To solve for three unknown numbers with given relationships, we set up algebraic equations. Using substitution, we find the three numbers by solving the linear system. The numbers are 21, 28, and 42.
Explanation:The problem presented is a typical linear equation problem found in mathematics where we need to find the values of three unknown numbers with the given relationships between them. To find the three numbers, we set up algebraic equations based on the information provided. Let's denote the first number as x, the second number as y, and the third number as z.
According to the problem:
The sum of the three numbers is 91: x + y + z = 91.The third number is 2 times the first: z = 2x.The first number is 7 less than the second: x = y - 7.Let's now use substitution to solve for the numbers. Substituting the value of x from the third equation into the second equation, we get z = 2(y - 7). Plugging the expressions for x and z back into the first equation, we have y - 7 + y + 2(y - 7) = 91. Simplifying this equation gives us 4y - 21 = 91, which solves to y = 28. Using y = 28, we find x = 21 and z = 42.
Therefore, the three numbers are 21, 28, and 42.
Find the median of the following set of data. $12.50, $13.23, $11.20, $14.50, $12.50, $13.23, $15.60, $15.75
Answer:
The answer is 13.23
Step-by-step explanation:
In order to determine the median of the set of data, we have to know about median and how applicate it.
The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.
Also, if there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.
So, we arrange the set of data:
11.20
12.50
12.50
13.23
13.23
14.50
15.60
15.75
The data set is an even number.
The two middlemost numbers are: 13.23; 13.23.
So, the mean (average) is:
(13.23+13.23)/2=13.23
Finally, the median of the set of data is 13.23
The sum of 2 consecutive odd interferes is 92 find the numbers
92/2 = 46
46-1 =45
46+1 =47
45+47 = 92
numbers are 45 & 47
Find the 13th term of the sequence 8, -16, 32, -64, ...
A. 32768
B. -16384
C. -65536
D. None of these
What is the angle of rotation of the minute hand of a clock moving from 11:15 to 11:40? Include direction
convert 0.0000001 to a power of 10.
107
10−7
106
10−6
Answer:
Its actually 10 to the power of -7.
Step-by-step explanation:
This is because it can be written as:
1/10000000
Because there is 7 0's it becomes -7
Therefore its 10 to the power of -7
The graph shows the location of Grant's, Hannah's, and Isobel's houses. Each unit on the graph represents 1 block. A coordinate plane graph is shown. Grants house is located at negative 4 comma 3. Hannahs house is located at 1 comma 3. Isobels house is located at 1 comma negative 4. If Grant walks from his house to Isobel's house, then on to Hannah's house along the path shown, how far will he have walked in blocks? Round your answer to the nearest tenth.
The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given coordinate has been drawn in the graph below,
The locus of the path from Grant's house to Isobel's house and then Hannah's house is making a right-angle triangle.
By Pythagoras' theorem,
Distance from Grant's house to Isobel's house ⇒
√(4² + 7²) = 8.06
The distance from Isobel's house to Hannah's house ⇒ 3 + | -4| = 7
Therefore, 8.06 + 7 = 15.06.
Hence "The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06".
To learn more about graphs,
brainly.com/question/16608196
#SPJ5
Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.
The interior angle of a regular hexagon is 120 degrees, and the exterior angle is 60 degrees.
Explanation:To find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides, we will use the fact that the sum of interior angles of a polygon is given by (n-2)×180°, where 'n' is the number of sides of the polygon. Thus, a regular hexagon will have its interior angles sum to (6-2)×180° = 720°. Since all interior angles in a regular polygon are equal, each interior angle will be 720° ÷ 6 = 120°. The exterior angle of a regular polygon is calculated as 360° ÷ n. Therefore, an exterior angle of a regular hexagon will be 360° ÷ 6 = 60°.
So, the interior angle of a regular hexagon is 120°, and the exterior angle is 60°.
Person 1 can do a certain job in twenty-one minutes, and person 2 can do the same job in twenty-eight minutes. When completing the job together, which expression would be used to represent the amount of work done by person 1?
21
1/21
x/21
21x
Answer:
[tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.
Step-by-step explanation:
When someone does a work in x time,
Then, the work done by the person in one day = [tex]\frac{1}{x}[/tex]
Given,
Time taken by person 1 = 21 minutes
Thus, by the above statement,
The one day work of person 1 = [tex]\frac{1}{21}[/tex]
Hence, [tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.
Second option is correct.
Find the next term in the sequence:
1/3,2/9,3/27,...
A. 4/36
B. 4/54
C. 4/81
D. 4/109
Please help me with math question
J is on -8, so it is 8 places to get to zero
K is on 4
so you have 8 + 4 = 12 units
Eight two-person teams are participating in a three-legged race. Find the number of orders in which all 8 teams can finish the race.
Answer:
thx for points man
Step-by-step explanation:
The area of a triangle is ½ (b) (h), where the base and height are always two sides of the triangle.
a. True
b. False
need help: write the expression in a complete factored form: x²-9x+xy-9y
A standard die is rolled. P(A)= the probability of rolling a three
P(B)= the probability of rolling a even number
What is P(A or B)
Identify the function as either a constant, direct variation, absolute value or greatest integer function f (x)=-4
Pleaseeeeeeeeeee help what is circle b
ne S is the blue line, where does it contact circle B?
it touches at Point K,
so that would be the tangency.
Answer Point K
#10 with explanation please
10. 4x = 1
x = 1/4
since there is no y if you graph x = 1/4 you would get a straight vertical line at x = 1/4
since it is a vertical line it is symmetric about the x axis ( it looks the same on both sides of the x axis)
Kieran’s wallet contains 7 bills: three $5 bills, two $10 bills, one $20 bill, and one $100 bill. if kieran pulls out two bills at random, what is the probability that he selects exactly two $5 bills?
