The domain of function, (cd)(x) is all real values of x except x = 2, i.e., (−∞,2)∪(2,∞).
The domain of a function is defined as a set of values accepted by function. In this case, we have a rational function. A rational function will only be defined if the denominator is not equal to zero. We have, two functions, c(x) = 5/ x - 2 and
d(x) = x + 3. We should determine the domain of (cd) (x). The product of two is (cd) (x) = c(x) . d(x)
=> (cd)(x) = (5/(x - 2) )(x + 3) = 5(x+3)/(x -2)
Which is a rational function. So, the function will be defined if the denominator is not equal to zero, i.e., x - 2 ≠ 0 => x ≠ 2. Thus, domain set of function contains all real numbers values except 2. Therefore, the required domain of function (cd) (x) is all real values of x except 2.
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Complete question:
If c(x) = 5 / x - 2 and d(x) = x + 3. What is the domain of (cd)(x)?
15/20, 20/21 determine if the ratio are proportional
According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.
How to determine whether that two ratios are proportional
In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:
15 / 20
Second, multiply numerator and denominator by 4 / 3:
[15 · (4 / 3)] / [20 · (4 / 3)]
20 / 26.667
Ratio 15 / 20 is not proportional to ratio 20 / 21.
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A pair of shoes regularly cost $45. Today, they are marked down 25%. What is the sale price of the pair of shoes?
Answer:
$33.75
Step-by-step explanation:
25% of 45 is 11.25 meaning you would get that much off as a discount making the shoes be $33.75
A spherical toy needs a triangular sticker (with a base of 12cm and height of 15cm) on it. The sphere has a diameter of 50cm what is the surface area not covered by the sticker?
Answer: 65.65
Step-by-step explanation:
Carry over the decimals in each number.
2) Multiply. This will give you 6,565.
3) Carry the decimal place and count how many times you moved it over. (2=1+1) Therefore, it gives you 65.65
Compute Autin' total ocial ecurity and Medicare taxe for the fourth quarter, if he i elf-employed and earn $5,000. 00 on a emimonthly bai. (For elf-employed peron, ocial ecurity tax i 12. 4% of wage up to $128,400, and Medicare tax i 2. 9% of all wage. )
The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.
The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.
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do you have 8 cups of flour a recipe calls for 2/3 cup of flour of the recipe calls are 1/4 cup of flour how much flour do you have left after making the recipes
Answer: Total cup of flour=8 cups
One recipe calls for cup of flour=2/3
Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour
Another recipe calls fro cup of flour=1/4
Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.
Amount of Floor left=7.08
Step-by-step explanation:
A village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. The village plans to increase the length by 30%.
Answer:
A) 234 feet
B) Area of new parking lot = 28080 square feet
C) The new parking lot will be able to fit 20 more cars than the original parking lot.
Step-by-step explanation:
We are given the following information:
Length of parking lot = 180 feet
Width of parking lot = 120 feet
Number of cars that can be parked = 75
A) Increase in length = 30%
New length =
B) New area =
C) Space required by 1 car = 288 square feet
Number of cars we want to fit = 75 + 20 = 95
Area required =
Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.
Please help me with this Geometry Question
The value of x from the given figure is 12 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔADC and ΔABC,
∠C=∠C (Reflex property)
AC=AC (Reflex property)
∠BAC=∠CDA=90°
By AA similarity, ΔADC ~ ΔABC
So, AC/BC = DC/AC
x/36 = 4/x
x²=36×4
x²=144
x=12 units
Therefore, the value of x from the given figure is 12 units.
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Express the lengths a and b in the figure in terms of theta. If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and pi/2, evaluate sin(x + y) Find all values of x such that sin 2x = sin x and 0 le x le 2pi. (List the answers in increasing) If you have had difficulty with these problems, you may wish to consult the Review of Trigonometry.
In the given figure, the length b is opposite the angle theta, and the length a is adjacent to the angle theta, so we can use the trigonometric ratios to express a and b in terms of theta:
What does trigonometry mean in plain English?
