[tex]\bf 3^2\cdot 3^3\implies 3^{2+3}\implies 3^5\implies 243[/tex]
Final answer:
To simplify 3 to the 2nd power times 3 to the third power, we add the exponents because the base is the same, resulting in 3 to the 5th power, which equals 243.
Explanation:
To simplify 3 to the 2nd power times 3 to the third power, we need to apply the rule of multiplying exponential terms with the same base. When multiplying terms like 32 and 33, we simply add the exponents together because the base (the number 3 in this case) remains the same. So this simplification process looks like:
32 × 33 = 3(2+3) = 35
The next step is to calculate the value of 3 raised to the 5th power:
35 = 3 × 3 × 3 × 3 × 3 = 243
Therefore, the simplified expression is 243.
Simplify this equation
Answer:
4/9 * -2/3= -8/27 is the solution
brandy is 4 years younger than twice amy’s age. if brandy is 18, how old is amy?
Answer:
Step-by-step explanation: 18x2+4=30
Answer:
amy is 11.
Step-by-step explanation:
in the problem it explains that brandy is 4 years younger than twice amys age. if we say that amy is 11 then we can verify the answer because 11*2 is 22-4 is 18.
hope this helps- cam:)
What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)?
Answer:
49
Step-by-step explanation:
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros.
Find the zeros by letting f(x) = 0, that is
- (x - 3)(x + 11) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 11 = 0 ⇒ x = - 11, thus
[tex]x_{vertex}[/tex] = [tex]\frac{-11+3}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for y- value of the vertex
f(- 4) = - (- 4 - 3)(- 4 + 11) = - (- 7)(7) = 49
What is the coefficient of each monomial a.5k b.t c.-9t d.-j
Step-by-step explanation:
Look at the picture
a. 5k → 5
b. t = 1t → 1
c. -9t → -9
d. -j = -1j → -1
find the solutions to the equation below x^2-25=0
Answer:
x = 5, -5
Step-by-step explanation:
Find the roots of [tex]x^{2} -25=0[/tex] by solving for x.
Add 25 to both sides
[tex]x^{2} =25[/tex]
Square root both sides
[tex]x = 5[/tex]
[tex]x=-5[/tex]
The solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The quadratic equation:
x² - 25 = 0
As we know,
a² - b² = (a + b)(a - b)
Using the above identity:
x² - 5² = 0
(x + 5)(x - 5) = 0
x + 5 = 0
x = -5
Or
x - 5 = 0
x = 5
We can also find the solution to the equation x² - 25 = 0 using the quadratic formula.
Thus, the solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).
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The expression 9X +5 and 11 X -25 represents the measures of two angles of regular nonagon. Find the Measure of an angle of a nonagon (question 16)
Answer:
140°
Step-by-step explanation:
The interior angles of a regular nonagon are equal.
Equate the 2 given angles and solve for x
11x - 25 = 9x + 5 ( subtract 9x from both sides )
2x - 25 = 5 ( add 25 to both sides )
2x = 30 ( divide both sides by 2 )
x = 15
Substitute this value into one of the given angles
9x + 5 = (9 × 15) + 5 = 135 + 5 = 140
Thus the interior angle has a measure = 140°
The interior angle of a nonagon measure is 140°.
The given expressions are 9x+5 and 11x-25.
What is a regular nonagon?A regular nonagon is one in which all the 9 sides are of equal length and the 9 interior angles are of equal measure. On the other hand, when the sides of a nonagon are of unequal lengths and the angles are of different measures, it is called an irregular nonagon.
Now, equate the 2 given angles and solve for x.
That is, 11x - 25 = 9x + 5 ( subtract 9x from both sides )
⇒2x - 25 = 5 ( add 25 to both sides )
⇒2x = 30 ( divide both sides by 2 )
⇒x = 15
Substitute x = 15 value into one of the given angles
9x + 5 = (9 × 15) + 5 = 135 + 5 = 140
Therefore, the interior angle of a nonagon measure is 140°.
