Answer:
[tex]\huge\boxed{x=1\ \vee\ x=2}[/tex]
Step-by-step explanation:
[tex]3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}[/tex]
[tex]\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}[/tex]
Final answer:
To solve the given equation involving exponents, convert 3^(x+1) and solve as a quadratic equation.
Explanation:
The equation is: 3^(2x) - 4*3^(x+1) + 27 = 0. To solve this, we can use the rules of exponents to change 3^(x+1) into 3*3^x.
Step-by-step solution:
Substitute 3^(x+1) with 3*3^x in the equation.
Now, you have a quadratic equation in terms of 3^x, solve it to find the value of 3^x.
Once you find the value of 3^x, proceed to find the value of x.
Chloe is a pharmacist and wants to know the
height of a medicine bottle received from a
supplier. The supplier informed her that the
radius of the medicine bottle is one-fourth its
height. Chloe knows that the medicine bottle
has a volume of V cubic inches.
Which of the following functions would best model the situation above?
O
cube root
O
square root
O
exponential
O
step
The given situation would be a best model of cube root.
Solution:
Generally, medicine bottles will be cylindrical in shape. Since the shape of the bottle is not given we can assume that the bottle is in cylindrical shape.
Given information:
Radius of the bottle (r) = one fourth of its height (h)
[tex]\Rightarrow r=\frac{1}{4}\times h[/tex]
Volume of the bottle = V cubic inches
The formula of the volume of a cylinder is as follows,
[tex]\Rightarrow V=\pi r^{2} h[/tex]
This can be re-written as [tex]h=\frac{V}{\pi r^{2}}[/tex] as we do not know the height.
On plugging-in the given values we get,
[tex]\Rightarrow h=\frac{V}{\pi \times(\frac{h}{4})^{2}}\rightarrow \frac{V}{\pi \times\frac{h^2}{16}}\rightarrow \frac{16V}{\pi\times h^2}[/tex]
On solving we get,
[tex]\Rightarrow h\times h^2 = \frac{V}{\pi}[/tex]
[tex]\Rightarrow h^3 = \frac{V}{\pi}[/tex]
On taking the cube root on both sides we get,
[tex]\Rightarrow h=\sqrt[3]{\frac{V}{\pi}}[/tex]
Therefore, cube root would be the best model of the given solution.
Combine like terms to simplify the expression: 9 + 3b − 1 + 7b − 2 = ______ 9 − 10b 6 + 10b 8 + 10b 16b 9 + 10b
Answer:6 +10b
Step-by-step explanation:
Like terms 9-1-2 =6 and 3b + 7b = 10b
Is this a linear f(x)= 7x^2+4
Answer:
Yes
Step-by-step explanation:
What was the population density per square meter ?
Answer:
The population density in people per square meter is 0.005377 people per square meter.
Answer: [tex]0.005377\frac{people}{m^{2}}[/tex]
Step-by-step explanation:
You want to convert [tex]\frac{people}{km^{2} }[/tex] to [tex]\frac{people}{m^{2}}[/tex]
To do this, multiply [tex]\frac{people}{km^{2} }[/tex] * [tex]\frac{1 km}{1000 m}[/tex] * [tex]\frac{1 km}{1000 m}[/tex]=[tex]\frac{people}{1000 * 1000 m^{2}}[/tex]
sub in 5377 for people to get
[tex]\frac{5377people}{1000 * 1000 m^{2}}=0.005377\frac{people}{m^{2}}[/tex]
it costs $6 for a dozen donuts how much does 1 donut cost
Answer:
.50 for one donut
Step-by-step explanation:
do a ratio 6$ for 12 donuts
so for $ for 1 donut
reduce the first equation for a ration of $1 per two donuts
so it be 50 cents
$6. $0.50
____ = ______
12 donuts. 1 donut
sam has a collection of 76 marbles. In the collection, 25% of the marbles are red and the rest are blue. Which statement accurately describes Samuel's marble collection? 19 marbles are red and 57 marbles are blue. 57 marbles are red and 19 marbles are blue. 16 marbles are red and 60 marbles are blue.
Answer:
Red is 19
Blue is 57
Step-by-step explanation:
According to the question,it says Sam has 25% red marble out of the 76.
