Answers
Answer:
1. The given equation is presented as follows;
[tex]3^{2 \cdot x - 1} = \dfrac{1}{9}[/tex]
The above equation can be rewritten as follows;
[tex]3^{2 \cdot x - 1} = 3^{-2}[/tex]...(1)
Therefore, taking logarithm to base 3 of both sides of the equation, the above equation can be rewritten without an exponent as follows;
[tex]log_3 \left (3^{2 \cdot x - 1} \right) =log_3\left(\dfrac{1}{9} \right) = log_3 \left( 3^{-2} \right)[/tex]...(2)
2. Inverse relationship of exponents is given as follows;
(1/a)ˣ = a⁻ˣ
Therefore, we have;
1/9 = 1/(3²) = (3²)⁻¹ = 3⁻²
Taking log of both sides of [tex]\left (3^{2 \cdot x - 1} = \dfrac{1}{9} = 3 ^{-2}\right)[/tex] gives;
[tex]log_3 \left (3^{2 \cdot x - 1} \right)= log_3 \left( 3^{-2} \right)[/tex]
From logarithm rules, we have;
From equation (2), we have;
[tex](2 \cdot x - 1) \cdot log_3 3 = -2 \cdot log_3 3[/tex]
Therefore, the equation can be simplified by dividing both sides by the common factor, [tex]log_3 3[/tex], as follows;
[tex]\dfrac{(2 \cdot x - 1) \cdot log_3 3 }{log_3 3} = \dfrac{-2 \cdot log_3 3}{log_3 3}[/tex]
Therefore, we get;
2·x - 1 = -2...(3)
3. Solving 2·x - 1 = -2, gives;
2·x - 1 = -2
2·x = -2 + 1 = -1
x = -1/2 = -0.5
x = -0.5
EQUATION 3
The given equation is presented as follows;
[tex]125^{x - 1} = 5^x[/tex]
1. By the property of exponents, we have;
[tex]\left(a^b \right)^x = a^{b \times x}[/tex]
125 = 5³
Therefore, we get;
[tex]125^{x - 1}= \left(5^3\right)^{x - 1} = 5^{3\times (x - 1)} = 5^{(3\times x - 3)}[/tex]
[tex]125^{x - 1}= 5^{(3\times x - 3)}[/tex]
2. Given that we can rewrite the given equation as follows;
[tex]125^{x - 1} = 5^{(3\times x - 3)} = 5^x[/tex]
Therefore;
[tex]5^{(3\times x - 3)} = 5^x[/tex]
Both sides of the equation are given in powers of 5, therefore, the appropriate base logarithm to use on both sides to rewrite the equation is logarithm to base 5
3. Using logarithm, by applying logarithm to both sides, we get;
[tex]log_5 \left (5^{(3\times x - 3)} \right) = log_5 \left(5^x \right)[/tex]
[tex](3\times x - 3) \cdot log_5 5 = x \cdot log_5 5[/tex]
Dividing both sides by log₅5 gives;
[tex]\dfrac{ (3\times x - 3) \cdot log_5 5}{log_5 5} = \dfrac{ x \cdot log_5 5}{log_5 5}[/tex]
∴ 3 × x - 3 = x
3 × x - x = 3
2·x = 3
x = 3/2 = 1.5
x = 1.5
Step-by-step explanation:
Related Questions
plsssss help meeee ....i need the answerrrr
Answers
Answer:
20
Step-by-step explanation:
[tex] = \dfrac{ \sqrt[3]{125} \times \sqrt[3]{64} }{ \sqrt[3]{125} - \sqrt[3]{64} } [/tex]
[tex] = \dfrac{5 \times 4}{5 - 4} [/tex]
[tex] = \dfrac{20}{1} [/tex]
[tex] = 20[/tex]
help help help due today
Answers
Answer:
sin 52°= AB/x
sin 52°=AB/7.7
AB= 6.06 m
For the following set of data, find the percentage of data within 2
population standard deviations of the mean, to the nearest percent.
58, 77, 31, 54, 58, 54, 56, 58, 56
Answers
Answer:
58,+77,+31,+54+,58+,54+,46+,58+,56/9
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
The data set is given below.
58, 77, 31, 54, 58, 54, 56, 58, 56.
