The value of x is equal to 85°.
What is the exterior angle theorem?In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the given triangle is equal to the measure of angle 125 degrees;
∠x + 40° = 125°
∠x = 125° - 40°
∠x = 85°
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Given the function f(x) = -x + 4, then what is f(-3x) as a simplified
polynomial?
Answer:
3x+4
Step-by-step explanation:
f(x) = - x+4
Substitute in x=-3x
f(-3x)= - (-3x) + 4 = 3x+4
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Thomas has some leftover paint that he would like to sell. He mixes
4 3/8
gallons of blue paint with 6 5/8
gallons of white paint. Then, he pours this light-blue mixture into
1/4
gallon containers. To find out how many of these
1/4
gallon containers he can fill, which two equations would you need?
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Answer:
4 3/8+6 5/8=x and x÷1/4=number of gallons
Step-by-step explanation:
You are planning a vacation and have found a great rate on a hotel. The hotel is $99 per night, plus tax and a
resort fee. The expression 99(1.05)+ 25 represents the total cost of the hotel for nights. What is the tax
rate and the resort fee? Explain how you know
Answer:
resort fee is 25
tax rate is 1.05
Step-by-step explanation:
What is the formula for the circumference of a circle? c = pi r squared c = 2 pi r c = 2 pi r squared c = pi r cubed
The formula for the circumference of a circle is "c = 2 pi r", where "c" represents the circumference, "pi" represents the mathematical constant pi (approximately equal to 3.14159), and "r" represents the radius of the circle.
This formula relates the distance around a circle to its size, and is useful for calculating various measurements related to circles, such as arc length and sector area. It is important to note that the formula for the circumference of a circle assumes the circle is a perfect, unbroken curve, and thus may not be accurate for circles that are not perfectly round.
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The cost of 2 rugby balls and 3 golf balls is £18.39.
The cost of 5 rugby balls and 7 golf balls is £45.10.
Work out the cost of
a) a rugby ball.
b) a golf ball.
The cost of a rugby ball is $6.57
The cost of a golf ball is $1.75
How to calculate the cost of a rugby and golf ball ?Let x represent the cost of a rugby ball and y represent the cost of a golf ball
2x + 3y= 18.39.........equation 1
5x + 7y= 45.10.........equation 2
multiply equation 1 by 5 and equation 2 by 2
10x + 15y= 91.95
-
10x + 14y= 90.2
y= 1.75
Substitute 1.75 for y in equation 2
5x + 7(1.75)= 45.10
5x + 12.25= 45.10
5x= 45.10-12.25
5x= 32.85
x= 32.85/5
x= 6.57
Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75
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Write a quadratic function f whose zeros are -3 and -8
Answer:
y = x² + 11x + 24
Step-by-step explanation:
y = (x + 3)(x + 8)
Expand
y = x² + 8x + 3x + 24
Combine like terms
y = x² + 11x + 24
Out of 113 students, it was found that 18 drink neither tea nor coffee, 67 drink tea and 37 drink coffee.Find:
i) How many students drink coffee only?
ii) How many students like tea only?
Also show in the Venn diagram?
Answer:
Step-by-step explanation:
find the slope. (no units needed)
Answer: 4/5
Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.
Using the linear function created, find f(x)=8500. What does it mean in this context?
(Just look at the table for the info)
Which equation has the solution x = 2?
A 2x-3=19
B 3x+2=8
C 4x-4=-4
D 5x+1=10
Answer:
The answer is B.
Step-by-step explanation:
You can solve this problem by plugging in 2 for x in the given equations.
2(2) - 3 = 19 is false
3(2) + 2 = 8 is true
4(2) - 4 = -4 is false
5(2) + 1 = 10 is false
SOMEBODYY HELPPPPPOOPPPPOOPPPPP
Answer:
y^2+z^2= x^2
Step-by-step explanation:
y^2+z^2= x^2 is the correct answer because the formula to find the hypotenuse (longest side in a triangle) is to add up the value of the squares (y^2+z^2 as an example to find for x^2).
