Solving as exponents
[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]
[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]
[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]
[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]
[tex]\\ \rm\Rrightarrow -2x=4[/tex]
[tex]\\ \rm\Rrightarrow x=-2[/tex]
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex]9^{x-8}=3^{4x-12}[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]
[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 2x-16=4x-12[/tex]
Subtract 2x from both sides:
[tex]\implies 2x-16-2x=4x-12-2x[/tex]
[tex]\implies -16=2x-12[/tex]
Add 12 to both sides:
[tex]\implies -16+12=2x-12+12[/tex]
[tex]\implies -4=2x[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies x=-2[/tex]
Find the area of the parallelogram.
Answer: 25 in.
Step-by-step explanation:
A = bh
A = 5 x 5
A = 25
8.2.PS-10
8.8 cm
A company is designing a new cylindrical water
bottle. The volume of the bottle will be 198 cm³.
The height of the water bottle is 8.8 cm. What is
the radius of the water bottle? Use 3.14 for .
The radius of the water bottle is about
cr
cm. (Round to the nearest tenth as needed.)
Questio
Answer:
Step-by-step explanation:
Givens
Volume = 198 cm^3h = 8.8 cmpi = 3.14r = ?Formula
V = pi * r^2 * h Substitute givens into formula
Solution
198 cm^3 = 3.14 * 8.8 * r^2 Combine the right
198 = 27.632 * r^2 Divide both sides by 27.632
198 / 27.632 = 27.632 * r^2 / 27.632
7.1656 = r^2 Switch the equation
r^2 = 7.1656 Take the square root of both sides
√r^2 = √7.1656
r = 2.6768
Answer
r = 2.7 rounded to the nearest tenth
FInd the measure of angle 1.
Answer:
48 degrees.
Step-by-step explanation:
Adjacent angles add up to 180 degrees. 132 degrees and angle 1 should add up to 180 when added together.
132+angle 1 =180
angle 1=180-132
angle 1=48 degrees
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textsf{According to given question, lines k and l are parallel to each other } [/tex]~
[tex] \textsf{and we can clearly observe that} [/tex][tex] \sf{ \angle 1} [/tex][tex] \textsf{forms Co- interior angle pair with 132° } [/tex]
[tex] \textsf{[ sum of co - interior angle pair = 180° ] } [/tex]
[tex]\qquad \sf \dashrightarrow \: \angle1 + 132 = 180[/tex]
[tex]\qquad \sf \dashrightarrow \: \angle1 = 180 - 132[/tex]
[tex]\qquad \sf \dashrightarrow \: \angle1 =48 \degree[/tex]
[tex] \texttt{So, the correct choice is C} [/tex]
Match the transformation with the description.
Answer:
Translation = Slide
Reflection = Flip
Rotation = Turn
Step-by-step explanation:
Giving Brainiest help me pleasee tyyy <3
Answer:
252 in^3
Step-by-step explanation:
Multiply all 12 x 7 x 3 = 84 x 3 = 252 in^3.
Hope this helps!
GIRL NO!!!! IM FAILING CAN SOMEONE HELP ME ASAP ON THIS SCREEN SHOT
Answer:
d = 306 m
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates
d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]
= [tex]\sqrt{270^2+144^2}[/tex]
= [tex]\sqrt{72900+20736}[/tex]
= [tex]\sqrt{93636}[/tex]
= 306 m
Answer:
The distance from Francesca's house to the beach is 306 meters.
Step-by-step explanation:
Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.
Step 1 Find the length of the horizontal leg.
The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).
|280 - 10| = 270
The length of the horizontal leg is 270 meters
Step 2 Find the length of the vertical leg.
The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)
|164 - 20| = 144
The length of the vertical leg is 144 meters.
Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.
a² + b² = c²
270² + 144² = c² Substitute into the formula.
72900 + 20736 = c² Simplify.
93636 = c² Add.
√93636 = c Take the square root of both sides.
306 = c Simplify.
The distance from Francesca's house to the beach is 306 meters.
pleaseeeee help ill give u brainliest
The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $250 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following.
C=250n+6500
Answer the following questions.
(a)
What is the total cost of transporting 11 tons?
$?
(b)
If the total cost is $11,750, how many tons is the company transporting?
? tons
Answer:
(a) C = $9250
(b) n = 21 tons
Step-by-step explanation:
(a) 11 tons being transported, so n = 11.