It means 25/100×76
It gives 19
To get the value for blue
Blue + red=76
Red is 19
Blue + 19=76
Blue=76-19
Blue=57
Therefore,red is 19 and blue is 57
Two triangles have a scale factor of 5:7, If the area of the smaller triangle is 225cm squared what is the area of the larger triangle
Answer:
441
Step-by-step explanation:
The ratio of sidelengths squares is the ratio of the areas, so the ratio of the area of the smaller triangle's area to the larger triangle's is 25:49.
Using ratios, you figure out that the area of the larger triangle must be 225/25 *49, which is equal to 9*49 = 441
Final answer:
The area of the larger triangle, given a scale factor of 5:7 and the smaller triangle's area of 225cm squared, is 441cm squared. The areas scale as the square of the scale factor, in this case, 25:49.
Explanation:
The question involves working with the scaling of the area of a triangle when given a scale factor between two similar triangles. Since the scale factor of the linear dimensions between the two triangles is 5:7, the ratio of the areas is the square of the scale factor, which is (5:7)2 or 25:49.
If the area of the smaller triangle is 225 cm², to find the area of the larger triangle, we need to use the area ratio. Given that 25 parts correspond to 225 cm²in the smaller triangle, we can calculate the value of 1 part as 225 cm² / 25 = 9 cm2. Hence, the area of the larger triangle corresponds to 49 parts, which gives us 49 * 9 cm² = 441 cm².
mel paid for three-fourths of the cost of a cake and Gretchen paid the rest. If Mel paid $21, how much did Gretchen pay
Multipli the numbers
$7.00
21/3=7, and 21 is 3/4 of 7*4
How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or differs from its neighbors exactly by 1 (from one smaller by 1, and from the other larger by 1) and which contain the digit 5?
The question is about finding the total count of possible 5-digit numbers that either has identical adjacent digits or differ from its neighbor digits by exactly 1 and containing at least one 5. Providing an exact solution without knowing students' pre-existing knowledge on the subject can be difficult. This kind of problem typically involves methodologies like recursive relationships.
Explanation:This question pertains to combinatorics, a topic in mathematics that deals with countable structures. Specifically, the question is asking how many five-digit numbers are there that follows the conditions given in the question.
The condition that the number contains the digit 5 is applicable for both the cases where the digit is the same as or differs by 1 from its neighbors. This is because 5 is a middle digit from 0 to 9, and it can satisfy both conditions.
The problem can be approached by finding the total count of five digit numbers that satisfy just the adjacent difference conditions, and then subtracting the count of such numbers that do not contain the digit 5.
However, providing a step-by-step solution to this problem would be complex and lengthy, especially without the proper context of the student's pre-existing knowledge. The method to solve it would involve recursive relationships and possibly programming or usage of a suitable mathematical software.
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What value of x makes this equation true? 13 - 4x = 1 - x
4
-4
−125
125
Answer:
x = 4
Step-by-step explanation:
Given
13 - 4x = 1 - x ( add x to both sides )
13 - 3x = 1 ( subtract 13 from both sides )
- 3x = - 12 ( divide both sides by - 3 )
x = 4
Simplify this algebraic expression completely 9x-6(x+4)
Answer:
3x - 24
Step-by-step explanation:
9x - 6x - 24
3x - 24
The price per month for the Blue-tooth is $12 more than the cost for the car-phone. The sum of both items is $58. Find the cost of the Blue-tooth and car-phone. Let x equal the cost per month of the car-phone.
Answer:
Bluetooth = $41
Car Phone = 17
Step-by-step explanation:
Answer:
the bluetooth was $35 and the carphone was $23.
Step-by-step explanation:
What missing number would complete the factorization?
k2 + 5k + 6 = (k + 2)(k + ?)
