Answer:
2
Step-by-step explanation
Let's complete the square. We get:
(x^2-30x)+y^2+221=0
(x^2-30x+225)+y^2+221-225=0
(x-15)^2+y^2-4=0
(x-15)^2+y^2=4
By analyzing this, we see that the radius is just :[tex]\sqrt{4}[/tex]=2
A current flows at 5 mph. A boat can travel 20 mi downstream in the same amount of time it can go 12 mi upstream. What is the speed of the boat in still water?
If a current flows at 5 mph. A boat can travel 20 mi downstream in the same amount of time it can go 12 mi upstream. The speed of the boat in still water is 20mph.
How to find the speed?Boat speed x mph
Current speed 5 mph
Against current x - 5 mph
With current x + 5 mph
Distance against current 12
Distance with current 20
Time = same equate the time against with time with current
t=d/r
12 /(x- 5)= 20 /(x+ 5)
12 ×(x+ 5 )= 20 ×(x- 5 )
12 x + 60= 20 x -100
12 x -20 x = -100 + -60
-8x = -160
x = -160/-8
x= 20 mph
Therefore the speed of the boat in still water is 20mph.
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40 points Is this correct please help
Select the correct answer.
Which graphs represent functions?
-4
14
●
4-
24
+2
4
Graph A
y
4
-2
4
2
2
2
4
X
-2
F
4
2
2
>4
Graph B
4
•
2
2 4
x
►x
Answer:
Graph B
Step-by-step explanation: No point has the same x-axis
Find the area. Simplify your answer.
x+8
x+5
Answer:
9x+5
Step-by-step explanation:
Add x and 8x
35 POINTS TO WHOEVER CAN ANSWER THIS!!!!!
Answer:
y = (-5/2)x + 8
slope = -2.5
b = 8
x-intercept = 3.2
y-intercept = 8
Step-by-step explanation:
is 3(5a + 9) + 5a and 4(5a+6) equivalent
Answer:
no although they were close
Step-by-step explanation:
Find the perimeter of the polygon if
5cm, 4cm, and 3cm
P=
The perimeter of the polygon is found as the 42 cm.
Define the term perimeter of the polygon?The perimeter of an enclosed plane figure is referred to in geometry. The perimeter of an enclosed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.For the shown polygon:
Points A, B, C and D are tangents on the circle.
Thus, these tangent will subtend equal length from the points.
So,
AB = 3 + 4 = 7 cm
BC = 4 + 5 = 9 cm
As, ∠B ≅ ∠D, sides must also be equal.
CD = 5 + 4 = 9 cm
DA = 4 + 3 = 7 cm
Perimeter = AB + BC + BC + BC
= 7 + 9 + 9 + 7
Perimeter = 42 cm
Thus, the perimeter of the polygon is found as the 42 cm.
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What does 2x² mean?
A quadratic equation is a second-degree equation, meaning it contains at least one squared term.
what is quadratic equation ?A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.
given
2x2-7x = 0.
As we already know, a quadratic equation is a second-degree equation, meaning it contains at least one squared term.
Regarding comparing the quadratic equation in standard form with the equation 2x27x=0
ax ²+bx+c=0:
We get a=2, b=7, and c=0.
The equation 2x27x=0 is therefore a quadratic equation.
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Which expressions have a product of 10? Options A. 5/14x14, B. 5/6 x14, C. 3/5 x 20, 2/3 x 15. Please help this assignment is due tomorrow
The expressions that have a product of 10 are:
Option B: 5/6 x 14 = (5/6) * 14 = (514)/6 = 70/6 = 10
Option C: 3/5 x 20 = (3/5) * 20 = (320)/5 = 60/5 = 12
Option A: 5/14 x 14 = (5/14) * 14 = (514)/14 = 70/14 = 5
Option D: 2/3 x 15 = (2/3) * 15 = (215)/3 = 30/3 = 10
So options B and D have a product of 10.
Marvin is about to play tag with his friend Paul in a circular field. Paul is away from Joshua, and the field has a diameter of 12m. How far is the distance between the two friends?
Distance between Marvin and Joshua is less or equal to 12 meter.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given,
Marvin and Joshua are about to play in a circular field.
Diameter of the field D = 12m
Let distance between two friends is x
Since, Diameter is the longest chord in a circle
Thus, x ≤ D
Distance between two friends ≤ 12 meter.
Hence, Marvin and Joshua are 12 meter or less far away from each other.
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How do you solve a 3d triangle?
If the base of the prism has dimensions x and y, and the diagonal along the base is represented by c, then x² + y² = c². The longest diagonal in the solid, s, is the hypotenuse of the triangle formed by the sides c and the height of the solid, z. So we know that, c² + z² = s².
What is a triangle in 3D called?