Then the mean of the data set will be
Mean = (58 + 77 + 31 + 54 + 58 + 54 + 56 + 58 + 56) / 9
Mean = 502 / 9
Mean = 55.78
Then the standard deviation will be
[tex]\rm SD = \sqrt{\dfrac{(58 - 55.78)^2+(77-55.78)^2 + ..... + (56-55.78)^2 }{9}}\\\\SD = \sqrt { \dfrac{1085.5}{9}}\\[/tex]
On further solving we have
SD = 10.98
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
More about the standard deviation link is given below.
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which inequality is represented by this graph
Answers
Answer:
[tex]x\geq -53[/tex]
Step-by-step explanation:
Answer:
x ≥ -53
Step-by-step explanation:
Here is a trick the arrow is going to the right so the arrow in the inequality must go to the right and if the circle is closed there must be a line under the arrow in the inequality.
Can I get Brainliest please!
plzz help............
Answers
Answer:
14. (8,9,10)
15.no(A)
this is the answer
Which equation has the least steep graph A. y = 2x + 1 B. y = -7x-2 C. y=-3/4x-9 D. y = 1/4x+6
Answers
Answer:
D. y = 1/4x + 6
Step-by-step explanation:
In the linear equation y = mx + b, m is the slope.
A graph will be steeper if it has a larger slope, and less steep if it has a smaller slope.
So, to find which equation has the least steep graph, find which one has the smallest slope.
Out of the 4 equations, the smallest slope is 1/4. Although -7 is the smallest number, it still has a steep slope. The negative sign just makes it go in the other direction.
So, the equation with the least steep graph is D. y = 1/4x + 6
Answer:D
Y= 1/4x +6
Step-by-step explanation:
Diane has $814 in her checking account. If she writes five checks for a total of $287, how much does she have left
in her account?
Answers
Answer:
$527
Step-by-step explanation:
Find how much she has left by subtracting 287 from 814:
814 - 287
= 527
So, she has $527 left in her account
Please help I’ll give brainliest
Answers
Answer:
285.214 cubic meters
Step-by-step explanation:
So I use this equation V=πr2h
All because this equation have a radius and so I put it in this form
V= π5.5^2 x 3
V=285
(I hope this help and if it’s wrong I am truly sorry)
The required volume of the given cylinder is 285.214 cubic meters. Option A is correct.
For a cylinder,
Height = 3m
Radius = 5.5m
Volume = ?
Volume is defined as the ratio of the mass of an object to its density.
Here,
The volume of the cylinder is given as,
Volume = πr²h
Substitute the value in the equation,
Volume = 3.14×5.5²×3
volume = 285.214 cubic meters.
Thus, the required volume of the given cylinder is 285.214 cubic meters. Option A is correct.
Learn more about Volume here:
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Solve the inequality for x
3^(6x+18)<27^(3x)
Answers
Answer:
[tex]\displaystyle x > 6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsFactoringAlgebra II
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Solving exponential equationsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 3^{6x + 18} < 27^{3x}[/tex]
Step 2: Solve for x
Rewrite: [tex]\displaystyle 3^{6x + 18} < 3^{3(3x)}[/tex]Set: [tex]\displaystyle 6x + 18 < 3(3x)[/tex]Factor: [tex]\displaystyle 3(2x + 6) < 3(3x)[/tex][Division Property of Equality] Divide 3 on both sides: [tex]\displaystyle 2x + 6 < 3x[/tex][Subtraction Property of Equality] Subtract 3x on both sides: [tex]\displaystyle -x + 6 < 0[/tex][Subtraction Property of Equality] Subtract 6 on both sides: [tex]\displaystyle -x < -6[/tex][Division Property of Equality] Divide -1 on both sides: [tex]\displaystyle x > 6[/tex]Answer:
[tex]x>6[/tex]
Step-by-step explanation:
When given the following equation;
[tex]3^(^6^x^+^1^8)<27^(^3^x^)[/tex]
One is asked to solve for ([tex]x[/tex]). The inequality has exponents, hence, it appears daunting at first, however, the easiest way to deal with exponents is to bring them to the same base. This allows for one to have the ability to treat the exponents like an ordinary number. Since ([tex]27=3^3[/tex]) one can rewrite ([tex]27^(^3^x^)[/tex]) as ([tex]3^3^*^(^3^x^)[/tex]). This is possible because raising a number to an exponent when it already has an exponent is the same as multiplying the two exponents. Rewrite the inequality in this format;
[tex]3^(^6^x^+^1^8)<3^3^(^3^x^)[/tex]
Simplify,
[tex]3^(^6^x^+^1^8^)<3^(^9^x^)[/tex]
Since the bases are the same they no longer have any relevance, so one can ignore the bases and only work with the exponents,
[tex]6x+18<9x[/tex]
Now solve this inequality like a normal inequality. Use inverse operations;
[tex]6x+18<9x[/tex]
[tex]18<3x[/tex]
[tex]6<x[/tex]
Help me with this one plz
Answers
Answer:
-1 is the only number there that is an integer as all the rest of them are mixed fractions.
