The solution is x = 6
Step-by-step explanation:
Let us revise some rules of the exponents
If [tex]a^{n}=a^{m}[/tex] , then n = m[tex](a^{n})^{m}=a^{nm}[/tex]∵ [tex]9^{(x+15)}=3^{7x}[/tex]
∵ 9 = 3 × 3
∴ 9 = 3²
- Substitute 9 by 3² in the equation above
∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]
- Use the second rule above for the left hand side
∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]
∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]
∴ [tex]3^{2x+30}=3^{7x}[/tex]
- By using the first rule above
∴ 2x + 30 = 7x
- Subtract 2x from both sides
∴ 30 = 5x
- Divide both sides by 5
∴ 6 = x
The solution is x = 6
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What is the answer ?
Answer:
353
Step-by-step explanation:
355-42=x-40
I just need to subtract 2 from 355 to get x because I subtracted 2 from 42 to get 40.
355-2=353=x
What is the simplified form of the fraction below 6/24
1/4 is the simplified fraction for 6/24.
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
you can divide the numerator and denominator of [tex]\frac{6}{24}[/tex] by 6, resulting in [tex]\frac{1}{4}[/tex]
24.5 written in scientific notation
Answer:24.5
=
2.45
×
10
=
2.45
×
10
1
⇒
24.5
×
10
−
5
=
2.45
×
10
1
×
10
−
5
=
2.45
×
10
−
4
Step-by-step explanation:
Answer:
[tex]2.45*10^1[/tex]
Step-by-step explanation:
You move the decimal point of a number until the new form is a number from 1 up to 10 (N), and then record the exponent (a) as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.
what is the inverse of f(x)=2x^3
Answer:
f^-1 (x)=(x/2)^(1/3)
Step-by-step explanation:
y=2x^3
x=2y^3
2y^3=x
y^3=x/2
y=(x/2)^(1/3)
The mean of 20 observations is 50. If the observation 50 is replaced by 140, what will be the resulting mean?
Answer:
24.5
Step-by-step explanation:
20 + 140-50/20
= 20 + 4.5
=24.5
on average a person blink 16 times per minute how many times does a person blink in one day. there are 1,440 minutes in a day
Answer:
16 times 1440= 23040 blinks a day
Step-by-step explanation:
So umm... 16 blinks a minute so for every minute is 16 blinks so just multiply the 1440 minutes so yeah..
The quadrilateral shown is a rhombus. If AB = 17 and AE = 8, what is the measure of BE
Answer:
[tex]BE=15\ units[/tex]
Step-by-step explanation:
we know that
In a rhombus the diagonals are perpendicular
so
The triangle ABE is a right triangle
see the attached figure to better understand the problem
Applying the Pythagoras Theorem to the right triangle ABE
[tex]AB^2=AE^2+BE^2[/tex]
where
AB is the hypotenuse of the right triangle (greater side)
AE and BE are the legs of the right triangle
we have
[tex]AB=17\ units\\AE=8\ units[/tex]
substitute
[tex]17^2=8^2+BE^2[/tex]
solve for BE
[tex]289=64+BE^2[/tex]
[tex]BE^2=289-64[/tex]
[tex]BE^2=225[/tex]
[tex]BE=15\ units[/tex]
Answer:
C) 16
Step-by-step explanation:
Line has the equation y=2x+2. Write the equation of the image of after a dilation with a scale factor of 4, centered at the origin.
Write your answer in slope-intercept form.
Final Answer:
The equation of the image after a dilation with a scale factor of 4, centered at the origin, is y = 8x + 8.
Explanation:
When a function undergoes dilation centered at the origin, each coordinate (x, y) is transformed to (kx, ky), where k is the scale factor. In this case, the original equation y = 2x + 2 is dilated by a factor of 4. Therefore, the new equation becomes y' = 4(2x + 2), which simplifies to y' = 8x + 8. The scale factor of 4 multiplies both the coefficient of x and the y-intercept, resulting in a steeper slope and a vertical shift.
In the original equation, the coefficient of x was 2, indicating a slope of 2. After the dilation, the coefficient becomes 8, indicating a steeper slope of 8. Additionally, the y-intercept of 2 is multiplied by 4, yielding a new y-intercept of 8. This transformation preserves the line's direction while magnifying its steepness and shifting it vertically. The equation y' = 8x + 8 represents the dilated image of the original line.
To summarize, the process involves multiplying both the coefficient of x and the y-intercept by the scale factor. This scaling maintains the line's direction while adjusting its steepness and vertical position. The resulting equation, y' = 8x + 8, accurately describes the image of the original line after dilation by a factor of 4 centered at the origin.
If I have a shirt that's 15 dollars how do I take 20% off the price
Well, first find out what 20% of $15 is.
20% x $15 = $3
Take that from the original price.