∴ C = 250 (11) + 650
C = $9250
(b) C = $11,750
∴ 11750 = 250n + 6500
250n = 5250
n = 21 tons
Hope this helps!
Please help me and hurry
Answer:
1.5 x 10 ^4
Step-by-step explanation:
Answer:
1.5 x 10 ^4
Step-by-step explanation:
hello hope this helps
find x so that x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence
Answer:
x = -3/2
Step-by-step explanation:
x + 3 + d = 2x + 1 First term plus common difference = 2nd term
x -2 = d
x + 3 + 2d = 5x+2 First term + 2 d = third term re-arrange:
4x-1 = 2d sub in the definition of d from above
4x -1 = 2 (x-2)
4x-1 = 2x-4
2x = -3
x = -3/2
If x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The sequence in which consecutive terms will have common difference is called as Arithmetic sequence.
x+3, 2x+1, and 5x+2
The common difference between first term and second term
d=2x+1-x-3
d=x-2
The common difference between second term and third term
5x+2-2x-1=d
3x+1=d
Now plug in d value
3x+1=x-2
Subtract x from both sides
3x-x=-3
2x=-3
Divide both sides by 2
x=-3/2
Hence, if x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
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What is 1/2 + blank = 7/8?
find the surface area of the pyramid. the surface area of the pyramid is __in squared.
Answer:
[tex]561.08in^{2}[/tex]
Step-by-step explanation:
[tex]S A = lw + l[/tex] [tex]\sqrt{(\frac{w}{2})^{2} + h^{2} } + w[/tex] [tex]\sqrt{(\frac{l}{2})^{2} + h^{2} }[/tex]
[tex]SA = 14(14) + 14 \sqrt{(\frac{14}{2})^{2} + 11^{2} }+ 14 \sqrt{(\frac{14}{2})^{2} + 11^{2} } = 561.08in^{2}[/tex]
PLease Help me its a math problem see image attached
Answer:
the second one
Step-by-step explanation:
If an object is rotated 360 degrees then what will the figure look like?
1. The exact same as the pre-image
2. An upside down version of the pre-image
3. A sideways version of the pre-image
Answer:
the exact same as the pre image
What’s the probability Cecilia picks a plastic marble from the bag?
Answer:
Answer. = 2/2.
Step-by-step explanation:
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost? Show your work.
wierd circles i dont like using pi please help
Can anyone explain how to work this equations pls?
Answer:
[tex]\frac{3}{y^{2} }[/tex]
Step-by-step explanation:
This question is asking you to simplify using the law of indices:
Just to write out the question in fraction form:
[tex]\frac{12y^{7} }{4y^{9} }[/tex]
Cancel out the 4:
[tex]\frac{3y^{7} }{y^{9} }[/tex]
Cancel out y^7:
[tex]\frac{3}{y^{2} }[/tex]
Hope this helped and brainliest please
Answer:
3/y^2
Step-by-step explanation:
1. Rewrite the division as a fraction.
= 12y^7/4y^9
2. Cancel the common factor of 12 and 4
= 4(3y^7)/4y^9
= 3y^7/y^9
3. Cancel the common factor of y^7 and y^9
= y^7 ⋅ 3/y^9
= 3/y^2
what’s the circumference, to this problem ?
Answer:
The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex] but in this case we see that a diameter is being used therefore we can get rid of the 2 and the r because that is what the diameter and just replace d into there like this [tex]C=d*\pi[/tex].
We can then input the value and we get that [tex]C=1*\pi[/tex] which then just narrows down to [tex]C=3.142[/tex].
Hope this helps! Let me know if you have any questions
Question 6
Points 1
Anne measured the volume of an object and recorded it as 46 cubic cm which
was 15% high from the actual volume. Find the actual volume.
Answer:
Actual volume = 40 cm^3.
Step-by-step explanation:
15% = 0.15 as a decimal fraction.
Let the actual volume be x cm^3, then we have the equation:
x + 0.15x = 46
1.15x = 46
x = 46 / 1.15
= 40 cm^3.
Emily is a songwriter who collects royalties on her songs whenever they are played in
a commercial or a movie. Emily will earn $40 every time one of her songs is played in
a commercial and she will earn $120 every time one of her songs is played in a movie.
Emily earned a total of $600 in royalties on 11 commercials and movies. Graphically
solve a system of equations in order to determine the number of commercials, x, and
the number of movies, y, on which Emily's songs were played.
a
✓Click twice to plot each line. Click a line to delete it.
Answer:
x + y = 12
40 x + 120 y = 640
Step-by-step explanation:
which expression is equivalent to the given expression?