Triangular Prism (3D shape with identical triangle bases) Cone (3D triangle with a circular base)
In the case of a cylinder, one or several of the following data must be provided: the total area/lateral area and the circumference/area of the base or the area of the base and the volume. Ex: provided the circumference of the base = 10π inches, and the lateral area = 50π inches², the equation can be written as 50π ÷ 10π = 5 inches.
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Select the correct answer from each drop-down menu.
As x approaches positive infinity, m(x) approaches positive infinity.
As x approaches negative infinity, m(x) approaches negative infinity.
What is meant by function?An expression, rule, or law in mathematics that establishes a connection between one variable (the independent variable) and another variable (the dependent variable).
A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.
If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.
A function is a rule that is applied to a number, known as an input, in order to produce a result, known as an output.
when [tex]$x^n$[/tex] ( n is odd number and n > 0), a > 0 and c is any constant,
[tex]$$x \rightarrow \infty, a x^n+c \rightarrow+\infty[/tex]
[tex]$x \rightarrow-\infty, a x^n+c \rightarrow-\infty$[/tex]
The complete question is;
The function f(x) = x^3 has been transformed, resulting in function m.
m(x) = 1\3x^3 + 6
As x approaches positive infinity, m(x) approaches___
As x approaches negative infinity, m(x) approaches___
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What is a domain of the functions Mcq?
A function's range is the collection of all possible values that it can accept, and its domain is the set of all values for which the function is defined.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x. The following requirements are frequently verified when a function's output y-value is required to be a real number:
1. The numerator cannot be zero.
2. Even roots (square roots, etc.) radicands (expressions denoted by a radical symbol) cannot have a negative value.
3. Only positive values can be used in logarithms.
4. Physical or other real-world constraints may be placed on word problems, such as the fact that time is not negative or that the number of items is an integer.
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Which of the following is the solution of the equations: 2x+3y=3, 3x+2y=7
The solution of the equations: 2x+3y=3, 3x+2y=7 is x =0 and y =1.
Equation:
An equation is a mathematical formula containing two algebraic expressions on either side of an equal sign (=). It shows the equivalence relation between the formula written on the left and the formula written on the right. In any formula, L.H.S = R.H.S (left side = right side). We can solve equations to find the values of unknown variables that represent unknown quantities. If a statement doesn't have an equals sign, it means it's not an equation. considered to be an expression.
According to the question:
Given in the question:
2x+3y=3 --------------------------------------- (1)
3x+2y=7 ---------------------------------------- (2)
Multiplying Equation (1) by 3 and (2) by 2, we get:
6x + 9y = 9 --------------------------------- (3)
6x + 4y = 14 --------------------------------- (4)
Now,
Subtracting equation (4) from (3)
5y = 5
⇒ y = 1
Now, putting y = 1 in equation (1) we get:
2x + 3 × 1 = 3
⇒ 2x + 3 = 3
⇒ x = 0
Therefore, x =0 and y=1.
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How would the equation f (x) = log (x - 2) + 8 be shifted with respect to the parent function
Answer:
right 2 up 8 units
Step-by-step explanation:
the (x-2) is basically the opposite of what u think so it goes right
and +8 is normal so its up 8
Which doesn't belong and
why?
64
289 81 363 121
The number 363 does not belong to the set.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
The given numbers are 64, 289, 81, 363 and 121.
The numbers 64, 289, 81 and 121 is a perfect square of integers.
64 = 8²
289 = 17²
81 = 9²
121 = 11²
But 363 is not a perfect square of any integer.
Hence the number which is odd in the list is 363.
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What is the 15th digit of pi
What is the difference between expression and polynomial class 8?
Expression and polynomial are both mathematical terms that are used to represent mathematical equations.
An expression is any combination of symbols, numbers, and operations that represent a value or a quantity. Expressions can be represented as algebraic equations, numerical equations, or verbal phrases. A polynomial is a specific type of expression that is composed of one or more terms with each term containing a power of a single variable. A polynomial can be represented with a single variable or multiple variables.
A formula is an expression or equation that represents an idea or a relationship between two or more variables. A calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
In summary, an expression is any combination of symbols, numbers, and operations that represent a value or quantity, while a polynomial is a specific type of expression composed of one or more terms with each term containing a power of a single variable. A formula is an expression or equation that represents an idea or relationship between two or more variables, while a calculation is the actual process of evaluating an expression or equation to determine a numerical value or answer.
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Taylor writes an expression with 5 terms. All 5 terms are like terms. How many terms are in the equivalent expression with the least number of terms
Answer:
An equivalent expression with the least number of terms will have 1 term if all 5 original terms are like terms. This is because like terms can be combined using the distributive property and addition, resulting in a single term with a combined coefficient.
Step-by-step explanation:
pls helppppppp dont worry abt the one i have marked
What is the exponential of 0?
Answer:
The exponential form of 0 is 0.