$15-$3=$12
Hello, i need help!
5/2 multiplied by what equals 1?
equation: 5/2×?=1
Answer:
[tex]\large\boxed{\dfrac{2}{5}}[/tex]
Step-by-step explanation:
[tex]\text{The product of the number and its reciprocal gives us 1.}\\\text{Reciprocal of }\ \dfrac{5}{2}\ \text{is equal}\ \dfrac{2}{5}.\\\\\dfrac{5}{2}\times\dfrac{2}{5}=\dfrac{5\!\!\!\!\diagup}{2\!\!\!\!\diagup}\times\dfrac{2\!\!\!\!\diagup}{5\!\!\!\!\diagup}=\dfrac{1}{1}\times\dfrac{1}{1}=1\times1=1[/tex]
Kayla receives a bill for $754 for a new sofa. The bill includes a 6.2% tax on the sofa selling price and a $26 delivery fee. To the nearest cent, what was the selling price of the sofa?
Answer:
685.50
Step-by-step explanation:
754 - 26 = 728
728 / 1.062 = 685. 50
Answer: $685.50
Step-by-step explanation:
1.062x+26=754
1.062x=728
x=685.499
to nearest cent $685.50
twinlakes on the shelf of a covenience store lose their fresh tastines over time. we say that the taste quality is 1 when the twinkies are first put on the shelf at the store, and that the quality of tastiness declined according to the function Q(t)=0.85^t. Graph this function on a graphing calculator, and determine when the taste will be half of its original value?
Answer:
The graph is shown below.
The time to make the taste to half is 4.265 s.
Step-by-step explanation:
Given:
Initial value of the taste is, [tex]Q_0=1[/tex]
Therefore, the quality of taste over time 't' is given as:
[tex]Q(t)=Q_0(0.85)^t\\Q(t)=1(0.85)^t[/tex]
Now, when the taste reduces to half, [tex]Q=0.5[/tex]
Therefore,
[tex]0.5=1(0.85)^t[/tex]
Taking natural log on both the sides, we get:
[tex]\ln(0.5)=\ln(0.85)^t\\\ln(0.5)=t\ln(0.85)\\t=\frac{ln(0.5)}{\ln(0.85)}=4.265\ s[/tex]
Therefore, the time to make the taste to half is 4.265 s.
is (1 2) a solution of 6x-y>3
Answer:This can be checked by the following steps;
Step-by-step explanation:
The pair (1,2) is a solution to the inequality 6x - y > 3 because when these values are substituted into the inequality, the result is 4 > 3, which is a true statement.
Explanation:The question is asking if the pair of numbers (1,2) is a solution to the inequality 6x - y > 3. We can evaluate this by substituting the pair of values (1, 2) into the inequality in place of x and y. This gives us 6*1 - 2 > 3, or 6 - 2 > 3, which simplifies to 4 > 3. Since 4 is indeed greater than 3, we can conclude that the pair (1,2) is a solution to the inequality 6x - y > 3.
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Students were surveyed about their wither break plans.Of the people that stated they were going skiing, 25% did not actually go.How many students actually went skiing?
Answer:
The total number of students actually went for skiing is 0.75 times the total students .
Step-by-step explanation:
Given as :
Some Students were surveyed about their wither break plans.
The percentage of students who actually did not go for skiing = 25 %
So , The percentage of students who actually go for skiing = 100 % of students - 25 %
I.e The percentage of students who actually go for skiing = 75 %
Let The total number of students = x
So, out of x students , The The percentage of students who actually go for skiing = 75 % of the total students
I.e The The percentage of students who actually go for skiing = 75 % of x
Or, The The percentage of students who actually go for skiing = 0.75 × x
So, The number of students for skiing = 0.75 x
Hence The total number of students actually went for skiing is 0.75 times the total students . Answer
3(x-4)=12 solve for x
Step-by-step explanation:
Step 1: Distribute the 3 to (x-4)
⇒ 3(x)-3(4) = 12
Step 2: Calculate the left side!!
⇒ 3x-12= 12
Step 3: Add 12 to both sides!
⇒ 3x= 24
Step 4: Divide 3 by both sides!
⇒ 3x/3= 24/3
Step 5: YOUR ANSWER!!
⇒ 8
ANSWER: 8
WRITE THE TERM,FILL IN THE BLANK
When we rewrite an expression so that it has no grouping symbols and all of the like terms have been combined, we ___ it.
Example: The process of turning (5x - 6) + 10x into 15x - 6.
The answer you’re looking for is: simplify.
When you rewrite an expression, we are simplifying it. We first use the distributive property through any groupings symbols, then evaluate terms we exponent that are given. Lastly, we combine any like terms, weather they are constants or variables.
Hope this helps! :)
Answer:
It is simplify. It is what you do when like terms are combined in order to get your answer.