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Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y= -x + 5 y= x - 3
Answer:
The system has one solution: (4,1)
Step-by-step explanation:
We have the equations:
1) Y = -X + 5
2) Y = X - 3
Replace the "value" of Y of the 2nd eq into the 1st eq:
(X - 3) = -X + 5
Now let's leave X alone in one side of the iquality:
X + X = 5 + 3
2X = 8
X = 8/2
X = 4
Now, having the value of X, replace it into any of the aquations, let's use the 2nd:
Y = X - 3
Y = 4 -3
Y = 1
The ONE solution of this equations system is (4,1), which is the point in the xy plane where the two lines intersect.
The following equation has:
Unique solution (one solution i.e. (4,1) )
Step-by-step explanation:The system of equation is given by:
y= -x + 5-----------(1)
and y= x - 3------------(2)
Now, on substituting the value of y from equation (1) into equation (2) we have:
[tex]-x+5=x-3[/tex]
On adding x on both the sides of the equation we have:
[tex]5=x+x-3\\\\5=2x-3[/tex]
on adding 3 on both the sides of the equation we have:
[tex]2x=5+3\\\\2x=8\\\\x=\dfrac{8}{2}\\\\x=4[/tex]
Now, on putting the value of x into equation (2) we have:
[tex]y=4-3\\\\y=1[/tex]
Hence, the solution is unique (one solution )
Also, the point of intersection of the graph of two equations is solution to the system of equations.
A dog owner records the weight of her dog. She finds that from the age of 20 weeks to the age of 48 weeks, the dog’s weight can be modelled by the equation w = 0.92t−0.15 (20 ≤ t ≤ 48),
Explain why the model cannot be extended to model accurately the dog’s weight at birth
Answer:
See explanation
Step-by-step explanation:
A dog owner records the weight of her dog. She finds that from the age of 20 weeks to the age of 48 weeks, the dog’s weight can be modelled by the equation
[tex]w = 0.92t-0.15\ \ \ (20\le t\le 48)[/tex]
where
w = weight
t = number of week from 20 weeks to 48 weeks
If we want to extend this model to the dog's weight at birth, then find the dog's weigth when it was born.
At t = 0,
[tex]w=0.92\cdot 0-0.15\\ \\w=-0.15\ kg[/tex]
We get the dog's weight -0.15 kilograms at the day the dog was born. But this is impossible, because the dog's weight cannot be negative.
The model cannot predict the dog's weight at birth due to negative values and unrealistic linear growth for early development.
The equation w = 0.92t - 0.15 describes the weight of the dog as a function of time t in weeks, specifically for the age range of 20 weeks to 48 weeks. When t is set to 20 weeks, we can calculate the weight:
w = 0.92(20) - 0.15
= 18.4 - 0.15
= 18.25 kg.
However, if we try to extend this model to predict the dog's weight at birth (t = 0 weeks), we would get:
w = 0.92(0) - 0.15
= -0.15 kg.
A negative weight is nonsensical in this context, as animals cannot have negative weight. Moreover, the biological growth of a dog does not follow a linear pattern from birth to maturity. The model is designed to represent a specific growth phase after the initial rapid growth and development that occurs in the early weeks of life.
Growth models typically start with an exponential phase during early life, which cannot be accurately captured by a linear equation.
How to make 36/80 as a fraction but In the simplest form
[tex]\bf \cfrac{36}{80}\implies \cfrac{~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3\cdot 3}{2\cdot 2\cdot ~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 5}\implies \cfrac{9}{20}[/tex]
Answer:
9/20
Step-by-step explanation:
find a common factor and divide both the numerator and the denominator by that factor until there's no way to keep simplifying anymore. or use a calculator. but don't do that. you won't learn that way. im a bad teacher sorry.
At a particular restaurant, each onion ring has 40 calories and each mozzarella stick has 60 calories. A combination meal with onion rings and mozzarella sticks has a total of 14 onion rings and mozzarella sticks altogether and contains 800 calories. Write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of mozzarella sticks in the combination meal. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
Writing a system of equations is really just writing an equation for each part of the problem. The parts here being the calories, and number of items. It's not asking to solve it, so I will not unless you do want me to.
First variables, let's keep it simple. O will be onion rings and M will be mozzarella sticks.
