Explain how to solve 3^x-4=6 using the change of base formula log base b of y equals log y over log b. include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
x = log 10/log 3
Step-by-step explanation:
3^x - 4 = 6
3^x = 10
We take log base 3 of both sides since log_3 3^x is simply x.
log_3 3^x = log_3 10
x = log_3 10
We have an answer for x, but it is a log base 3. We want log base 10.
Now we use the change of base formula.
log_b y = log y/log b
x = log 10/log 3
PLEASE HELP!!!!!! URGENT!!!!!!!!! ALGEBRA! Hannah, Yu, and Becky went to buy groceries together. All three of them bought pasta, noodles, and split peas. Hannah bought 3 packs of pasta, 10 packs of noodles, and 2 packs of split peas. Yu bought 5 packs of pasta, 12 packs of noodles, and 1 pack of split peas. Becky bought 3 packs of pasta, 15 packs of noodles, and 2 packs of split peas. Hannah, Yu, and Becky spent $8.41, $9.42, and $9.66 respectively on these items. What are the costs of a pack of pasta, a pack of noodles, and a pack of split peas? A) Pasta: $0.69 per pack, Noodles: $0.25 per pack, Split peas: $0.99 per pack B) Pasta: $1.09 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack C) Pasta: $0.99 per pack, Noodles: $0.25 per pack, Split peas: $1.47 per pack D) Pasta: $0.69 per pack, Noodles: $0.20 per pack, Split peas: $1.97 per pack
Answer:
option d
sorry it took so long.
Write as an equation: Sara spent $2 more than Lauren, and together they spent $19.
Answer:
Equations:
a + b = 19
a = b + 2
a = Money that spent Laura
b = Money that spent Laureen
then:
(b+2) + b = 19
2b + 2 = 19
2b = 19-2
2b = 17
b = 17/2
b = 8.5
a = b + 2
a = 8.5 + 2
a = 10.5
Check:
10.5 + 8.5 = 19
which is the solution set of 18 - 3n + 2 = n + 20 - 4n Ф 0 all reals
Answer:
all reals
Step-by-step explanation:
Simplified, you have ...
20 -3n = 20 -3n
The equation is a tautology, true for all values of n.
The solution set is "all reals."
. A salesman sold 300 bags of maize to a retailer at Kshs .2000 each .He was given a commission of 3%.The salesman allowed a discount of 0.2% on the maize sold. This discount was deducted from his commission. (a) Calculate (i) The discount allowed
Answer:
The discount allowed per bag is kshs 4
while the discount allowed on all the 300 bags is kshs 1,200
Step-by-step explanation:
Here, we are interested in calculating the discount allowed on the sales of the bag of maize.
From the question, we are told that the sales man allowed a discount of 0.2% on the maize sold.
Now, to find the amount of this, we proceed as follows;
What we simply need to do is to find 0.2% of the each of the price of the maize bags, and then we can proceed to find the total discount given on all maize bags sold.
The discount on each bag of maize would be;
0.2% of kshs 2000
That would be;
0.2/100 * 2,000 = 400/100 = kshs 4
Since there are 300 bags, the total amount of discount allowed is 300 * kshs 4 = kshs 1,200
What is the real part of 4 - 5i
Answer:
5i is an imaginary number
In these questions it contains two parts
real and imaginary parts . thus answer to these questions is 5i
Explanation
Complex Number is the number which contains both real and imaginary numbers i is the specified elements. 5i is an imaginary parts number and 4 is real part number.
Thus we conclude that above statement for the question is correct.
To know more about the complex number
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Create a scatterplot for the following population data, using t = 0 to stand for 1950. Then
estimate the population of Namibia in the years 1940, 1997, and 2005. Note: Population
values are in thousands. (Hint: Begin by determining which row is the x-value and which row
is the y-value)
Answer:
The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.
