The value of the logarithm expression [tex]log_{0.5}(16)[/tex] evaluated is given by : Option A: -4.00
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = log_a(c)[/tex]
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) + log_b(c) = \log_a(c)\\[/tex]
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
For this case, we have to simplify the expression [tex]log_{0.5}(16)[/tex]
Let this is equal to 'a', then:
[tex]a = \log_{0.5}(16)\\\\0.5^a = 16\\(\dfrac{1}{2})^a = 16\\\\1^a/2^a = 2^4\\\\1 = 2^4 \times 2^a\\2^0 = 2^{4+a}\\\\0 = 4 + a\\a = -4[/tex]
(we used the property that: [tex]b^0 = 1[/tex] and [tex]k^m \times k^n = k^{m+n}[/tex] )
Thus, the value of the logarithm expression [tex]log_{0.5}(16)[/tex] evaluated is given by : Option A: -4.00
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Solve for x in the equation x ^ 2 + 2x + 1 = 17
O x = - 1 plus/minus sqrt(13)
O x = - 2 plus/minus 2 * sqrt(5)
O x = - 1 plus/minus sqrt(17)
O x = - 1 plus/minus sqrt(15)
Answer:
[tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
Step-by-step explanation:
[tex]x ^ 2 + 2x + 1 = 17[/tex]
[tex]\mathrm{Subtract\:}17\mathrm{\:from\:both\:sides}[/tex]
[tex]x^2+2x+1-17=17-17[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x^2+2x-16=0[/tex]
[tex]\mathrm{Solve\;with\;Quadratic\;formula}[/tex]
[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}[/tex]
[tex]\sqrt{2^2-4 \cdot1\cdot(-16)} =\sqrt[2]{17}[/tex]
[tex]x_{1,\:2}=\frac{-2\pm \:2\sqrt{17}}{2\cdot \:1}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-2+2\sqrt{17}}{2\cdot \:1},\:x_2=\frac{-2-2\sqrt{17}}{2\cdot \:1}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
Hence, Answer is [C] [tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
~Lenvy~
Answer:C
Step-by-step explanation:
Help marking as braninliest answer if gotten right!
Answer:
k=60
Step-by-step explanation:
k+2k=180
3k=180
k=60
Answer:
k = 60
Step-by-step explanation:
Because supplementary angles are either 2 angles where the sum equals 180, if we take 60 for [tex]\angle {1}[/tex], and then add it to [tex]\angle {2}[/tex], we get 2(60) = 120 for [tex]\angle 2[/tex] and 60 for [tex]\angle 1[/tex], meaning that if we add the values of both angles together, it will be 120 + 60 = 180.
A certificate of deposit with $600 principal earns 2. 5% interest for 6 years. How much is the interest earned for 6 years?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (600)(0.025)(6)\implies I=90[/tex]
I need help wit the answer
Answer:
Triangle STU is not similar to Triangle VWU
Step-by-step explanation:
For two triangles to be similar, they both should have the same angle measures. To find out if they have the same angle measures, we have to solve for the unknown angles. Remember, a triangle is worth 180°.
Triangle STU:
x + 90 + 42 = 180x + 132 = 180x = 48Triangle VWU:
x + 58 + 90 = 180x + 148 = 180x = 32As you can see, the angles don't have the same angle measures. Thus, they are not similar.
which expression represents half of a number,n,plus 3?
16 with the exponent of 2
Answer: 256
Step-by-step explanation:
that is just gonna be 16 x 16 which is 256
Answer:
16x2=32
Step-by-step explanation:
Multiple 16 twice, then you get 32!
What is the area of the rectangle shown on the coordinate plane?
3
2+
Х
12 square units
18 square units
21 square units
28 square units
Answer:
21 units
Step-by-step explanation:
7x3 is 21
Which of these is the absolute value parent function?
O A. f(x) = |x-1|
O B. f(x) = |3x|
O C. f(x) = |X|
O D. f(x) = |x|+ 2
Answer:
option 'C' is the correct one or parent function of linear.