Hope this helps!
Which of the following represents a geometric series
2+6+18
2,6,10
2+6+10+
2,6,18
good morning,
Answer:
2,6,18
Step-by-step explanation:
6/2=3 and 18/6=3 then 2,6,18 represent a geometric series.
6/2=3 and 10/6≠3 then 2,6,10 doesn’t represent a Géométric series.
:)
So how am I supposed to get my.anwsers
You can look them up on here or other apps/websites.
last year, Mr. Petersen's rectangular garden had a width of 5 meters and an area of 20 square meters.
This year, he wants to make the garden three times as long and two times as wide.
a
Solve for the length of last year's garden using the area formula. Then, draw and label the
measurements of this year's garden
Last Year
This Year
20
square
meters
Answer:
Last year: length of 4 meters
This year: width of 10 meters and a length of 12 meters
Step-by-step explanation:
A crane is lowering a concrete block from a height of 270 feet above the ground at a constant rate of 2.5 feet per second. Which function can be used to determine h, the height , in feet above the ground of the concrete block after “s” seconds ?
The function would be h = 270 - 2.5s, where h is the height (in feet) and s it the time (in seconds) that has passed.
The 270 represents the initial value, which is given. We are told that the initial height of the block is 270 feet.
2.5s represents the feet that it has descended. We know the block is lowered at a rate of 2.5 feet per second. Multiplying this by s, the time, will give us how much it has descended.
The height at any point is can be given by function f(s) = 270 - 2.5s.
Given to us,
concrete block top height, H = 270 feet,
speed of the block, v = 2.5 feet/second,
We know that [tex]\rm \bold{speed = \dfrac{Distance}{Time} }[/tex],
thus, [tex]\rm \bold{Distance = speed\times Time}[/tex]
So, we can write, height (distance from the top height) covered is "s" seconds as,
[tex]\bold{h = v \times s}=\bold{2.5\times s} = \rm \bold{2.5s}[/tex]
therefore, we can write,
Height at any point = Top height - height covered
= 270 - 2.5s
Hence, the height at any point is can be given by function f(s) = 270 - 2.5s.
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urgent, please help, I really appreciate (100 points)
Which sequence isn't a geometric
progression?
Answer:
3, 6, 9, 12 is not geometric
Step-by-step explanation:
A geometric progression has a common ratio r between consecutive terms.
3, 6, 9 , 12
has a common difference of 3 between terms and is arithmetic
1, 5, 25, 125
r = 5 ÷ 1 = 25 ÷ 5 = 125 ÷ 25 = 5 ← geometric
4, 8, 16, 32
r = 8 ÷ 4 = 16 ÷ 8 = 32 ÷ 16 = 2 ← geometric
2, 6, 18, 54
r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 ← geometric
Answer:
3, 6, 9, 12 would not be a geometric sequence.
Step-by-step explanation:
The reason for this is because, geometric sequence is multiplication or division while arithmetic is addition and subtraction.
1, 5, 25, 125 is multiplication. x5
4, 8, 16, 32 is multiplication as well. x2
2, 6, 18, 54 is multiplication as well. x3
While 3, 6, 9, 12 would be +3.
Therefore, 3,6, 9, 12 would not be a geometric sequence.
if an airplane consumes 30.25 gallons of fuel in 2.8 hours of flying how many gallons will it consume and 4.3 hours of flying?
Answer:
46.46 gallons
Step-by-step explanation:
we know that
An airplane consumes 30.25 gallons of fuel in 2.8 hours of flying
so
using proportion
Find out how many gallons will it consume in 4.3 hours of flying
[tex]\frac{30.25}{2.8}\ \frac{gal}{h}=\frac{x}{4.3}\ \frac{gal}{h}\\\\x=30.25*(4.3)/2.8\\\\x= 46.46\ gal[/tex]
Which of the following equations is equivalent to y + 3 = -4(x - 2)?
Answer:
D. y= -4x +5
Step-by-step explanation:
The equation [tex]y+3=-4(x-2)[/tex] can be transformed by doing some algebra.If we solve the second term of the equation -4(x-2)= 8 - 4x, then we have [tex]y+3=8-4x[/tex] (this is done by distributing the multiplication into the two terms: remember that the product of -4x(-2)=+8 because the product of two negative numbers is a possitive number).Then, by subtracting both sides 3, we have [tex]y=5-4x[/tex]. Rearranging terms in the right side, we have [tex]y=-4x+5[/tex], which is option D.To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form.
Explanation:To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form. Here are the steps:
Distribute -4 to (x - 2): y + 3 = -4x + 8Move y to the right side: -4x + y + 3 = 8Combine like terms: -4x + y = 5Therefore, the equation that is equivalent to y + 3 = -4(x - 2) is -4x + y = 5.
