Answer:
7.07 units
Step-by-step explanation:
T(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. Which statement must be true?
A: Fewer tickets were sold on the fourth day than on the tenth day.
B:No tickets were sold on the fourth day and tenth day.
C: The same number of tickets was sold on the fourth day and tenth day.
D: More tickets were sold on the fourth day than on the tenth day.
The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:
C: The same number of tickets was sold on the fourth day and tenth day.
What is the average rate of change?The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.
Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.
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hey free 100 points :) (not really) please help!
Complete the square in the quadratic function f given by
f(x) = 2x2 - 6x + 4
Answer: x = 2, 1
Step-by-step explanation:2x^2 - 6x + 4 = 0
Firstly, simplify. Divide by 2 to get
2(x^2-3x+2) = 0
Move the constant to the other side.
2(x^2-3x) = -2
Divide the x term by 2 and square it
-3/2^2 = 9/4
Add this result to both sides.
2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:
take the sqrt of both sides and isolate x for each solution
x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1
What additional information must be known to prove the triangles similar by SSS?
A)
The lengths of and
B)
∠F ≅ ∠K
C)
No additional information is needed.
D)
∠D ≅ ∠J
The angle also should be known to prove congruency.
What is congruence?It states that two triangles are said to be congruent if they are exact copies of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equal to those of the first triangle.
A congruence theorem, is AAA?It is ineffective to only know angle-angle-angle (AAA), as this can result in triangles that are similar but not congruent. There are four short cuts that can be used to check whether two triangles are congruent.
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analyze the two equations: 12y= -3x+8 and 6y =kx-5 for what value of k are the graphs equal
The value of k are the graphs (equations) equal is k = -3/2
What are equations?Equations are mathematical expressions that show the relationship between two variables.
How to find for what value of k are the graphs equal?Since we have the two equations 12y = -3x + 8 and 6y = kx -5, re-writing them, we have
12y = -3x + 8
3x + 12y - 8 = 0 (1)
Also, 6y = kx - 5
-kx + 6y + 5 = 0 (2)
Condition for equal (consistent) equations?For a pair of equations ax + bx + c = 0 (3) and a'x + b'x + c' = 0 (4) to be equal (or consistent), then
a/a' = b/b' = c/c'
Comparing with (1) and (2), with (3) and (4) above, we have that
a = 3, b = 12c = -8a' = -kb' = 6 andc' = 5So, using a/a' = b/b', we find k.
So, substituting the values of the variables into the equation, we have that
a/a' = b/b'
⇒ 3/-k = 12/6
Cross-multiplying, we have that
3 × 6 = -k × 12
k = -3 × 6/12
k = -3/2
So, the value of k = -3/2
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What is 3X3X3X3X3 in exponential form?
3×3×3×3×3 in exponential form is 3⁵.
When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.
For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is
a×a×a×a×a = a⁵
Where
a is the base
5 is the power of a
We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,
3×3×3×3×3 = 3⁵
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Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.
what is trigonometry ?Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.
given
a/sinA = c / sinB
12 / sin19 = c / sin90
36.85 = c /1
c = 36.85
Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.
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Line m passes through point (5, 8) and has a slope 3/5. What is the equation for the line
The equation for the line is y = 3/5x + 5.
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
y = mx + b
8 = 3/5(5) + b
8 = 15/5 + b
b = 5
∴ equation is y = 3/5x + 5
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Need help pls and thanks
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.
The table depicts a proportionate relationship if all of those ratios are the same.
If all of the ratios of the variables are equal, then there is a proportional link between the two variables.
In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable. The proportionality constant is the name given to the constant value. A mathematical equation of the form y=kx, where k is the proportionality constant, can be used to model any proportional relationships. The unit rate is another name for the proportionality constant.
Dustin, for instance, spends $8 each month for a music streaming service. The total cost of the service, c, and the number of months Dustin pays for the streaming service, m, are proportionate.
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A baker sells bread for $3 a loaf and rolls for $1 each. The baker needs to sell $27 worth of baked goods by
the end of the day.
Graph the linear equation 3b + r = 27, where b is the number of loaves of bread sold and r is the
number of rolls sold.
Answer:
4 loaves of bread
Step-by-step explanation:
Cost of 1 loaf of bread = $3
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $24.
To find the linear equation,
Suppose, the baker sells
x
loaves of bread and
y
rolls.
Then the total cost of the sales has to be $24.
So, the linear equation will be:
3
x
+
1
y
=
24
.......................(A)
Now, it is given that the baker sold 12 rolls and we need to know how many loaves he has to sell.
For that, replace the
y
in equation (A) with 12 as
y
represents number of rolls sold.
