Answer: Given the log function ln(100), this can therefore be written as loge(100)
Step-by-step explanation: Logarithmic functions
Logarithmic functions are inverse of exponential functions. There are different ways to write log function;
Some are written as a exponent base
Some to the base of 10
Loga is also written as log10(a)
lna is written as loge(a)
Given the log function ln(100), this can therefore be written as loge(100)
Answer: C log(10).
Step-by-step explanation: When you calculate In (10), you would be finding the value of log(10).
In mathematics, the logarithm function is used to express the exponent to which a base must be raised in order to produce a given number. The base of the logarithm is usually denoted by "b" and the number whose logarithm is being taken is denoted by "x". The logarithm of x to base b is denoted as logb(x).
For example, the logarithm of 10 to base 10 is denoted as log10(10), which is equal to 1. The logarithm of 100 to base 10 is denoted as log10(100), which is equal to 2.
In general, the logarithm of x to base b can be calculated as follows:
logb(x) = y
This equation states that b raised to the power of y is equal to x.
The natural logarithm, denoted as In, is a special case of the logarithm function where the base is the mathematical constant e (approximately 2.718). The natural logarithm of x, denoted as In(x), is equal to the logarithm of x to base e.
Therefore, when you calculate In (10), you are finding the value of the natural logarithm of 10, which is the logarithm of 10 to base e.
Option A log (10) is incorrect because it is missing the base of the logarithm (e).
Option B log₁0(e) is incorrect because it is the logarithm of e to base 10, which is not the same as the natural logarithm of 10.
Option D 10 In(e) is incorrect because it is the value of 10 raised to the power of the natural logarithm of e, which is not the same as the natural logarithm of 10.
Option C log(10) is correct because it is the natural logarithm of 10, which is the value we are trying to find. Therefore, the correct answer is C log(10).
Todd orders pictures from a photographer. Each picture costs $7.50 A one time shipping fee of
$3.25 is added to the cost of the order.
Write an algebraic expression that reflects this situation.
Answer:
1.25 es la respuesta
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given:
Each picture costs $7.50
One time shipping cost = $3.25
Total cost of the order = $85.75
To FInd:
An equation to determine the number of pictures ordered.
Solution:
Define x:
Let x be the number of pictures bought.
Let y be the total amount of money collected.
Form the equation:
The $3.25 one time shipping cost is a fixed cost.
The $7.50 is a variable cost depending on the number of pictures ordered.
Therefore the equation:
⇒ y = 3.25 + 7.5x
Find the number of pictures bought.
The total cost is $85.75
3.25 + 7.5x = 85.75
7.5x = 82.50
x = 11
Answer: The equation is y = 3.25 + 7.5x and Todd bought 11 pictures.
PLS HELPPPPPPPPPPPPPPP
Answer:
1: 50
2: 1
3: 2
4: 36
5: 0
6: -12
7: -2
8: 3
Step-by-step explanation: Use PEMDAS
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5. Use Table 2. a. Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places. Round "Sample mean" to 3 decimal places and "Sample standard deviation" to 2 decimal places.) Sample mean 17.000Sample standard deviation 79.42 b. Construct the 95% confidence interval for the population mean (Round "t" value to 3 decimal places and final answers to 2 decimal places.) Confidence interval 83.41 to -49.418 c. Construct the 90% confidence interval for the population mean. (Round "t" value to 3 decimal places and final answers to 2 decimal places.)Confidence interval 70.21 to -36.218 d, what happens to the margin of error as the confidence level increases from 95% to 90%?as the confidence level increases, the margin of error becomes smaller
For the given data
(a) sample mean is 17 and sample standard deviation = 8.91 .
(b) the 95% confidence interval is (9.551 , 24.449) .
(c) the 90% confidence interval is (11.032 , 22.968) . .
In the question ,
the data is given as 25, 11, 12, 27,26, 22, 8,5.