Plato Question!!!!
Type the correct answer in each box.
What is a polar form of (-1, √3 ) is ( _ , _ ) ?
Answer:
(2, 120° )
Step-by-step explanation:
To convert from rectangular to polar form, that is
(x, y) → (r, Θ ), use
r = [tex]\sqrt{x^2+y^2}[/tex]
Θ = [tex]tan^{-1}[/tex]( [tex]\frac{y}{x}[/tex])
here (x, y ) = (- 1, [tex]\sqrt{3}[/tex])
r = [tex]\sqrt{(-1)^2+(\sqrt{3} }[/tex] )^2
= [tex]\sqrt{1+3}[/tex] = [tex]\sqrt{4}[/tex] = 2
Θ = [tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]) = 60° ← related acute angle
Note (- 1, [tex]\sqrt{3}[/tex]) is in the second quadrant so Θ must be in the second quadrant.
Θ = 180° - 60° = 120°
(- 1, [tex]\sqrt{3}[/tex]) → (2, 120°)
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
The polar form of a Cartesian coordinates is given by (r, @) where r = √x^2 + y^2
@ = tan^-1 y/x
r = √-1^2 + √3^2
r = √4
r= 2
@ = tan ^-1 √3/-1 -tan √3/1 = -60°
@ = 180-60 = 120°
solve the systems of equations by subsiturion
y=x+15
y=2x
next question
y=x+12
4x+2y=27
Answer:
1) x = 15, y = 30 is the solution of the given system of equation.
2) x = 0.5 , y = 12.5 is the solution of the given system of equation.
Step-by-step explanation:
First QUESTION:
Here the given set if equation are:
y = x + 15
y = 2 x
Substituting the value of y = 2 x in the first equation, we get:
y = x + 15 ⇒ 2 x = x + 15
or, 2 x - x = 15
⇒ x = 15
⇒ y = 2 x = 2 ( 15) = 30, or y = 30
Hence, x = 15, y = 30 is the SOLUTION of the given system of equation.
Second QUESTION:
Here the given set if equation are:
y = x +12
4 x + 2 y = 27
Substituting the value of y = x + 12 in the second equation, we get:
4 x + 2 y = 27 ⇒ 4 x + 2 (x + 12) = 27
or, 4 x + 2(x) + 2 (12) = 27
⇒ 6 x = 27 - 24 = 3
⇒ x = 3 /6 = 0.5
Now, y = x + 12 = 0.5 + 12 = 12.5 or y = 12.5
Hence, x = 0.5 , y = 12.5 is the SOLUTION of the given system of equation.
Mathematical
PRACTICE 5 Use Math Tools Sarah buys a pen that costs
$0.75. How much will 2 pens cost?
Answer: 1.5
Step-by-step explanation:
0.72 • 2 = 1.5
Answer:1.50
Step-by-step explanation: 75•2 = 1.50
Use the expression to complete the table.
**Look above for the picture.
Answers:
110
95
80
65
75
Yay
please help asap im stuck
Answer: 65%
Step-by-step explanation:
2258 glove-784 remaining = 1474 gloves used
now create part to whole relationship
1474 gloves used/2258 total gloves = 0.65 approx or 65%
Tristan took a math quiz last week. He got 26 out of 52 problems correct. What percentage did Tristan get correct? Write your answer using a percent sign (%).
Answer:
50%
Step-by-step explanation:
To find the percentage of his correct answers, divide the amount of correct answers he got by the total number of problems.
26 out of 52 is another way to say
26/52
= 26 ÷ 52
= 0.50
0.5 is the decimal form of the answers Tristan got correct.
To convert it to a percentage, more the decimal two places to the right.
0.50 => 50%
Tristan got 50% of the problems correct.
Which of the following could be the first step in solving this problem? 9(12-3)+4
The first step in solving the expression 9(12-3)+4 is to perform the operation within the parentheses, subtracting 3 from 12. This operation adheres to the Order of Operations (PEMDAS) and simplifies the expression for further steps.
Explanation:The first step in solving the problem 9(12-3)+4 involves using the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, according to PEMDAS, we start with the operation within the parentheses. So, we subtract 3 from 12, resulting in 9 times 9, plus 4. The operation within the parentheses simplifies the problem and sets the stage for the subsequent multiplication and addition.
After simplifying the operation within the parentheses, we multiply the result by 9 and then add 4 to get the final answer. This step-by-step approach helps in solving the problem accurately.
Step One: Identify the unknown in the problem. In this case, the unknown is the result of the expression 9(12-3)+4.
Step Two: The first step in solving this problem is to simplify the expression inside the parentheses using the order of operations (PEMDAS/BODMAS).
Step Three: Perform the operations within the parentheses first, then multiply the result by 9 and finally add 4. This will give you the solution to the given expression.