Then the new equation becomes:
3
x
+
1
×
12
=
24
0r
3
x
=
24
−
12
or
3
x
=
12
Solving for
x
,
x
=
12
3
=
4
loaves
A phone company offers a monthly data plan for $10 a month. The planincludes 2 megabytes of data, and charges $0.10 per megabytes above the2 megabytes of data. Write a piecewise-defined function forM(x), the cost forxmegabytes of data used in a month.
The piecewise-defined function for M(x), the cost for x megabytes of data used in a month [tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex].
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;
The cost per month for x MB of data is:
Up to 2 Mb of data utilized; $10
Data use of over 2 MB
One off charge = $ 10
Charge for data over 2 Mb is $ 0.10 per MB
The monthly charge for x MB data is:
Data ta used up to 2 Mb
$ 10
Data used more than 2 Mb
m(x) = 10 + 0.1(x-2)
m(x) = 10 + 0.1 x-0.2
m(x) = 0.1 x + 9.8
So the function is:
[tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex]
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What is the height of a triangle if its base is 24 cm and its area is 216 cm2?
The height of a triangle if its base is 24 cm and its area is 216 cm² is 18 cm.
The area of triangle is calculated using the below mentioned formula -
Area = 1/2 × base × height. We will use the formula of area of triangle to calculate the height of triangle.
Keep the values in formula -
216 × 2 = 24 × height
Firstly multiplying the values given on Left Hand Side of the equation
height × 24 = 432
Shifting 24 to Right Hand Side of the equation
Height = 432/24
Now dividing the values
Height = 18 cm
Thus, the height of the triangle is 18 cm.
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Gabi is helping her friend Joaquin create a square tile design in his backyard. Joaquin has one large square tile that is no longer being manufactured. He also has eight rectangular tiles that have the same side length as the large tile, and one small square tile that has the same width as the rectangular tiles. Gabi gets her algebra tiles to model the situation. How many small square tiles does Joaquin need to buy to complete a square tile design? please help
Answer:
Step-by-step explanation:
15 tiles
6. Which of the following is not a way to name the plane?
b. Plane IGF
a. Plane P
c. Plane HDG
d. Plane HDF
Answer: P
Step-by-step explanation:
What is the constant of Y 10x?
For y = 10x the constsnt of proportionality is 10
We know that the quantity m is proportional to quantity n if there is a constant p such that m = pn
Here, p is called as the constsnt of proportionality.
This means, the constsnt of proportionality is nothing but the ratio between two proportional quantities.
Two variables are proportonal to each others means, when the variable increase the other one would also increase at some rate and that rate is the constant of proportionality.
We have been given an equation y = 10x.
Comparing given equation y = 10x with y = kx (here k is the constsnt of proportionality)
we have k = 10
This means, the constsnt of proportionality is k = 10
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Elena and Jada each make money by helping out their neighbor. Elena babyit. Her earning are given by the equation y=8. 40x, where x repreent how many hour he work and y repreent how much money he earn. Jada earn $7 per hour mowing her neighbor' lawn. How long would it take to make each peron 150$?
If Elena earn y = 8.40x dollars where x represent how many hours she work and Jada earn $7 per hour, it would take Elena approximately 17.86 hours and Jada approximately 21.43 hours to earn $150
To find out how many hours it would take for Elena to earn $150, we need to solve the equation:
y = 8.4x
150 = 8.4x
x = 150/8.4
x ≈ 17.86 hours
So it would take Elena approximately 17.86 hours to earn $150.
To find out how many hours it would take for Jada to earn $150, we divide 150 by her hourly rate:
= $150 /( $7/ hour)
≈ 21.43
So it would take Jada approximately 21.43 hours to earn $150.
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How do I covert between VOLUME units??
We will convert between volume units by multiplication or division process depending on the standard metric units.
What is unit conversion?
Unit conversion is done either by multiplication or division process between numerical values. There are some standard metric units. By following the standard, we can convert one unit to another. As example we have a box that is 2 square feet area, now we want to know the area in inches. So, we will multiply it by 144 to convert in square inches.
How do we convert between volume units?
We convert between volume units either by multiplication or division process depending on the standard unit. If we find a volume in liter and we can convert it in cubic meter by multiplying the number by 0.001. Assume, we measured a volume in cubic feet, but someone want to know this volume in cubic meter that time we divide this value by 35.32 to convert in required unit.
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Find an expression to present the perimeter of the rectangle below
An expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
What is the perimeter?
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.
Here, we have
Given: Sides = 10/(x² + 11x +24) and (x+1)/(x+3)
The perimeter is when you add all the sides of a shape.