So , the number of terms (n) = 8
Part(a)
the sample mean(μ) is = (25+11+12+27+26+22+8+5)/8 = 17
the standard deviation is calculated as :
= √[(25 - 17)² + (11 - 17)² + (12 - 17)² + (27 - 17)² + (26 - 17)² + (22 - 17)² + (8 - 17)² + (5 - 17)²)]/7
Simplifying the above data further ,
we get
= 8.91
Part(b)
we know that at 95% confidence interval , the critical value is t₀.₀₂₅,₇ = 2.3646
So , the 95% confidence interval is :
= μ ± t₀.₀₂₅,₇*s/√n
= 17 ± 2.3646*8.91/√8
= 17 ± 7.449
So , the interval is ⇒ (9.551 , 24.449) .
Part(c)
we know that at 90% confidence interval , the critical value is t₀.₀₅,₇=1.8946
So , the 90% confidence interval is :
= μ ± t₀.₂₅,₇*s/√n
= 17 ± 1.8946*8.91/√8
= 17 ± 5.968
So , the interval is ⇒ (11.032 , 22.968) .
Therefore ,(a) the sample mean and standard deviation are 17 and 8.91
(b) the 95% interval is (9.551 , 24.449) .
(c) the 90% interval is (11.032 , 22.968) .
The given question is incomplete , the complete question is
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5.
(a) Calculate the sample mean and the sample standard deviation.
(b) Construct the 95% confidence interval for the population mean.
(c) Construct the 90% confidence interval for the population mean.
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Inequalities in the real world
Pls help
WHat is 64% as a fraction
Answer:
64/100
Step-by-step explanation:
Answer: 16/25or64/100
Step-by-step explanation: 64/100 and divide it by 4 . To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary
Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the
area under the graph using first two and then four rectangles.
f(x) = x³ between x = 2 and x = 4
The area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.
Here a=0, b=1 and n=2( two rectangles), so
Δx = (1 - 0)/2
Δx = 1/2
Δx = 0.5
M2 = (0.5) * ( f((0+0.5)/2)) + f((0.5+1)/2)) )
= (0.5) * ( f(0.25) + f(0.75) )
Using f(x) = x^3
=(0.5) * ( 0.015625 + 0.421875 )
=0.21875
Here a=0, b=1 and n=4( four rectangles), so
Δx = (1 - 0)/4
Δx = 1/4
Δx = 0.25
M4 = (0.25) * ( f((0+0.25)/2)) + f((0.25+0.5)/2)) + f((0.5+0.75)/2)) + f((0.75+1)/2)) )
=(0.25) * ( f(0.125) + f(0.375) + f(0.625) + f(0.875) )
Using f(x) = x^3
= (0.25) * ( 0.001953125 + 0.052734375 + 0.244140625 + 0.669921875 )
= 0.2421875
Hence, the area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.
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what is the equation of the line that passes through the point (3, -4) and had an undefined slope
The equation of the line that passes through the point (3,4) and has an undefined slope is y = 3
What is an Undefined Slope?An undefined slope is an infinite slope. This is the slope of a vertical line. The x values never changes no matter the changes in the y values.
The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope
c = y-intercept
Since the slope, m is undefined, the expression that has an undefined slope is a vertical line
Therefore,
y = 3
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Let f(x)= -4x-1 and g(x)= x^2 +3. Find (f o g)(-6).
The value of (f o g)(-6) will be;
⇒ (f o g)(- 6) = - 157
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (x) = - 4x - 1
And, g (x) = x² + 3
Now,
Since, The values are,
⇒ f (x) = - 4x - 1
And, g (x) = x² + 3
Hence, The value of function (f o g)(x) is,
⇒ (f o g)(x) = f (g (x) )
= f (x² + 3)
= - 4 (x² + 3) - 1
= - 4x² - 12 - 1
= - 4x² - 13
Thus, (f o g)(- 6) = - 4 (-6)² - 13
= - 4 × 36 - 13
= - 144 - 13
= - 157
So, The value of (f o g)(-6) will be;
⇒ (f o g)(- 6) = - 157
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find the point at which the given lines intersect find a n equation of the plamn tjat cpontains these lines
The point at which the given lines intersect is (6,0,2) and an equation of the plane that contains these lines is x+y=6.
