Answer:
First of all, this equation is defined on ]3,+∞[ because you need x+3>0 and x−3>0 at the same time or the log won't be defined.
The log function maps a sum into a product, hence log(x+3)+log(x−3)=27⇔log[(x+3)(x−3)]=log27.
You now apply the exponential function on both sides of the equation : log[(x+3)(x−3)]=log27⇔(x+3)(x−3)=27⇔x2−9=27⇔x2−36=30. This is a quadratic equation that has 2 real roots because Δ=−4⋅(−36)=144>0
You know apply the quadratic formula x=−b±√Δ2a with a=1 and b=0, hence the 2 solutions of this equation : x=±6
−6∉]3,+∞[ so we can't keep this one. The only solution is x=6.
Step-by-step explanation:
I THINK IT HELP U
99. Savings Bronwyn wants to buy a house, so she has decided
to save one quarter of her salary. Bronwyn earns $47.00 per hour
and receives an extra $28.00 a week because she declined
company benefits. She wants to save at least $550.00 each week.
How many hours must she work each week to achieve her goal?
Answer:
46.5 hours per week
Step-by-step explanation:
At least 550 a week.
Which is 1\4 of Bronwyn salary.
550 x 4 = 2200
To find minimum work hours
2200-28 = 2172
2172 \ 47 = 46.212 hours per week
So, bronwyn needs to work at least 46.5 hours per week
Answer:
Bronwyn must work nearly 47 hours each week to achieve her goal.
Step-by-step explanation:
Let x be the number of hours Bronwyn works per week.
If Bronwyn earns $47 per hour, if x is the number of hours she works per week and if Bronwyn earns $28 per week because she declined company benefits, lets assume that the left hand side of the equation is:
[tex]47x + 28[/tex]
Now onto the salary. Since Bronwyn wants to save $550 each week and since she also wants to save one quarter of her salary, her salary becomes $2200 for each week she works
Making the equation...
[tex]47x + 28 = 2200[/tex]
Time to solve for x
[tex]47x = -28 + 2200\\47x = 2172\\x = 46.2[/tex]
Since its at least, you can round it up to 47 making 47 the number of hours she must work each week to achieve her goal.
Is (6,0) a solution of 5x-y=9?
Answer:
No
Step-by-step explanation:
5(6)-(0)≠95(6)-(0)=30Songs on a band's set list are an example of which type of data?
Answer
O Discrete
O Continuous
O Neither
Here we want to see which type of set is a band's setlist.
We will see that it is a discrete set.
We can define two types of sets
Continue sets are those, like the name implies, continuous (or dense). Examples can be the set of real numbers.
Discrete sets are those that have "gaps" between consecutive elements. For example, the integer set is a discrete set. Particularly, discrete sets can be quantized (counted).
Now, we have a list of songs, that can be written as:
L = {song 1, song 2, song 3, ...}
Here we can see that we have separated elements. Thus, this is a discrete set. This happens because we clearly can separate the element "song 1" from "song 2" (there may be a lapse of time between them, defining the end of the first one), so we have the "gaps" mentioned above.
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10 pounds of egg whites. You have 6 ounces to make one serving. How many servings can you make?
Identify which of the twelve basic functions listed below fit the description given.
y = x, y = x2, y = x3, y = , y = , y = ex, y = , y = ln x, y = sin x, y = cos x, y = int (x), y = 1/1+e-x
The two functions with infinitely many zeros
Try this option:
only periodical functions have many zeros, that is why y=sinx and y=cosx are the correct answer.
The functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.
The two functions with infinitely many zeros from the given list of twelve basic functions are y = x and y = x³
The function y = x has infinitely many zeros because any value of x that equals zero will result in y also being zero.
In other words, for every x value of 0, the corresponding y value is also 0.
This makes the function pass through the origin (0, 0) and have an infinite number of zeros.
2. The function y = x³ also has infinitely many zeros because the cube of any real number is zero if and only if the number itself is zero.
This means that for every x value of 0, the corresponding y value is also 0. Hence, the function y = x³ passes through the origin (0, 0) and has an infinite number of zeros.
In summary, the functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.