In a rectangle, two sides are the same, and so are the other two. therefore, if the two sides are 10/(x² + 11x +24) and (x+1)/(x+3) the expression will be:
= 2(10/(x² + 11x +24)) + 2(x+1)/(x+3)
= 20/(x² + 11x +24) + 2(x+1)/(x+3)
= 20/(x+8)/(x+3) + 2(x+1)/(x+3)
= {20 + 2(x+1)(x+8)}/(x+8)/(x+3)
= {20 + 2(x² + 9x + 8)}/(x+8)/(x+3)
= { 20 + 2x² + 18x + 16}/(x+8)/(x+3)
= {2x² + 18x + 36}/(x+8)/(x+3)
= (x+12)(x+6)//(x+8)/(x+3)
Hence, an expression to represent the perimeter of the rectangle with 10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).
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The volume of a right cone is 4487 units³. If its height is 21 units, find its radius.
Answer:
Step-by-step explanation:
V=(1/3)hπr^2
<=> 4487 = 1/3x21πxr^2
<=> r^2 = 641/π
<=> r = squrt( 641/π)
What does a scale factor of 1.5 mean?
Scale Factor. To create a scaled copy, we multiply all the lengths in the original figure by the same number.
What does the number 1.5 signify on a scale?A 1.5 GPA, or Grade Point Average, is comparable to a D+ letter grade on a scale of 4.0 GPA. This corresponds to a grade of around 69%. The Scale Factor. To make a scaled replica, multiply all of the original figure’s lengths by the same number. This figure is known as the scaling factor. The scale factor in this case is 1.5 since 4(1.5)=6, 5(1.5)=7.5, and 6(1.5)=9.
An Over 1.5 Goals bet is simply a betting on there being two or more goals scored in a given game. The scoreboard is irrelevant; as long as the two sides collaborated for at least two goals, your bet will win.
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Isabel chooses one ball from the bag at random. She wins 1 if the number 1 is selected, 2 if the number 2 is selected,5 if the number 3 is selected, 6 if the number 4 is selected 8 if the number 5 is selected and 10 if the number 6 is selected. She loses 16 if 7 or 8 is selected
The expected value of Isabel's game is given as follows:
E(X) = 0.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
The game is composed by choosing eight balls, which are equally as likely to be chosen.
Then the probability distribution of earnings is given as follows:
P(X = 1) = 1/8.P(X = 2) = 1/8.P(X = 5) = 1/8.P(X = 6) = 1/8.P(X = 8) = 1/8.P(X = 10) = 1/8.P(X = -16) = 2/8.Hence the expected value of the price is given as follows:
E(X) = 1/8 x (1 + 2 + 5 + 6 + 8 + 10) - 16 x 2/8.
E(X) = 0.
Missing InformationThe problem asks for the expected earnings.
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find the area of STUV.
1. Find the midpoint of the line segment joining (–4, –2) and (2, 8).
The midpoint of the line segment joining (–4, –2) and (2, 8) is calculated to give: (-1, 3)
What is a line's midpoint?The centroid of a line segment is its middle point. Since it is equally far from both ends, it divides the region in half.
How to determine a line segment's midpointIn coordinate geometry, the midpoint formula is the method for calculating the center point of a straight line given its endpoints' coordinates.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
For points (–4, –2) and (2, 8).
X= (-4 + 2)/2 = -1
Y = (-2 + 8)/2 = 3
The midpoint is solved to be (-1, 3)
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Which of the following angles are congruent to ∠5? Select all that apply.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
What is Congruency ?When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.
It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.
Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
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Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
What is Congruency ?When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.
It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.
Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.
Angle 5 is congruent to angle 8 by (vertically opposite angle )
Angle 5 is also Congruent to Angle 4 (alternate Angles)
Angle 5 is also Congruent to Angle 1 ( corresponding Angles )
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Multiply the first number by its reciprocal:
6
X
6
42
The result after multiplication = 6/X, 1, 1/ 7
What is reciprocal?When one is divided by a number or value it is called the reciprocal of that number or value. It is also said the inverse form of the value or number. As example, reciprocal of 12 is written as 1/12.
What is the result?
There are four values 6, X, 6 and 42.
multiply the first number by the reciprocal of others.
reciprocal of X = 1/X
reciprocal of 6 = 1/6
reciprocal of 42 = 1/42
now we multiply, 6×1/X = 6/X
6×1/ 6 = 1
6×1/ 42 = 1 /7
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decide if the absolute value inequality is an “and” compound inequality, an “or” compound inequality, or neither.
1. |5+m|<13
a. “and” b. “or” c. neither
2. 4|y + 6| ≥ 3
a. “and” b. “or” c. neither
3. Choose the answer to | g – 3 | = -2
a. g = 5 or -5
b. g = 1 or -1
c. null set
1. |5+m|<13 is an "or" compound inequality. 2. 4|y + 6| ≥ 3 is neither compound inequality. 3. null set.
