Answer:
2,129
5 times 2129 = 10645
Step-by-step explanation:
Hope it helps! =D
Write each logarithmic expression as a single logarithm.
1/4 log₃2+ 1/4 log₃x
For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
We are given the logarithm expression as:
1 / 4 log₃ 2 + 1 / 4 log₃ x
Now, take 1 / 4 common from the expression:
1 / 4 ( log₃ 2 + log₃ x)
Now, we know that log₃ a + log₃ b = log₃ ( a b)
So, we get that:
1 / 4 ( log₃ ( 2 x) )
1 / 4 log₃ 2 x
Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.
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Which of the following points lie on the line whose equation is y + 4= 3/5 ( x- 2)?
The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)
What points do belong to a given linear equation?
In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.
Now we proceed to check the expression for each case:
(x, y) = (1, - 5)
- 5 + 4 = (3 / 5) · (1 - 2)
- 1 = (3 / 5) · (- 1)
- 1 = - 3 / 5 (FALSE)
(x, y) = (- 8, - 12)
- 12 + 4 = (3 / 5) · (- 8 - 2)
- 8 = (3 / 5) · (- 10)
- 8 = - 30 / 5
- 8 = - 6 (FALSE)
(x, y) = (- 3, - 8)
- 8 + 4 = (3 / 5) · (- 3 - 2)
- 4 = (3 / 5) · (- 5)
- 4 = - 3 (FALSE)
(x, y) = (12, 10)
10 + 4 = (3 / 5) · (12 - 2)
14 = (3 / 5) · 10
14 = 30 / 5
14 = 6 (FALSE)
(x, y) = (7, - 1)
- 1 + 4 = (3 / 5) · (7 - 2)
3 = (3 / 5) · (5)
3 = 3 (TRUE)
The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).
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1) what is the answer to this
Answer:
Slope: 2/1
equation: y=2/1x+2
-40 -2 (3m + 1/2) = 7m -2
Answer:
m = -3
Step-by-step explanation:
A football team has a win to loss of 5:8. What is the ratio of losses to total games played
Solve each equation.
3⁻²x⁺²=81
After solving the equation, x = -1 is the value of x in [tex]3^{(-2x)+2} = 81[/tex]
⇒ [tex]3^{(-2x)+2} = 81[/tex]
⇒ [tex]3^{(-2x)+2} = 3^4[/tex]
⇒ -2x + 2 = 4
⇒ -2x = 2
⇒ x = 2/(-2)
⇒ x = -1
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
Answer:
g(f(x)) = 4x^2 + 8x + 4
Step-by-step explanation:
If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).
You are asked to find g of f of x.
This means your x value for the equation g(x) is f(x), hence g(f(x)).
g(2x+1)=(2x+1)^2 + 2(2x+1) +1
g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1
Combine like terms.
g(2x+1) = 4x^2 + 8x + 4
g(f(x)) = 4x^2 + 8x + 4
Grapes are selling for $0.26 a pound. Ashley spent $3.77 on grapes. How many pounds of grapes did Ashley buy?
Use natural logarithms to solve each equation.
ex/₄-8=6
39.16 approx. is the value of x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 solved by using natural logarithm
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to find x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 using natural logarithm
⇒ [tex]e^{\frac{x}{4} -8}[/tex] = 6
⇒ [tex]\frac{x}{4} - 8[/tex] = ㏑6
⇒ [tex]\frac{x}{4}[/tex] = ㏑6 + 8
⇒ x = ln(1296) + 32
= 39.16 approx.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^{\frac{x}{4} -8}[/tex] = 6
Each ordered pair is from an inverse variation. Find the constant of variation. (6,3)
The value of constant variation is 18.
Constant is what?A key integer with a stable value determined by a clear specification is referred to as a mathematical constant.
Inverse variation: what is it?connection in mathematics between two variables that may be described by an equation in which the sum of their products equals a constant
Inverse variation is y = k. 1/x
given y = 3
x = 6
So, 3 = k. 1/6
So, the value of k = 18.