What is the midpoint of the line segment with endpoints (-1,3) and (-5,5)?
Answer:
(4, 5)
Step-by-step explanation:
Calculate the midpoint using the midpoint formula
midpoint = [( + ), ( + ) ]
with (, ) = (1, 2) and (, ) = (7, 8)
midpoint = [(1 + 7), (2 + 8) ]
= (4, 5)
( -6p - 8 ) - ( 2p - 6 ) plz :)
Answer:
-8p-14
Step-by-step explanation:
the stream function for a two dimension, nonviscous, incompressible flow field is given by the expression where the stream function has the units of ft^2/s with x and y in feet. is the continuity equation satisfied? g
The continuity equation is satisfied and the flow is incompressible.
To check if the continuity equation is satisfied, we need to take the partial derivatives of the stream function with respect to x and y and see if they satisfy the continuity equation
Continuity equation: ∂u/∂x + ∂v/∂y = 0
where u and v are the x and y components of the velocity field, respectively.
From the definition of the stream function, we have
u = ∂Ψ/∂y = -2
v = -∂Ψ/∂x = -(-2) = 2
Taking the partial derivatives of u and v with respect to x and y, we have
∂u/∂x = 0, ∂v/∂y = 0
Substituting these values into the continuity equation, we get
∂u/∂x + ∂v/∂y = 0 + 0 = 0
Since the continuity equation is satisfied (resulted in zero), the flow is incompressible.
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The given question is incomplete, the complete question is:
The stream function for a two-dimensional, nonviscous, incompressible flow field is given by Psi = -2(x-y) where the stream function has the units of ft^2/s with x and y in feet. (a) Is the continuity equation satisfied?
16047 divide by 60
4620 divide by 250
52080 divide by 15
brainleiest
Answer:
1) 267.45
2) 18.48
3) 3472
Exercise 14e Copy and complete Table 14.3 for circles. 22 (Use the value for x.) 7 a b C d e radius 7m 140 mm f Table 14.3 2.1 cm diameter 7 cm 28 m 3-1/2 cm 3 m area
The complete table for circle where π = 22/7 is below;
a. radius= 7 m
diameter = 14 m
Area = 154 m²
b. radius= 3.5 cm
diameter = 7 cm
Area = 38.5 cm²
c. radius= 140 mm
diameter = 280 mm
Area = 61,600 mm²
d. radius= 14 m
diameter = 28 m
Area = 616 m²
e. radius= 1¾ cm
diameter = 3½ cm
Area = 9.625 cm²
f. radius= 2.1 cm
diameter = 3m
Area = 13.86 cm² or 7.07 m²
What is the area of the circle?a. radius= 7 m
diameter = 7m × 2 = 14m
Area = πr²
= 22/7 × 7²
= 154 m²
b. radius= 7cm /2 = 3.5 cm
diameter = 7 cm
Area = πr²
= 22/7 × 3.5²
= 22/7 × 12.25
= 38.5 cm²
c. radius= 140 mm
diameter = 280 mm
Area = πr²
= 22/7 × 140²
= 61,600 mm²
d. radius = 14 m
diameter = 28 m
Area = πr²
= 22/7 × 14²
= 616 m²
e. radius= 1¾ cm
diameter = 3½ cm
Area = πr²
= 22/7 × (1¾)²
= 9.625 cm²
f. radius= 2.1 cm
diameter = 3 m
Area = πr²
= 22/7 × 2.1²
= 13.86 cm²
or
Area = πd²/4
= (22/7 × 3²) / 4
= (22/7 × 9) / 4
= 28.28571428571428 / 4
= 7.07 m²
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A car moving on a highway covers the first 400.0 m in 18.0s and then covers the next 250.0 m in 24.0 s.
What is the average speed of the car?