Answer:
[tex]\bf\textbf{Probability of selecting exactly two $5 bill }=\frac{1}{7}[/tex]
Step-by-step explanation:
Total number of bills in the wallet = 7
Total number of $5 bills in the wallet = 3
Total number of $10 bills in the wallet = 2
Total number of $20 bill in the wallet = 1
Total number of $100 bill in the wallet = 1
We need to find the probability that he selects exactly two $5 bills.
Number of favorable outcomes = 3
[tex]\text{Probability of selecting one $5 bill }\frac{3}{7}[/tex]
[tex]\text{Probability of selecting second $5 bill }\frac{2}{6}[/tex]
[tex]\bf\textbf{Probability of selecting exactly two $5 bill = }\frac{3}{7}\times \frac{2}{6}=\frac{1}{7}[/tex]
PLEASE HELP!!!!!!!!!!!!! GEOMETRY
a country's population in 1995 was 175 million. In 2000 it was 181 million. Estimate the population in 2020 using exponential growth formula. Round you answer to the nearest million
Which is the graph of f(x)=3/2(1/3)^x
Answer:
Graph B
Step-by-step explanation:
Given is a function as
[tex]f(x) = \frac{3}{2} (\frac{1}{3} )^x[/tex]
There are 4 graphs given.
Out of the 4 options we have to select one which suits this graph
Let us study about f graph
X intercept is at infinity.
Or y=0 is asymptote for this curve
y intercept is when x =0
i.e. y intercept =3/2 (1) = 3/2
Only A and B satisfy this value of y intercept
Out of A and B we have to select one option
When x=1, we get
f(1) = 3/2 (1/3) = 1.5
This is satisfied only by Graph B.
Hence answer is graph B.
When x tends to -infinity y
simplify the expression r^-3s^5t^2/r^2st^-2
Quadrilateral ABCD is an Isosceles Trapezoid. Which angle is congruent to Angle C?
Answer:
The reason why any angles coming out from D and C are congruents is because of the geometry coungruence's concept of 2 items having the same pattern, shape or form and size as the mirror image of the other.
2 angles would be congruent by being the same angle in degrees or radians.
Thereby any angle coming out from C as vertex would be congruent with any other vertex point angle mirroring the resulting figure shaped by the radiants or degrees of such angle.
Step-by-step explanation:
Find the domain of f of x equals negative square root of the quantity two x plus four, plus 3?
What is the center and radius of the circle with equation x2 + y2 + 6x + 16y + 64 = 0?
Which shows the graph of the solution set of 3y – 2x > –18? Mark this and return
A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. how many square inches of wrapping paper are needed to wrap the box?
The surface area of the rectangular box is equal to 488 square inches.
What is surface area?The area of the surface of the rectangular box is equal to the total surface area of the rectangular box.
Given that, a gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches.
The surface area will be calculated as,
SA = 2(6 x 14) + 2(6 x 8) + 2(14 x 8)
SA = 2(84) + 2(48) + 2(112)
SA = 168 + 96 + 224
SA = 488 square inches of paper to wrap the box.
Therefore, the surface area of the rectangular box is equal to 488 square inches.
To know more about surface area follow
https://brainly.com/question/26759265
#SPJ5
Final answer:
To find the square inches of wrapping paper needed for a gift box, calculate the surface area of the box by using its length, height, and width dimensions.
Explanation:
To calculate the square inches of wrapping paper needed to wrap the box, you need to find the surface area of the box.
Calculate the surface area of each side of the box: 2(length x width) + 2(width x height) + 2(length x height).
Plug in the given dimensions: 2(14 x 6) + 2(6 x 8) + 2(14 x 8).
Calculate the total: 2(84) + 2(48) + 2(112) = 168 + 96 + 224 = 488 square inches needed.
A club has 12 members. In how many ways can we select four members to go on a trip?
When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither numerator determinant is zero, then the system _______.
A. has infinite solutions
B. is inconsistent
C. is dependent
D. is consistent
If the determinant of the coefficient matrix is zero and neither numerator determinant is zero when using Cramer's Rule to solve a system of equations, then the system is inconsistent, meaning there's no solution.
Explanation:When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither numerator determinant is zero, then the system is inconsistent.
Cramer's Rule is a method applied in linear algebra to solve a system of linear equations. The rule states that the system is inconsistent if the determinant of the coefficient matrix is zero (meaning the equations do not intersect) but at least one of the numerator determinants are nonzero. This condition indicates that there's no solution to the system of equations.
On the contrary, if the determinant of the coefficient matrix is zero an all the numerator determinants are also zero, the system is said to be dependent, meaning it would have infinitely many solutions.
Learn more about Cramer's Rule here:https://brainly.com/question/30682863
#SPJ3
Choose the correct description of the graph of the compound inequality x - 3 less than or equal to 5
A- open circle on 8, shading to left
B- closed circle on 8, shading to left
C- open circle on 8, shading to right
D- closer circle on 8, shading to right
Answer:
B- closed circle on 8, shading to left.
Step-by-step explanation:
We have been given an inequality [tex]x-3\leq 5[/tex]. We are asked to choose the correct description of the graph of the compound inequality.
Let us solve for x.
[tex]x-3+3\leq 5+3[/tex]
[tex]x\leq 8[/tex]
Since we have been given a less than or equal to sign, so we will have a solid dot at [tex]x=8[/tex].
Since the solutions for our given inequality are less than and equal to 8, so we will shade in all values of x that are to the left of 8.
Therefore, option B is the correct choice.