A. 3
B. 6
C. 12
D. 4
Answer:
A. 3Step-by-step explanation:
[tex]k^2+5k+6=k^2+2k+3k+6=k(k+2)+3(k+2)\\\\=(k+2)(k+3)[/tex]
Other method:
[tex]k^2+5k+6=(k+2)(k+x)\qquad\text{use}\ FOIL\\\\k^2+5k+6=(k)(k)+(k)(x)+(2)(k)+(2)(x)\\\\k^2+5k+6=k^2+kx+2k+2x\\\\k^2+5k+6=k^2+(x+2)k+2x\Rightarrow x+2=5\ \wedge\ 2x=6\\\\x+2=5\qquad\text{subtract 2 from both sides}\\x=3\\\\2x=6\qquad\text{divide both sides by 2}\\x=3[/tex]
Solve (x+4)2 – 3(x + 4) – 3 = 0 using substitution.
u=
Answer:
Step-by-step explanation:
(x+4)2-3(x+4)-3=0
2x+8-3x-12-3=0
-1x-4-3=0
-1x-7=0
-1x=7
x=7/-1
x=-7
Answer:
u= x + 4
Step-by-step explanation:
I just did the as. and quiz
Which function is the inverse of f(x) = -5x-42
Answer:
f'(x)=-(x+42)/5
Step-by-step explanation:
Rewrite f(x) as y:
y=-5x-42
Flip x and y and solve for y:
x=-5y-42
x+42=-5y
(x+42)/-5=y
So the inverse function is f'(x)=-(x+42)/5 (note that f' means inverse)
If a babysitter babysat for 2 hours each night for 10 night. she made $180. she wants to she how much she makes per hour
answer fast !!!!!!!!!!
Answer:
The answer would be $9 dollars per hour.
Step-by-step explanation:
Let's start off with getting the basics down. She babysits for 2 hours each night for 10 total nights, so we would multiply the two and get 20 hours of babysitting service. We would then take $180 and divide the total money amount by the number of hours to get your money per hour. In this case, the answer is $9 per hour.
what is the positive solution to the equation 4x^2 + 12x = 135
The positive solution to the equation 4x^2 + 12x = 135 is; x = 9/2
By quadratic formula;
x = {-b ±√(b² - 4ac)}/2awhere, a = 4, b = 12 and c = -135.
By solving the equation quadratically;
The solutions are;
x = 9/2. OR. x = -15/2In essence, the positive solution of the equation is; x = 9/2
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The positive solution to the equation 4x^2 + 12x = 135 is found using the quadratic formula, resulting in a positive root of approximately x ≈ 3.375.
Explanation:The positive solution to the equation 4x^2 + 12x = 135 can be found by first rearranging the equation into the standard quadratic form of ax^2 + bx + c = 0. Bringing all terms to one side gives us 4x^2 + 12x - 135 = 0. This equation can be solved by either factoring, completing the square or using the quadratic formula. Since the original equation does not easily factor into a product of binomials, and the instructions indicate a preference for recognizing a perfect square when possible, we should attempt to complete the square or use the quadratic formula.
To complete the square, we would add (b/2a)^2 to both sides of the equation after dividing the linear coefficient by 2 and squaring the result. However, in this case, it's more straightforward to employ the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values from our equation gives two roots, but since we are only interested in the positive root, we take the solution where the square root term is added to the negative b value.
After calculating, we find that the positive root is x ≈ 3.375, which is the solution to the equation in question.
find the circumference of each circle with the given radius or diameter round to the nearest tenth use 3.14 for pie r=9 cm
Answer:
d=2r
Step-by-step explanation:
A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches.
A square with diagonals is shown. The diagonals split the square into 4 congruent triangles. The uppercase left triangle is Fall, the uppercase right triangle is winter, the bottom left triangle is summer, and the bottom right triangle is spring.
What is the approximate total length of iron edging needed to create the square frame and the two diagonals?
43.5 inches
50.9 inches
54.0 inches
61.5 inches
Answer:
43.5 inches
Step-by-step explanation:
we know that
The approximate total length of iron edging needed to create the square frame and the two diagonals is given by the formula
[tex]L=4b+2d[/tex]
where
b is the length side of the square
d is the diagonal of the square
we have
[tex]d=9\ in[/tex] ----> given problem
Find the value of b
Remember that the diagonal in a square is given by
[tex]d=b\sqrt{2}\ in[/tex]
substitute the given value of d
[tex]9=b\sqrt{2}[/tex]
solve for b
[tex]b=\frac{9}{\sqrt{2}}\ in[/tex]
Find the total length
[tex]L=4(\frac{9}{\sqrt{2}})+2(9)=43.5\ in[/tex]
Answer:
43.5 in
Step-by-step explanation:
ed said it was right lol
nononononononononono
Answer:
yesyesyesyes
Step-by-step explanation:
yesyesyesyesyes
Answer:
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what are the measures of center
Answer: mean, median, mode and range
Step-by-step explanation:
The measures of centre are referred to as mean, median, mode and range.