1. The inequality is given in the question, is as follows:
|5+m| < 13
The absolute value of the expression "5+m" is less than 13.
To solve the inequality, we need to split the inequality in two separate inequalities: 5+m < 13 and -5-m < 13.
Thus, |5+m|<13 is an "or" compound inequality.
2. 4|y + 6| ≥ 3 is neither compound inequality because we have just one inequality.
3. The absolute value of a number is always positive, so it is impossible for |g - 3| = -2. So the answer is c. null set.
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A ceiling fan has 19-inch blades(so the radius of the circular fan is 19 inches). Suppose the dan turns at a rate of 69 revolutions per minute.
a) Find angular speed of the fan in radians per minute
b) Find the linear speed of the tip of a blade in inches per minute
Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is
What the linear speed and angular speed?Suppose the dan turns at a rate of 69 revolutions per minute.
Angular speed of the fan in radians per minute is
According to the problem
w = 2zn
(a) w = 2z * 67
= 134z
≈ 421 crad /min)
Angular speed of the fan in radians per minute is 421 (crad /min)
The linear speed of the tip of a blade in inches per minute is
(b) v = 2z * 19 * 67
{ v = 2zrn}
=2546z
7988(cin / m * in)
The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)
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I NEED HELP WITH 4 ,5, 6 and 7 PLEASE ???
The Wien Apetrol UC 20142000 was a unique and innovative venture that aimed to provide clean energy solutions to the people of Austria.
Solve for x ?x = -7
ma = 54
m23 = 54
The project was a collaboration between the Austrian government, private companies, and research institutions.It focused on developing and implementing renewable energy sources such as solar, wind, and hydropower, as well as energy storage systems. The project showcased the potential of renewable energy sources to provide a sustainable and affordable energy solution to citizens.It also promoted the use of energy efficiency measures to reduce energy consumption and costs. The project was a success, and it achieved its goal of providing reliable and affordable energy to the people of Austria.The project has been cited as a model for renewable energy projects around the world and has served as an example of how collaboration between different sectors can be successful.To learn more about Wien Apetrol refer to:
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Help please due by tonight
The table shows the temperature of a substance at the start of a science experiment which - 16.8°C and we were told that it changed by 3/4 of the value which therefore means that the final temperature at 2:35pm is - 29.4°C.
What is Temperature?This is referred to as the degree of hotness or coldness of a substance and it is measured in Celsius, kelvin etc.
In this scenario we were told that the temperature - 16.8°C changed by 3/4 of the value which means that:
3/4 × - 16.8°C = - 12.6°C
The temperature at 2:35pm will therefore be - 16.8°C - 12.6°C = - 29.4°C.
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What is the name of a triangle when all 3 sides are the same length?
The name of a triangle when all 3 sides are the same length is Equilateral Triangle
What is an Equilateral Triangle ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
Equilateral Triangle Properties
Equal on all three sides.
The sum of the three congruent angles is 60 degrees.
It has three regular sides and is a polygon.
The equilateral triangle is divided into equal halves by the perpendicular that is traced from its vertex to the other side. Additionally, the perpendicular's origin vertex's angle is split into two equal angles of 30 degrees each.
The centroid and ortho-centre are located at the same location.
The median, angle bisector, and altitude of an equilateral triangle are all the same.
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For what value of A is x 4 a factor of 5x³ 7x² ax 28?
(x - 4) is a factor of the expression 5x³ − 7x² − ax − 28, when a = 28
Here we are given the expression 5x³ − 7x² − ax − 28
now we need to find a value of a for which (x - 4) is a factor of
5x³ − 7x² − ax − 28
This implies that 5x³ − 7x² − ax − 28.must be divisible by (x - 4)
On dividing 5x³ − 7x² − ax − 28. by x - 4 will give us
[tex]x-4) \overline{5x^{3}-7x^{2}-ax-28.}(5x^{2}+14x+(56-a)\\{\hspace{1cm} 5x^{3}-20x^{2}\\\\\hspace{2cm}\overline{14x^{2}-ax}\\{\hspace{2cm}14x^{2}-56x\\\\{\hspace{3cm} \overline{(56 - a)x - 28}\\{\hspace{3cm} (56-a)x-(56-a)\\{\hspace{5cm} \overline{28-a}[/tex]
Since (x - 4) is a factor of 5x³ − 7x² − ax − 28, there should not be any remainder left
Hence, 28 - a = 0
or, a = 28
Hence (x - 4) is a factor of 5x³ − 7x² − ax − 28, when a = 28
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Correct Question
Find the value of a such that (x−4) is a factor of 5x³ − 7x² − ax − 28.