Step-by-step explanation:
Refer the attached figure
We will use equation calculator to find the equation of given plot
[tex]y = 483.36 \times e^0.0264x[/tex]
We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.
x values are years
y values are population
For 1940, [tex]x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2[/tex]
For 1997, [tex]x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64[/tex]
For 2005,[tex]x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74[/tex]
Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.
Identify the sample as biased or unbiased and describe its type. John wanted to know about the popularity of a particular movie. He surveyed 20% of the people in 5 different theaters.
Answer: unbiased; simple random sampling
Step-by-step explanation:
From the question, we are informed that John wanted to know about the popularity of a particular movie and that he surveyed 20% of the people in 5 different theaters.
This is an unbiased sample. This is because everybody at the theaters have an equal chance of being chosen by John.
Also, it's a simple random sampling. This is because a subset of the entire population is randomly selected.
in the equation x=c-b/a, find the value of x when c=10, b=2, and a=2
Answer:
9
Step-by-step explanation:
x = c - b/a
x = 10 - 2/2
x = 10 - 1
x = 9
Answer:
x = c - b (divided by) a
Step-by-step explanation:
x = 10 - 2over2
x = 10 - 1
x = 9
try 18/2 since that part is a fraction.
Pls help me... Need proper working .. Answer all questions and explain a bit, a bit..... OK?if anything that you don't understand.... Ask me.
Step-by-step explanation:
for no .5.no.6...you must understand that if u want to get speed,distance must multiple with time
the volume of a solid come is 616cm^3. Find it's height if the base radius is 7cm
Answer:
height = 4cm
Step-by-step explanation:
volume = п r² h
п = 3.14 (aprox.)
r = radius
h = height
volume = 616cm³
then:
616 = 3.14 * 7² * h
616 = 3.14*49*h
616 = 153,86 * h
h = 616 / 153.86
h = 4
height = 4cm
Answer:
Your answer is
Step-by-step explanation:
If u multiply 616cm^3 multipied by 7 cm gives you the correct answer because volume multiplied by radius=height of that particular object.Hope this helps....
Have a nice day!!!!
When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
It should be written as 8x−15x.
It should be written as −2x−5x.
It should be written as x−8x.
It should be written as −x−7x.
I think its B but im not sure
Is the given equation a quadratic equation? Explain.
x(x−6)=−5
The equation is not a quadratic equation because there is no x2-term.
The equation is a quadratic equation because there is an x2-term.
The equation is not a quadratic equation because the expression is not equal to zero.
The equation is not a quadratic equation because there is a term with degree higher than 2.
Which of the following is an example of the difference of two squares? x2−9
x3−9
(x+9)2
(x−9)2
Answer:
(3x+4)(2x-5)
Step-by-step explanation:
Factor by grouping.
Which of the following shows the correct solution steps and solution to 7x-4= -18?
Answer:
x = -2
Step-by-step explanation:
To solve for x always get x on one side
First add 4 on each side, 4 + 7x - 4 = -18 + 4
Next subtract 18 from 4, making it -14 7x = -14
Now divide 7 on each side, x = -2
Today, Ling is going to an art museum to see a special exhibit. It takes Ling 45 minutes to walk to the subway station. She will ride the subway for 45 minutes and then walk 15 minutes to the art museum. If Ling needs to be at the art museum by 9:30 A.M., what is the latest time she can leave her house?
Answer: 7:55
Step-by-step explanation: in total the journey is 105mins so if she has to reach by 9:30. Then she has to leave her house 105mins before 9:30
there are how many times as many second in an hour as in a minute
Answer:
Step-by-step explanation:
1 hour=3600 sec
1 min=60 sec
Los jornales de dos obreros suman S/.60. Si uno de ellos gana S/.12
más que el otro. ¿Cuánto ganan cada uno de ellos?
Answer:
Cada uno de ellos gana:
S/. 24
S/. 36
Step-by-step explanation:
Planteamiento:
a + b = 60
a = 12 + b
Desarrollo:
sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:
(12+b) + b = 60
2b + 12 = 60
2b = 60 - 12
2b = 48
b = 48/2
b = 24
de la segunda ecuación del planteamiento:
a = 12 + b
a = 12 + 24
a = 36
Check:
24 + 36 = 60
Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively. At 5.00 p.m. all four machines give out a signal simultaneously. At what time will this happen again at the earliest?