Now, I mentioned the two parts are the calories and number of items so we'll take it one at a time. First calories.
The total calories will equal 800, so we know the answer to the equation. Now, how would we relate the variables? if you had two of each item what would the total calories be? it may be easy to figure out, but for our purposes we want to think of it as multiplying the calories of each by the number of each item, or in other words 40*O+60*M, where O and M equal 2. So for the general case we use the same thing, but we know what we want So our first equation is 40*O + 60*M = 800
The second is a bit simpler. It just wants to know the total amount of things ordered. So we are just adding O and M together. So this gets us O + M = 14, since there are 14 things together. Let me know if there's still something you don't understand though.
The system of equations is: [tex]\( x + y = 14 \)[/tex] and [tex]\( 40x + 60y = 800 \)[/tex], where \( x \) represents the number of onion rings in the combination meal and \( y \) represents the number of mozzarella sticks in the combination meal.
Let's define:
- \( x \) as the number of onion rings in the combination meal.
- \( y \) as the number of mozzarella sticks in the combination meal.
The system of equations would be:
1. [tex]\( x + y = 14 \)[/tex] (since the combination meal has a total of 14 onion rings and mozzarella sticks altogether)
2. [tex]\( 40x + 60y = 800 \)[/tex] (since each onion ring has 40 calories and each mozzarella stick has 60 calories, and together they contain 800 calories)
Solve
6(x-2)-4x=8+2x-20
Each of 6 students reported the number of movies they saw in the past year. This is what they reported:
16,9, 14, 16, 18, 15
Find the median and mean number of movies that the students saw.
If necessary, round your answers to the nearest tenth.
Mean: ? movies
Median: ? movies
Answer:
mean: 10
meidian; 9.5
Step-by-step explanation:
rasons
The mean of the movies that the students saw is, 14.67
The median of the movies that the students saw is, 15.5
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Each of 6 students reported the number of movies they saw in the past year. This is what they reported:
⇒ 16, 9, 14, 16, 18, 15
Now, The mean of the movies that the students saw is,
⇒ 16 + 9 + 14 + 16 + 18 + 15 / 6
⇒ 88 / 6
⇒ 14.67
And, We arrange the given data in ascending order,
⇒ 9, 14, 15, 16, 16, 18
Hence, The median of the movies that the students saw is,
⇒ (15 + 16) / 2
⇒ 31 / 2
⇒ 15.5
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Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a^4 and 16a^4.
Answer: [tex]48a^4[/tex]
Step-by-step explanation:
In this case we know that the legs of the given right triangle have these lenghts:
[tex]12a^4[/tex] and [tex]16a^4[/tex]
By definition, the sides of a right triangle are in the ratio [tex]3:4:5[/tex]
Since:
[tex]\frac{5}{4}=1.25[/tex]
We can multiply the lenght [tex]16a^4[/tex] by 1.25 in order to find the lenght of the hypotenuse of the right triangle:
[tex](16a^4)(1.25)=20a^4[/tex]
Since the perimeter of a triangle is the sum of the lenghts of its sides, we can write the following expression for the perimeter of the given right triangle:
[tex]12a^4+16a^4+20a^4[/tex]
Simplifying, we get:
[tex]=48a^4[/tex]
The expression in the simplest form that represents the perimeter of the right triangle with legs 12a⁴ and 16a⁴ is 48a⁴
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides can be found using pythagoras theorem.
Therefore,
The perimeter of the right triangle is the sum of the whole sides. Therefore, let's find the hyotenuse.
c² = a² + b²
c² = (12a⁴)² + (16a⁴)²
c² = 144a⁸ + 256a⁸
c² = 400a⁸
c = √400a⁸
c = 20a⁴
Therefore, the perimeter is as follows:
perimeter = 12a⁴ + 16a⁴ + 20a⁴
perimeter = 48a⁴
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Coach Smith went to the sporting goods store to get ready for tennis season. He bought 25 containers of tennis balls and 12 packs of grip tape. Sales tax is 5%. How much does Coach Smith owe?