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what is 63 divided by 1000
Answer:
0.063
Step-by-step explanation:
[tex]-7+1[3+8(2^2-8)][/tex]-7+1[3+8(2^2-8)]
Answer:
-36
Step-by-step explanation:
-7+1[3-32]
= -7-29
= -36
- Three times the quantity two decreased by x is nine.
Step-by-step explanation:
3(2-x)=9
this is the answer to the statement
The expression three times the quantity two decreased by x is nine is - 1
A quantity two decreased by x can be expressed thus :
(2 - x)Multiplying the quantity by 3 :
3(2 - x)The expression can be written Mathematically as thus : 3(2 - x) = 9
The expression can be expanded further as :
3(2 - x) = 9
6 - 3x = 9
Collect like terms
-3x = 9 - 6
-3x = 3
x = (3 ÷ -3)
x = - 1
Therefore, the expression equates to - 1
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Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?
Answer:
join me on no comments yet the story is about to the turf and a bagane and pinni geting step by step explanation friendship is not working properly and the story of a y I have a mantra and sister about your self and the story of the story is a bagane unda and the story and the portion of the story of the story of the story is about the event of a y you know if
Help please! Find the area of the shape below. (Show work)
9514 1404 393
Answer:
292 yd²
Step-by-step explanation:
We can find the area of the remaining L shape by subtracting the area of the 21×22 rectangle at lower left from the 26×29 overall rectangle.
shape area = (26 yd)(29 yd) -(21 yd)(22 yd) = 754 yd² -462 yd²
shape area = 292 yd²
__
Additional comment
The area of a rectangle is the product of its length and width.
There are many ways the area of this shape can be calculated. The area can be divided into two rectangles, two trapezoids, three rectangles, and other ways.
If you cut up the given shape into smaller pieces, you will generally need to know the widths of the arms of the L. One of those is shown as 7 yd. The other is 26-21 = 5 yd.
Using the method we did, we only needed the dimensions shown on the figure.
The inverse of the relation y = 9x – 4 can be obtained graphically by:
The inverse of the function y = 9x -4 is obtained by a reflection in the line at ( y = x ). Hence Option D is correct.
What is the reflection of a line?Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point but is on the other side of the line. This transformation is known as a reflection over the line.
The inverse relation for y= 9x -4 will be calculated by putting the value of x equal to y or replacing x by y and y by x in the equation.
Hence Option D is correct.
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twice a number added to the product of 14 and 2 is 30. find the number
Answer:
1
Step-by-step explanation:
2x + (14 • 2) = 30
2x + 28 = 30
2x = 30 - 28
2x = 2
x = 2/2
x = 1
Hope this helps you. Do mark me as brainliest.
Integration of x+4/(x+2)"2
Answer:
is this u want?
Step-by-step explanation:
if no so sorry..
A store is having a sale on jelly beans and trail mix. For 7 pounds of jelly beans and 9 pounds of trail mix is a total of $42. For 5 pounds of jelly beans and 3 pounds of trail mix is a total of $24. Find the cost for each pound of jelly beans and each pound of trail mix?
Answer:
One pound of jelly beans costs $3.75.
One pound of trail mix costs $1.75.
Step-by-step explanation:
Let [tex]x[/tex] be equal to one pound of jelly beans.
Let [tex]y[/tex] be equal to one pound of trail mix.
1) Form equations
We're given:
7 pounds of jelly beans + 9 pounds of trail mix = $42
⇒ [tex]7x+9y=42[/tex]
5 pounds of jelly beans + 3 pounds of trail mix = $24
⇒ [tex]5x+3y=24[/tex]
Now, we have our two equations:
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
2) Solve for x using elimination
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
Multiply the second equation by 3 to change 3y to 9y:
[tex]5x+3y=24\\3(5x+3y)=3(24)\\15x+9y=72[/tex]
Subtract the first equation from the second to eliminate y:
[tex]15x+9y=72\\- 7x+9y=42\\\rule{2.5cm}{0.4pt}\\8x=30[/tex]
Divide both sides by 8 to isolate x:
[tex]\displaystyle x=\frac{30}{8} \\\\x=3.75[/tex]
Therefore, one pound of jelly beans costs $3.75.
