Answer:
17x and 3x
Step-by-step explanation:
like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
S. Mr. Watkins looks up at the top of a tree. The tree is 10 m away, and he can see the top at an
angle of 25 degrees. How tall is the tree?
The problem does not mention the height of S. Mr. Watkins, so we are just going to assume its from his feet.
So, i made this drawing to represent him and the tree, at a distance of 10 meters looking up at a 25* angle.
I marked the opposite side, adjacent side, and hypotenuse.
x is angle where you are "looking" from. I.E., from the POV of mr watkins.
sin(x) = opposite/hyp
cos(x) = adj/hyp
tan(x) = opp/adj
So, we have an unknown side which is the opposite side, represented by length x.
The side adjacent is 10 meters.
The angle from him is 25 degrees.
What deals with adjacent and opposite? Tangent.
Tan(25) = x/10
Solve for x.
10tan(25) is the height of the tree = 4.66
The height of the tree is 5 meters.
Solve. Check for extraneous solutions. 2(x-1)⁴/₁+4=36
No extraneous solution to the equation
The equation is
2[tex](x - 1)^{4/1}[/tex] + 4 = 36
We have to find the extraneous solution of the equation and for this first, we need to find the value of x.
2[tex](x - 1)^{4}[/tex] + 4 = 36
2[tex](x - 1)^{4}[/tex] = 32
[tex](x - 1)^{4}[/tex] = 16
x - 1= 2
x = 3
Now we will put the value of x in the equation.
2[tex](3 - 1)^{4}[/tex] + 4 = 36
2 [tex]2^{4}[/tex] + 4 = 36
2 × 16 + 4 = 36
32 + 4 = 36
36 = 36
Therefore we get that there is no extraneous solution to the equation, x = 3 is the solution of the equation.
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hello can someone help please
Ken and Hamid run around a track.
It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap.
Ken and Hamid start running at the same time from the start line.
How many laps will they each have run when they next meet on the start line?
Evaluate each logarithm.
log₅125
the answer to the given logarithm expression is log₃ 125 = 3
Another technique to explain exponents in mathematics is through logarithms. A base number's logarithm equals another number.
The power's inverse function is the logarithm. For instance, log10 100 = 2 if 102 = 100. A power to which a number must be increased in order to achieve another value is referred to as a logarithm.
This is the most practical method for displaying enormous numbers. Logarithms have several important properties that prove that multiplication and division of logarithms can be written in terms of addition and subtraction logarithms. A second name for the common logarithm is the base 10 logarithm.. This is represented as log10 or simply log. The base 10 logarithm is another name for the common logarithm. The common logarithm specifies the number of times the number 10 must be multiplied in order to produce the desired result.. We need to evaluate log₃ 125
Using the property
logₐ (mⁿ) = n logₐ m
125 = 5³log₃ 125 can be written as log₃ 125= 3 log₅ 5
We know that logₐ a = 13 log₅ 5= 3
Therefore, we calculated the logarithm, which is log₃ 125 = 3
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barbara has 526 pieces of candy that she wants to share with the 19 students in her class.Barbara wants to make sure that each classmate gets the same amount of candy.How many pieces of candy will each of her friends recieve and how many pieces will she have left over for herself. Answers
Answer: they will get 27 each and their will be 13 left over
Step-by-step explanation:
What is the solution of each system of equations? Solve using matrices.
b. [4x-6y=9 -10x+15y = 8]
The system of equations which is as represented in the task content above when solved by elimination, substitution or matrices has no solution.
This goes to say that the above given system of equations ultimately has no solution using matrices
What is the solution of the system of equations given in the task content?It follows from the task content that the solution pair of the system of equation as given in the task content is to be determined.
Given system of equation;
4x-6y=9
-10x+15y = 8
By multiplying the first equation by 5 and the second equation by -2; we have;
20x - 30y = 45
20x - 30y = -16
Hence, it is evident that the system of equations above has equal slope but different intercept equations.
Consequently, subtract equation 2 from 1 so that we have;
0 = 61....an equality which doesn't hold true.
Ultimately, the system of equations has no solution.
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6 x 10^6 divided by 2 =
Answer:
3,000000
Step-by-step explanation:
10^6=1000000
1000000x6=6000000
6000000/2=3000000
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The midpoint of FG is M(4, 6). One endpoint is G(2, 8). Find the coordinates of the other
endpoint F.
Answer is the coordinates of endpoint F(6, 4).
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
let coordinate of F is (x,y).
4= (x + 2)/2
8= x +2
x = 6
6= (y +8)/2
12 = y + 8
y = 4
Answer is the coordinates of endpoint F(6, 4).
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How do I express the difference in the measures of center as a multiple of the measures of variation?
The difference between the measures of center is equal to the measure of variation.
How to illustrate the information?The IQR of the given box plot:
Q1 = 10
Q3 = 18
IQR = Q3 − Q1 = 18 − 10 = 8
Median = 15
Q1 = 4
Q3 = 12
IQR = Q3 − Q1 = 12 − 4 = 8
The difference between the measures of center as a multiple of the measure of variation:
Median of first data set - median of the second data set
IQR = 15 − 7 / 8
= 1
Therefore, the difference between the measures of center is equal to the measure of variation.