(a) In the given question we have to find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2]
r = [6,0,2] + s[-3,3,0]
The equations of the lines can be written as :
The points for first line is
L(1)⟹x=3+3t, y=3-3t, z=0+2t and
The points for second line is
L(2)⟹x=6-3s , y=0+3s , z=2+0s .
Set the z coordinates equal from the line one and two, and we get :
2t = 2
Divide by 2 we get
t=1 .
Substitute the value of t into the point of x of first line :
x=3+3(1)
x=3+3
x=6
Equating the value of x equal to the coordinate of x of line two
6=6-3s
Subtract 6 on both side, we get
-3s=0
s=0
Now substitute the value of t into the point of y of first line:
y=3-3(1)
y=3-3
y=0
Equating the value of y equal to the coordinate of y of line two
0=0+3s
s=0
Now substitute the value of t into the point of z of first line:
z=0+2(1)
z=2
Equating the value of z equal to the coordinate of z of line two
2=2+0(s=0)=2 .
We thus have the point of intersection is :
P=(x,y,z)
P=(6,0,2)
Hence, the point at which the given lines intersect is (6,0,2)
(b) The direction vector for the first line is
[tex]\vec{v_{1}}=3\hat{i}-3\hat{j}+2\hat{k}[/tex]
and the direction vector for the second line is
[tex]\vec{v_{2}}=-3\hat{i}+3\hat{j}+0\hat{k}[/tex]
We can find a normal vector to the line as :
[tex]\vec{N_{1}}=\vec{v_{1}}\times\vec{v_{2}}[/tex]
[tex]\vec{N_{1}}=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\-3 &3 &-2 \\ -3 &3 & 0 \end{vmatrix}[/tex]
[tex]\vec{N_{1}}=\hat{i}(0-(-6))-\hat{j}(0-6)+\hat{k}(-9-(-9))[/tex]
[tex]\vec{N_{1}}=6\hat{i}+6\hat{j}[/tex]
is a normal vector
But , we can also use
[tex]\vec{N}=\frac{\vec{N_{1}}}{6}[/tex]
[tex]\vec{N}=\hat i+\hat j[/tex]
as the normal vector to the plane .
We can thus use the point P=(6,0,2) and the normal vector [tex]\vec{N}=\hat i+\hat j[/tex] to write the equation of the plane :
1(x-6)+1(y-0)+0(z-2)=0
x-6+y+0=0
x+y=6
Hence, an equation of the plane that contains these lines is x+y=6.
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The right question is
(a) Find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2] r = [6,0,2] + s[-3,3,0]
(x,y,z) = ( )
(b) Find an equation of the plane that contains these lines.
The area of the triangle formed by the x and y intercepts of the parabola y=0.5(x-3)(x+k) is 1.5 find all possible values of k
Answer:
The possible values of k are -0.56, -3.56, -2 and -1.
Step-by-step explanation:
We have the equation of the parabola, .
Substituting x=0, we get that i.e. y = -1.5k
So, the y-intercept is (0,-1.5k).
Thus, the height of the triangle becomes |-1.5k| = 1.5k
Again, substituting y=0, i.e. i.e. x=3 and x=-k
So, the x-intercepts are (3,0) and (-k,0).
Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.
We see that 'k' cannot be 0 or -3 as if k=0, then height = 0, which is not possible. If k= -3, then the base = 0, which is also not possible.
As, area of a triangle = .
Substituting the values, we get,
1.5=
i.e.
i.e. k = -0.56 and k = -3.56
or
1.5=
i.e.
i.e. k = -2 and k = -1.
Thus, the possible values of k are -0.56, -3.56, -2 and -1.
PLEASE HELP!!!!!!!!!
3y^2 + 3(4y^2 - 2) please help
The roots of the quadratic equation 3y² + 3(4y² - 2) is ± √(1/7).
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, 3y² + 3(4y² - 2).
3y² + 12y² - 2.
14y² - 2.