Answer:
6:30 pm
Step-by-step explanation:
Given the following :
Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively.
Time when all four machines gave out signal simultaneously = 5:00 pm
To find the time all four will give out the next simultaneous signal :
Take the lowest common factor of the four intervals :
L. C. M of 24, 27, 30, 50
Using the Lowest Common Multiple calculator :
L. C. M. = 5400
5400 seconds.
Adding 5400 seconds to the last time a simultaneous signal was produced :
5:00 pm + 5400 seconds
5400 seconds = (5400/60) = 90 minutes = 1hour 30 minutes
5:00 pm + (1 hour 30 minutes)
= 6:30 pm
I need help. What is (-5/3)²
Answer:
Exact form:
25/9
Decimal form:
2.(7)
Mixed fraction form:
2 7/9
Step-by-step explanation:
Hope you found this helpful
Answer:
(-5/3)² = 25/9
Step-by-step explanation:
(a/b)ⁿ = aⁿ / bⁿ
(-5/3)² = -5² / 3² = 25 / 9
what is
[tex] \frac{3}{5} [/tex]
of 15
Answer:
9
Step-by-step explanation:
3/5 * 15
Rewriting as
3 * 15/5
3 * 3
9
The word "of" tells us we need to multiply.
So 3/5 of 15 means the same thing as (3/5) · (15).
Think of the 15 as 15/1 so when multiplying,
we can cross-cancel the 5 and 15 to 1 and 3.
So we have (3/1) · (3/1) which is 9/1 or just 9.
Draw the image of △ABC under a dilation whose center is P and scale factor is 1/2.
Answer:
See below
Step-by-step explanation:
Each point on the triangle moves to half its previous distance from P.
URGENTLY NEED THIS ASAP PLZ TYSM
Marcie solved the following inequality, and her work is shown below:
−2(x − 5) ≤ 6x + 18
−2x + 10 ≤ 6x + 18
−8x +10 ≤ 18
−8x ≤ 8
x ≤ −1
What mistake did Marcie make in solving the inequality?
She subtracted 6x from both sides when she should have added.
She subtracted 10 from both sides when she should have added.
She did not make a mistake.
When dividing by −8, she did not change the direction of the sign.
Answer:
fifth option
Step-by-step explanation:
Given
- 2(x - 5) ≤ 6x + 18 ← distribute left side
- 2x + 10 ≤ 6x + 18 ( subtract 6x from both sides )
- 8x + 10 ≤ 18 ( subtract 10 from both sides )
- 8x ≤ 8
Divide both sides by - 8, reversing the sign as a result of dividing by a negative quantity, thus
x ≥ - 1
Please help, i’ve never been good at this.
Answer:
x=4, x=-10
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
As per Pythagorean theorem:
10² = (x+2)² + (x+4)²100 = x² + 4x + 4 + x² + 8x + 16100 = 2x² + 12x + 2080 = 2x² + 12x40 = x² + 6xx² + 6x - 40 = 0Solving we get positive root of:
x = 4What part of the line does the midpoint identify?
The half-way coordinate between the end points.
The second quartile
The top part
The bottom quartile
Answer:
The half-way coordinate between the end points.
Step-by-step explanation:
The half-way coordinate between the end points.
What is 9x - 2 - 13x + 16 simplified ???
Answer:
Simplifying
9x + -2 + -13x + 16 = 0
Reorder the terms:
-2 + 16 + 9x + -13x = 0
Combine like terms: -2 + 16 = 14
14 + 9x + -13x = 0
Combine like terms: 9x + -13x = -4x
14 + -4x = 0
Solving
14 + -4x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-14' to each side of the equation.
