Knowing which x-values would result in division by zero can help you avoid using certain x-values. Finding the domains of rational functions is therefore likely to be your initial step.
What is a rational function?A function that measures two polynomials in comparison. Because one is divided by the other, just like a ratio, it is a "rational function."
All real numbers x, except those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.
For instance, the set of all real numbers other than x=0 is the domain of the parent function f(x)=1/x.
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A tourist in France wants to visit 12 different cities. How many different routes are possible?
A. 39,916,800
B. 144
C. 479,001,600
D. 12
The different routes are 479,001,600
How to determine the number of routes?The number of cities is given as:
n = 12
The cities are different.
So, the number of routes is:
Routes = 12!
Expand
Routes =12 * 11 * 10 * 9 * ..... * 1
Evaluate
Routes =479,001,600
Hence, the different routes are 479,001,600
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What is the area of the shaded portion of the circle?
A: (16pi-32) in^2
B: (16pi-8) in^2
C: (64pi- 32) in^2
D: (64pi - 8) in^2
Answer:
1st option
Step-by-step explanation:
the area of the shaded portion is calculated as
area of sector - area of white Δ
area of sector = area of circle × fraction of circle
= πr² × [tex]\frac{90}{360}[/tex] ( r is the radius )
= π × 8² × [tex]\frac{1}{4}[/tex]
= 64π × [tex]\frac{1}{4}[/tex]
= 16π in²
area of Δ = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = h = 8
area of Δ = [tex]\frac{1}{2}[/tex] × 8 × 8 = [tex]\frac{1}{2}[/tex] × 64 = 32 in²
then
area of shaded portion = (16π - 32 ) in²
If lines I and m are parallel, which pair of angles are congruent?
o 2 and 3
o 1 and 8
o 4 and 5
o 1 and 7
Answer:
last choice
angle 1 and 7 are alternet xterior angles
Step-by-step explanation:
The temperature outside is initially recorded, in Fahrenheit degrees at 8:00 AM and is re-recorded at various times throughout the day. The
temperature recordings are represented by the number line below.
The temperature in degrees Fahrenheit outside at various times throughout the day is given by the inequality x < 69°F
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A number line is a straight line with numbers placed at equal intervals.
Let x represent the temperature in degrees Fahrenheit, from the number line:
x < 69°F
The temperature in degrees Fahrenheit outside at various times throughout the day is given by the inequality x < 69°F
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A wheel with radius $1\text{ m}$ is rolled in a straight line through one complete revolution on a flat horizontal surface. How many meters did the center of the wheel travel horizontally from its starting location
The distance traveled by the center is equal to the distance traveled by the wheel 6.28m is traveled by the center.
Given: A wheel with a radius rolled in a straight line through one complete revolution on a flat horizontal surface.
To Find: How many meters did the center of the wheel travel horizontally from its starting location.
Solution:
consider the figure attached.
radius of wheel [tex]=1m[/tex]
Horizontal distance traveled by the wheel in one complete revolution
=circumference of the wheel
[tex]\\=2\pi r\\=2*3.14*1\\=6.28m[/tex]
Hence, the distance traveled by center is equal to the distance traveled by the wheel 6.28m is traveled by the center
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2. Use the Distributive Property to determine which of the following statements is equivalent to 5(6-2).
O11-2
30-2
O11-7
tive OR (JL22) 1 Tools Of The Trade
30 - 10
A
Answer:
30 - 10
Step-by-step explanation:
When you distribute, that means you multiply everything on the outside of the parentheses by everything on the inside.
5 (6-2)
is really
5*6 - 5*2
30 - 10
The following system of equation is given: -7x+7y=7\newline 2x-2y=-18−7x+7y=7
2x−2y=−18
Choose the correct solution for the system.
The given system of equation has no solution.
What is a System of Equation ?The set of equation that have common solution is called the system of equation
The equation given are
- 7x + 7y = 7
2x - 2y = -18
On simplifying the equations
- x + y = 1
x - y = -9
On adding these equations there is no solution
as
[tex]\rm \dfrac {a_1}{a_2 } = \dfrac{b_1} {b_2} \ne \dfrac{c_1}{c_2}[/tex]
The given system of equation has no solution.
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mark the congruent parts of the triangles and complete the proof
1) given
2) definition of an angle bisector
3) reflexive
4) [tex]\triangle ABD \cong \triangle CBD[/tex] (ASA)
5) [tex]\angle A \cong \angle C[/tex] (CPCTC)
5|x +9| < 10
x< ?
x> ?
Answer:
x<−7 and x>−11
Step-by-step explanation:
Let's solve your inequality step-by-step.