2x^2-14x+24
A.) 2(x-5)(x-2)
B.) 2(x-3)(x+3)
C.) 2(x-3)(x-4)
D.) (2x-12)(x-2)
Answer:
C.) 2(x-3)(x-4)
Step-by-step explanation:
I think so
What is the scale factor for the dilation below?
See picture for full problem. Please and thank you so very much!!!!
Answer:
The answer is 5
Step-by-step explanation:
Divide the original x-axis value by the x-axis value after dilation. So, point G' has an x-axis value of 2, and point G has an x-axis value of 10. If you divide 10/2, you get 5.
8.2, 5.1, 9.4, 9.2, 2.2, 4.9, 4.8, 3.3, 3.9state the median
Answer: Median=4.9
Step-by-step explanation:
If f(x)=3x²-4 and g(x) = x+2, find (f - g)(x).
Answer:
D. 3x² - x - 6
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = 3x² - 4 - (x + 2)(f - g)(x) = 3x² - x - 6Four friends are playing the board game Hidden Treasure. The game begins with 40 coins
divided evenly among the four players. Each player keeps 2 of their coins on the table and
keeps the rest of the coins inside their bag.
Let b equal the number of coins in each bag.
Which equation represents the total number
of coins the four players have?
4(b+2)=40
4b=40
b+2=49
4b+2=40
Answer:
I hope this helps 40 divided by 4 is 10 10 per person 10-2=8 8 coins in each players bag and the total amount of coins in bags is 8 times 4 which is 32
Lamar is cutting a piece of 15 foot rope into 1 and 1/3 foot long
sections. How many sections of rope will he end up with?
A: 11
B: 11 and 1/4
C: 8 and 1/3
D: 4 and 1/4
Answer:
B:11 and 1/4
Step-by-step explanation:
to divide 15 by 1 1/3 i used the Keep, Change, Flip method aka-KCF
i kept 15 over 1 changed the division sign into a multiplication sign and flipped 1 1/3 which is 4/3 to its reciprocal 3/4.
which got me the answer 45/4 i simplified it into 11 and 1/4
How do I do this????
Answer:
your answer will be 10 and that rounded to the nearest hundredth is 100.
Step-by-step explanation:
i really hope this is right
Need help please answer ASAP!
Let's see
3x²-9x3x(x-3)3x is one factor
Other one is x-3#2
Mass of 1000 protons
1000×Mass of one proton1.67×10^{-24}×10³1.67×10^{-21}gAnswer:
22. (3) x - 3
23. (4) [tex]1.67 \times 10^{-21}\: \sf g[/tex]
Step-by-step explanation:
Question 22Given expression:
[tex]3x^2-9x[/tex]
Factor out common term [tex]3x[/tex]:
[tex]\implies 3x \cdot x - 3 \cdot 3x[/tex]
[tex]\implies 3x(x-3)[/tex]
Therefore, the two factors are [tex]3x[/tex] and [tex]x-3[/tex]
Question 23[tex]\textsf{Mass of 1 proton}=1.67 \times 10^{-24}\: \sf g[/tex]
[tex]1000=10 \times 10 \times 10=10^3[/tex]
[tex]\begin{aligned}\implies \textsf{Mass of 1000 protons} & = \textsf{mass of 1 proton} \times 1000\\& =(1.67 \times 10^{-24}) \times 1000\\& =1.67 \times 10^{-24}\times 10^3\\ & =1.67 \times 10^{-24+3}\\ & = 1.67 \times 10^{-21}\: \sf g\end{aligned}[/tex]
Shirley has a collection of 50 stamps and adds 4 stamps daily to her collection. model this situation as a function of number of days (d).
Which expression represents the volume, in cubic units, of empty space in the cube? four-thirdsπ(4.53) – (4.5)3 (9)3 – four-thirdsπ(4.52) four-thirdsπ(4.53) – (9)3 (9)3 – four-thirdsπ(4.53)
The expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³
How to determine the volume of the empty space?The cube box has a side length of 9.
So, the volume of the box is:
V = 9³
The sphere has a radius of 4.5.
So, the volume of the sphere is:
v = 4/3π(4.5)³
Calculate the difference between both volumes:
d = 9³ - 4/3π(4.5)³
Hence, the expression that represents the volume of the empty space is 9³ - 4/3π(4.5)³
Read more about volumes at:
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Answer: that is answer d
Step-by-step explanation:
2023 edge