14 + -14 + -4x = 0 + -14
Combine like terms: 14 + -14 = 0
0 + -4x = 0 + -14
-4x = 0 + -14
Combine like terms: 0 + -14 = -14
-4x = -14
Divide each side by '-4'.
x = 3.5
Simplifying
x = 3.5
Step-by-step explanation:
Answer:
-4x+14
Step-by-step explanation:
Collect "Like Terms" (9x and -13) = -4x
-4x - 2 + 16= -4x + 14
Anyone know the answer or how to solve this
Answer:
9 for part b 40 for part a
Step-by-step explanation:
if u do 5 times the numbers it gives u the product so 45 is 9 times 5 and 40 os 8 times 5
Answer:
Part A: 9 orange beads
Part B: 40 blue beads
Step-by-step explanation:
Notice that you need to have the proportion of blue beads always 5 times larger than the number of orange beads. therefore you need to complete the table following such pattern:
Part A: for 45 blue beads, she needs to use : 45/5 = 9 orange beads
Part B: for 8 orange beads, she needs to use 8 * 5 = 40 blue beads
Solve the following formula for m v2=3Pmn
Answer:
m= 0 /(−3np+v2 )
Step-by-step explanation:
You store square notepaper in a cube shape box with an inside edge length of 3 inches. What is the volume of the box
A cube has sides that are all equal lengths .
Volume of a cube is S^3, where S is the length of the side.
Volume = 3^3 = 3 x 3 x 3 = 27 cubic inches.
The volume of box will be 27 inch³.
A square notepaper is stored in a cube shape box with an inside edge length of 3 inches.
We have to calculate the volume of the box.
What is the volume of a cube ?
The volume of a cube is the multiplication of the edge length (a) for three times i.e., a × a × a = a³ .
As per the question ,
Inside edge length of cube = 3 inches
So ,
the volume of box will be ;
= a × a × a
= 3 × 3 × 3
= 27 inch³
Thus , the volume of box will be 27 inch³.
To learn more about volume of cube click here ;
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How many terms are in 3x + 2y + 8z?
Answer:
three terms
Step-by-step explanation:
3x + 2y + 8z
Since we cannot simplify
There are three terms
3x, 2y, 8z
Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?
Answer:
FV(n)=42,000(1.04)^n
Step-by-step explanation:
FV=PV(1+r/n)^nt
Where
FV=future value
PV=present value
r=interest rate
n=number of periods
t=time (years)
PV=42,000
r=4%=0.04
n=1
t=n
FV(n)=p(1+r/n)^nt
=42,000(1+0.04/1)^1*n
=420000(1+0.04)^n
=42,000(1.04)^n
FV(n)=42,000(1.04)^n
Answer:
42000(1-1.04^n/-0,04)
Step-by-step explanation:
Based on the image below, if you know that , find the following:
a) sin A
b) cos A
c) tan A
d) tan B
Answer:
A. Sine A = 4/5
B. Cos A = 3/5
C. Tan A = 4/3
D. Tan B = 3/4
Step-by-step explanation:
We'll begin by calculating the value of b in the attached photo.
This can be obtained as follow:
Cos B = 4/5
Cos B = Adjacent /Hypothenus
Adjacent = 4
Hypothenus = 5
Using pythagoras theory, the value of b can be obtained as follow:
b² = 5² – 4²
b² = 25 – 16
b² = 9
Take the square root of both side.
b = √9
b = 3
A. Determination of Sine A
Sine A =?
Opposite = 4
Hypothenus = 5
Sine A = Opposite /Hypothenus
Sine A = 4/5
B. Determination of Cos A
Cos A =?
Adjacent = 3
Hypothenus = 5
Cos A = Adjacent /Hypothenus
Cos A = 3/5
C. Determination of Tan A.
Tan A =?
Opposite = 4
Adjacent = 3
Tan A = Opposite /Adjacent
Tan A = 4/3
D. Determination of Tan B
Tan B =?
Opposite = 3
Adjacent = 4
Tan B = Opposite /Adjacent
Tan B = 3/4