Natasha and Richard are making exam papers.Each set takes Natasha 45 minutes and Richard 1 hour.Express the times Natasha and Richard take as a ratio. Give your answer in its simplest form.
Answer:
3:4
Step-by-step explanation:
1=60 minutes
Natasha: Richard-----> 45:60
Simplify: 45/15= 3 60/15= 4
Ratio: 3:4
PLZ HELP FAST The amount of water in a tank is taken out of the tank by the equation g = -20h +100, when g represents the number of gallons of water left in the tank and h represents the number of hours that have passed by. How many gallons of water are left in the tank after 3.5 hours? Type your answer in the box provided.
Answer:120
Step-by-step explanation:
if you add 20 and 100 it gives you 120
Question 9 of 10
What is the area, measured in square centimeters, of the green shape
pictured below? Do not include units in your answer.
Answer:
I think it's 126cm not sure
PLZ PLZ HELP ASAP! I WILL MARK YOU BRAINLIEST!
Answer:
I can't see it redo it so I can answer
Answer:c,d,a,d
Step-by-step explanation:
Liam paid $13. 00 at a department store for 5 pairs of socks. When the number of pairs of socks is represented by p and the total cost (in dollars) is represented by c, which equation corresponds to this relationship?A. C = 2. 6pB. C = 1. 6pC. C = 3. 4pD. C = 0. 4t
.Brainliest please
Answer:
B. c = 2.6
Step-by-step explanation:
$13.00 / 5 = 2.6
PLSS HELPP
Two numbers a and b are in the ratio 3 : 4. If the first number is decreased by 4 and the second is decreased by 2, they are in the ratio 2 : 3. Find a and b.
a =
b=
The value of a = 24 and b = 32. Let the original numbers be 3x and 4x since they are in the ratio 3 : 4.
Step 1: Form the new ratios after the given decreases.
The first number decreased by 4 becomes 3x - 4, and the second number decreased by 2 becomes 4x - 2. The new ratio is 2 : 3.
Step 2: Set up the equation based on the new ratios.
We have the following equation based on the new ratios:
(3x - 4) / (4x - 2) = 2 / 3
Step 3: Solve the equation for x.
To solve the equation, we can cross-multiply:
3(3x - 4) = 2(4x - 2)
Expand and simplify:
9x - 12 = 8x - 4
Now, isolate the variable on one side:
9x - 8x = 12 - 4
x = 8
Step 4: Find the values of a and b.
Now that we have the value of x, we can find the values of a and b:
a = 3x = 3 * 8 = 24
b = 4x = 4 * 8 = 32
So, a = 24 and b = 32.
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A pump is removing water from a tank at a constant
rate. The graph shows the relationship between the
volume of water in the tank and the number of hours.
What is the y-intercept of the graph, and what does
it represent?
80
(0, 80)
60
Volume (liters)
40
1. Underline each question you need to answer.
20
0
0
2
4
6
8
X
Hours
2. On the graph, circle the point that corresponds to
the y-intercept. Explain how to use this point to
find the y-intercept.
to by Savvas Leam. What does the graph show about how the volume of water in the
tank changes over time?
4. Does the y-intercept represent a starting value or an ending value?
Explain.
5. On the graph, highlight the information that describes the
quantity represented on the y-axis. How does this help you
determine the meaning of the y-intercept?
Answer:
you can use a calculator and find the formula
Step-by-step explanation:
1/4 divided by 11.5
Help!
Answer:
1/46 as a fraction and 0.02 recurring as a decimal
Step-by-step explanation:
calculator
During his leg of the run, Shannon developed hypothermia, a dangerous condition caused by extreme cold. Normal body temperature is 98.5ºF. During hypothermia, it falls by at least 3.5º. If his temperature dropped by that amount, what was Shannon’s body temperature with hypothermia?
Find the area. Pls help I'm not smart and I cant do this
Show an example of a Multi step equation with an answer of -13.
Answer:
Step-by-step explanation:
x=338/2x
2x^2=338
x^2=169
x=13
Comments) How many of you go to K12 for school?