Let 14y² - 2 = 0.
14y² = 2.
y² = (2/14).
y = ± √(2/14) Or ± √(2/2×7) Or ± √(1/7).
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Evan added -2 1/2+4 and got 6 1/2 draw arrows on the number line to represent the problem and explains Evans error
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2. On adding he would be getting 1 1/2
What is number line?A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.
It is given that Evan added -2 1/2 and 4 but got 6 1/2
The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because
4 - (-2 1/2)
= 4 + 2 1/2
= 6 1/2
This is wrong as he was asked to add -2 1/2 and 4 not to subtract.
Therefore, on adding -2 1/2 and 4, we get,
= 4 - 2 1/2
= 1 1/2
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2 . On Evan's error was that he subtracted from 4, and thus he got . On adding he would be getting 1 1/2
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graph and label (-3.25,3)
Answer
hello I have provided a picture of the answer
Step-by-step explanation:
ur welcome and have a nice day
Which sequence of transformations could demonstrate the similarity of the two shapes from Part 1?
A. a rotation and then a reflection
B. a dilation and then a reflection
C. a rotation and then a dilation
D. a translation and then a reflection
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years.
In 11.61 years the given principal amount of $ 900 will be double.
What is Compound interest:Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.
The formula for the Amount when compound interest is calculated is given by
Amount, A = P(1+r/n)^ntP = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period in years
Here from the given data,
Principal amount = $ 900
Rate of interest = 6% = 6/100 = 0.06
Number of compounds = 12 [ ∵ compounded monthly]
Here we need to find the time period
Assume that after 't' years the amount will be doubled
From the given data and formula,
Amount, A = 900(1+0.06/12)^12t
= 900(1+0.06/12)^12t
= 900(1 + 0.005)^12t
= 900 (1.005)^12t
As we assumed after 't' years the amount is double
=> 900 (1.005)^12t = 2 × 900
=> (1.005)^12t = 2
Applying log on both sides
=> log (1.005)^12t = log 2
=> 12t log(1.005) = log 2
=> 12t = log 2/log(1.005)
[ we can use a calculator for log (1.005) and log 2]
=> 12t = 0.30108/ 0.00216
=> 12t = 139.888
=> t = 11.61
Therefore,
In 11.61 years the given principal amount of $ 900 will be double.
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e(x) = 10(4-x)
Find e(-3).
Answer:
70
Step-by-step explanation:
Substitute the value -3 into the expression and simplify:
10(4 - -3)
10(4 + 3)
10(7)
70
The same digits are used for the expressions 7² and 2⁷ . Explain how to compare the value of each expression.
Choose the correct answer below.
A. Write each power as repeated multiplication. These compare the bases of the exponents.
B. Write each power as repeated multiplication. Then compare the number of factors.
C. Write each power as repeated multiplication. Then evaluate and compare their values.
Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
What is the relation between power and base?
In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.Compare 7² and 2⁷.
7 ≠ 2
So, write the power as repeated multiplication of the given expression:
7² = 7 * 7
2⁷ = 2*2*2*2*2*2*2
Evaluate:
7² = 49
2⁷ = 128
Compare the values:
128 > 49
2⁷ > 7²
Hence, Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
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A credit card company determines a card holder's minimum monthly payment by adding all new interest to 1.5% of the outstanding principal. The credit card company charges an interest rate of % per day. On November , a customer used his credit card to pay for the following business expenses: van repairs ($), equipment maintenance ($), office supplies ($), and dinner with clients ($). Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer parts a and b below.
a. Assuming the card holder had no new interest, determine his minimum payment due on December 1, his billing date.
The card holder's minimum payment due on December 1 is ___$.
(a) Minimum payment to be paid is $22
(b) Minimum payment to be paid is $35
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.
The formula for simple interest is:
Simple Interest=P×R×T
where:
P=Principal Amount
R=Daily interest rate
T=Number of days between payments
(a)The minimum monthly payment is calculated by taking 1.5 percent of the outstanding principle
(0.015) ×$ (677+452+139+141) = $21.135
as there is no additional interest due.
