The equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 2)^2 + (y + 4)^2 = 50, is in standard form, then
h = -2
k = -4
r = 5√2
Hence, the equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
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How many times will the graph of y=x^2+3 interest the x-axis?
What’s this I need help asap
Answer:
see attached photo for the graph
i need help with this please please please !asap !
Answer:
18
7b² + 12b + 19 + -------
b - 1
Step-by-step explanation:
(7b³ + 5b² + 7b - 1) ÷ (b - 1)
1 | 7 5 7 -1
↓ 7 12 19
----------------------
7 12 19 18
18
7b² + 12b + 19 + -------
b - 1
I hope this helps!
Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.
(3,-5),(-3,3),(0,2)
Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.
Three or more points are said to be collinear if they lie on a single straight line.
To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
Getting the slope of each pair of points:
(3 , -5) and (-3 , 3)
m = (y2 - y1)/(x2 - x1)
m = (3 - -5)/(-3 - 3)
m = 8/-6
m = -4/3
(-3 , 3) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(0 - -3)
m = -1/3
(3 , -5) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - -5)/(0 - 3)
m = 7/-3
m = -7/3
Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.
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Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x + 2)^2 - 16
Answer:
x = 2, x = -6
Step-by-step explanation:
Given quadratic function in vertex form:
[tex]f(x)=(x+2)^2-16[/tex]
The zeros of a function occur when f(x) = 0:
[tex]\implies (x + 2)^2 - 16 = 0[/tex]
Add 16 to both sides:
[tex]\implies (x + 2)^2 - 16+16 = 0+16[/tex]
[tex]\implies (x + 2)^2 =16[/tex]
Square root both sides:
[tex]\implies \sqrt{ (x + 2)^2} =\sqrt{16}[/tex]
[tex]\implies x+2= \pm 4[/tex]
Subtract 2 from both sides:
[tex]\implies x+2-2= -2 \pm 4[/tex]
[tex]\implies x= -2 \pm 4[/tex]
Therefore:
[tex]\implies x=-2+4=2[/tex]
[tex]\implies x=-2-4=-6[/tex]
The zeros of the given quadratic function are x = 2, x = -6.
Determine whether the given conclusion is based on inductive or deductive reasoning.
Andrew's mom makes spaghetti for dinner on Mondays. Today is Monday. He concludes that his mom will make spaghetti for dinner.
Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. The given conclusion is deductive reasoning.
What are Inductive reasoning and Deductive Reasoning?Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.
Given the statements,
Andrew's mom makes spaghetti for dinner on Mondays. Today is Monday. He concludes that his mom will make spaghetti for dinner.From the given sentences, the first sentence is a general statement, the second statement is a specific statement. And, at the last, the third statement is a conclusion statement.
Hence, the given conclusion is deductive reasoning.
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Construct a true table. Use tea for true enough for falls
Truth Table is used to perform logical operations in Maths. These operations comprise boolean algebra or boolean functions. It is basically used to check whether the propositional expression is true or false, as per the input values. This is based on boolean algebra.
A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.
Here we construct truth table for And operation -
see attachment below -
So because we don't have statements on either side of the "and" symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p.
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داند
14) The weight of Callie's backpack is 2 ½ times the weight of Carl's backpack. If
Carl's backpack weighs 3 pounds, how much does Callie's backpack weigh?
The weight of Callie's backpack is 7½ pounds which is calculated by multiplication of the number of times the bag is heavier with the weight of the bag.
Multiplication or product of two constants is defined as the number of times a particular constant is added . If we want to multiply a and b then their product is equal to b times a added.
a+a+a+a....... b times=ab
The multiplication is one of the four basic arithmetic operations that are used in mathematics and everyday lives.
Given the weight of Callie's bag is 2 ½ times the weight of Carl's backpack.
Therefore to calculate the the weight of Callie's backpack we multiply the weight of Carl's backpack with 2 ½.
Weight of Carl's backpack=3 pounds
Therefore weight of Callie's backpack= 2 ½×3 pounds= 7½ pounds
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which picture has an area equivalent to 8/12 shaded?
Answer:
B)1/3 + 1/3 = 2/3 or 8/12Step-by-step explanation:
semplify
8/12 = 2/3
B)
1/3 + 1/3 = 2/3
Select the correct answer. histogram is plotted between x-axis (ranging from 0 to 5) and y-axis (ranging from 1 to 7). the histogram exhibits negative skewness. what type of skew is observed in this histogram? a. symmetry b. zero skew c. negative skew d. positive skew
Answer:
C. Negative skew
Step-by-step explanation:
I did the test and got it right, plato / edmentum
If x2+y2 = 12 and x2-y2=18, what is the value of x4-y4?