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
a = bsec(theta)
b = acosec(theta)
To evaluate sin(x+y), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
We can use the given information to substitute the values of sin(x) and cos(y)
sin(x) = 1/3, cos(y) = sqrt(1 - (5/4)^2) = sqrt(9/16)
sin(x+y) = (1/3) * sqrt(9/16) + sqrt(9/16) * (1/3) = (3sqrt(9) + 9) / 48
To find all values of x such that sin 2x = sin x and 0 le x le 2pi, we can set sin 2x = sin x and solve for x.
sin 2x = sin x
2sinxcosx = sinx
cosx = 1/2
x = pi/3,5*pi/3
So the values of x that satisfy the equation are x = pi/3 and 5*pi/3
Note that these values are in radians, if you need in degree, x=60°, 300°
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Solve the equation 6z2-7z-5=0
Answer:
-1/2, 5/3
Step-by-Step Explanation:
6z^2 - 7z - 5 = 0
=> 6z^2 - 10z + 3z - 5 = 0
=> 2z(3z - 5) + 1(3z - 5) = 0
=> (2z + 1)(3z - 5) = 0
=> z = -1/2, 5/3
Hope it helps.
If you have any query, feel free to ask.
When Gabriella moved into a new house, she planted two trees in her backyard. At
the time of planting, Tree A was 34 inches tall and Tree B was 14 inches tall. Each
year thereafter, Tree A grew by 2 inches per year and
Tree B grew by 6 inches per
Let A represent the height of Tree A t years after being planted and let B
present the height of Tree B t years after being planted. Write an equation for each
situation, in terms of t, and determine the height of both trees at the time when they
have an equal height.
PLEASE ANSWER ITS DUE TODAY!!!!!!
The equation for Tree A's height t years after being planted is:
[tex]A = 34 + 2t[/tex]
The equation for Tree B's height t years after being planted is:
[tex]B = 14 + 6t[/tex]
To determine the height of both trees at the time when they have an equal height, we can set the two equations equal to each other:
[tex]A = B[/tex]
[tex]34 + 2t = 14 + 6t[/tex]
And solving for t, we find that:
[tex]t = 10[/tex]
So, 10 years after being planted,
Tree A will be 54 inches tall [tex](34 + 2 * 10)[/tex] and Tree B will be 74 inches tall [tex](14 + 6 * 10)[/tex].
At this point, both trees will have an equal height.
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set of points is shown on the graph.
Scatter plot with a point at negative 3 comma 9, a point at 0 comma 5, a point at 1 comma 8, a point at 6 comma 7, and a point at 8 comma 3.
Which of the following equations is the best model for a line of fit for the data?
y equals 2 thirds times x plus 7
y equals negative 2 thirds times x plus 7
y equals 1 third times x plus 7
y equals negative 1 third times x plus 7
An equation which represents the best model for a line of fit for the data is: y equals negative 2 thirds times x plus 7. The correct option is A.
How to find a line of fit for the data?A scatter plot should be used to determine a linear equation of the line of best fit (trend line) that models the data points described above.
In this scenario, the x-values would be plotted on the scatter plot's x-axis, while the y-values would be plotted on the scatter plot's y-axis.
Right-click on any data point on the scatter plot in Excel, select the format trend line, and then check the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear equation for the line of best fit is given by:
y = -0.33x + 7.
Rewriting the equation as an improper fraction, we have:
y = -2/3(x) + 7
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How many times more intense is an earthquake that measures 8 on the Richter scale than an earthquake that measures 4 on the Richter scale?.
A measures magnitude 8 on the Richter scale of an earthquake is 10,000 times stronger than a magnitude 4 measure on the Richter scale.
Earthquake Intensity: An earthquake is the release of energy from the movement of tectonic plates. Earthquakes can be measured on the Richter scale, which ranges from 2 to 10 and measures the magnitude of an earthquake.
Earthquake intensity is a qualitative estimate of the effects caused by an earthquake, so it has no numerical value. The Richter scale is a logarithmic scale. This means that as you move up each digit, the power increases by a factor of 10. So let's set the damage from 4 earthquakes to X. Then, 5 = 10X
=> 6 = 100X
=> 7 = 1,000X
=> 8 = 10,000X
Hence, the required intensity is 10,000.
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What is the value of a in the following image?
Check the picture below.
Sara drives 72 miles on 3.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 12.3 gallons of gas?