Mean also referred to as average, it is the sum of values in a data set divided by the number of values in the given data set.
Median is the middle point number in a given data set. Median of an even data set is the average of two values in the middle of the data set.
Mode is the most occurring number in the given data set. It is the number with the highest frequency in the set.
Range is the difference between the highest number and the lowest number in a given data set.
I hope this answers your question.
The measures of center in a dataset are statistical values that represent the central point of the data. These include the mean (arithmetic average), median (middle value), and mode (most frequent value). Another common measure of center is the weighted mean, which is used when some data points carry more significance than others.
Explanation:Measures of the center are statistical measures that provide information about the central point of a dataset. The main measures include the mean, median, and mode.
The mean is the arithmetic average of the data set. This is usually the sum of all data points divided by the number of data points.
The median is the middle value of the data set when it is ordered from smallest to largest. If there is an even number of data points, the median would be the average of the two middle numbers.
The mode is the data point that occurs most frequently in the data set. A data set may have one mode, more than one mode, or no mode at all.
Another common measure of center is the weighted mean, which is useful when some data points carry more significance than others. For example, you might want to calculate the average grade in a class where some assignments are worth more than others.
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The measure of an angle is 63.7°. What is the measure of its supplementary angle?
Answer:
116.3
Step-by-step explanation:
Supplementary angles add to 180
One angle is 63.7, the other is x
63.7+x = 180
Subtract 63.7 from each side
63.7-63.7+x = 180-63.7
x = 116.3
Assuming that c represents a positive number, which pair best represents f(x) and g(x)?
Answer:
Option A
Step-by-step explanation:
From the graph, we can see both f(x) and g(x) are parabolas that turns upside down.
The parent function for both f(x) and g(x) is
[tex]y = - {x}^{2} [/tex]
We can see that , f(x) is obtain by shifting the parent function up, by c units.
Therefore
[tex]f(x) = - {x}^{2} + c[/tex]
Also we can see that g(x) is half way between f(x) and the origin.
Therefore
[tex]g(x) = - {x}^{2} + \frac{c}{2} [/tex]
Therefore the correct option is A .
Jeremy wants to buy a desktop
computer that costs $1,600. He has
already saved $1,280. What percent
of the total has he saved?
Answer:
80%
Step-by-step explanation:
1280/1600=0.8=80%
What is the equation of the line that passes through the point (-4, 4) and has a
slope of -3
Answer:
[tex]y=-3x+4[/tex]
- A flow of 250 GPM is to be treated with a 2.4 percent (0.2
pounds per gallon) solution of sodium fluoride (NaF). The
water to be treated contains 0.5 mg/L of fluoride ion and
the desired fluoride ion concentration is 1.4 mg/L. What is
the sodium feed rate in gallons per day? Assume the sodium
fluoride has a fluoride purity of 43.4 percent. Select the
closest answer.
1. 19 gal/day
2. 22 gal/day
3. 25 gal/day
4. 28 gal/day
5. 31 gal/day
ANSWER FAST
The net of a cube is shown. If the length of each edge of the cube is 5 cm, find the surface area of the cube.
Answer:
150 cm²
Step-by-step explanation:
A cube has 6 surfaces.
A cube has equal length for all edges.
Area of 1 surface = 5 x 5 = 25 cm²
Area of 6 surfaces = 25 x 6 = 150 cm²
Answer:
Step-by-step explanation:
its 600 dont belive those liers.
Tammy is going for a walk she walks at a speed of 3 miles per hour for 7.5 miles. For how many hours does she walk.
Tammy does walk a time of 3.75 hours
Explanation:
Given-
Speed, (which can be represented as s) = 2 miles/hour
Distance, (which can be represented as d) = 7.5 miles of distance .
Time, t = ?
We know,
d = s t
7.5 miles of distance = 2 miles/hour × t
3.75 hour of time = t
Therefore, Tammy does walk a time of 3.75 hours
Write a sequence that has two geometric means between -6 and 2/9
An item on sale costs 30% of the original price. The original price was $17.
Answer:
$11.90
Step-by-step explanation:
30% of 17 is 5.10 which means you have to subtract 5.10 from 17