Answer:
B
Step-by-step explanation:
the total number of adult/ children tickets sold was 95 , then
a + c = 95
the ticket sales totalled $1380 , then
9a + 16c = 1380
the system of equations is
a + c = 95 , 9a + 16c = 1380
simplify 6^5 * 2^3 * 6^4 / 12^3
^ is elevated
* multiplication
/ division
The simplified form of the expression is 6⁶
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6^5 * 2^3 * 6^4 / 12^3
That is,
6⁵ × 2³ × 6⁴ / 12³
Simplifying
6⁵ × 2³ × 6⁴ / 12³
6⁵ × 6⁴ × 2³ / 12³
Applying the exponents rule
6⁵ ⁺ ⁴ × 2³ / 12³
6⁹ × 2³ / 12³
Expanding 12³, we get
6⁹ × 2³ / 6³ × 2³
= 6⁹ / 6³
= 6⁹ ⁻ ³
= 6⁶
Hence, the simplified form of the expression is 6⁶
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Question 4 of 10
If you subtract 13 from an even number, the answer will be odd.
A. True
OB. False
SUBM
Solve each equation. Check your answers.
2 log (x+1)=5
2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: 2 log (x + 1) = 5
=> log (x + 1) = [tex]\frac{5}{2}[/tex]
Raising both sides by 10, in order to remove the logarithm:
=> [tex]10^{log_{10}(x+1)} = 10^{2.5}[/tex]
=> x + 1 = 316.22 ( as [tex]a^{log_a(x)} = x[/tex])
=> x = 315.22
Hence, 2 log (x + 1) = 5 => x = 315.22, by properties of logarithm.
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a root of the equation 3x-8=13
Answer:
x= 7
Step-by-step explanation:
3x= 13+8
3x= 21
x= 21/3
x= 7
Find the midpoint M of the line segment joining the points S= (-5, 1) and T = (3, -3).
M=
Answer:
The answer is (−1,−1)
Step-by-step explanation:
Hope this helps!
Sorry If I'm wrong
Suppose
f
(
x
)
=
−
2
x
2
+
6
x
+
4
. Compute the following:
f
(
−
4
)
=
f
(
3
)
=
we get f(-4)= -52 and f(3)=4
suppose f(x)= -2x^2+6x+4
we have to compute f( -4) and f(3)
The value of f(-4) is found by substituting -4 into the equation per variable, solving and simplifying as needed, to get the answer.
f(x)= -2x^2+6x+4
we have to compute f( -4)
then f( -4)= -2(-4)^2+6(-4) +4
= -32-24+4
= -52
similarly ,The value of f(3) is found by substituting 3 into the equation per variable, solving and simplifying as needed, to get the answer.
f(x)= -2x^2+6x+4
we have to compute f( 3)
then f( 3)= -2(3)^2+6(3) +4
= -18+18+4
=4
Hence we get f(-4)= -52 and f(3)=4
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According to the box-and-whisker plot shown above, identify the following:
5) The 25th quartile
6) The 75th quartile
7) The range
According to the box-and-whisker plot,
5)The 25th quartile = 60
6)The 75th quartile = 100
7)The range = 40
Box-and-whisker plot allows us to determine the mean, the largest or the lowest number in the data set as well as the quartiles in the data.
In this case, from the given figure,
Median is equal to = 80,
The range is equal to = 110-40
We can subtract the value,
So we can write,
The range is equal to = 70.
The 25th quartile is equal to = 60
The 75th quartile is equal to = 100.
The range is equal to = 100-60
We can subtract the value,
So we can write,
The range is equal to = 40.
So,
Then,
The median=80
The range=70
Therefore,
According to the box-and-whisker plot,
5)The 25th quartile = 60
6)The 75th quartile = 100
7)The range = 40.
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Question 2: Write each of the following in index form
(a) √√
(b) √y
(c) √
Va
(d) √ (e) x (1) c
The area of a rectangle is 108.35 in² and the length is 7.8 in. Find the width.
A) 6.95 in.
B) 13.89 in.
C) 27.78 in.
D) 21.44 in.