Tennis Ball Containers, each $5.75
Packs of Grip Tape, each $2.50
A) $185.00 C) $182.44
B) $180.75 D) $173.75
Answer:
C
Step-by-step explanation:
143.75+ tax(7.1875)= 150.9375 <-- Tennis Ball Containers
30+ tax(1.5)= 31.5 <-- Packs of Grip Tape
150.9375+31.5= 182.4375
This can be rounded up to 182.44 (which is your final answer)
Use a distributive property to rewrite (4+5)6
Answer:
54
Step-by-step explanation:
First you would distribute 6 into 4 and 5. 6 times 5 is 30, and 4 times 6 is 24. the equation is now (24 + 30), which equals 54.
Find the GCF for 15az and 25az
Answer:
The GCF for 15az and 25az is marked below.
15az = 3*5*a*z
25ab - 5*5*a*b
GCF = 5a
Step-by-step explanation:
Answers above! Hoped this helped :)
Answer:
GCF=5az.
Step-by-step explanation:
First, find a number that is the largest to be multiplied by something else to get both of these numbers. 5 is the correct number. az is also applicable, so therefore 5az is correct. you can multiply 5az by 3 to get 15az or by 5 to get 25az
18. There are 8 teachers going to the science museum. If each teacher pays
$15 to get inside, how much did the teachers pay?
$
Answer:
120$ altogether
Step-by-step explanation:
There are 8 teachers and they have to pay 15 dollars so do
8×15=120
or
15+15+15+15+15+15+15+15=120
Solve for x.
logx+log3=log18
Answer:
The value of x in log x + log 3 = log 18 is 6.
Solution:
From question, given that log x + log 3 = log 18 ---- eqn 1
Let us first simplify left hand side in above equation,
We know that log m + log n = log (mn) ----- eqn 2
Adding log m and log n results in the logarithm of the product of m and n (log mn)
By using eqn 2, log x + log 3 becomes log 3x.
log x + log 3 = log 3x ---- eqn 3
By substituting eqn 3 in eqn 1, we get
log 3x = log 18
Since we have log on both sides, we can cancel log and the above equation becomes,
3x = 18
[tex]x = \frac{18}{3} = 6[/tex]
Thus the value of x in log x + log3 = log18 is 6
Answer:
the answer is 6
I even toke the test as well.
it is not 6.00001
Step-by-step explanation:
The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in your paper homework and respond to questions or statements online.
Show that AB = 2AO, where O is the origin
Good evening ,
___________________
Step-by-step explanation:
AO=[tex]\sqrt{p^{2}+q^{2} }[/tex]
AB=[tex]\sqrt{( p+2q-p)^{2} + (q+2p-q)^{2}[/tex]
=[tex]\sqrt{(2q)^{2}+(2p)^{2} }[/tex]
=[tex]\sqrt{4(q^{2}+p^{2} ) }[/tex]
=[tex]2\sqrt{p^{2}+q^{2} }[/tex]
=2AO.
:)
How many times greater is the first 5 than the second 5 in 853,539
Answer:
100 times greater is the first 5 than the second 5 in 853,539.
Step-by-step explanation:
To find : How many times greater is the first 5 than the second 5 in 853,539?
Solution :
According to place value system,
Hundred Th. Ten Th. Thousand Hundred Tens Ones
8 5 3 5 3 9
The value of first 5 in the number 853,539 is at ten thousand place
So, The value of first 5 is 50000.
The value of second 5 in the number 853,539 is at hundred place
So, The value of second 5 is 500.
The times greater is the first 5 than the second 5 in 853,539 is
[tex]\frac{50000}{500}=100[/tex]
Therefore, 100 times greater is the first 5 than the second 5 in 853,539.
Final answer:
The first 5 in the number 853,539 is 1,000 times greater than the second 5 because it is in the ten thousands place, while the second 5 is in the tens place.
Explanation:
The question asks how many times greater is the first 5 compared to the second 5 in the number 853,539. To answer this, we compare the place values of each 5. The first 5 is in the ten thousands place while the second 5 is in the tens place.
The ten thousands place is 1,000 times greater than the tens place. Therefore, the first 5 (50,000) is 1,000 times greater than the second 5 (50).