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Express the difference between the measures of center as a multiple of the measure of variation.
Given is a box plot for the number of questions attempted in subject 1 by different students.
Simplify the following expression using Distributive Property ½(x+10)
Answer:
I think the answer is
1/2x + 5
Step-by-step explanation:
Evaluate each logarithm. log₃ 1/9
According to the given the given logarithm log₃ 1/9 the value is = -2
What is Logarithmic functions?Logarithmic functions are significant due of their link to exponential functions. Logarithms are useful for solving exponential equations and investigating the properties underlying exponential functions.
According to the given information:log₃ 1/9
Can be written as:
log₃ (1/9) = x
using the log definition in exponential form. if x and b are positive real number and b dose not equal 1 then log_b (x) = y is equivalent to b^y = x.
3^x = 1/9
creating equivalent expression in the equation that all have equal base.
3^x = 3^-2
if the base are the same, two expression are only equal if the exponential are also equal
x = -2
the variable x is equal to -2
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PLEASE HELP ASAP
Compute the requested average. The balance forward of the account is $358.27.
In dollars and cents, the average payment above was $___
The average payment will be $611.64.
How to compute the average?It should be noted that average means mean. This implies that we will add the numbers and then divide.
This will be:
= ($23.42 + $14.95 + $276.50 + $219.93 + $76.84) / 5.
= $611.64
Therefore, the average payment will be $611.64.
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Answer:
All these added amount to $611.64, yes.
However, to find average, you then divide by 6.
Which equals; $101.94.
That is the average payment.
Step-by-step explanation:
Hope it helps.
Need some help with this..
Answer:
Step-by-step explanation:cevaplandıında banada haber verin rez kardeşlerim
Can someone to help me answer this
I am pretty sure it is the top right graph
For each annual rate of change, find the corresponding growth or decay factor.+ 500%
The corresponding growth factor of +500% is 6
The formula for the annual rate of change is
1 ± r (1)
where r = rate of change
and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.
According to the question we have been given the growth that is +500%. Since there is plus sign therefore it is a growth factor.
Thus, r = + 5
Putting this value in equation (1) we get
= 1 + 5
= 6
Hence the corresponding growth factor of +500% is 6
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5/14
April has 2/3 cup sugar and Mike has 1 3/6 cups of sugar. How much do
they have together?
Mauna Loa depresses the sea floor,
resulting in 26,400 more feet added to
its height. What is the total height of
Mauna Loa?
In linear equation, 40100 is the total height of Mauna Loa .
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."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.the total height of Mauna Loa
26400 +13700 = 40100
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The complete question is -
Mauna Loa depresses the sea floor, resulting in 26400 more feet added to its height. If Mauna Loa is 13700 ft tall. What is the total height of Mauna Loa?
What is the decimal of thirty five hundred thousandths?
Answer:
0.0035
Step-by-step explanation:
In front of the decimal point is the ones place. After that is the tenths place, hundredths place, and then thousandths place.
Mariam took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.25 per mile. The total fare was $6.65, not including the tip. Write and solve an equation which can be used to determine m, the number of miles in the taxi ride.
Equation:
Answer: m =
Answer:
are there options?
Step-by-step explanation:
the question is in the picture! i need help ASAP!
Answer:
The answer I think is
No points of intersectionStep-by-step explanation:
(0,-6) (-3,-8) (2,-4)
Are these points collinear or no??
RIGHT ANSWERS ONLY, PLS AND TY
Line that passes through (0,-6) and (2,-4)
[tex]y = mx + c \\ m = \frac{ - 6 + 4}{0 - 2} = \frac{ - 2}{ - 2} = 1 \\ c = y - mx = - 4 - 1(2) = - 6 \\ y = x - 6[/tex]
If the third point (-3,-8) belongs to this line, then it must satisfy its equation and be collinear to the other two points, if not, then these points are not collinear, check:
[tex] - 8 = - 3 - 6 \\ - 8≠ - 9 \\ so \: nopeeee[/tex]
Example 2
14. TURNPIKE The total cost for cars entering President George Bush Turnpike at Beltline Road is
related to the number of cars entering the turnpike at Beltline Road. The costs of different numbers
of cars entering the turnpike at Beltline Road are as follows: 1 car, $0.75; 2 cars, $1.50; 3 cars, $2.25; 4
cars, $3.00; 5 cars, $3.75. function
a. Make a table.
b. Determine the domain and range of the relation.
c. Determine whether the relation is a function.
15. HOME VALUE The average value of a house changes over time. The average values of a house in
2010 $350.000: 2015 $293.000:
The domain of the relation is {1, 2, 3, 4, 5} and the range of the relation is {0.75, 1.50, 2.25, 3.00, 3.75}
As per the question statement, the total cost for cars entering President George Bush Turnpike at Beltline Road is related to the number of cars entering the turnpike at Beltline Road. The costs of different numbers of cars entering the turnpike at Beltline Road are as follows: 1 car, $0.75; 2 cars, $1.50; 3 cars, $2.25; 4 cars, $3.00; 5 cars, $3.75.