We can conclude that the value of constant variation is 18.
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Sandy is training for a triathlon. Between running and bicycling, she covers a
distance of 200 miles every week. Her average speed on a bicycle ride is 20
mph. Her average speed running is 8 mph. If she spends 16 hours per week
training, how many hours does she spend on each sport?
Answer:
Step-by-step explanation:
A line passing through point (-6, 1) and has a slope of -3
Write an equation in Ax+By=C
Use integers A, B and C
Answer:
y=-3x-17
Step-by-step explanation:
y=mx+b (slope-intercept form) b=y-intercept= (0,?) m=slope
y=-3x+b substitute values
y+3x=b isolate b to find b
1+3(-6)=b substitute given ordered pair
-17=b
y=-3x-17
What inscribed polygon is being constructed? Explain how you know.
With an equilateral triangle, only two circles are formed.
In geometry, what is an inscribed polygon?An inscribed polygon is one whose vertices are circle points. "In" denotes "in" and "scribed" denotes "written." Connect the points in a straight line with segments.What kind of polygon is carved into the circle?
A cyclic polygon is one that is inscribed in a circle, and the circle is its circumscribed circle or circumcircle.So, according to the given figure, we know that an equilateral triangle and only two circles are formed.Therefore, with an equilateral triangle, only two circles are formed.
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Given: m<4 + m<7 = 180 degrees
Prove: c || d
1) m∠4 + m∠7 = 180° (given)
2) ∠4 is congruent to ∠6 (vertical angles)
3) m∠4 = m∠6 (definition of congruent angles)
4) m∠6 + m∠7 = 180° (substitution)
5) c is parallel to d (converse of same side interior angles theorem)
Use the properties of logarithms to evaluate each expression.
1/2 log₅15 - log₅√75
Using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
According to the question the expression that we have been given is
= [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75}[/tex]
Now solving it step by step using the properties of logarithm which are
[tex]log a^{m} = m*loga[/tex] , [tex]log \frac{x}{y} = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
As √75 is also equal to [tex](75)^{1/2}[/tex]. Thus equating in the equation we get
Therefore ,
[tex]= \frac{1}{2}log_{5} 15 - log_{5} 75^{\frac{1}{2} } \\= \frac{1}{2}log_{5} 15 - \frac{1}{2} log_{5}{75} \\[/tex]
As we can see that 1/2 is common in both the terms we will take out 1/2 common from both terms, by which we get
[tex]= \frac{1}{2} [log_{5} 15 - log_{5}{75} ] \\= \frac{1}{2} [log_{5} \frac{15}{75} ] \\\= \frac{1}{2} [log_{5} \frac{1}{5} ] \\= \frac{1}{2} [log_{5} 1 - log_{5}{5} ]\\= \frac{1}{2} [0 - 1]\\= -\frac{1}{2}[/tex]
Hence using the properties of logarithm the value of the expression is [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]
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(a +11)(11a +1)
Simplify
Answer:
11a^2 + 122a + 11
Step-by-step explanation:
First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.
the dum of twice a number and 15
3 identical circles inside a rectangle each circle touches the other two circles and sides of a rectangle
the radius of each circle is 2mmworkout the exact area of the rectangle
give your answer in the form a√ 3+b
where a and b are integers
The area of the rectangle having three identical circles inside is calculated as: (16√3 + 32) mm².
What is the Area of a Rectangle?Area of rectangle = (length)(width)
The image of the three identical circles in the rectangle has been labelled as shown in the diagram attached below.
We need to find the measure of the length and width of the rectangle.