Answer:
not me
Step-by-step explanation:
why?
m=1/2 and the y intercept is (0,-5) what is the equation of the line in slope intercept form
Which value for x makes the equation x -4.21 = 6.047 true? A. x = 10.68 C. X = 10.247 B. x = 10.257 D. x = 1.837
Answer:
C. X = 10.247
Step-by-step explanation:
X -4.21 = 6.047
just you will add 4.21 to both sides of the equation
X -4.21 + 4.21 = 6.047 + 4.21
X = 10.247
Answer: the answer is B.
m(x) =5
Find m(2)
I have no idea how to do this help me
Answer:
10
Step-by-step explanation:
All this is saying is when there is one x value it is equal to 5
so, applying that logic, 2 fives is equal to 2*5=10
so when x=2, it is equal to 10
Hope this helps you out!!!
how do scientists know about the ordovician period
Answer:
they do know true the callender
At a particular school 20% of children travel by bus.
If this represents 280 children, how many children attend the school?
Answer:
1,400 children attend the school
Step-by-step explanation:
If 20% is 280, we can set up a proportion to solve for how many attend the school. I will put the percentages on top and the number of children on the bottom:
-> Please note that a percentage divided by 100 becomes a decimial
[tex]\frac{20}{280}=\frac{100}{x}[/tex]
Cross multiply:
.2 * x = 280 * 1
.2x = 280
Divide both sides of the equation by .2:
1,400 children attend the school
We can check our work by multiplying 1,400 by 0.2:
1,400 * 0.2 = 280 ✓
what is (3-8y)x(-2.5)
Answer:
20xy−7.5x
Step-by-step explanation:
Solve 6x² +11x -35 =0
Step-by-step explanation: If you're asked to solve a quadratic equation by the method of your choice, you should always check to see if the quadratic factors before you try any other method.
In this case, we have a trinomial that
factors as the product of two binomials.
In the first position for each binomial, we will use
our factors of 6x² which are either 6x · x or 3x · 2x.
It's a good idea to try less extreme extreme factors.
That means choose factors a little closer together.
So 3x and 2x would be first on our list.
We do the same for the factors of -35.
Since our constant term is negative, it will factor
as the product of a positive times a negative.
So the factors of -35 are +7 · -5, -5 · +7, -7 · +5, +5 · -7.
Remember to reverse the order of the
factors is your lead coefficient is not 1.
The factors that work in this case are -5 and +7.
So we have (3x - 5)(2x + 7).
To check, take the product of the outer terms and inner terms.
So we have -21x + 10x which is our middle term.
Now set it equal to 0.
So we have (3x - 5)(2x + 7) = 0.
Now use the zero product property.
So either 3x - 5 = 0 or 2x + 7 = 0.
Solving each equation from here, we have x = 5/3 or x = -7/2.
Felicia is considering two companies for the installation of her new carpet. The carpet companies installation rates are shown.
Carpet Company A: C = 1.35y + 100 where c is the cost and y is the number of square yards.
Carpet Company B: This company charges $2.05 per square yard for the carpet and the installation.
Identity the unit rate in dollars per square yard for each carpet company.
Using linear function concepts, it is found that:
The unit rate for company A is of $1.35.The unit rate for company B is of $2.05.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.For Company A, the equation is:
y = 1.35y + 100.
The slope is of m = 1.35, hence the unit rate is of $1.35.
For Company B, as already stated in the problem, the unit rate is of $2.05.
More can be learned about linear function concepts at https://brainly.com/question/24808124
What is the x and y ??????????
Answer:
The points on an axis
Step-by-step explanation:
There are two points on an axis and they are x and y. x goes across and y goes up and down
8 is what percent of 2
Answer: 400%?
Step-by-step explanation: 2 is 1/4 of 8 which means to get from 2 you need to multiply it by 4, 1=1.00 which is 100% so it is 400%
Answer:
0.25 or 25%
Step-by-step explanation:
p x 8 = 2
= 2/8
Then turn this into a percent which is 25% hope this helped