5(|x+9|)<10
Step 1: Divide both sides by 5.
5(|x+9|)/5 < 10/5
|x+9|<2
Step 2: Solve Absolute Value.
|x+9|<2
We know x+9<2 and x+9>−2
x+9<2(Condition 1)
x+9−9<2−9(Subtract 9 from both sides)
x<−7
x+9>−2(Condition 2)
x+9−9>−2−9(Subtract 9 from both sides)
x>−11
Answer:
x<−7 and x>−11
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{5|x + 9| < 10}[/tex]
[tex]\huge\textbf{Solving:}[/tex]
[tex]\mathbf{5|x + 9| < 10}[/tex]
[tex]\huge\textbf{DIVIDE 5 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{5|x \ + \ 9|}{5} = \dfrac{10}{5}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{|x + 9| < 2}[/tex]
[tex]\huge\textbf{Solve the absolute value:}[/tex]
[tex]\mathbf{|x + 9| < 2}[/tex]
[tex]\huge\textbf{Possibly we know that:}[/tex]
[tex]\mathbf{x + 9 < 2 \ and\ we\ know\ that \ x+9 > -2}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\mathbf{x + 9 < 2}[/tex]
[tex]\huge\textbf{SUBTRACT 9 to BOTH SIDES:}[/tex]
[tex]\mathbf{x + 9 - 9 < 2 -9}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x < -7}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\mathbf{x + 9 > -2}[/tex]
[tex]\huge\textbf{SUBTRACT 9 to BOTH SIDES:}[/tex]
[tex]\mathbf{x + 9 - 9 > -2 - 9}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x > -11}[/tex]
[tex]\huge\textbf{Answer(s):}[/tex]
[tex]\huge\boxed{\mathsf{x < -7\ or\ x > -11}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve for X. HELP?!
Answer:
x = 90
Step-by-step explanation:
In this figure the exterior angle is 130°
An exterior angle is the sum of the interior angles. The interior angles are x and 40 so x + 40 = 130 giving x = 130-40 = 90
Answer:
∠ x = 90°
(90 degrees)
Step-by-step explanation:
When two angles combine to make a straight line, we know that their angle values must add up to 180
Here, we can see that 130 combines with an inner angle to form a straight line. (I will be calling this interior angle z )
So, 130 + z = 180
130 + z = 180
- 130 -130
z = 50
We also know that all angles in a triangle must add up to 180 degrees, and because we know the two other angles of our triangle now, we can find x
z + x + 40 = 180
50 + x + 40 = 180
90 + x = 180
- 90 -90
x = 90
So, the measure of angle x is 90°
hope this helps!! have a lovely day :)
PLEASE HELP
A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18)? a It has the same slope and the same y-intercept. b It has the same slope and a different y-intercept. c It has the same y-intercept and a different slope. d It has a different slope and a different y-intercept.
The given function: B. has the same slope and a different y-intercept.
What is the Equation in Slope-intercept Form of a Linear Function?The linear function is expressed in slope-intercept form as, y = mx + b, where b is the y-intercept and m is the slope.
Slope (m) of the first function is: -7/9.
Its y-intercept (b) is: 3.
Given the equation, y + 11 = -7/9x - 18, rewrite in slope-intercept form:
y + 11 = -7/9x - 18
y = -7/9x - 18 - 11
y = -7/9x - 29
The slope (m) is: -7/9
Its y-intercept (b) is: -29
Therefore: B. It has the same slope and a different y-intercept.
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What is the value of Lilly’s expression when x=5? Show or explain how you got your answer
Answer:
what is lollies expression. I need to now what the expression is in order to plug 5 in for x.
Step-by-step explanation:
we need the expression first
anybody can help me?
The proportional graph that corresponds to the situation is: Graph C.
What is a Proportional Graph?A proportional graph is a straight line graph with a constant of proportionality, k = y/x. The equation of the graph is defined as, y = kx.
The equation, M = 3n, has a constant of proportionality as, k = 3.
In graph C, using a point on the line, (400, 1,200), the constant of proportionality, k = 1,200/400
k = 3.
Therefore, the answer is: C.
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How many apples?
Help me please, thanks so much
The number of Apples that were in the given fruit salad is approximately; 2170 Apples.
How to work with ratio questions?We are given the ratio of apples to oranges as;
A:O = 31:11
Now, we are told that there are 2940 apples and oranges in total.