Answer:
276.75
Step-by-step explanation:
one gallon lets sara drive 22.5 miles. multiply that by 12.3 and u get 276.75 !
ΔRST is reflected across the line y = x to form ΔR’S’T’. Find the coordinates of the points R’, S’ and T’.
R(1,-2)
S(2,-8)
T(7,-4)
Answer:
R' ( -2,1)
S' (-8,2)
T' ( -4,7)
Step-by-step explanation:
(06.01 LC)
The distance formula can be used to prove that a triangle has (5 points)
O congruent sides
O a right angle
O parallel sides
O congruent angles
The distance formula can be used to prove that a triangle has congruent sides.
What is congruent sides?If two sides in geometry are congruent, then they have the same length. Since a square has four sides that are all the same length, it has four congruent sides. We refer to a triangle as being equilateral when its three sides are congruent. We use a slash mark to indicate the congruent sides. An equilateral triangle always has 60° angles. An isosceles triangle is one that possesses two congruent sides.Congruent sides are those in any shape that have sides that have the same length. We can say that two triangles are congruent if, for instance, all three of their sides are the same length and equal to one another. The SSS congruence rule stands for (side-side-side).
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How do you multiply 3-digit numbers by 2 digit numbers with regrouping?.
Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.
Follow along with example 343 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.
3 4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.
3 4 3
×3 2
_________
6 8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.
3 4 3
×3 2
__________
6 8 6
10 2 9×
__________
10 976
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How do you use the sine rule for a triangle?.
To use the sine rule for a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides.
What is triangle ?
A triangle is a geometric shape that has three straight sides and three angles. Triangles are classified based on the measures of their angles and the lengths of their sides.
What is law of sine ?
The law of sines, is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. Specifically, the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
It can be written as
[tex]a/sin(A) = b/sin(B) = c/sin(C) = 2R[/tex]
where R is the circumradius of the triangle.
To use the sine law to solve for an unknown side or angle in a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides. Once we have that information, we can use the sine law to find the measure of the unknown angle or the length of the unknown side.
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The support for a window air-conditioning unit forms a triangle and an exterior angle. What is the measure of the exterior angle?.
The measure of the exterior angle in this case is 60+60 = 120 degrees.
What is exterior angle ?
An exterior angle of a polygon is an angle formed between one side of the polygon and a line extended from the endpoint of the opposite side. An exterior angle can be formed by standing outside of the polygon and looking at it.
In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it. In any convex polygon, the sum of the measures of the exterior angles is always 360 degrees.
The support for a window air-conditioning unit forms a triangle. A triangle is a three-sided polygon, and all the interior angles in a triangle add up to 180 degrees. Therefore, the measure of each interior angle of a triangle is (180/3) = 60 degrees.
An exterior angle of a triangle is the angle formed between one side of the triangle and a line extended from the endpoint of the opposite side. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it.
Therefore, the measure of the exterior angle in this case is 60+60 = 120 degrees.
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please help, i dont understand!
10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the area of rectangle is 70y⁸+30y⁶
The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶
70y⁸+30y⁶
10y⁶(y²+3)
10y⁶ is the width of the rectangle.
y²+3 is the length of the rectangle.
Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
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URGENT!
find the value of x in each supplementary angle pair
Answer:
x = 14°
Step-by-step explanation:
We know that,
→ Straight line is always 180°.
Forming the equation,
→ 156° + (x + 10°) = 180°
Now the value of x will be,
→ 156° + (x + 10°) = 180°
→ x + 166° = 180°
→ x = 180° - 166°
→ [ x = 14° ]
Hence, the value of x is 14°.
The value of x in the given supplementary angle pair is 14°.
Explain the term supplementary angle?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° as well as angle 50° are complementary angles since the sum of these two angles is 180°.Two angles are classified as supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are thought to be complimentary angles and together they make a right angle.Then,
156 + (x + 10) = 180
166 + x = 180
x = 180 - 166
x = 14°
Thus, the value of x in the given supplementary angle pair is 14°.
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Please help me understand
The perimeter of the horse corral is 600 feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and
p is the perimeter of the polygon.
Given that area of the horse corral is 3000 ft²
Length of the apothem is 10 ft
We need to find the perimeter.