Answer: 13.89 in ==> B
Step-by-step explanation:
A=area of rectangle, l=length, w=width
A=l*w
108.35=7.8*w
108.35/7.8=7.8w/7.8
w=108.35/7.8
w=13.891 ==> w=13.89 in==> B
what is the range of the data set: 7, 12, 15, 4, 23, 15, 25, 9
Answer: 21
Step-by-step explanation:
When it comes to finding the range, you must take the biggest number and subtract it from the smaller number, therefore in your question the answer is
25 - 4 = 21
Hope it helped :D
If f(x) = 3x + 2 and g(x) = xsquared − x, find the value. f(x) + 1
The value of the function f(x) + 1 is 3x + 3
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of the function?The functions are given as
f(x) = 3x + 2
g(x) =x^2 - x
To calculate the value of the function f(x) + 1, we use the following definitions:
New function = f(x) + 1
Substitute f(x) = 3x + 2 in New function = f(x) + 1
So, we have
New function = 3x + 2 + 1
Evaluate the sum
So, we have
New function = 3x + 3
Rewrite as
So, we have
f(x) + 1 = 3x + 3
Hence, the value of the function f(x) + 1 is 3x + 3
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Simplify each number. 81¹/₄
[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 81 = 3 x 3 x 3 x 3 = [tex]3^{4}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
According to the given condition,
∴ [tex]81^{\frac{1}{4} }[/tex] = [tex](3^{4} )^{\frac{1}{4} }[/tex]
Applying the law of indices mentioned above,
[tex](3^{m})^{n} = 3^{4 X\frac{1}{4} }[/tex]
= 3.
Thus, the
[tex]81^{\frac{1}{4} }[/tex] can be simplified into 3.
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(5/2-3/4)-1/4(1-x)=1/2
Answer:
Step-by-step explanation:
[tex](\frac{5}{2} -\frac{3}{4} )-\frac{1}{4} (1-x)=\frac{1}{2}[/tex]
[tex](\frac{10}{4} -\frac{3}{4}) -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]
[tex]\frac{7}{4} -\frac{1}{4} -\frac{1}{4} x=\frac{1}{2}[/tex]
[tex]\frac{6}{4} -\frac{1}{4}x=\frac{1}{2}[/tex]
[tex]1=\frac{1}{4} x[/tex]
[tex]4=x[/tex]
[tex]x=4[/tex]
Hope this helped! Have a great day!
what is the general process for solving an equation with one variable
Answer:
Typically when solving an equation with one variable, your objective is to isolate the variable on one side of the equation. This can be done adding/subtracting number to cancel them out on one side. You can also multiply/divide coefficients in order to isolate a variable.
Example:
Add -4 to both sides to isolate the variable.
Simplify.
Divide both sides by 2 to isolate the variable on one side.
Step-by-step explanation:
Solve this equation. Enter your ans
-4(x-26) = -200
Three times a number, increased by one, is between negative eight and thirteen. Find all the numbers.
Answer:
l speak frenchjwhehdgdhehdhs
5. The function m(x) = |x - 79| represents the absolute deviation (in inches) of a
man's height x (in inches) from the average height of men on a college basketball
team. The function w(x) = |x - 72 represents the absolute deviation (in inches)
of a woman's height x (in inches) from the average height of women on a college
basketball team. Compare the absolute deviations for a man and a woman who are
both 76 inches tall.
Step-by-step explanation:
Reread the underlined sentence on page 4.
What does the figurative language in this
sentence suggest about the narrator?
He feels that people should have used better tools
to help them detect advanced life forms on other
planets.
He sympathizes with people for not apprehending
that there was advanced life on other planets.
He is unable to believe that there could be any
form of life more advanced than humans.
He blames people's exaggerated idea of their
superiority for their failure to imagine life more
advanced than themselves.
Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₃ 8
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 8}{log \\3}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
[tex]log_38[/tex]
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
[tex]log_38[/tex] = [tex]\frac{log \ 8}{log \ 3}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 8}{log \\3}[/tex]
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Juan and his children went into a restaurant where they sell drinks for $2 each and
tacos for $4 each. Juan has $40 to spend and must buy a minimum of 11 drinks and
tacos altogether. If a represents the number of drinks purchased and y represents
the number of tacos purchased, write and solve a system of inequalities graphically
and determine one possible solution.
The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
How to generate Inequality Graph?We are given that;
a represents the number of drinks purchased.
y represents the number of tacos purchased
He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;
2a + 4y ≤ 40
a + y ≥ 11
The inequality graph that represent the given system of inequalities is as shown in the atatched file.
From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)
Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
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A health food company packs almond butter in jars. some jars hold 250 kg. other jars hold 500g. on tuesday, the company packed 186.5 kg of almond butter in 511 jards. how many jars of each size did they pack
In linear equation, there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Let the number of 250g=0.25 kg jars be x and that of 500g=0.5 kg jams be y;
therefore:
total number of jars was
x+y=511
x=511-y..........i
total amount kg was:
0.25x+0.5y=186.5....ii
substituting i in ii
0.25(511-y)+0.5y=186.5
127.75-0.25y+0.5y=186.5
solving for y we get:
0.25y=186.5-127.75
0.25y=58.75
y=58.75/0.25
y=235 jars
and
x=511-x
=511-235
=276
hence , there was 235 jars with 0.5 kg almond and 276 jars with 0.25 kg almonds.