Radius = AB = BD = DF = FG = CD = HI = 2 mm
Length of the rectangle = AB + BD + DF + FG = 2 + 2 + 2 + 2
Length of the rectangle = 8 mm
Width of the rectangle = CD + DH + HI
CD = 2 mm
HI = 2 mm
Use the Pythagorean theorem to find the measure of DH
DH = √(FH² - DF²)
FH = 2 + 2 = 4 mm
DF = 2 mm
Substitute
DH = √(4² - 2²)
DH = √(16 - 4)
DH = √12 = 2√3 mm
Width of the rectangle = CD + DH + HI = 2 + 2√3 + 2
Width of the rectangle = 2√3 + 4
Area = (2√3 + 4)(8)
Area = (16√3 + 32) mm²
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Find the real and imaginary solutions of each equation.
x⁴-14 x²+49=0
The given 4th order polynomial equation only has real solutions, x = √7 and x = –√7
The given equation is x⁴-14 x²+49 = 0.
This is a 4th degree polynomial equation.
Let p = x².
Then we can write x⁴-14 x²+49 = 0 as:
p²- 14p +49 = 0
This is a quadratic equation.
There are three ways to find the solutions of a quadratic equation:
By factoringBy completing the squareBy applying the quadratic formulaNotice that p²- 14p +49 = 0 can be written as a perfect square:
(p - 7)² = 0
Hence, it has only single real solution:
p - 7 = 0
p = 7
Substitute p = 7 into p = x², we get:
x² = 7
x = ± √7
The solutions are, therefore, x = √7 and x = –√7
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Jack bought 8 drill bits for aed11.22 each, 10 washers for aed10.11 each and 2 hammers for aed 545.59 each. a. calculate the total cost? b. later he bought a box to keep all the items. he paid aed 1500 altogether including box and received aed 12 as balance. find the cost of the box?
Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
No. drill bits = 8 drill bitscost of drill bits = AED 11.22/ drill bitsNo. washers = 10 washers cost of washers = AED 10.11 / washers No. hammers = 2 hammers cost of hammers = AED 545.59 / hammersPaid = AED 1500Balance = AED 12Total cost = ?Box cost = ?Calculating the total cost Jack spend before bought the box:
Total cost = (No. drill bits*cost of drill bits) + (No. washers *cost of washers ) + (No. hammers *cost of hammers)
Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)
Total cost = AED 89.76 + AED 101.1 + AED 1091.18
Total cost = AED 1282.04
Calculating the box cost:
Balance = Paid - (Total cost + box cost)
Balance = Paid - Total cost - box cost
box cost = Paid - Total cost - Balance
box cost = AED 1500 - AED 1282.04 - AED 12
box cost = AED 205.96
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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A computer is rendering two scenes. The computer has already rendered 540540540 thousand pixels (\text{kpx}kpxstart text, k, p, x, end text) of a kitchen scene and renders another 90\,\text{kpx}90kpx90, start text, k, p, x, end text each minute. The computer has rendered 960\,\text{kpx}960kpx960, start text, k, p, x, end text of a garden scene and renders 60\,\text{kpx}60kpx60, start text, k, p, x, end text more pixels each minute.
Answer: 14 min
Step-by-step explanation:
After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
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 computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.
Let after t minutes the scene will have the same amounts rendered.
The linear equation in one variable can be framed as:
540 + 90t = 960 + 60t
After solving the above linear equation in one variable:
90t - 60t = 960 - 540
30t = 420
t = 14 minutes
Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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what is the equation for this graph in slope intercept form?
Solve. Check for extraneous solutions. (x-2)¹/₂ -(28-2 x)¹/₄=0
-4 is an extraneous solution.
The equation is
[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0
To know whether the given equation has an extraneous solution or not we need to find the value of x.
[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]
Multiply both sides with the power of 4, and we get
[tex](x- 2)^{2}[/tex] = 28-2x
[tex]x^{2}[/tex] - 4x + 4 = 28-2x
[tex]x^{2}[/tex] - 2x - 24= 0
[tex]x^{2}[/tex]- 6x + 4x -24=0
x(x-6) +4(x-6)=0
(x-6)(x+4) = 0
x = 6 , -4
Now put both the value of x in the equation
x=6
[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0
[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0
2-2=0
0=0
Now
x = -4
[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0
[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0
[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0
Which is not possible and a negative integer is not present in the square root.
Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.