2) Solve for y using substitution
[tex]\displaystyle\left \{ {{7x+9y=42} \atop {5x+3y=24}} \right.[/tex]
Now, we know that x=3.75. Plug this value into one of the equations and solve for y:
[tex]5x+3y=24\\5(3.75)+3y=24\\18.75+3y=24\\3y=24-18.75\\3y=5.25\\\\\displaystyley=\frac{5.25}{3} \\\\y=1.75[/tex]
Therefore, one pound of trail mix costs $1.75.
I hope this helps!
Find an equation of the set of all points equidistant from the points
A(−2, 6, 3) and B(5, 3, −3).
We need to find the equation which is equidistant to the given points.
[tex]A(-2,6,3)[/tex] and [tex]B(5,3,-3)[/tex]
This can be done using the distance formula.
Let us take a point [tex]P(x,y,z)[/tex] which is equidistant from both points so
[tex]\sqrt{(x+2)^2+(y-6)^2+(z-3)^2}=\sqrt{(x-5)^2+(y-3)^2+(z+3)^2}\\\Rightarrow y^2-12y+x^2+4x+z^2+49-6z=y^2-6y+x^2+z^2+6z+43-10x\\\Rightarrow 7x-3y-2z+1=0[/tex]
The required equation is [tex]7x-3y-2z+1=0[/tex]
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Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(-7,9) and (-2,4)
solve the equation 6 = 5 x -2
Answer:
8/5 = x
Step-by-step explanation:
6 = 5x - 2
~Add 2 to both sides
8 = 5x
~Divide 5 to both sides
8/5 = x
Best of Luck!
Can someone help me with this one pleaseee!!!!
Find the midpoint of the segment with the given endpoints.
(-7, -9) and (-2,7)
Answer:
(-9/2,-1)
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
This year Amanda watched 80 movies. She thought that 56 of them were very good. Of the movies she watched, what percentage did she rate as very good?
Helppp
Find the measure of ∠3.
Answer:
90°
Step-by-step explanation:
diagonals of a kite intersect each other at 90°
:)
ANSWER :
third option 90 degrees
Step-by-step explanation:
the opossite adjasent angle is 1 that is 90 so angle 3 is opposite adjacent angle of angle 1
*The opposite adjacent angles will always be same
Will mark as brainliest!
Answer:
[tex]f=12-\frac{t}{20}[/tex]
Step-by-step explanation:
What is the value of the expression?
3 * [(2 * 6 - 5) + (8 divided by 4)] - 1
A. 9
B. 11
C. 26
D. 32
Show Work!
[tex]3\cdot[(2\cdot6-5)+(8:4)]-1=\\\\=3\cdot[(12-5)+2]-1=3\cdot(7+2)-1=\\\\=3\cdot9-1=27-1=\boxed{26}[/tex]
Please urgent
please solve
Answer:
1
Step-by-step explanation:
steps are in picture.Ignore hand writing
What is the decimal equivalent for a centimeter?
Chase thought that only 23 people would come to the banquet, but 48 people ended up coming. What was his percent error?
Answer:
The answer is 52%
ssmoga membantu
brainiest to whoever right
Answer:
Area of a triangle
Step-by-step explanation:
1/2bh is used to find the area for a triangle
What is the measurement??
Answer:
83°
.......................
Answer:
83
Step-by-step explanation:
Identify the segment bisector of RS.
12
S
R
M
OMS
RM
6
OS
O lines
The length of RS is O
Answer:
s
RS = 24
Step-by-step explanation:
A bisector, in mathematics, is a two-dimensional line or line segment that divides another two-dimensional shape in half. In this case, as per the given drawing line (s) divides the line (RS) in half. This is indicated by the two small red lines on either side of the line (s) on the line (RS), signifying that the two segments are congruent. Thus, proving that line (s) bisects line (RS).
The length of line (RS) is is twice the length of line (RM), thus line (RS) is (24).
multiply 18/-57 and 7/6
Answer:
-7/19
Step-by-step explanation:
First simplify the fractions. 18/-57= -6/19.
-6/19x7/6=-42/114
-42/114=-7/19
I hope this helps! I also put it into an online calculator to make sure it is right and it is!
