The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:
x = -6/5.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]
Both 8 and 4 are powers of 2, as follows:
8 = 2³.4 = 2².Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]
The subtraction is obtained as follows:
3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.
(as the least common factor of 2 and 3 is of 6).
Then the simplified expression is of:
[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]
As the exponential function y = 2^x is injective, the solution is obtained as follows:
5x/6 = -5/2.
10x = -12
x = -6/5.
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Use the Pythagorean theorem to find the missing area
Answer:
28 cm^2
Step-by-step explanation:
a^+21^2=36^2
a^2+441=1225
a=28
What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Consequently, it follows that the greatest possible quotient as required is; 25.
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Abby earns $7 per hour working as a cashier at a cafe.
She earned $ in a week in which she worked 28 hours. She earned $ in a month in which she worked 112 hours. She earned $ more in the month than she did in the week.
Answer:
1. So $7 per hour
For 24 hour =7×24= $168
28-24=4
4×7=28
168+28=$196
or
For 28 hour
7×28
= $196
2. 7×112
=$784
3. To find the difference subtract
784-196=$588
Answer:
196; 784; 588
Step-by-step explanation:
Jen's car used 10 gallons of gas to travel 300 miles. How many miles did her car travel per gallon of gas?
Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6
Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).
Function 3x²+24x-6 does not belong with the other three
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the option we have to simplify each function
a. f(x)=3x²+6x-24
b. f(x)=3x²+24x-6
c. f(x)=3(x-2)(x+4)
=3(x²+4x-2x-8)
=3x²+6x-24
d. f(x)=3(x+1)²-27
3(x²+1+2x)-27
3x²+3+6x-27
3x²+6x-24
So function 3x²+24x-6 does not belong with the other three
Hence, function 3x²+24x-6 does not belong with the other three
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What type of triangle do the points 3 2 (- 2 3 and 2/3 form a right triangle B equilateral triangle C isosceles triangle d none of these?
Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).
Let the given points be,
A = (3, 2), B = (-2, -3) and C = (2, 3)
The formula for the distance between two points:
The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].
Therefore,
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)
[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex] units
B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex] units
A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)
[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex] units
By using the Pythagorean theorem:
According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Now, we can see that,
[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]
[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]
Therefore, the given triangle is a right angled triangle.
Therefore, option(A) s correct.
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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.
A. right triangle
B. equilateral triangle
C. isosceles triangle
D. none of these
80, 84, 79, 44, 87, 73, 89, 90, 82, 89, 93, 97, 77, and 71 whats the mean
Answer:
sum up the numbers and divide by the numbers of values.
80+84+79+44+87+73+89+90+82+89+93+97+77+71 / 14
1135/14
= 81•1 is the mean
Angle 1 and Angle______ are alternate exterior angles.
It’s angle 1 and angle 8
The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal
goodluck
Round 9,888,000 to the nearest whole number as needed
Idek :|
Regular hexagon $ABCDEF$ is the base of right pyramid $\allowbreak PABCDEF$. If $PAD$ is an equilateral triangle with side length 8, then what is the volume of the pyramid
The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .
The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.
so the height becomes,
√3a/2 = 4√3
The area of the hexagon is calculated using the formula ,
=3√3/2 x a²
=3√3/2 x 64
= 963√3
=332.553 square units.
Volume of a pyramid is calculated as ,
1/3 x base x height
= 1/ 3 x 8 x 8
= 1/3 x 64
=21.33 cubic units answer.
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where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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Which techniques can be used to evaluate the expression 12. 75÷1. 5? Select all that apply.
The division technique can be used to evaluate the given expression
12.75÷1. 5
The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/).
“p divided by q” can be written as: (p÷q) or (p/q).
The method of verification can be expressed as:
Dividend = (Divisor × Quotient) + Remainder.
The given equation is:12.75÷1.5
We'll first write the above decimal numbers in fractional form.
12.75÷1.5
1275/100÷15/10
2. Now we'll divide it further.
⇒1275/100÷15/10
⇒1275/100×15/10
⇒1275/10×15
⇒225/10×3
⇒88/10
3. And finally, we'll write our quotient in decimal form.
⇒88/10
⇒8.8
ㅤ
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tomatoes cost 1.19 per pound which equation best represents y the total cost of x pounds of tomatoes
Answer:y=1.19x
Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.
2. 15 - |-4a|
It says evaluate the expression.
If a = 2
Answer:
7
Step-by-step explanation:
So first you substitute A in
15-|-4(2)|
Then you multiply first because of GEMDAS or PEMDAS
15-|-8|
And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation
15-8
=7
What is quadrant 3 on a graph?