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need help with question in pic
Answer:
x = 2 + [tex]\sqrt{3}[/tex] i
x = 2 - [tex]\sqrt{3}[/tex] i
Step-by-step explanation:
3(2x-2)=6(x-1)
How do you do this
[tex]\large\bf\implies{infinitely \:many\: solutions}[/tex]
Alternate forms :
[tex] \large \bf \implies{x \in ( - \infty \: , \infty)}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow{3(2x - 2) = 6(x - 1)}[/tex]
Apply the Distributive Property[tex] \bf \longrightarrow{6x - 6 = 6x - 6}[/tex]
Rearrange variables to the left side of the equation[tex] \bf \longrightarrow{6x - 6x = - 6 + 6}[/tex]
Apply the inverse property of addition[tex] \bf \longrightarrow{0 = 0}[/tex]
Bases on the given conditions, the (system of) equation(s) has[tex]\bf \longrightarrow{infinitely \:many\: solutions}[/tex]
Given the product (x+8) (x+3) do the following.
(a) Show that this product is equivalent to x² +11x + 24 by using any acceptable method.
(b) Test the equivalency by using x= 1. Show the intermediate calculations.
The product or multiplication of the polynomials is given as
x² +11x + 24.
A result or product is produced by multiplication or a statement that lists the factors to be multiplied.
The commutative law of multiplication states that the product is independent of the sequence in which real or complex numbers are multiplied.The order of the factors often determines the outcome of multiplying matrices or the constituents of other associative algebras.For instance, multiplication in general and in matrices are non-commutative operations in other algebras.Additionally, two complex numbers can be multiplied to get a complex number. When we multiply two integers, we always get back an integer.Given (x+8) (x+3)
let us find the product :
= x² + 8x + 3x + 24
= x² +11x + 24
Let us now test the equivalency .
(x+8) (x+3) = (1+8)(1+3) = (9)(4) = 36
x² +11x + 24 = (1)² + 11(1) + 24 = 36
Hence we can see that the product is same in both the cases.
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Earth is approximately 5 x 109 years old. For which of these ages could this be an approximation?
A 4,762,100,000 years
B 48,000,000,000 years
4.45 x 10⁹ years
4.249999999 × 10⁹ years
Answer:
The answer is around 50,000,000,000 years so its E
Step-by-step explanation:
( 4, -3 ) ( 8 , -3 ) slope
Can someone help me with this one
Answer:
#9 has 8 vertices
# 10 has 5 vertices
Step-by-step explanation:
A vertex is is a point where two or more curves, lines, or edges meet. The word "vertices" is the plural of the word "vertex."
A baker needs to make eight batches of cookies for a party. If each batch requires 2 2/4 cups of flour, how many cups will he need?
Answer:
20
Step-by-step explanation:
8x2=16 and 2/4 times 8 is 4 so 20
How do you model a situation in which a function behaves differently over different parts of its domain?
Enter your answer.
The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable
Such a situation can be explained through an example:
f(x) = { x, for x > 0
{ 1, for x = 0
{ -x, for x < 0
now, when we take x value less than 0, say x= -1
thus, f(x)= f(-1)= -(-1) = 1 , here we used f(x) given x<0
now, when we take x value more than 0, say x= 1
thus, f(x)= f(1)= (1) = 1, here we used f(x) given x>0
now, when we take x = 0,
thus, f(x)= f(0)= 1, here we used f(x) given x=0
this is how we model piecewise function, we use f(x) as per the value of x. Following image shows plotted answer for this example.
Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we pointed a point at (0,1)
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Write each logarithmic expression as a single logarithm. log₂4+3 log₂9
The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).
What are the logarithmic expression?A logarithmic equation is one that includes a logarithm in the variable x.
An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿNow, as per the stated condition in question;
The expressed equation is;
= log₂4+3 log₂9
Using the Power Rule in the second term.
= log₂4+log₂9³
= log₂4+log₂729
As, the base of each log term is 2. We can use product rule to simplify the equation.
= log₂(4×729)
= log₂ (2916) [As a single log function]
Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).
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Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 4),
radius 3
Answer:
(x +3)² +(y -4)² = 9
Step-by-step explanation:
You want the equation of a circle with center (-3, 4) and radius 3.
Circle equationThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
ApplicationYou have a circle with center (h, k) = (-3, 4) and radius r = 3. Using these values in the above equation, we find the circle equation to be ...
(x -(-3))² +(y -4)² = 3²
(x +3)² +(y -4)² = 9