In simple words, the exponents can said to be the powers of the base. For example, in 2³, the exponent will be 3. If a number is given without any power then its power is 0. The exponential form is simply the number with exponents.
Find the value of the remainder. Enter the value of the remainder (only the number, you do not need to place it over the divisor)
It is simple to locate the rest. Simply divide the number by another number with its multiples to obtain the remaining.
What is a remainder?Always less than the divisor is the remainder. It indicates that the division is not complete if the remainder exceeds the divisor. It might either be higher or lower than the quotient. For instance, the remaining is six when the number seven is divided by 41, leaving five as the quotient.
It's simple to locate the rest of them. To obtain the remainder, we simply divide the number by a different integer that is one of its multiples.
the surplus after division (happens when the first number does not divide exactly by the other). Example: Dividing 19 exactly by 5 is not possible. The closest you can go to 19 without going over is 3 x 5, which is 15 and 4 less. 4 remains as a result.
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What is the degree of the polynomial 3x² 5x¹ 7?
The degree of the polynomial 3x² 5x¹ 7 is 2.
This can be calculated by examining the highest exponent of the variable in the polynomial. Since the highest exponent is 2, the degree of the polynomial is 2.
Formula: Degree = Highest Exponent of the Variable
To calculate the degree of the polynomial 3x² 5x¹ 7, we first need to examine the highest exponent of the variable. The highest exponent is 2, therefore, the degree of the polynomial is 2.
3x² = 3x2 = 3x2 = Degree = 2
5x¹ = 5x1 = 5x1 = Degree = 1
7 = 7 = 7 = Degree = 0
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Darren randomly selected fifty 10th grade students at his high school and asked how they normally get to school. The results are shown in the
table.
Mode of
Number of
Transportation Students
Bus
38
Car
Walk
Which inferences can be made from the results? Choose all correct statements.
Approximately 3% of the 10th graders at Darren's school take
car.
E
Approximately 18% of the 10th graders at Darren's school walk.
C. Approximately 18% of all the students at Darren's school walk.
D. Approximately 38% of the students at
Darren's school ride the bus.
Approximately 76% of the 10th
graders at Darren's school ride the bus.
B} Approximately 18% of the 10th graders at Darren's school walk.
E} Approximately 76% of the 10th graders at Darren's school ride the bus. Options B and E are correct options
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Total students = 50
Number of students in bus = 38
Number of students in car = 3
Number of students in Walk = 9
Percentage student go to school by bus = 36 / 50 × 100% = 76%
Similarly,
Percentage students go to school by car = 6%
Percentage of students who go to school by walk = 18%
From the above calculation, the Correct options,
B} Approximately 18% of the 10th graders at Darren's school walk.
E} Approximately 76% of the 10th graders at Darren's school ride the bus.
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.
The graph shows the location of the entrance to a state park each unit on the graph represents 1 km Rodrigo uses the graph to locate a waterfall the waterfall is located 3 km to the left and 4 km down from the park entrance Rodrigo says we ordered pair for the waterfall is three, nine use the drop-down menus to explain Rodrigo
The location of the waterfall on the graph will be (3,1). Instead of going down down, Rodrigo goes 4 units upward direction.
What are the coordinates of a point?
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).
Given that the location of the entrance is at (6,5).
To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.
The x-coordinate decreases to the left side of a point and increases to the right side of a point.
The y-coordinate decreases to a downward point and increases upward a point.
The x-coordinate of the waterfall is 6 - 3 =3
The y-coordinate of the waterfall is 5 - 4 = 1.
The coordinate that represents the location of a point is (3,1).
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1. During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?
Yesterday, between noon and midnight, the temperature dropped by 29.6°F. If the temperature was -8.6°F at midnight, what was it at noon?
Why is it called substitution method?
It is called the substitution method because we substitute the value of one variable with another one and solve the equation.
By changing the value of another variable in an equation, the variable can be eliminated using this method. Thus, the elimination by substitution method is the name given to this technique.
As we are aware, the substitution approach entails solving the equation to determine the value of the variable, which is then substituted in the other equation. The elimination approach, in contrast, involves removing variables from the equation such that the equation's system can be reduced to being the function of a single variable.
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(-6) to the power of -2
Answer: -1/36
Step-by-step explanation:
Answer: - 1/36
Step-by-step explanation: exponet rule a^-b=1/a^
WILL MARK BRAINLEST 40 POINTS Simplify three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed.
−18
−12
36
42
The value of the expression is -5.84
How to find the value?The question is mathematically expressed as follows
The question reads: three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed
[(3/5*1 + √16)]² - (5-2)³
Simplify the brackets first
This implies that
(3/5 + 4)² - (3)³
Simplify further to have
[(3+20)/5]² - 27
⇒(23/5) -27
Simplify to get
529/25 - 27
= 21.16 - 27
=-5.84
Therefore the expression gives -5.84
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