The lower left-hand corner of the graph is the third quadrant.
It contains the negative values of both x and y.
Quadrant
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.
Cartesian system
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
coordinates
Coordinates are numbers which determine the position of a point or a shape in a particular space.
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Ill mark brainly if its correct. a,b,c, or d ~ quickly please ~
Answer:
B
Step-by-step explanation:
A bag contains 2 green disks,2 yellow disks, and 5 black disks. What is the probability of drawing two green disks without replacement?
Answer: 1/36
Step-by-step explanation: 2/9 x 1/8 =2/72 = 1/36
can someone please help me?
What is 35% of 35!!
Answer:
12.25
Step-by-step explanation:
Solution for What is 35 percent of 35:
35 percent *35 =
( 35:100)*35 =
( 35*35):100 =
1225:100 = 12.25
Now we have: 35 percent of 35 = 12.25
Question: What is 35 percent of 35?
Percentage solution with steps:
Step 1: Our output value is 35.
Step 2: We represent the unknown value with x.
Step 3: From step 1 above, 35 = 100%
Step 4: Similarly, x = 35%
Step 5: This results in a pair of simple equations:
35 = 100% (2)
x = 35% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have
[tex]\frac{35}{x} =\frac{100}{35}[/tex] (with % for 100 and 35)
Step 7: Again, the reciprocal of both sides gives
[tex]\frac{x}{35} =\frac{35}{100}[/tex]
⇒ x=12.25
Therefore, 35% of 35 is 12.25
The geometric sequence LaTeX: a_n=125\left(\frac{1}{5}\right)^{n-1}a n = 125 ( 1 5 ) n − 1 represents the sales of a specific product at a store, where n is the number of years after its release. What is the sum of the first 6 terms?
The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.
The sum of the first 6 terms of the geometric sequence is calculated as follows:
[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]
[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]
[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]
Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75
The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.
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A rectangular prism has a length of 2cm, a height of 13cm, and a width of 9cm. What is its volume, in cubic cm?
Answer:
2 x 13 x 9 = 234 cm3 is your answer.
Step-by-step explanation:
Whenever given 3 side lengths of a rectangular prism you ALWAYS have to multiply those in order to get the volume..
Ten gallons of a sugar solution were mixed with 7 gallons of a 76 percent sugar solution to make a 64 percent sugar solution. Find the percent concentration of the first solution.
answers-
a. 51%
b. 60%
c. 48%
d. 56%
7 gallons of 76% solution contain 0.76×(7 gal) = 5.32 gal of sugar
10 gal of c% solution (c for concentration) contain c/100×(10 gal) = c/10 gal of sugar
(for example, if you have 10 gal of 50% solution, then it contains 50/10 = 5 gal of sugar)
Mixing the two gives a new solution with a total volume of 17 gal. If its concentration ends up at 64%, then it must contain 0.64×(17 gal) = 10.88 gal of sugar. This means
(sugar in 76% solution) + (sugar in c% solution) = 10.88 gal
5.32 gal + c/10 gal = 10.88 gal
c/10 gal = 5.56 gal
c = 50.56 ≈ 51
which makes the answer A.
Answer:
d. 56
Equation:
Let x = the percent of the 10 gallon sugar solution
10x + 76(7) = 64(10 + 7)
10x + 532 = 1088
10x = 1088 - 532
10x/10 = 556/10
x = 55.6
55.6 is closest to 56, therefore, the answer is 56%
what is the decrease of 3/2
Answer:
3/2
Step-by-step explanation:
3/2 is in the simplest form; it can't be decreased any more.
Please help I’m going to fail this grade
The result of the operation between two mixed numbers are listed below:
99 / 104 4 / 3 6 / 5 52 / 25 57 / 53 33 / 100 1 / 2 8 / 5 4 4 / 3How to solve an operation between mixed numbers
Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:
a b / c = a + b / c
Where a, b, c are integers and c is a non-zero number.