Answer:
- 1
Step-by-step explanation:
Determina la masa molar y el volumen que ocupa la siguiente sustancia CO2, si su masa es de 28 gr. *
Answers
Answer:
Para el CO₂ sabemos que:
densidad = 0,001976 g/cm³
Sabemos que:
densidad = masa/volumen
Entonces, si tenemos una masa de 28 g, podemos escribir:
volumen = masa/densidad
volumen = (28g)/(0,001976 g/cm³) = 14,170 cm^3
Para obtener la masa molar (es decir, la masa de un mol de esta sustancia) simplemente sumamos la masa de un mol de cada componente.
Carbono: tiene una masa molar de 12 g/mol
Oxígeno: tiene una masa molar de 16 g/mol (y tenemos dos oxígenos)
entonces la masa molar va a ser:
masa molar = 12g/mol + 2*16g/mol = 44 g/mol
Es decir, un mol de CO₂, pesa 44 gramos.
A line passed through the point (8,5) and has a slope of 2. Write an equation for this line
Answers
Answer:
y = 2x -11
Step-by-step explanation:
The equation of a line that passes through point x1, y1 is given as
y - y1 = m (x - x1)
where m is the slope of the line
Given that the line passes through the point (8,5) and has a slope of 2, the equation of the line
y - 5 = 2 (x - 8)
y - 5 = 2x - 16
add 5 to both sides
y = 2x - 16 + 5
y = 2x -11
How can we do this math problem?
Answers
Answer:
b) 92
Step-by-step explanation:
1. if according to the condition the triangle is equilateral, then every inside angle (m∠F=m∠G=m∠H) is 60°.
2. it is possible to substitute the value 60 (F=60) into the given equation:
[tex]60=(\frac{Z}{2}+14);[/tex]
3. if to solve the equation above, then Z=92
Which calculation shows the best method for estimating the result of 384 divided by three-sixteenths?
Answers
Answer:
the answer to this is 2048
Step-by-step explanation:
Answer: B
Step-by-step explanation: Just round
The diameter of a circle is 9 m. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answers
Answer:
[tex]C=28.3m[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter [tex]d=9m[/tex]
Radius[tex]r=4.5m[/tex]
Generally the equation for Circumference of a circle is mathematically given by
[tex]C=2\pi r\\\\\C=2*\pi*4.5m[/tex]
[tex]C=28.3m[/tex]
Answer:
Step-by-step explanation:
From the question we are told that:
Diameter
Radius
Generally the equation for Circumference of a circle is mathematically given by
Have a good day
Step-by-step explanation:
HELP PLEASE I HAVE 15 MINS LEFT
In AABC median AM is drawn from vertex A to BC, BM = 14x and MC = 6x + 56. Determine and
state the value of x.
Answers
Answer:
x = 7
Step-by-step explanation:
A median bisects the opposite side length, therefore
14x = 6x+56
8x = 56,
x = 7
Answer:
x = 7
Step-by-step explanation:
given:
AM is the median
BM = 14x
MC = 6x + 5x
since the median is drawn fron vertex A to BC it bisects the BC into two equal halves. So,
14x = 6x + 54
14x - 6x = 54
8x = 54
x = 54/8
x = 7
the coordinates of three vertices of a rectangle are -2, 3, -2, -1, and 3, -1. what are the coordinates of the fourth vertex
Answers
Answer:
(3,-5)
Step-by-step explanation:
We first cal ulate the distance
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in second, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of a second
Answers
10.17 seconds
hope this helps
The volume of a cylinder is 1280pi cm cubed. The radius is 8cm. Find the missing length.
