Answer: [tex]x=\pm \sqrt{22}[/tex]
Step-by-step explanation:
[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]
Answer:
sqrt(22) = [tex]\sqrt{22}[/tex]
Step-by-step explanation:
we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem
log(x-1) + log(x+1) = = [tex]log((x-1)(x+1))[/tex] = log(21)
this means that x^2 - 1 equals 21
xx-1 = 21
xx=22
x=sqrt(22)
Is this the right answer?
Answer:
Step-by-step explanation:
Yeah you have the correct answer.
In the original line you solve for y where the slope is given -3.
Then it is up to you but I like using the point slope formula so I'll plug in the values and the result is the same as the picture.
y-y=m(x-x)
y-(-6)=-3(x-1)
Graph a line with a slope of 1/5 and passes through the point (-2, 2).
The equation of line in slope intercept form
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Slope = [tex]\frac{1}{5}[/tex]
Point = (-2, 2)
Required equation of line =
[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]
The graph has been attached here.
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The graph of g(x) is the graph of f(x)=x−2reflected across the y-axis. Which equation describes function g?
The required equation of g(x) for reflection of f(x)=x-2 across the y-axis is g(x)=-x-2.
What is reflection?Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.
Given that,
f(x)=x-2
To find the required equation for g(x) that is reflected across the y-axis, Use reflection property,
According to reflection property,
Reflection Across the y-axis, the x change in -x and the remaining part of the equation remains same.
The equation of f(x) changes in g(x) as g(x)=-x-2,
So, the equation of g(x)=-x-2 .
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need help with this asap first answer will get brainliest
Answer:
x° = 34°
Step-by-step explanation:
First, find the interior angle supplementary to the given exterior angle 124°.
I will label it y.
124° + y° = 180°
y° = 180° - 124°
y° = 56°
Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.
x° + y° + 90° = 180°
x° + y° = 90°
x° + 56° = 90°
x° = 90° - 56°
x° = 34°
Answer:
x = 34---------------------------
Exterior angle in the triangle is the sum of remote interior angles124 = x + 90x = 124 - 90x = 34Define rational number in your own words.
Answer:A rational number is a number thats a quotient or fraction
Step-by-step explanation:
4\6 would be a rational number 8 over 4 as well.
Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answer: 324
Step-by-step explanation: 10% is the same as 1/10
360/10 is 36
360-36= 324
meaning 324 students now attend Haley elementary school <3
hope this helps <33
Fwam is preheating his oven before using it to bake. Fwam wants to predict the final
temperature after a minutes. He wrote the equation y = 40x+79, where y represents the final temperature in degrees Fahrenheit. What is the meaning of the y- value when x = 1?
The solving linear equation states that the temperature of the oven is 119 after an minute.
What is a linear equation?A linear equation is just an algebraic equation of something like the form y=mx+b that only contains a constant and a first-order (linear) component, where m represents the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are now the variables.
According to the given data:Given:
y = 40x+79
X = number of minutes using it to bare:
When X = 1
y = 40(1)+79
y = 119
It means that the temperature of the oven is 119 after an minute.
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A dictionary costs $15.00 and a map costs $5.00. If you want to
spend exactly $60.00 and you need to buy 3 dictionaries, how
many maps can you buy? Write an equation in standard form
modeling this situation then see how many maps you can buy.
Let a represent the number of dictionaries you buy and b
represent the number of maps you buy.
maps
Answer:
15.00x +5.00y = 60.00
Step-by-step explanation:
answer is to the equation is 3 because u plug in 3 to x given information provided to get 45.00 dollars. u then subtract 60 and 45 to see how much money u have left for maps. each map is 5.00 dollars and with 15.00 dollars remaining, u can get three maps and three dictionaries to equal 60.00 dollars!! Hope this helps!
Answer:
You can buy 3 maps. Equation: 15a + 5b = 60 ⇒ 15(3) + 5(3) = 60
Step-by-step explanation:
15 multiplied by 3 equals 45. Now you have $15 left. 15 divided by 5 equals 3. Therefore, you can buy 3 maps. Hope that helped! :)
Find the probability.