Thus, the fractions of apples and oranges of the total will be;
Apple fraction = 31/(31 + 11) = 31/42
Orange Fraction = 11/42
Thus;
Number of Apples = (31/42) * 2940
Number of Apples = 2170 Apples
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please help I need help ill pick brainlyist
20points
Hello and Good Morning/Afternoon
Let's take this problem step by step:
What the problem wants to find:
⇒ area of a parallelogram
What is the area formula of the parallelogram:
⇒ Area = Base * Height
Let's gather the information necessary:
Base: 12 inHeight: 11 inLet's solve:
⇒ Area = 12 * 11 = 132 in²
Answer: 132 in²
Hope that helps!
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Answer:
132 inches squared
Step-by-step explanation:
Area is 132 inches squared
Method 1:
Area of parallelogram = base x height = 11inches x 12 inches = 132 inches squared
Method 2:
Move the triangle divided by the dotted line on the right to the left.
It becomes a rectangle of 11 inches by 12 inches. 11 inches x 12 inches = 132 inches squared.
Carson is a salesman at an insurance company. He receives a monthly salary of $1,027.00 and a $185.00 commission on each
policy he sells. If Carson receives his commission check at the end of the month along with his salary check, which of the following
functions can be used to determine his total pay for the month?
(Let x represent the number of policies sold and f(x) represent the total amount of pay for the month.)
Answer: He receives a monthly salary of $1,478.00 and a $249.00 commission on each policy he sells. If Carson receives his commission check at the end of the month ...
Step-by-step explanation:
Triangle L N M is cut by a bisector that forms a right angle with the base and splits the base into 2 congruent lengths. The lengths of sides L N and N M are congruent. Angle L N M is (6 x + 1) degrees. Angle N M L is (4 x minus 11) degrees.
What is the measure of ∠NLM?
m∠NLM =
The value of ∠NLM = 29 degree
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that a Δ LNM is cut by a bisector
The bisector forms a right angle at the base and splits in tnto two congruent lengths
LN = NM
∠LNM = 6x +1
∠NML = 4x -11
∠NLM = ?
∠NLM =∠NML = 4x -11
as 6x +1 is the value of the angle bisector
By the angle sum property
4x -11 +4x -11 + 12x+2 = 180
20x = 200
x = 10
The value of ∠NLM =
4x - 11 = 4 * 10 - 11 = 29 degree
Therefore the value of ∠NLM = 29 degree
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Answer: A.) ✔ 29 degrees
Step-by-step explanation: i hope this helps :)
A sum of money in a savings account is represented by the following function:
A = 9, 000(1. 03)t where t is the number of years the money is invested.
What is the initial sum of money in the account?
The initial sum of money in the account is 9000
How to determine the initial sum of money?The function is given as:
A = 9, 000(1.03)^t
The above function is an exponential function.
An exponential function is represented as:
A = ab^t
Where
a represents the initial value
By comparison;
a = 9000
Hence, the initial sum of money in the account is 9000
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You should be able to find this
without a calculator.
sin cos
(co
1
√√3
2
?]
[ ]
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
sin([tex]cos^{-1}[/tex] [tex]\frac{\sqrt{3} }{2}[/tex] )
using the sides of the 30- 60- 90 triangle
with legs 1, [tex]\sqrt{3}[/tex] and hypotenuse 2 , then
[tex]cos^{-1}[/tex] [tex]\frac{\sqrt{3} }{2}[/tex] = 30° and
sin30° = [tex]\frac{1}{2}[/tex]
answer:
1/2
Step-by-step explanation:
sin 30º=-√3/2, 1/2 or π/6
cos=√3/2
sin= 1/2
Mark has 580 stamps. Debbie has 720 stamps than Mark. How many stamps must Debbie give to mark so that Mark have 120 more than she?
480 stamps must be given to Mark
Answer: 130 stamps.
Step-by-step explanation:
Let amount оf the stamps Debbie must give to Mark so that Mark have 120 more than she is x.
Hence,
(580+x)-(720-x)=120
580+x-720+x=120
2x-140=120
2x=260
2*x=2*130
x=130.
So, 130 stamps Debbie must give to Mark so that Mark have 120 more than she.
Good luck an' have a nice day!
The kind of statistics that focuses on providing a description that illuminates some characteristic of a numerical dataset and has value as an estimate of a real-world measure is called
The kind of statistics that provides a description that illuminates some characteristic of a numerical dataset and has an estimate is called descriptive.
What does descriptive statistics mean?Descriptive statistics is a branch of statistics field that sheds light on a given feature of datasets.
Descriptive statistics uses numerical coefficients to analyze datasets that may represent the overall population or only a sample.
In conclusion, the statistics that provides a description that illuminates some characteristic of a numerical dataset is called descriptive.
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Quick algebra 1 assignment for 50 points!
