primary procedure).
In an office there was a small cash box.One day ann took half of the money plus$1 more.Then dan took half of the remaining money plus$1 more.Stan then took the remaining $11.How many dollars were originally in the box?
Answer:
this as a equation looks like this
-1/2x+1+x=11
1/2x=10
x=20
Hope This Helps!!!
20 dollars were originally in the box
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
In an office there was a small cash box.
One day ann took half of the money plus$1 more
Then dan took half of the remaining money plus$1 more
Stan then took the remaining $11
-1/2x+1+x=11
Subtract 1/2x from both sides
1/2x=10
Multiply 2 on both sides
x=20
Hence, 20 dollars were originally in the box
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(e) Dhanu plays with his model railway from 06 50 to 11 15. He then rides his bicycle for 3 hours. Find the ratio time playing with model railway : time riding bicycle. Give your answer in its simplest form.
Answer:
53:36
Step-by-step explanation:
53:36
265:180
The ratio of time Dhanu spent playing with model railway to the time riding bicycle is 53 : 35.
What is the ratio of the time spent playing with model railway to the time riding bicycle ?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
Time spent playing with the model railway = 4 hours 25 minutes.
Converting the time to minutes = (4 x 60) + 25 = 265 minutes
Time in minutes spent riding a bicycle = 60 x 3 = 180
Ratio of the minutes - 265 : 180
53 : 35
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the ratio of boys to girls is 4 :3,if there are 24boys and how many girls will be there?
Answer:
There are 18 girlsStep-by-step explanation:
explanation given in the image ❣️◕Jess bregoli◕❣️#keep learning!!Laura bought some movie tickets. The graph represents
the
proportional relationship between the cost and the number of movie
tickets. Find the cost of seven tickets
Answer:
it must be 85 (approx.)
Step-by-step explanation:
Use the quadratic formula to find the solution to the quadratic equation given
below.
X^2-x+1/4=0
Answer:
[tex]\displaystyle x=\frac{-1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]Step-by-step explanation:
Step 1: Define
Identify
x² + x + 1/4 = 0
↓ Compare to Standard Form
a = 1, b = 1, c = 1/4
Step 2: Solve for x
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1^2 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 4(1)(\frac{1}{4})}}{2(1)}[/tex][√Radical] Multiply: [tex]\displaystyle x=\frac{-1 \pm \sqrt{1 - 1}}{2(1)}[/tex][√Radical] Subtract: [tex]\displaystyle x=\frac{-1 \pm \sqrt{0}}{2(1)}[/tex][√Radical] Evaluate: [tex]\displaystyle x=\frac{-1 \pm 0}{2(1)}[/tex]Simplify: [tex]\displaystyle x=\frac{-1}{2(1)}[/tex]Multiply: [tex]\displaystyle x=\frac{-1}{2}[/tex]The x-intercept, or zero, of function g is x = . Function g is over the interval [-5, 5]. As the value of x approaches positive infinity, the value of g(x) approaches infinity.
Answer:
boom box second one one my bad just need points my g
Step-by-step explanation:
Answer:
3
decreasing
negative
Step-by-step explanation:
The graph of function g crosses the x-axis at (3,0), so there is a zero at x = 3.
As the values of x increase, the values of g(x) decrease, so function g is decreasing along all intervals, including the interval [-5, 5].
As the values of x approach positive infinity, cube root functions either approach positive infinity or negative infinity. Since this function is decreasing, the values of g(x) approach negative infinity.
What is a set ? Give an example of a set .
Answer: 24
Step-by-step explanation:
an apple farm costs $5 to get in and $0.75 per pound of apples, what is the y intercept? (Number answer only, no symbols)
Answer:
(0, 5).
Step-by-step explanation:
$5 is the base fee, so when x = 0, y = 5. 0.75 won't come into play yet.
(not really a math problem) I have a 125 gallon tank, 5ft long and 6ft in circumfrence 3 inches of fuel in the tank how much gallons is that ` - `
Answer:
6.25 gallons
Step-by-step explanation:
If 125 gallon tank in equivalent to 5ft
1 foot is equal to 12inches...
5 ft ×12 =60 inches
So 125 gallon tank= 60 inches
If 60 inches = 125 gallon
3 inches = 125 × 3 / 60
= 375/60
= 6.25 gallons
general solution
4sin^x+9 cosx-6=0
Answer:
if this is helpful to you...
plz do follow
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The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by more than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected? Round your answer to four decimal places.
Answer:
Probability[(X - μ) < 1.1] = 0.6046
Step-by-step explanation:
Given:
σ² = 64
Mean μ = 34
Find:
Probability[(X - μ) < 1.1]
Computation:
Standard deviation σ = √σ²
Standard deviation σ = √64
Standard deviation σ = 8
Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]
Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]
Using z table
Probability[(X - μ) < 1.1] = 0.6046
Which shows the correct solution of the equation + so, when 6-30?
Answer:
-24
Step-by-step explanation:
rest 6 minus 30 and it give you -24
I need help pls !!!!!!!
Which linear inequality represents the graph below? (-2, 3) & (0, -2)
Answer:
no hablo inglés wey perdón corona y gracias
A bag contains 13 blue marbles, 12 red marbles, 6 yellow marbles, and 8 green marbles. What is
the probability of picking a red marble, putting that one back and then picking another red
marble?
4. Assume you have the same bag of marbles as the previous question. What is the probability of
selecting a yellow marble, then another yellow marble, then a red marble, and finally another
yellow marble, without replacing in between?
Answer:
12 in 29. uou add all the number together then and it is 12 red marbles in 29 chancesso you take one marble out and put the exact marble back in having no effect.