3000=10p/2
6000=10p
Divide both sides by 10
600=perimeter
Hence, the perimeter of the horse corral is 600 feet.
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Tristan has a points card for a movie theater.
He receives 25 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 110 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Tristan can make to earn his first free movie ticket.
The inequality that represents the number of visits Tristan can make to earn his first free movie ticket is 8.5x + 25 ≥ 110.
What is the inequality?In mathematics, an inequality is a relationship between two expressions or values that are not equal to each other.
In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).
Here,
Let us refer to x as the number of visits.
He receives 8.5 points for each visit,
That is he receives 8.5x points for x visits. i
Then there are the 25 reward points for simply signing up.
So the total points expression would be 8.5x + 25.
He needs at least 110 points to get a freebie,
Therefore the inequality is 8.5x + 25 ≥ 110.
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Help me find x please!
Answer:
PSQ = x since PSQ + 3 x = 4 x
So the triangle PQS is an equilateral triangle
2 x + y = 180 (y = PQS the angle opposite 68)
y + 68 = 180 these must add to 180
x = 34 subtracting the previous two equations
What is the slope of the line that passes through the points (-9,-5) and (-1,-9)
Answer:
-1/2
Step-by-step explanation:
slope is rise over run so find the difference between the y values (-9-(-5)) and divide that by the difference between the x values (-1-(-9)).
Per company charge $20 per day to rent a car and $. 10 for every mile driven. Addion want to rent a car knowing that he plan to drive 100 mile and he ha at mot $80 to pend right and olve an inequality which can be ued to determine X the number of day Addion can afford to rent or tay within her budget
Considering the definition of inequality, the inequality that can be used to determine x is 20x + 10 ≤ 80.
According to the question,
Addison wants to rent a car, we know that:
She plans to drive 100 miles.She has at most $80 to spend.On the other hand, x denotes the maximum number of days. Alyssa can afford to rent while staying within her budget.
Then, the inequality that can be used to solve x is:
20x + 0.1×100≤ 80
so,
20x + 10≤ 80
Hence, the inequality which can be used to determine x is 20x + 10≤ 80.
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Which graph shows the solution to this inequality? 15≤−3x+6
Answer: Look below
Step-by-step explanation:
What is the argument of 4 3i?.
The Argument of 4 + 3i is arg(z) = 36.97◦.
Now, According to the question:
Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The standard format of a complex number is:
[tex]a +bi[/tex]
In which:
a is the real part.b is the imaginary part.Given,
The complex number is:
z = 4 + 3i
We have to find the argument of the 4 + 3i.
The argument is given by:
θ = [tex]tan^-^1\frac{b}{a}[/tex]
tan θ = [tex]\frac{3}{4}[/tex]
θ = [tex]tan^-^1\frac{3}{4}[/tex]
θ = 36.97◦
The argument is θ = 36.97◦
We also have an abbreviation for argument: we write arg(z) = 36.97◦
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Is 6(4b + 3d) and 24b + 3d equivalent or not
Answer:
No
Step-by-step explanation:
You must distribute 6 to BOTH numbers in the bracket
[tex]6(4b + 3d) = 24b + 18d[/tex]
Answer:
No, they are not equivalent !
Step-by-step explanation:
Simplify 6(4b + 3d)....
6(4b + 3d)
→ 6*4b+6*3d
→ 24b+18d
and we have....
→ 24b + 3d
So, no 6(4b + 3d) and 24b + 3d are not equivalent.
PLEASE HELP ME I NEED TO TURN THIS IN BY TMMR!!
Answer:
[tex]\frac{4}{3}cm/s[/tex]
Step-by-step explanation:
By looking at the graph, we can use the slope formula.
[tex]slope=\frac{y^2-y^1}{x^2-x^1}[/tex]
We can substitute the point values into the equation.
[tex]\frac{16-0}{12-0}[/tex]
Then simplify.
[tex]\frac{16}{12}[/tex]
This fraction has the greatest common denominator of 4, so we will divide the numerator and the denominator.
[tex]\frac{16}{12}=\frac{4}{3}[/tex]
Therefore, the speed of the snail has a unit rate of [tex]\frac{4}{3} cm/s[/tex].