Before solving the question we need to know what is domain and range basically.
Ordered pair : {(1,0.750 , (2,1.50) , (3,2.25) , (4,3.00) , (5,3.75)}
Domain is the set which consists of all the first elements of all the ordered pair of the given relation, therefore Domain is {1, 2, 3, 4, 5}.
Range is the set which consists of all the second elements of all the ordered pair of the given relation, therefore Range is {0.75,1.50,2.25,3.00,3.75}
And yes, the given relation is also a function because as the number of cars increases the total cost is also increasing but gradually with a constant value.
Domain: It the set which consists of all the first elements of all the ordered pair of the given relation.Range: It is the set which consists of all the second elements of all the ordered pair of the given relation.To learn more about domain and range, click on the link given below:
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2 1/6 + 3 4/9
Need help with this mixed number problem:)
Answer:
5.611 or 5 11/18
Step-by-step explanation:
hope this is helpful!
Answer:5/3
Step-by-step explanation:
Write each expression in simplest form. (x⁴/x⁻¹)⁻¹/₅
The simplest form of the expression [tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} }[/tex] is [tex]\frac{1}{x}[/tex].
The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).
A fraction is a number that has been expressed as a quotient by dividing the numerator by the denominator. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator.
An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions joined by an equal sign form an equation.
Consider the expression,
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} }[/tex]
Now we know,
[tex]x^{-1}=\frac{1}{x}[/tex]
Therefore,
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{1}{\frac{x^4}{x^{-1}} })^{\frac{1}{5} }[/tex]
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{x^{-1}}{x^4})^{\frac{1}{5}[/tex]
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } =(\frac{1}{x \times x^4})^{\frac{1}{5}[/tex]
Using the exponential rule,
[tex]n^{b} \times n^{a} = n^{a+b}[/tex]
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = (\frac{1}{x^{5}} )^{\frac{1}{5}[/tex]
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = \frac{1}{x^{5 \times \frac{1}{5} }}[/tex]
[tex](\frac{x^{4}}{x^{-1}} )^{\frac{-1}{5} } = \frac{1}{x}[/tex]
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There are 62 people at the commuter area waiting to catch carpool vans. Each van can fit 9 people. How many vanes will be needed to transport everyone so that no one is left behind?
Answer:
7 vans
Step-by-step explanation:
62 ÷ 9 = 6.86.8 is not a whole number, so when you round it to the nearest whole number you get 7.[Also, 9 × 7 = 63, which is close to 62]∴ 7 vans will be needed.
Answer:
7 vans
Step-by-step explanation:
Each van can take 62 people so you share the 62 among the vans, and each van is 9,therefore 62÷9=6.888889 and people cannot be in decimals so you round the figure to a whole number which is equal to 9.
Simplify the expression.
164[3+2+ (9-7)] =
After thoroughly calculating the simplifying the expression 164[3+2+ (9-7)] is 1148
What is mathematical expression?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
The following are some examples of expressions and word phrases that they relate to:
Formula: 3 + 7
Expressions and equations are different from one another because an expression consists of a combination of numbers, variables, and operation symbols, whereas an equation consists of two different expressions joined together by an equals sign. This shows that the expression's two sides have the same value.
Simplification of the expression 164[3+2+ (9-7)]
⇒ 164[3+2+ (9-7)] =
⇒ 164[5+(2)] =
⇒ 164[5+(2)]
⇒ 164(7)
⇒ 1148
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Which statement is true about the ray passing through points B and C?
Answer:
The ray extends infinitely in one direction.
Step-by-step explanation:
It starts at the point and the arrow at the ends mean it extends in that direction away from the point infinitely.
Write 0.33 as a percentage.
Answer:
33%
Step-by-step explanation:
moving the decimal two places to the right
Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. f(x)=g(x)
The domain of the function h(x) = x² - x - 12 when the function operation f(x) = g(x) is performed is ( - ∞ , ∞ ).
A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The collection of potential output values represented on the y-axis is known as the range.
Consider the two functions,
f(x) = x - 4 and g(x) = x² - 16
The function operation f(x) = g(x).
g(x) - f(x) = h(x)
x² - 16 - ( x + 4 ) = h(x)
h(x) = x² - x - 16 + 4
h(x) = x² - x - 12
The collection of input or argument values for which a function is actual and defined is known as its domain.
So, the domain of the function h(x) is ( - ∞ , ∞ ) or - ∞ < x < ∞.
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In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 9.5 in Valdivia, Chile, in 1960
The intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.
We use the following formula for comparing the intensity level of earthquakes-
Log (i1 / i2) = M1 - M2
where i = intensity level determined by a seismograph
M = magnitude on a Richter scale.
Now, from the given information-
magnitude of earthquake in New Madrid = 7.9
Thus, M1 = 7.9
Then intensity of the earthquake in New Madrid = i1
magnitude of earthquake in Chile = 9.5
Thus, M2 = 9.5
Then intensity of the earthquake in Chile = i2
⇒ log (i1 / i2) = 7.9 - 9.5
log (i1 / i2) = -1.6
This means that the intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.
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