The minimum monthly payment required on December 1 is $22, rounded up to the nearest whole dollar.
(b) The minimum monthly payment will be equal to 1.5 percent of the outstanding principle plus the new interest charges.
We will apply the simple interest formula, S.I = p×r×t, to get his new interest costs.
Because Dec contains 31 days, the
Principle amount, p = (677+452+139+141) - 300 = 1109,
the rate, r = 0.05163% each day
Time, t = 31 days.
S.I =p×r×t=1109×0.0005163×31= $17.75
0.015×1109 = 16.64, which is 1.5 percent of the outstanding amount.
To reach $17.75 + $16.64 = $34.39, we must now add the additional interest to 1.5 percent of the outstanding principal.
The minimum monthly payment required on January 1 is $35, rounded up to the next whole dollar.
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Ima needs an at least B help me out here Please.
What number makes the expressions equivalent?
−1.1−1.4m + 0.4 = ? − 1.4m
By using the concept of algebraic expression, it can be calculated that
The number that makes the expressions equivalent is -0.7
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
The given algebraic expression is
−1.1−1.4m + 0.4
On simplifying −1.1−1.4m + 0.4
−1.1−1.4m + 0.4
-0.7 - 1.4m
So the number that makes the expressions equivalent is -0.7
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18. Find the total length of segment A E.
Using Pythagorean Theorrem the length of AE = 46 units
What is a Right Angle Triangle?
A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Solution:
In Triangle ABC using Pythagorean Theorem
AC = √(21*21 + 20*20)
AC = √841
AC = 29
In Triangle CDE using Pythagorean Theorem
CE = √(8*8 + 15*15)
CE = √289
CE = 17
From the figure we can say that AE = AC + CE
AE = 29 + 17
AE = 46 units
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a number squared divided by 15
Answer:
Step-by-step explanation:
If a number is squared and then divided by 15, the resulting expression can be written as (x^2)/15, where x is the number. For example, if the number is 5, then the expression can be written as (5^2)/15 = 25/15. In general, the value of the expression (x^2)/15 will be the square of the number x divided by 15.
How do I find the inverse of the relation
Answer:
5, -11. -3, 8. 10, 17. -15, 13.
Step-by-step explanation:
All you have to do is switch x and y
In a busy airport, aeroplanes from EZPlanes Airways depart every 264 minutes
whilst aeroplanes from Bryanair Airlines depart every 198 minutes. If both airlines
have aeroplanes departing at 06:20 when is the next time they will depart from
the airport together again?
The next time they will meet again is 08:44 (next day)
How to determine the next time they will meet againFrom the question, we have the following parameters that can be used in our computation:
EZPlanes Airways depart = every 264 minutes
Bryanair Airlines depart = every 198 minutes
Both airlines depart = at 06:20
Using the above as a guide, we have the following departure times
EZPlanes Airways depart = 264, 528, 792, 1056, 1320, 1584, 1848, 2112, 2376 and 2640 minutes,
Bryanair Airlines depart = 198, 396, 594, 792, 990, 1188, 1386, 1584, 1782 and 1980 minutes
The common departure time in the above is
Time = 1584 minute
So, we have
Common departure time = 06:20 + 1584 minutes
Evaluate the sum
Common departure time = 06:20 + 26 hours + 24 minutes
Evaluate the sum
Common departure time = 08:44 (next day)
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Find the cost of installing a fence around all sides of a rectangular
yard that is 50 feet by 90 feet. The fence that is being used costs
$8.50 per foot.
$1,190.00
$2,380.00
$3,825.00
$38,250.00
The total cost of installing a fence around all sides of the rectangular yard would be $38250.
What is the area of the rectangle?
For the dimensions of the rectangle of length 'l' and breadth 'b', the area can be computed by using the formula,
Area = Length × Breadth
Given data:
The length of the yard is 90 feet. and the breadth is 50 feet.
Area of the yard = length * breadth
= 90 * 50
= 4500 square foot
Now per square foot, the cost is $8.50 so the total cost of installing a fence around all sides of the yard would be = 4500 * 8.5
= $38250.
Hence, the total cost of installing a fence around all sides of the rectangular yard would be $38250.
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Solve 8x - 2y = 0 and -6x + 14y = 50 using elimination. Show steps. Put your answer in coordinate form (x,y)
The required solution (1, 4) of a linear system of the equation is determined by the elimination method.
Given the linear system of equations:
8x - 2y = 0 or 4x - y = 0 …(i)
-6x + 14y = 50 or -3x + 7y = 25 …(ii)
Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.
So, we have to find out the value of 'x’ and 'y’.
By multiplying 7 by equation (i) and adding both equations
28x - 7y -3x + 7y = 25
25x = 25
x = 25/25
x = 1
Substitute the value of x = 1 in the equation (i), and solve for y
4(1) - y = 0
y = 4
Hence, the required solutions are x = 1 and y = 4.
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Please help
Find the angles:
Arc QR =
Arc RS =
QPS =
PSR =
SRQ =
The angles of the cyclic quadrilateral and the arc angle is as follows:
arc QR = 48°arc RS = 96°∠QPS = 72°∠PSR = 87°∠SRQ = 108°How to find the angles in a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral drawn inside a circle. In other words, a cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
A cyclic Quadrilateral's opposite angles add to 180°.
Therefore,
∠PSR = 180 - 93 = 87 degrees.
An inscribed angle is one-half of the measure of the arc that it intercepts.
Therefore,
87 = 1 / 2 arc PQR
cross multiply
arc PQR = 87 × 2
arc PQR = 174 degrees
Hence,
arc QR = 174 - 126
arc QR = 48 degrees
arc RS = 360 - 90 - 174
arc RS = 96 degrees.
∠QPS = 1 / 2 (96 + 48)
∠QPS = 1 / 2 (144)
∠QPS = 144 / 2
∠QPS = 72 degrees
∠SRQ = 180 - 72
∠SRQ = 108 degrees
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Answer:
48°
96°
72°
87°
108°
Step-by-step explanation:
arc QR = 48°
arc RS = 96°
∠QPS = 72°
∠PSR = 87°
∠SRQ = 108°
A group spends $277.50 to rent 15 tubes for a float down the Ichetucknee River. One person tubes cost $12.50 and two person tubes cost $20. How many of each type of tube does the group rent?
The number of One-person tubes and two-person tubes is 3 and 12 respectively.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
A group spends $277.50 to rent 15 tubes for a float down the Lchetucknee River. One-person tubes cost $12.50 and two-person tubes cost $20.
The equation can be written as,
12.5x + 20y = 277.5
Here, x is the number of One-person tubes and y is two-person tubes.
Also, x + y = 15
Solve the above equation by elimination method,
x = 3 and y = 15 - 3 = 12
Therefore, the number of One-person tubes and two-person tubes is 3 and 12 respectively.
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Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
What are Equivalent expressions:A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.
In general, if anything is considered equal then the two of them are said to be equivalent. Similarly to this, if any two or more algebraic equations have identical solutions or roots then the equations are Equivalent expressions even they look different.
Here we have
Expressions
3a +b +13a
20b +11a -3b
20b -5b +2b
To simplify given expressions add or subtract like terms as given below
3a +b +13a => (3a+13a) +b = 16a + b
Therefore,
The equivalent expression of 3a +b +13a is 16a + b
20b +11a -3b => (20b-3b) + 11a = 17b + 11a
Therefore
The equivalent expression of 20b +11a -3b is 17b + 11a
20b-5b+2b => 20b+2b - 5b = 22b -5b = 17b
Therefore,
The equivalent expression of 20b-5b+2b is 17b
Therefore,
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
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Use the distance formula to find the distance between the points (−1,6) and (−1,7).
The required distance between the points (−1,6) and (−1,7). is 1 unit.
Given that,
using the distance formula to evaluate the distance between the points (−1,6) and (−1,7).
Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1
Thus, the required distance between the points (−1,6) and (−1,7). is 1 unit.
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