Answer:
1. graphing a linear using slope
2. Determine the learning goals of your tutoring session
- convert equations to slope-intercept forms.
- graph linear equations from the slope-intercept form.
3. Provide a brief overview of the graphing method that you will be demonstrate.
- use this formula y=mx+b to make the equation into slope intercept form
- Then graph the line equation using the slope intercept form
4. Plot the line Y = 2x+3 starting with the y-intercept and then using the slope
Steps on how to do number 4
1. Find the y-intercept = b of the equation y = mx + b.
2. Plot the y-intercept. The point will be (0, b).
3. Find the slope=m of the equation y = mx + b.
4. Make a single step, using the rise and run from the slope. (Make sure you go up to the right if it's positive and down to the right if it's negative.)
5. Connect those two points with your line.
Should look like the first graph below
5. Plot the line y= -3x+2 starting with the y-intercept and then using the slope.
Answer key
Use these steps
Find the y-intercept = b of the equation y = mx + b.
2. Plot the y-intercept. The point will be (0, b).
3. Find the slope=m of the equation y = mx + b.
4. Make a single step, using the rise and run from the slope. (Make sure you go up to the right if it's positive and down to the right if it's negative.)
Second graph is what number 5 question is supposed to look like
A jar contains 18 jelly beans: 7 purple jelly beans, 3 green jelly beans, and 8 orange jelly beans. Without looking. Travis picks 1 jelly bean from the jar. What is the probability of each of the following outcomes? [ P(green) - 2 P(purple) 3 P(orange) - 4 P(not green) 5. P(purple or green) 6. P(not orange)
Answer:
1/6, 7/18, 4/9, 5/6, 5/9, 5/9
Step-by-step explanation:
Ariana bought 153 ounces of flour and she used 21.4 ounces of it to make biscuits. How much is left?
What is the value of x in the figure shown below?
3.6
A
C
57⁰
80⁰
4.5
4.5
D
3.6
B
Answer: [tex]57^{\circ}[/tex]
Step-by-step explanation:
[tex]\triangle ACB \cong \triangle DBC[/tex], so by CPCTC, [tex]x=57^{\circ}[/tex]
can someone please please help me with this question !!!
Answer: b and d
Step-by-step explanation:
Since the roots are x=2 and x=6, we can write the equation as
[tex]f(x)=a(x-2)(x-6)[/tex]
Substituting in the coordinates of the vertex,
[tex]-4=a(4-2)(4-6)\\\\-4=a(2)(-2)\\\\-4=-4a\\\\a=1[/tex]
So, the equation is [tex]f(x)=(x-2)(x-6)[/tex].
On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]
Cooper weighs 20 pounds. when he is an adult dog, he will weigh about 350% as much as his current weight. how much will cooper weigh as an adult dog. show each step of your solution.
The cooper's weight as an adult dog will be 90 pounds.
What is percentage?Percentage, which is a relative figure used to denote hundredths of any quantity. One percent (symbolized as 1%) is equal to 100 parts; hence, 100 percent denotes the complete amount, and 200 percent designates double the amount specified.
A typical method for calculating a percentage is the formula shown below:
Determine the total amount of what you want to find a percentage. Divide the number to determine the percentage. Multiply the value by 100.Calculation for the weight of Cooper as an adult;
Cooper's present weight is 20 pounds.
He will weigh about 350% as much as his current weight.
Calculate 350% of 20 pounds.
= (350×20)/100
= 70
The increment of the weight of Cooper will be 70 pounds.
Thus, the total weight is 20 + 70 = 90.
Therefore, the weight of Cooper after 350% as an adult would be 90 pounds.
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3. 46,386
4. 1,020,615
Write in word form
Answer:
46,386=Forty six thousand three hundred eighty six.
1,020,615=One million twenty thousand and six hundred fifteen.
Can someone help me with this problem having trouble
If mauricio does a job in 6 hrs less time than Alyson, and they can do the job together in 4 hrs, how long will it take to do the job alone
Mauricio takes 24 hours, and Alyson takes 24/5 hours if the Mauricio does a job in 6 hrs less time than Alyson.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let x and y be the time to take the job for Mauricio and Alyson respectively
1/x = 1/y - 1/6 ..(1)
1/x + 1/y = 1/4 ..(2)
After solving the equations:
[tex]\rm \dfrac{1}{\dfrac{6y}{6-y}}+\dfrac{1}{y}=\dfrac{1}{4}[/tex]
y = 24/5 hours
x = 24 hours
Thus, Mauricio takes 24 hours, and Alyson takes 24/5 hours if Mauricio does a job in 6 hrs less time than Alyson.
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