Answer: 15.48 m/s
Step-by-step explanation:
The following information can be gotten from the question:
Total distance covered by the car will be:
= 400m + 250m
= 650m
Total time taken = 18.0s + 24.0s = 42s
Average speed = Distance/Time
= 650/42
= 15.48 m/s
A rectangle that is 2" x 3" has been scaled by a factor of seven suppose you want to scale the copy back to its original size what scale factor should you use
Answer:
Scale factor of \(\frac{1}{7}\).
Step-by-step explanation:
scale = \(\frac{scaled length}{actual length}\)
The rectangle has been scaled by a factor of seven implies that its real dimensions has been multiplied by seven. Therefore, to scale the copy back to its original size, its dimension should be multiplied by a scale factor of \(\frac{1}{7}\).
Example:
when the scale is 7;
2 x 7 = 14
3 x 7 = 21
when the scale is \(\frac{1}{7}\);
14 x \(\frac{1}{7}\) = 2
21 x \(\frac{1}{7}\) = 3
Finding Angles (Level 1)
PLEASE full explanation :))
Answer:
59°Step-by-step explanation:
A and B are complementary angles since C is right angle.
m∠A + m∠B = 90°31° + m∠B = 90°m∠B = 90° - 31°m∠B = 59°which of the following cannot be determined from the information collected by the system? responses the total number of books borrowed in a given year the total number of books borrowed in a given year the total number of books that were never borrowed in a given year the total number of books that were never borrowed in a given year the total number of books that were returned past their due date in a given year the total number of books that were returned past their due date in a given year the total number of people who borrowed at least one book in a given year
The total number of books that were never borrowed in a given year. Option B
What can not be seen?A library system is a piece of software made specifically for managing a library's activities and inventory of books, periodicals, magazines, and other materials.
It offers a centralized database that librarians may use to manage the library's collection, keep track of borrowing, and keep an eye on other activities related to the library.
This is the kind of software used to collect the information in the question above.
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#Missing parts;
A library system contains information for each book that was borrowed. Each time a person borrows or returns a book from the library, the following information is recorded in a database.
Name and the unique ID number of the person who was borrowing the book
Author, title, and the unique ID number of the book that was borrowed
Date that the book was borrowed
Date that the book was due to be returned
Date that the book was returned (or 0 if the book has not been returned yet)
Which of the following CANNOT be determined from the information collected by the system?
A
The total number of books borrowed in a given year
B
The total number of books that were never borrowed in a given year
C
The total number of books that were returned past their due date in a given year
D
The total number of people who borrowed at least one book in a given year
What is the equation that moves g(x) = log2 x down 3 units?
When we want to translate the function to the right or left, we add a constant to its argument.
\(f(x)\rightarrow f(x+a)\)If a is positive the function goes to the left, and if a is negative the function goes to the right.
When we want to translate the function up or down, we add a costant to the function value
\(f(x)\rightarrow f(x)+a\)If a is positive, the function goes up, and if a is negative the function goes down.
Since we want to translate our function 3 units down, we need to subtract 3 from the original function
\(g(x)\rightarrow g(x)-3\)Since our original function is
\(g(x)=\log _2x\)The translated function is
\(h(x)=\log _2x-3\)Which regular polygon can be used to form a tessellation?
I need help
Answer: Option 4 (Hexagon)
Step-by-step explanation:
A equilateral triangle, square and hexagon can be used to form a tessellation.
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In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16. what is the mean for this sample?
The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.
Then the data set will be given below.
10, 10, 10, 10, 10, 16
Then the mean of the data set will be
Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6
Mean = 66/6
Mean = 11
Thus, the mean of the sample will be 11.
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Which is equal to 1/58^8 ? a.58^-8 b.-1/58^-8 c.58^8 d.1/(58)^-8
a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.
How to evaluate this expression ?To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.
Applying this rule to the expression 1/58^8, we get:
1/58^8 = 1/(58^8) = 58^-8
Therefore, the correct answer is 58^-8.
It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:
1/58^8 = (1/58)^8 = 58^-8
This simplification shows that the correct answer is still 58^-8.