The procedure to simplify the operation is described below:
Transform mixed numbers into improper fractions. Divide the resulting two fractions. Simplify the expression.Case 1
1 3 / 8 ÷ 1 4 / 9
(1 + 3 / 8) ÷ (1 + 4 / 9)
(11 / 8) ÷ (13 / 9)
(11 / 8) / (13 / 9)
99 / 104
Case 2
2 1 / 3 ÷ 1 3 / 4
(2 + 1 / 3) ÷ (1 + 3 / 4)
(7 / 3) ÷ (7 / 4)
(7 / 3) / (7 / 4)
28 / 21
4 / 3
Case 3
4 1 / 5 ÷ 3 1 / 2
(4 + 1 / 5) ÷ (3 + 1 / 2)
(21 / 5) ÷ (7 / 2)
42 / 35
6 / 5
Case 4
5 1 / 5 ÷ 2 1 / 2
(5 + 1 / 5) ÷ (2 + 1 / 2)
(26 / 5) ÷ (5 / 2)
(26 / 5) / (5 / 2)
52 / 25
Case 5
9 1 / 2 ÷ 9 4 / 6
(9 + 1 / 2) ÷ (9 + 4 / 6)
(19 / 2) ÷ (58 / 6)
114 / 106
57 / 53
Case 6
2 2 / 10 ÷ 6 2 / 3
(2 + 2 / 10) ÷ (6 + 2 / 3)
(22 / 10) ÷ (20 / 3)
(22 / 10) / (20 / 3)
(66 / 200)
33 / 100
Case 7
2 1 / 4 ÷ 4 1 / 2
(2 + 1 / 4) ÷ (4 + 1 / 2)
(9 / 4) ÷ (9 / 2)
(9 / 4) / (9 / 2)
18 / 36
1 / 2
Case 8
2 2 / 3 ÷ 1 2 / 3
(2 + 2 / 3) ÷ (1 + 2 / 3)
(8 / 3) ÷ (5 / 3)
(8 / 3) / (5 / 3)
8 / 5
Case 9
5 3 / 5 ÷ 1 2 / 5
(5 + 3 / 5) ÷ (1 + 2 / 5)
(28 / 5) ÷ (7 / 5)
(28 / 5) / (7 / 5)
28 / 7
4
Case 10
4 2 / 3 ÷ 3 1 / 2
(4 + 2 / 3) ÷ (3 + 1 / 2)
(14 / 3) ÷ (7 / 2)
(14 / 3) / (7 / 2)
28 / 21
4 / 3
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What is the plotting method?
Plotting method is the graphical representation of mathematical expression.
What is mean by plotting?A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.
What are the steps of plotting method?At first, we need to choose the coordinate system by which we plot the point.
suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.
besides, we need to determine the required value that will be plotted on the plan.
if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.
we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.
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The table shows data for 4 cyclists during one day of training.
Complete the table by finding the rate of speed for each cyclist. Use the formula r = d ÷ t.
Cyclist Distance (mi) Time (hr) Rate (mi per hr)
Alisha 40 4
Jose 30 2
Raul 40 4
Ruthie 80 5
Rate of speed of each cyclist is:
Alisha 10mi/hr
Jose 15mi/hr
Raul 10mi/hr
Ruthie 16mi/hr
Data given of each cyclist;
Formula used: [tex]r=\frac{d}{t}[/tex]
here,
r=rate of speed
d=distance
t=time
Alisha: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]
Jose: Distance=30mi; Time=2hr
applying the formula
[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]
Raul: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]
Ruthie: Distance=80mi; Time=5hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]
Alisha= 10mi/hr
Jose= 15mi/hr
Raul= 10mi/hr
Ruthie= 16mi/hr
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fast please! Which measure of center is best to use for this set of data?
45, 39, 49, 37, 3, 51
Question 1 options:
Mean
Median
Mode
Range
Answer:
Median
Step-by-step explanation:
Mean: Add up all the numbers, then divide by how many numbers there are.
Median: Arrange your numbers in numerical order. Count how many numbers you have. Go to the number in that position and average it with the number in the next higher position to get the median.
Mode: Put the numbers in order from least to greatest and count how many times each number occurs.
Range: The difference between the smallest and highest numbers
Answer:
Mean:
[tex]mean = \frac{(45 + 39 + 49 + 37 + 3 + 51)}{6} \\ = 37.3[/tex]
Median:
[tex]3 \: \: 37 \: \: 39 \: \: 45 \: \: 49 \: \: 51 \\ median = ( \frac{n}{2} + 1) {}^{th} \\ = ( \frac{6}{2} + 1) {}^{th} \\ = 4 {}^{th} \: value \\ median = 45[/tex]
Mode:
[tex]mode = none \\ all \: digits \: are \: repeated \: once[/tex]
Range:
[tex]range = 51 - 3 \\ = 48[/tex]
a=___
b=___
c=___
Solve for θ and round your answer to the nearest degree.
θ =___ degrees
Answer:
a= -2,3*4,-1
b=u
c=w
Step-by-step explanation:
Polygon measurement include which of the following?
Answer:
Length and Width
The graph below shows the relationship between average heart rate (in beats per minute) of several mammal
species and their life expectancy (in years).
Which statement is the best description of the association between these variables?
Answer:
Nonlinar assosion
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation: