In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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What is the area of FGH? (Please help it’s due tmrw !! I’ll mark you brainliest)
Answer:
102.0625 square units
Step-by-step explanation:
First determine the length of each side using the distance formula for two points. Then use Heron's formula to determine the area of a triangle given three sides
Distance Formula
The distance between two points is the length of the path connecting them
The distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
Let's compute the lengths of the sides FH, FG and HG
The three vertices are F(-2, 5) G(7, -10) and H(-9, -6) as indicated on the graph
So length FG between (-2,5) and (7,-10)
[tex]FG= \sqrt {(7 - (-2))^2 + (-10 - 5)^2}[/tex]
[tex]= \sqrt {(9)^2 + (-15)^2}[/tex]
[tex]= \sqrt {{81} + {225}}[/tex]
[tex]= \sqrt {306}[/tex]
FG [tex]= 17.492856[/tex] (round to 17.5)
Length FH between(-2,5) and (-9, -6) is
[tex]FH = \sqrt {(-9 - (-2))^2 + (-6 - 5)^2}[/tex]
[tex]= \sqrt {(-7)^2 + (-11)^2}[/tex]
[tex]= \sqrt {{49} + {121}}[/tex]
[tex]= \sqrt {170}[/tex]
FH [tex]= 13.038405[/tex] (can be rounded to 13.04
Length GH between (7, -10) and (-9, -6) is
[tex]GH = \sqrt {(-9 - 7)^2 + (-6 - (-10))^2}[/tex]
[tex]= \sqrt {(-16)^2 + (4)^2}[/tex]
[tex]= \sqrt {{256} + {16}}[/tex]
[tex]= \sqrt {272}[/tex]
GH [tex]= 16.492423[/tex] (can be rounded to 16.5)
Determining the area of a triangle given 3 sides
Heron's formula allows us to find the area of a triangle given 3 sides If the sides are a, b and c the general form of Heron's formula is
[tex]Area = \sqrt {s(s-a)(s-b)(s-c)}[/tex]
where s is the semi-perimeter = [tex]\frac{a+b+c}{2}[/tex]
Substituting values we get
s = [tex]\frac{17.5+13.04+16.5}{2} = 23.52[/tex]
[tex]Area = \sqrt {23.52(23.52-17.5)(23.52-13.04)(23.52-16.5)}[/tex]
[tex]= \sqrt{23.52\cdot6.02\cdot10.48\cdot7.02}[/tex]
[tex]102.0625[/tex] square units
A serviceman charges ₱450 per hour for doing mechanical jobs. How much does he get for 6.75 hours of doing the job?
Pa help po
Answer:
450×6.75 = 2 956.5
So the serviceman will get 2 956.5 after 6.75 hours of doing the job
Which data set has the same standard deviation as the data set {1, 1, 3, 5, 8} ?
{9, 8, 9, 8, 9}
{2, 2, 4, 6, 9}
{1, 2, 6, 6, 9}
{1, 1, 1, 2, 2}
The data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
How to Find the Standard Deviation of a Data Set?Given the data set, {1, 1, 3, 5, 8}, the standard deviation (σ) is calculated as shown below:
Standard deviation (σ) = √(SS/n)
Count (n) = 5
Mean (μ) = 3.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Also, the standard deviation of {2, 2, 4, 6, 9} is calculated as shown below:
Count (n) = 5
Mean (μ) = 4.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Therefore, the data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
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Aisha wants to ride her bicycle 18.2 miles this week. She has already ridden 5 miles. If she rides for 4 more days, write and solve an equation which can be used to determine mm, the average number of miles she would have to ride each day to meet her goal.
The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles (m) is 3.3 miles to ride each day to meet her goal.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Total distance of ride Alisha wants by her bicycle (d) = 18.2 miles.
And, She has already ridden 5 miles.
She rides for 4 more days.
Now, Let the average number of miles = m
She has already ridden 5 miles.
And, She rides for 4 more days.
The number of miles she needs to ride more is
18.2 miles - 5 miles
= 13.2 miles
If m is the average number of miles she must cycle in 4 days to reach her objective,
Hence, we can formulate;
4m = 13.2
Divide both side by 4,
m = 3.3 miles
So, The equation that could be used to determine, m, is 4m = 18.2 - 5
The average number of miles is 3.3 to ride each day to meet her goal.
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What is the distance of this line segment?
Answer:
5 studs (3^3)
(3^3) = 5
Step-by-step explanation:
M is the midpoint of AB. Q is the midpoint of AM. and T is the midpoint of QM. If the coordinates of A and B are a and b. find the coordinates of Q and T in terms of a and b.
The the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4].
What is Mid-point of a Line segment?
The mid-point of a line segment is a point on the line segment which divides it into two equal parts.
Given is a line segment AB whose mid-point is M with a and b being the coordinates of A and B respectively. Further, Q is the midpoint of AM and T is the midpoint of QM.
[Refer to the image attached for clear explanation]
Since M is the mid-point of AB, therefore the coordinates of point M will be = M [(a + b)/2]
Now, Q is the mid-point of AM. Therefore, the coordinates of Q will be =
[(a + b)/2 + a]/2 = Q [(3a + b)/4]
and
T is the mid-point of QM. Therefore, its coordinates will be =
(a + b)/2 + (3a + b)/4 = T [(5a + 3b)/4]
Hence, the the coordinates of Q and T in terms of a and b is -
Q [(3a + b)/4] and T [(5a + 3b)/4]
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Name all the line segments that are skew to line segment BF
The line segment that is skew line to line segment BF is CD.
Skew line:
Skewed lines are two lines that are not parallel to one another, and neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist on several planes. Two lines in two-dimensional space can either intersect or run parallel to one another. Therefore, skew lines are impossible in 2D space.
The line segment AB is perpendicular to the line segment BF which means it is not the skew line to line segment BF
The line segment CD is not parallel and not perpendicular to the given line segment BF which means it is a skew line to the given line segment BF.
Therefore, The line segment that is skew line to line segment BF is CD.
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Help fast please pamdas
What is the third common multiple of two numbers is 72
Answer:
x-2-10123
y0.1 0.3 0.9 2.7 8.1 24.3
A soccer coach purchased one goal and some soccer balls for the team. The expression 180 + 15x represents the cost before tax. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. cost of goal total cost of soccer balls
The meaning of the terms and factors in the expression are
180 ⇒ cost of goal15x ⇒ total cost of soccer ballsx ⇒ Number of soccer balls180 + 15x ⇒ total cost of soccer balls and goalHow to determine what the different parts of the expression model represents?The expression is given as
180 + 15x
The above expression can be split as follows:
180 15xx180 + 15xThe meaning of the above terms and factors are
180 ⇒ cost of goal15x ⇒ total cost of soccer ballsx ⇒ Number of soccer balls180 + 15x ⇒ total cost of soccer balls and goalRead more about linear functions at
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Express in interval in set builder notation and graph the interval on a number line (-infinity,-6)
The interval on a number line (-∞, -6) using set-builder notation is;
{ x | x ∈ R, x ≤ -6 }
How to express an interval in set builder notation?Set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.
Real numbers (R) include all rational and irrational numbers. Thus, If we need to write the interval on a number line (-∞, -6) using set-builder notation, we will write as:
{ x | x ∈ R, x ≤ -6 }
In words : "x such that x belongs to R, x is less than or equal to -6"
This shows that x is any real number less than or equal to -6
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This question: Submit Fritz plans to fence off a square feed lot and then cross-fence to divide it into four smaller feed lots. If he uses 924 feet of fencing, then how much area will be fenced in?
Answer:
23,716 ft
Step-by-step explanation:
Let the side length of each of the four smaller lots be s.
Then, Fritz will use 12s feet, which is equal to 924.
This means s=77.
This means the area of each smaller square is 77²=5929, and thus the total area is 23,716 ft.
Select the expression that has a quotient greater than 1. Explain your reasoning PLEASE ANSWER THIS
1. 4 2/3 ÷ 5 1/4
2. 3 1/8 ÷ 2 2/5
3. 1 6/7 ÷ 2 1/3
4. 5 3/4 ÷ 7 3/8
The expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
How to Solve Fractions?To solve each of the expressions involving fractions, convert mixed fractions into improper fractions before finding the quotient of each.
1. 4 ⅔ ÷ 5 ¼
Convert to improper fractions
14/3 ÷ 21/4
14/3 × 4/21
= 56/63 (less than 1)
2. 3 ⅛ ÷ 2 ⅖
Convert to improper fractions
25/8 ÷ 12/5
25/8 × 5/12
125/96 (greater than 1)
3. 1 6/7 ÷ 2 1/3
13/7 ÷ 7/3
13/7 × 3/7
= 39/49 (less than 1)
4. 5 3/4 ÷ 7 ⅜
23/4 ÷ 59/8
23/4 × 8/59
= 184/236 (less than 1)
Therefore, the expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
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3. An object is dropped from a 450-meter tower. The height of the falling object is given
by y(t) = 450-4.9t2, with height y in meters and time t in seconds.
(a) Use the basic derivative rules to compute y' (2).
Using basic derivative rules the value of y' (2) is 19.6 .
Derivative rules in calculus square measure accustomed realize the derivatives of various operations and differing types of functions like power functions, exponent functions, exponential functions, etc. Some vital spin off rules are:Power Rule ,Sum/Difference Rule ,Product Rule ,Quotient Rule,Chain Rule The power rule of derivatives says d/dx (xⁿ) = nxⁿ⁻¹We have given a function of t y(t) = 450-4.9t².
On differentiating with respect t , we get
y'(t) = 2 × 4.9t
y'(t) = 9.8 t ......(1)
Putting t = 2 in equation (1) , we get
y'(2) = 9.8 × 2
= 19.6
Hence , value of y'(2) is 19.6
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Which graph represents the function h(x)=−x√+2?
Of like f(x)= - √x+2
A b c d
Answer:
use air math
Step-by-step explanation:
hope that helps
The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each
The salaries of each will be 127975 and 182875.
How to compute the value?Lat the salaries of B = b
Let the salary of A = b + 54900
Therefore, we will add them together to get the value:
b + b + 54900 = 310850
2b + 54900 = 310850
2b = 310850 - 54900
2b = 255950
b = 255950/2
b = 127975
a = b + 54900 = 127975 + 54900 = 182875
Therefore, the salaries of each will be 127975 and 182875.
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The sales tax in Jorge's state is 7%. Jorge bought a Ford Mustang having a sales tax of $1,928.22. What was the cost of the car?
The cost of the car is $27,546
How to calculate the cost of the car ?The sales tax is 7%
Jorge bought a ford mustang having a sales tax of $1,928.22
Therefore the cost of the car can be calculated as follows
1928.22÷ 7/100
= 1928.22/0.07
= 27,546
Hence the cost of the car is $27,546
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#17 Write an inequality for
the situation below:
Bring at least $9 for dinner
tomorrow.
The inequality will be:
x ≥ $9
Which says that x can be equal to or larger than $9.
How to write an inequality?An inequality is a mathematical statement that relates two or more mathematical elements (variables, expressions, etc.) in such a way that there is not a equality like in an equation (an equality can be a solution, but not necessarily)
For example, if x represnts what you bring for dinner, we know that x needs to be at least $9.
So x = $9 is a solution.
But if x is a larger value than $9, it also is a solution.
This situation is represented by the inequality:
x ≥ $9
Which says that x can be equal to or larger than $9.
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The equation
3x-15
= 4x models temperature change, where x represents the difference in degrees in the last 24 hours. Solve for x.
Answer:
15
Step-by-step explanation:
[tex]3x-15=4x \\ \\ x-15=0 \\ \\ x=15[/tex]
Mike took a loan of $20,000 from a bank on 4 February 2009 at the rate of 8% p.a and paid back the same on 6th July 2009. Find the total amount paid by Mike
A. N20,666.30
B. N21,777.40
C. N22,888.50
D. N24,999.60
12x + 36 -14 -8x +5 =
Answer:
4x + 27
Step-by-step explanation:
12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)
12x + 27 - 8x Combine like terms (12x, -8x)
Divide 38 in two parts such that one part is 18 more than the other
Answer:
10 and 28
Step-by-step explanation:
let x be one number then the other is x + 18 ( 18 more than the other ), then
x + x + 18 = 38
2x + 18 = 38 ( subtract 18 from both sides )
2x = 20 ( divide both sides by 2 )
x = 10
and x + 18 = 10 + 18 = 28
the 2 numbers which divide 38 into the 2 parts are 10 and 18
whats the meaning of literature
Answer:
literature most commonly refers to works of the creative imagination, including poetry, drama, fiction, nonfiction, and in some instances, journalism, and song.
find the sum of the sequence 33 + 34 + 35 + 36 + . . . + 100
Answer:
230
Step-by-step explanation:
Calculate the area of a rhombus with vertices A(0,-5), B(9,2), C(12,13), and D(2,7) to the nearest tenth of a unit.
Answer:
93 square units (the figure is not a rhombus)
Step-by-step explanation:
You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).
Area from coordinatesThe formula for the area of a polygon based on its coordinates might be written ...
[tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]
where coordinate indices wrap around from the end to the beginning.
Using this formula, we find the area to be ...
A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|
A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93
The area of the figure is 93 square units.
DiagonalsThe area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.
Here, the differences between diagonally opposite coordinates are ...
AC = (12, 18) . . . . slope = 18/12 = 3/2
BD = (-7, 5) . . . . slope = 5/-7 = -5/7
If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...
(3/2)(-5/7) = (-15/14) ≠ -1
The given figure is not a rhombus.
If we assume the diagonals are perpendicular, then the area would be ...
A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048
Rounded to the nearest tenth, this area would be 93.0 square units.
The diagonals actually cross at an angle of about 88.152°, so the area is actually ...
93.048·sin(88.152°) = 93 square units (exactly)
(Development of this formula is beyond the scope of this answer.)
PLEASE HELP
In horse racing, a trifecta is a race in which you must pick the first-, second-, and third-place winners in their proper order to win a payoff. If horses are racing, and you randomly select three as your bet in the trifecta, what is the probability that you will win? (Assume that all horses have the same chance to win)
0.0030 is the probability that you will win .
In statistics, what does a probability mean?
The likelihood that an event will occur in a Random Experiment is measured by probability. A number between 0 and 1 is used to quantify probability, where, broadly speaking, 0 denotes impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.Here order of selection is important, so we will use permutation.
Total number of ways to choose 3 horses out of 8 = 8P3 = 8! / (8 - 3)! = 336
P(win) = 1/336 = 0.0030
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I need help with 4B please. Thank you!
The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:
y = 2e(x - 1).
What is the equation to the tangent line of a function of a point?Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:
[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]
In which f' is the derivative.
In this problem, the function is:
[tex]f(x) = e^{(x^2)}[/tex]
Applying the chain rule, the derivative is:
[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]
At x = 1, the derivative is:
[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]
Hence the tangent line at point (1,0) is given by:
y = 2e(x - 1).
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Write 670,000,000 in scientific notation.
6.7 × 109
0.67 × 109
67 × 108
6.7 × 108
6.7×10 8 is your correct answer
Answer:
the scientific notation is: [tex]6.7 ~x~10^{8}[/tex]
Step-by-step explanation:
The proper format for scientific notation is;
[tex]a~x~10^{b}[/tex]where a is a number or decimal number such that the absolute value of a is greater than or equal to one.
Given:
[tex]670,000,000[/tex]Thus, the scientific notation is:
[tex]6.7 ~x~10^{8}[/tex]Hope this helps!Answered by:AshTheNekoIan drove home from college traveling an average speed of 61.5 mph and drove back to the college the following week at an average speed of 65.2 mph. If the total round trip took 11 hours, how much time did it take Ian to drive from home back to college? Express the time in hours and minutes. Round to the nearest minute.
(Blank) hours (Blank) minutes
Show your work!
Explain your answer!
Do not spam answers!
Thanks!
Time taken in hours from home to college is; 5 hours 20 minutes
How to calculate time from speed?We are given;
Going home DATA:
Speed rate = 61.5 mph
Distance = x miles
Time taken = distance/speed = x/61.5 hrs
Going to college DATA:
Speed rate = 65.2 mph
Distance = x miles
Time taken = x/65.2 hrs
Thus, the equation set up is:
x/61.5 + x/65.2 = 11
Multiply through by (61.5 * 65.2) to get;
65.2x + 61.5x = 11 * (61.5 * 65.2)
126.7x = 44107.8
x = 44107.8/126.7
x = 348.1279 miles
Thus;
Time in hours from home to college = 348.1279/65.2
Time in hours from home to college = 5.34 hours = 5 hours 20 minutes
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