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If a system of two linear equations has infinitely many solutions, which of the following statements describes the graph of the corresponding two lines in the Iy-plane?
A The lines are coinciding.
B The lines are intersecting at only one point.
c The lines are parallel.
The lines are perpendicular.
Answer:
A.
Step-by-step explanation:
The lines touch along every point so they are on top of each other.
The given system of equations represent two coinciding lines.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
A linear equation in two variables represent a straight line.
As system of equations in two variables can be represented as
a₁x + b₊y + c₁ = 0
a₂x + b₂y + c₂ = 0
When there are two such equations having infinite solutions the relation between the coefficients is given as,
a₁/a₂ = b₁/b₂ = c₁/c₂
It implies that there are infinite points common between them which is possible only when these two lines are coinciding.
Hence, the graph of corresponding two lines in the x- y plane represents coinciding lines.
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It takes two points to define a plane.
Answer:
In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines.
Step-by-step explanation:
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HELP MEE PLZZZZ I DON'T UNDERSTAND THIS
Answer: Choice D. \(6.44 \times 10^{-4}\)
========================================================
Work Shown:
We multiply the coefficients 9.2 and 7 to get 64.4, which is the same as 6.44*10^1 in scientific notation. When multiplying exponential expressions with the same base, we add the exponents
This is what the steps could look like
\(\left(9.2 \times 10^{-9}\right)\times\left(7 \times 10^{4}\right)\\\\\left(9.2\times7\right)\times\left(10^{-9} \times 10^{4}\right)\\\\\left(64.4\right)\times\left(10^{-9+4}\right)\\\\\left(6.44\times 10^{1}\right)\times\left(10^{-5}\right)\\\\6.44\times\left(10^{1}\times 10^{-5}\right)\\\\6.44\times\left(10^{1+(-5)}\right)\\\\6.44\times 10^{-4}\\\\\)
The final result is in scientific notation as the coefficient c is restricted such that \(0 \le c < 10\)
Find the digits x and y such that number 90x0y07 is divisble by 2017
No digit with the format 90x0y07 is divisible by 2017
How do determine the digits x and y?The given parameters are:
Dividend = 90x0y07
Divisor = 2017
The dividend is a 7-digit number, and the divisor is a 4-digit number
So, the quotient must be 3 to 4 digits.
Comparing the first and last digits of 90x0y07 and 2017;
The first and last digits of the quotient must be 4 and 1, respectively
So, we have:
90x0y07 = 2017 * 4a1
Assume a = 9.
So, we have:
90x0y07 = 2017 * 491
90x0y07 = 990347
The above is 6-digit.
So, we make use of a 4-digit quotient
This gives
90x0y07 = 2017 * 4ab1
Next, we make use of trial by error.
After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017
The closest attempt is
90x0y07 = 2017 * 4471
90x0y07 = 9018007
Where:
x = 1, y = 0 and the digit between x and y is 8, not 0
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Write an equation of the circle with center (9,-2) and diameter 8
Step-by-step explanation:
Equation of circle with center h,k and radius r
(x-h)^2 + (y-k)^2 = r^2
for this one this becomes (center 9,-2 and radius 4 )
(x-9)^2 + ( y+2)^2 = 16
Solve the equation. (Enter your answers as a comma-separated list.)x210x − 6x10x = 27(10x)x =
Answer:
x = -3, 9
Explanation:
First, let us divide both sides of the equation by 10^x; this gives,
\(\frac{x^210^x-6x\times10^x}{10^x}=\frac{27\times10^x}{10^x}\)\(\Rightarrow x^2-6x=27\)subtracting 27 from both sides gives
\(x^2-6x-27=0\)The left-hand side can be factored as
\((x-9)(x+3)=0\)which gives us two further equations
\(\begin{gathered} x-9=0 \\ \boxed{x=9.} \end{gathered}\)\(\begin{gathered} x+3=0 \\ \Rightarrow\boxed{x=-3.} \end{gathered}\)Hence, the two solutions we get are x = 9 and x = -3.