Um A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the
probability that a 4 is drawn from A followed by a 2 from B?
The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is 1/40 .
In the question ,
it is given that
the number of balls in Urn A is 8
which are {1,2,3,4,5,6,7,8}
the probability of getting a 4 from Urn A is (P₁) = 1/8
the number of balls in Urn B is 5 .
which are {1,2,3,4,5}
the probability of getting 2 from Urn B is (P₂) = 1/5
So ,the required probability is = P₁ × P₂
On substituting the values of P₁ and P₂ ,
we get
= 1/8 × 1/5
= 1/40
Therefore , the required probability is 1/40 .
The given question is incomplete , the complete question is
Find the probability.
Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?
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4x/3 -x=x/15-12/5 x =??????????
5- (8 - 6) + 3 times 4 +6
-----------------------------------------
5(4 -5)
The dash lines are for a fraction line. :)
The result of the fractional operation in this problem is given as follows:
-21/5 = -4.20.
How to solve operations with fractions?A fraction is represented by the division of a term x by a term y, as follows:
Fraction = x/y.
The terms that represent x and y are given as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.The numerator in this fraction is given as follows:
5 - (8 - 6) + 3 x 4 + 6.
The parenthesis and the multiplication have precedence, hence:
5 - (8 - 6) + 3 x 4 + 6 = 5 - 2 + 12 + 6 = 21.
The denominator in this fraction is given as follows:
5(4 - 5) = 5(-1) = -5.
The result is the division of the numerator by the denominator, hence:
21/(-5) = -21/5 = -4.20.
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-353.92 - (-283.56) -131.29
-353.92-(-283.56)-131.29= -20,165
(Lesson 22)
P=L(+)
a. Find the monthly payment P on a $75,000 loan with an
annual interest rate of 4% (let r= .9967) and a term of
20 years (n = 240 months). Show your work below and
circle your final answer.
The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
Given that,
We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).
We know that,
Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)
Here,
P is principal amount $75,000
n is number of months 240 months
i is interest rate 4% is 0.04
=P(i(1+i)ⁿ/(1+i)ⁿ-1)
=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)
=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)
=75,000(0.04(12246.20236)/(12245.20236)
=75,000(0.04×1.000081665)
=38455
Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.
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PLEASE HELP
19- 4x + x² can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Step-by-step explanation:
so, let's do the multiplications and squaring. and then compare the result with the target.
(x + a)² + b = x² + 2ax + a² + b
and the original expression is
x² - 4x + 19
x² = x² done
2ax = -4x
2a = -4
a = -2
a² + b = 19
(-2)² + b = 19
4 + b = 19
b = 15
so, the result is
(x - 2)² + 15
Answer: (x-2)^2+15
Step-by-step explanation:
Given x^2-4x+19
=here b=-4 and c=19
B=b/2=-4/2=-2
C=c-B^2=19-(-2)^2=19-4-15
so
(x-B)^2+C
(x-2)^2+15
it costs a paper company 4x+185 dollars to produce x notebooks. how many notebooks can they produce for $285
The paper company can produce 25 notebooks for $285
How to determine the number of notebooks?From the question, the equation of the total cost is given as
Equation = 4x + 185
Rewrite as
Cost = 4x + 185
Express the equation as a cost function
So, we have the following representations
C(x) = 4x + 185
When the total cost is $285, we have
C(x) = 285
This gives
4x + 185 = 285
Subtract 185 from both sides
4x = 100
Divide by 4
x = 25
Hence, the number of notebooks is 25
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Help Need ASAP
Paula makes purses. The materials cost $2.25 per purse. She sells them for $5.00 each. Paula wants to invest $5000 for some new equipment. Which of these could be used to determine x, the number of purses Paula must sell to pay for the new equipment?
Responses
5.00x - 2.25x = 5000
5.00x + 2.25x = 5000
5.00x = 5000
2.25x = 5000
The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Paula makes purses and the materials cost $2.25 per purse.
She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.
Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.
The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.
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Answer: 5.00x - 2.25x = 5000
Step-by-step explanation:
The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
Answer: 2 ft.
Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2
Pls help urgent someone hurry please
Proved that the triangle ABW ≅ triangle DCW
In the given question,
The length of WA = The length of WD
The measure of angle 5 = The measure of angle 7
Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW
Consider the triangle ADW,
In the triangle ADW the length of the WA is equal to the length of WD.
Therefore the measure of angle A is equal to the measure of angle D.
So in triangle ABW and the triangle DCW, one side and two angles are equal.
Therefore the triangle ABW and triangle DCW are congruent
Hence, proved that the triangle ABW ≅ triangle DCW
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plseas help
There are 7 students in grade 11 and 15 students in grade 12 that are part of the VSS robotics club. A committee consisting of a president, vice president, media rep, and accountant is being chosen.
a. In how many ways could the panel be chosen if the president and vice president must be from different grades?
b. In how many ways could the panel be chosen if it must include at least one grade 11 student and at least one grade 12 student?
The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:
a) President and vice from different grades: 79,800.
b) At least one from each: 141,960.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, there are two possible cases for the parameters, as follows:
[tex]n_1 = 7, n_2 = 15, n_3 = 20, n_4 = 19[/tex]: President from grade 11, vice from grade 12, the remaining two roles can be chosen from any student.[tex]n_1 = 15, n_2 = 7, n_3 = 20, n_4 = 19[/tex]: President from grade 12, vice from grade 11, the remaining two roles can be chosen from any student.Hence the number of ways is:
N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.
For item b, the total number of outcomes is obtained as follows:
N = 22 x 21 x 20 x 19 = 175,560.
The number of outcomes with only grade 11 students is:
N = 7 x 6 x 5 x 4 = 840.
The number of outcomes with only grade 12 students is:
N = 15 x 14 x 13 x 12 = 32760.
Hence the number of students with at least one of each is:
N = 175,560 - (840 + 32,760) = 141,960.
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A motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 5.5 hours. Use this information to find the speed of the current.
The speed of the current is 9 miles per hour
How to determine the speed of the current?
Given that: the motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning.
Total time = 5.5 hours
Let s = speed of the current
speed downstream relative to land = 11 + s
speed upstream relative to the land = 11 - s
speed = distance/time
time = distance/speed
upstream time + downstream time = total time
10/11-s + 10/11+s = 5.5 (find LCM of 11-s and 11+s)
10(11+s) + 10(11-s) /(11-s)(11+s) = 5.5
110+10s+110-10s /(11-s)(11+s) = 5.5
220 = 5.5(11-s)(11+s)
220 = 5.5(121 - 11s + 11s - s²)
220 = 5.5(121 - s²)
220 = 665.5 - 5.5s²
5.5c² = 665.5 - 220
5.5c² = 445.5
s² = 445.5/ 5.5
s² = 81
s = √81 = 9
Therefore, the speed of the current is 9 miles per hour
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I can't do math so I need someone to help me. what's the answer?
The value of TV for the similar triangles is 25
What are similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
Similar triangles are not the same as congruent triangles though.
triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.
Let UV = p, it means also that WV = P. which means WU = 2p
so since the two triangles are similar, the ratio of their corresponding lengths are equal
meaning,
UV/UW = TV/XW
substituting their values, we have
p/2p = TV/50
by cross multiplying,
2p x TV = 50p
2TV = 50
TV = 50/2 = 25
In conclusion, the value of TV is half the value of WX = 25
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Given: ST=3x+3 and TU= 2x+9
What is the value of TU?
The value of TU is 21
From the question, we have
ST=3x+3 and TU=2x+9
ST = TU
3x + 3 = 2x + 9
3x - 2x = 9 - 3
x = 6
substituting the value, we get
TU = 2x + 9
= 2 (6) + 9
= 12 + 9
TU = 21
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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Consider the equation and the following ordered pairs: (−3,y) and (x,2). y=−3x−1 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation. Answer Keyboard Shortcuts Complete the table below. x y row 1−3 Answer row 2 Answer 2
Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.
How to Compute Missing Values that Satisfies an Equation?An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.
Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:
y = -3(-3) - 1
y = 9 - 1
y = 8
The missing value in the ordered pair is: (-3, 8).
To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:
2 = -3x - 1
2 + 1 = -3x
3 = -3x
3/-3 = x
x = -1
The missing value is (-1, 2).
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The annual average price per square foot for office space in a city was $30.18 in 2004, and it was $66.85 in 2015.
(a) Find an exponential function of the form f(t)=y0b^t to model these data in which t=0 corresponds to 2004.
The exponential model of the given data is f(t) = 30.18 × 1.06^t.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
Given that,
The average price for office space in 2004 is $30.18.
The average price for office space in 2015 is $66.85.
Suppose the average price in 2004 is taken as y₀.
The given situation can be represented in the form of exponential function f(t) = y₀b^t as,
Take t = 0 for 2004
Then, f(0) = y₀b^0
⇒ f(0) = y₀ = $30.18.
Then, at 2015, t = 12. Substitute the respective values to get,
f(12) = 30.18 × b^12
⇒ 66.85 = 30.18 × b^12
⇒ b^12 = 66.85 / 30.18
⇒ b = 1.06
Thus in exponential form the given situation can be written as,
f(t) =30.18 × 1.06^t
Hence, the given data can be modeled in exponential function as f(t) =30.18 × 1.06^t.
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PLEASE HURRY I WANT TO FINISH MY TEST AND I NEED THE ANSWER!!
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
The value to make the inequality true is n > 3
InequalityInequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
We need to solve this problem and determine what value will solve this problem.
2(n + 2) < 5(n - 1)
2n + 4 < 5n - 5
Collect like terms
4 + 5 < 5n - 2n
9 < 3n
3n > 9
n > 3
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What must be added to this expression
to make it a perfect square?
9/16 must be added to this expression [tex]x^{2} -3x/2[/tex] to make it a perfect square.
According to the question,
We have the following expression:
[tex]x^{2}[/tex] -3x/2
Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.
Now, 9/16 is the square of 3/4.
So, we will first solve it using 9/16:
[tex]x^{2}[/tex]-3x/2+9/16
Now, this formula is of identity [tex](a-b)^{2}[/tex] where we have a = x and b = 3/4.
The formula of the identity [tex](a-b)^{2} = a^{2} + b^{2} -2ab[/tex].
Now, adding 9/16 make it a perfect whole square.
(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)
Hence, the correct option is C.
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There are 10 applicants applying for 3 positions Hostess server and busier how many ways
The number of ways to select 3 position out of 10 applicant is 120 ways
What is combination?Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Since there are 10 applicants applying for 3 positions. This will be:
= 10! / (10 - 3)!3!
= 10! / 7!3!
= 10 × 9 × 8 / 3 × 2
= 120
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please help and please use the diagram
7
8
9
Answer:
↓ ↓ ↓
Step-by-step explanation:
7) Name of plane to piano CIJ:-
Plane AGL8) Name a segment parallel to BC:-
FE9) Which segment is not skew to EK:-
C. CI______________________
Hope this helps!
Have a great day!
For what value of x does the graph of f(x) = e* - 2x have
a horizontal tangent?
The value of x=0.301 at the x the graph of the function have a horizontal tangent.
Given that,
The function is f(x)=eˣ-2x
We have to find the value of x does the graph of the function have a horizontal tangent.
What is the horizontal tangent?Where the derivative of a function is zero, a graph's horizontal tangent line is a mathematical feature. This is so that the derivative, by definition, can provide the slope of the tangent line. The slope of horizontal lines is zero. As a result, when the derivative is zero, the tangent line is horizontal.
For horizontal tangent line,
f'(x)=0
The differentiation of the function is
eˣ-2=0
eˣ=2
Taking logarithm on both sides.
logeˣ=log2
We know that loge=1
So,
x loge=log2
x(1)=log2
x=log2
x=0.301
Therefore, the value of x=0.301 at the x the graph of the function have a horizontal tangent.
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Adaim has a goal to reach 70 miles. If he hikes 8 miles per day, how long will it take him to hike all 70 miles?