Order the numbers from least to greatest.
-4,8, -2, -6, 3
A. -2,-4,-6, 3, 8
B. 8 ,3,-2,-4,-6
c. -2, 3,-4, 6, 8
D. -6,-4,-2, 3, 8
How many centimeters are in 9.49
Answer:
949 centimeters
Step-by-step explanation:
100 centimeters = 1 meter
We have to multiply by 100 to find the values
9.49 meters = 9.49 * 100 = 949 m
Answer:
949 cm.
Step-by-step explanation:
1 m. = 100 cm.
100 × 9,49 = 949
⤻⤻
According to the Power of 10 rule, whenever you divide by 10 [⅒], you move the decimal mark to the left each time, and of course, whenever you multiply by 10, you move the decimal mark to the right each time. In this case, since you are multiplying by 100, you move the decimal mark twice to the right to get 949.
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At tryouts for the school talent show, 60% of
30 performers played a musical instrument.
How many performers played a musical instrument?
Answer:
18 performers
Step-by-step explanation:
I just multiplied 30 by 0.6 (the decimal form of 60 percent) and got 18
18 kids played a musical instrument
6 < 3x + 9 ≤ 18
please help me I will mark brainiest answer thanks
Answer:
Step-by-step explanation:
6< 3x + 9
-3x < 9-6
-3x < 3 .( -1 )
3x > 3
x > 3/3
x > 3
3x + 9 ≤ 18
3x ≤ 18-9
3x ≤ 9
x ≤ 9/3
x ≤ 3
S = {XeIR/ 3 > x ≤ 3 }
Not sure if the solution looks like this
Answer:
Step-by-step explanation:
Manuel takes a job translating English instruction manuals to Spanish. He will receive $15
per page plus $100 per month. Manuel would like to work for 3 months during the summer and make at
least $1500. Write and solve an inequality to find the minimum number of pages Manuel must translate
in order to reach his goal.
Answer:
15x+100(3) ≥ $1500
x ≥ 80 pages
Step-by-step explanation:
Let x represent the number of pages.
Manuel receives $15 per page = 15x
Plus $100 per month. Manuel would like to work for 3 months = 15x+100(3)
He wants to make at least $1500 during the summer
Thus the inequality we get is:
15x+100(3) ≥ $1500
Now solve the equation to find minimum number of pages:
15x+300 ≥ $1500
Combine the like terms:
15x ≥ 1500-300
15x ≥ $1200
Divide both sides by 15
15x ≥ $1200/15
x ≥ 80 pages
The radius of a circle is 6 yards. What is the circle's area?
Answer:
the answer is 113.1yd²
Step-by-step explanation:
Answer is provided in the image attached.
Factor the polynominal. t^2+8t
Answer:
t = 8 t = 0
Step-by-step explanation:
The factored form is t(t + 8).
Certainly! Let's factor the given polynomial t^2 + 8t step by step.
Identify Common Factors: Factor out the common factor, which is t in this case.So, the factored form of t^2 + 8t is t(t + 8).
what is the answer to -2 (6n-5) = 26? PLEASE ANSWER CORRECTLY
Answer:
n = 1.33 repeating
Step-by-step explanation:
first you distribute the -2 by everything in the parenthesis so then you get -12 + 1- = 26 the you subtract 10 from each side which leaves you with -12 = 16 then you devide -12 by both sides and you get the decimal 1.33 repeating.
a bycicle tire completes 9/10 of a revolution every 1/3 of a second. how many revolutions will the tire complete every minute?
Answer:
162 RPM
Step-by-step explanation:
Start by multiplying 9⁄10 by the Multiplicative Inverse of ⅓, which is 3:
9⁄10 ÷ ⅓ → 9⁄10 × 3 = 2 7⁄10
After this, multiply the result by sixty seconds, since there are sixty seconds in one minute:
60 × 2 7⁄10 = 162
So, it will make 162 RPM.
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what is the least common multiple of the numbers 5,25, and 15
Answer:
5
Step-by-step explanation:
Hold on I am doing it right now
Your answer is 75 hope this helps you