Answers
find the value of x and y, (3x - 2y, 7) = (11, x + y)
Answers
Answer:
Step-by-step explanation:
Given,(3x-2y,7)=(11,x+y)
So,3x-2y=11...............(i)
7=x+y
or,x+y=7................(ii)
Now,Multiplying eqn.(ii) by 2,we get,
2x+2y=14...........(iii)
Adding eqn(i) and eqn(iii),
3x-2y+2x+2y=11+14
or,5x=25
or,x=5
Substituting value of x in eqn(i),
5+y=7
or,y=2
Hence,the values of x and y are 5 and 2 respectively.
What percent is represented by the shaded area?
Answers
173/200=(convert to decimal)86.5
Please help I need help
Answers
Answer:
2 1/3
Step-by-step explanation:
PLS HELP ILL GIVE U BRAINLIST
A vector is 2.5 kilometers per hour at a bearing of of 50° West of North.
Find the magnitude of its vertical component.
lyl = v sin ©
A. lyl = - 1.9
B. lyl = 1.6
C. lyl = 2.5
D. lyl = 50°
Answers
B. |y| = 1.6
Step-by-step explanation:A sketch of the vector is attached to this response.
As shown, the vector lies on the second quadrant and its horizontal and vertical components are given by x and y respectively.
Where;
|x| = v cos θ -----------------(i)
|y| = v sin θ -----------------(ii)
and
v = magnitude of the vector = 2.5km/hr
θ = angle that the vector makes with the +x axis = 90° + 50° = 140°
To get the magnitude of the vector's vertical component
Substitute these values into equation(ii) as follows;
|y| = 2.5 sin 140°
|y| = 2.5 x 0.6428
|y| = 1.607
|y| ≅ 1.6 km/hr
Therefore, the vertical component of the vector has a magnitude of 1.6 km/hr.
12 more than the quotient of a number and eight
Answers
Answer:
X÷8+12 is how this would look
Answer:
x/8 + 12
Step-by-step explanation:
Find the area of the following shape:
Answers
Answer:
19 cm²
Step-by-step explanation:
→ Work out the area of the rectangle
1 × 7 = 7
→ State the formula for the area of the triangle
0.5 × base × height
→ Find the base and height
Base = 3 and height = 8
→ Substitute values into formula
0.5 × 3 × 8 = 12
→ Add this total to the rectangle formula
12 + 7 = 19 cm²
Question 6 (1 point)
Simplify 5/11-12 11-2/11 (1 point)
o
a
-33ſ9
Oь
-119
ос
-9/11
Od
-9/33
Answers
Answer:
-9√11
Step-by-step explanation:
Simplify 5√11-12√11-2√11
Applying,
The law of surd,
Step 1: factor out the common surd or irrational number i.e √11
√11(5-12-2)
√11(-9)
Step 2: Multiplying the whole number and the surd
-9√11
Therefore,
5√11-12√11-2√11 = -9√11
Hence the right option from the list of option is
c -9√11
Encik Basra’s age is four times his child’s age. 4 years ago, Encik Basri’s age is six times his child age. Find the age of Encik Basri’s child now.
Answers
Answer:
4 + 6 = 10 * 4 =40
Step-by-step explanation:
sana makatulong
His child is 10 years old.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Given
Assume now his child's age is x
4x-4 = 6(x-4)
4x-4 = 6x - 24
-4+24 = 6x-4x
20 = 2x
x=10
His child is 10 years old.
To learn more about algebraic expressions refer to:
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a.)Would the equation be sine or cosine if the situation was someone being on a roller coaster that starts 15 ft above ground level, goes up to 45 feet above ground level, and goes down 20 feet under ground level?
b.) What would the equation be? ford monition and the terminal is in the third quadrant
Answers
La fórmula correcta para encontrar el valor del coseno de un ángulo agudo en un triángulo rectángulo dado es:
Answers
Answer:
El coseno del ángulo esta dado por:
[tex]cos(\theta)=\frac{CA}{H}[/tex]
Step-by-step explanation:
Si tenemos un triángulo recatángulo, el coseno del ángulo está dado por:
[tex]cos(\theta)=\frac{CA}{H}[/tex]
Donde:
CA es el cateto adyacenteH es la hipotenusa del triánguloEspero te haya sido de ayuda!
After a 20% discount the phone cost is $70.40. What was the original price?
Answers
Answer:
$84.48
Step-by-step explanation:
Multiply the price before discount by 1.2 (100% + 20%) to get 70.40 x 1.2 = 80.48; $80.48
Hope this helps!
:)