Answer:
Step-by-step explanation: add the equations
2x² = 30
x² = 15
y² = 12 - 15
= -3
x4 -y4 = 15² - (-3)²
= 216
Help Please
An employee earns $17.55 per hour after receiving a 8% raise. What was the employee's hourly pay before raise? Round your answer to the nearest cent. The employee's pre-raise salary was $____.
Answer:
Step-by-step explanation:
17.55 x 0.92 = $16.15
HELP ASP SHOW UR WORK YOULL GET BRAINILEST IF UR CORRECT
Answer:
x = 5
Step-by-step explanation:
[tex]12x = 70 - 2x[/tex]
[tex]14x = 70[/tex]
[tex]x = 5[/tex]
Answer:
Here :))
Step-by-step explanation:
a. What is an equation of the circle for a circular irrigation field that has radius 12 and center (7,-10) ?
The equation of the circle for a circular irrigation field with radius 12 and center at (7 , -10) is (x - 7)^2 + (y + 10)^2 = 144.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circular irrigation field, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (7 , -10)
r = 12
(x - 7)^2 + (y - -10)^2 = 12^2
(x - 7)^2 + (y + 10)^2 = 144
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Which one of the following is testable?
A) science
B) pseudoscience
Answer: science
Step-by-step explanation:
Rosa is building a guitar.The second fret is 33.641 mm from the first fret.The third fret is 31.749 mm from the second fret
How far is the third fret from the first fret?
The required distance between the third and first fret would be 64.390 mm.
What are Arithmetic functions?Arithmetic functions are defined as adding, subtracting, dividing, and multiplying built-in functions.
- Subtraction operation: calculates the difference between the right-hand and left-hand operands.
for example 4 -2 = 2
+ Addition operation: on either side of the operator, additional significances are added.
For example 4 + 2 = 6
We have been given that the distance between the first and second frets is 33.641 mm.
The distance between the second and third frets is 31.749 mm.
So the distance between the third and first fret will be:
⇒ 33.641 + 31.749
Apply the addition operation, and we get
⇒ 64.390 mm
Therefore, the required distance between the third and first fret would be 64.390 mm.
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Solve each equation. Check each solution. 2x / 3 - 1/2 = 2x + 5/6
The solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1
In this question, we have been given an equation.
2x / 3 - 1/2 = 2x + 5/6
We need to find the solution of given equation.
⇒ 2x / 3 - 1/2 = 2x + 5/6
⇒ (4x - 3)/6 = (12x + 5)/6
⇒ 4x - 3 = 12x + 5
⇒ 4x - 12x = 5 + 3
⇒ -8x = 8
⇒ x = -1
We need to check above solution.
so, substitute x = -1 in LHS of given equation.
LHS
= 2(-1) / 3 - 1/2
= -2/3 - 1/2
= -(2/3 + 1/2)
= -[(4 + 3)/6]
= -7/6
Now, substitute x = -1 in RHS of given equation.
RHS
= 2(-1) + 5/6
= -2 + 5/6
= (-12 + 5)/6
= -7/6
For x = -1, LHS = RHS
Therefore, the solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1
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If h = 7, what is ✓-27 + 4h?
A room is (……) feet wide and 16 feet long.
Find the area of the room
What is the common ratio of the geometric sequence below?
18, −6, 2, - —–—‚ ...
OA.
113
OB. -3
OC.--1/3
OD. 3
y = 8x + 3
The rate of change is 1 and the y-intercept is 4
Answer:
False
Step-by-step explanation:
The rate of change/slope of the linear equation is 8.
The y-intercept is the point where x has no value and y does.
And in the linear equation y = 8x+3, the y-intercept is 3.
Therefore, false.
- Thanks.
Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary.
tossing a coin and getting heads or tails
According to the question, to calculate the probability of the event which states that tossing a coin to get either head or tail
The total number of a coin is [tex]1[/tex]
And total number of possibilities are {H,T}
Therefore, the total number of favorable outcomes in which either head or tail can come: [tex]1[/tex]
As per question, the probability can be written as:
P(h or t) = P(h) + P(t)
[tex]= \frac{1}{2} +\frac{1}{2} =1 = 100%[/tex]
Hence, the probability of getting either head or tail is [tex]1[/tex].