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Help for A Brainlist!!! geometry question!!! In the right triangle XYZ, angle X and angle Z are complementary angles. Given ( please see image attached below thank you for the help:) take care)
In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
In the right triangle XYZ, angle X and angle Y are complementary angles.
The complementary angle is either of two angles whose sum is 90 degrees
Therefore,
Angle X + Angle Z = 90 degrees
In trigonometry,
sinθ = Opposite side / Hypotenuse
sin z= 36/85
z= [tex]sin^{-1}(\frac{36}{85} )[/tex]
z= 25.06
Then the value of cos z is
cos 25.06 = 77/85
Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85
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HELP ASAP I DONT WANT TO FAIL
Answer:
16.3p + (-10)
Step-by-step explanation:
3. Noemi's team is working together to write a quadratic equation to model the path of the golf ball question in graphing form.
She calculated the value of `a=-\frac{1}{90}` is she correct?
Include detailed work that supports your answer on the left.
Begin with your equation for this golf ball situation from the previous slide.
The value of a calculated by Noemi is not correct as the correct value is
a = -1/45
We know that the general form of the quadratic equation is given as
y = ax² + bx + c
where, a and b are coefficients of the variable x and c is the constant term.
Now according to the question the path of the golf ball is parabola whose coordinates will be
(0,0) = origin where it starts
(60,80) = vertex or the maximum point
(120,0) = end point
Now putting the value of (x,y) in the above formula to find the value of a,b and c
when (x,y) = (0,0)
0 = a0² + b0 +c
c = 0
when (x,y) = (60,80)
80 = a60² + b60 +c
80 = 3600a + 60b + 0 (1)
when (x,y) = (120,0)
0 = a120² + b120 +c
0 = 14400a + 120b + 0
120b = -14400a
b = -120a
Putting the value of a in equation (1) we get
80 = 3600a + 60(-120a)
80 = 3600a - 7200a
80 = -3600a
a = - 1/45
⇒ b = 8/3
Hence the equation will be y = -1/45x² + 8/3x
and the value of a calculated by Noemi is not correct as the correct value is a = -1/45
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Factor the expression. 25-40 x+16 x²
Factor the expression 25-40 x+16 x² is [tex](4x-5)^2[/tex]
In mathematics, factorization is defined as breaking down or decomposing an entity (such as a number, matrix, or polynomial) into another entity or product of coefficients. Splitting the mean term means that the mean term of the quadratic must be rewritten as the sum or difference of two terms. The middle term should be split into two parts in terms of the sum or difference of the terms. The general form of the quadratic equation is [tex]ax^2+ bx +c=0[/tex]On rearranging the equation , we get
[tex]16x^2-40x+25=0[/tex] ...(1)
To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.
Midterm is 40 x , to split the middle term, use the sum-and-product form which is
" The sum-product form is the product of intermediate terms after splitting and must equal a × c and the sum must equal b "
[tex]f(x)=16x^2-40x+25[/tex]
here a = 16 , b = -40 and c = 25
We need to divide into 40x in two parts
40x = 20x + 20x
The product of the terms is [tex]16\times25=400[/tex]
Now we can rewrite 40x as 20x + 20x
Putting in equation (1) , we get
[tex]16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0[/tex]
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23
−
1/9
= ?????
I really need help please help me...
Answer: 22.8888888889 but rounded 22.9
Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9
Incorrect Work/Solution
-7x-3y + x + 2y
-7x-3y + 1/2x+y
-5-x-2y
Identify and explain the error (2 points)
The ratio of Richard and Ben's speed is 4:5. The ratio of Richard and Kim's speed is 3:2. If it takes Ben 8 minutes to get to a location, it's going to take Kim _____ minute(s) for the same distance. (FILL IN THE BLANK)
The time it would take Kim running the same distance is 15 minutes.
How long would it take Kim?
Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.
Speed = distance / time
The first step is to determine the time spent by Richard running:
(4 x 1/8) / 5 = 1/10 or 10 minutes
The second step is to determine the time spent by Kim running:
(2 x 1/10) / 3 = 1/15 = 15 minutes
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