The given event is mutually exclusive because it has [tex]100[/tex] percent which is close to tenth of a percent. And these two events cannot happen at the same time also, so they are mutually exclusive.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.
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Which two segments have the same length?
The two segments having the same length are line VW and line YZ. Option D
What is a number line?A number line can simply be defined as a straight line with numbers that are placed at equal intervals or segments along its length.
It is also known as a visual picture or representation of numbers.
From the number line shown, we have the following deductions;
Line XY = 10- 3 = 7Line YZ = 18 - 10 = 8Line WX = 3 --3 = 3 + 3 = 6Line VW = -2 --10 = -2 +10 = 8From the above solutions, we can see that line
Line VW is equal in length to line YZ
Thus, the two segments having the same length are line VW and line YZ. Option D
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Find the indicated measure. Round to the nearest tenth.
The area of a circle is 201 square meters. Find the radius.
Radius = 799.877cm
or = 7.99877m(in meters)
Explanation
Radius of a circle from area: if you know the area A, the radius is r = √(A / π).
➟ r = √(201/3.142)
➟ r = √63.98
➟ r = 7.99877m
Question is below in the image. Please explain. Thanks
Answer:
E
Step-by-step explanation:
Substituting x=0 into 1-x², we get:
[tex]\lim_{x \to 0} f(1-x^2)=\lim_{x \to 1} f(x)[/tex]
which does not exist.
Evaluate |2x+y-3z| for x=-2, y=10, and z=3.
Answer:
|2x + y - 3z|
Plug in the values
|-4 + 10 - 9|
= |-3|
= 3
Step-by-step explanation:
the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.
Stella is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4. Stella spent $52.50 altogether at the carnival and the number of rides she went on is twice the number of games she played. Write a system of equations that could be used to determine the number of games Stella played and the number of rides Stella went on. Define the variables that you use to write the system.
Answer:
Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
The equations are 2.5g +4r = 52.5 and g=2r.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Cost of game = $2.50
Cost of ride = $4
let g be the number of games
and, let r be the number of rides taken
total they played = $52.50
So, the equation can be
2.5g +4r = 52.5
and, number of rides she went on is twice the number of games she played.
So, g = 2r
Hence, The equations are 2.5g +4r = 52.5 and g=2r.
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Tamika has a points card for a movie theater.
She receives 20 rewards points just for signing up.
She earns 10.5 points for each visit to the movie theater.
She needs 167 points for a free movie ticket.
Write and solve an equation which can be used to determine xx, the number of visits Tamika must make to earn a free movie ticket.
Tamika's number of visits required to earn a free movie ticket is 14 visits.
What is meant by a linear equation with only one variable?A linear equation for one variable has only one solution and therefore is expressed as ax+b = 0, where a and b are two integers and x is a variable.For example, 2x+23=18 is a linear equation with the a single variable.According to the question, the given data is;
Tamika has a points card for a movie theatre which are as follow;
Signup rewards = 20 points
Each visit reward = 10.5
Total points needed = 167
Let 'x' be the number of visits.
Total points earned for x number of visits: 10.5x.
Thus, the equation according to statement;
20 + (10.5 × x) = 167
10.5x = 167 - 20
10.5x = 147
x = 147/10.5
x = 14 visits.
Therefore, Tamika's number of visits required to earn a free movie ticket are 14 visits.
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PLEASE HELP QUICK !!!
Which function represents the equation of the line?
Answer:
y = 3x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 6) ← 2 points on the line
m = [tex]\frac{6-0}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
y = 3x ← equation of line
The spinner is divided into 8 equal sections.
a. If the arrow lands on a number, what is the probability that it will land on 3 ?
The probability for the arrow that land in the number 3 is 1/8.
Probability:
Basically, the word probability means the possibility of occurring the required event.
Given,
The spinner is divided into 8 equal sections.
Here we need to find if the arrow lands on a number, what is the probability that it will land on 3.
Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.
Since the sections have equal size, each section is equally probable.
The probability of falling on each section is therefore 1/8.
We know that, in the 8 sections,
There is only one 3 in this list.
So, the possibility of the event = 1
Hence, probability is
=> 1/8
Therefore, the probability for the arrow that land in the number 3 is 1/8.
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